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Numerical model for the prediction of total dynamic landslide forces on flexible barriers Ashwood, Wesley 2014

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    NUMERICAL MODEL FOR THE PREDICTION OF TOTAL DYNAMIC LANDSLIDE FORCES ON FLEXIBLE BARRIERS  by  WESLEY ASHWOOD    A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  in  THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Geological Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)    April 2014    ©Wesley Ashwood, 2014  ii ABSTRACT Physical barriers are effective tools in the mitigation of landslide hazards. Numerous case histories have been reported where flexible barriers have successfully contained debris flows, and more recently debris avalanches up to 10,000 m3. The current limitation in the design of such measures is quantifying the force imparted by the landslide on the structure. Standard practice limits the investigation to flow parameters, neglecting the behavior of the structure, which can significantly vary between designs and installations. Effort has been made to model the flow – structure interaction, but has thus far been limited to complex numerical models. This research focuses on the development and validation of a simple, numerical model to quantify the total force imparted by a flow-like landslide on a flexible barrier. The model is based on a previously validated code for analysis of landslide mobility, DAN-W. The current model, referred to as DAN-Barrier, uses stiffness as a key physical property of the flexible barrier. The numerical solution explicitly solves for the total force, fill height at the barrier face, and barrier deflection during each time step, and the landslide mass reacts to the addition of the barrier force resisting flow. In an attempt to validate the numerical model, a series of flume tests have been performed where granular material impacts a rigid wall and a flexible rubber barrier. With some calibration, reasonable results are obtained. The model was also used to simulate forces induced during full-scale impacts by back analyzing experiments performed at debris flow and debris avalanche test sites. DAN-Barrier requires further refinement and calibration before it could be used as a predictive tool, but is successful in showing the potential for a simple tool to quantify the flow – structure interaction that occurs when flow-type landslides impact flexible barriers.   iii PREFACE The work presented in this thesis, as well as all text, is original and has not been published. The numerical model described in Chapter 3 is an extension of a previously published and validated model by Prof. O. Hungr. The concepts fundamental to the expanded numerical model were proposed by Prof. O. Hungr and implemented within the original code by myself and Prof. O. Hungr. The laboratory apparatus described in Chapter 4 was designed by myself with guidance from Prof. O. Hungr. Construction of the steel sliding cart apparatus and flume were done by J. Unger of the UBC Earth and Ocean Science machine shop and myself. Data acquisition software used during experimentation was developed by D. Jones, a system analyst with the UBC Earth and Ocean Science computer staff. All laboratory results discussed in Chapter 5, and subsequent analysis, were performed by myself. The data used in the back-analyses presented in Chapter 7 were taken from previously published work by the United Stated Geological Survey, and through private correspondence with the Swiss Federal Institute for Forest, Snow and Landscape Research (WSL) with permission from Geobrugg.   iv TABLE OF CONTENTS Abstract ........................................................................................................................................ ii Preface ........................................................................................................................................ iii Table of Contents ..................................................................................................................... iv List of Tables ........................................................................................................................... vii List of Figures ......................................................................................................................... viii Acknowledgments ................................................................................................................ xiii 1 Introduction ....................................................................................................................... 1 1.1 Thesis objectives .................................................................................................................... 2 1.2 Layout of thesis ....................................................................................................................... 2 2 Background ......................................................................................................................... 3 2.1 Debris flows and debris avalanches ................................................................................ 3 2.2 Protective structures ............................................................................................................ 6 2.2.1 Flexible barriers ........................................................................................................................... 6 2.3 Flexible barrier components .......................................................................................... 10 2.4 Current approaches to the determination of impact forces ................................ 11 3 Numerical model for the determination of the total impact force of a landslide on a flexible barrier ........................................................................................... 18 3.1 The original dynamic model, DAN-W........................................................................... 19 3.2 Introduction of DAN-Barrier ........................................................................................... 24 3.2.1 General approach ...................................................................................................................... 25 3.3 Correlating deformed shape ........................................................................................... 27 3.4 Implementation of DAN-Barrier .................................................................................... 29 4 Physical tests – UBC test flume .................................................................................. 31 4.1 Apparatus design and setup ............................................................................................ 31 4.2 Test materials ...................................................................................................................... 36 4.3 Test procedure ..................................................................................................................... 38 5 Results ............................................................................................................................... 41 5.1 Calibration ............................................................................................................................. 41 5.2 Measurement and data ..................................................................................................... 42 5.2.1 Time series .................................................................................................................................. 42 5.2.2 Velocity ......................................................................................................................................... 43 5.3 Results for tests with thin flow front ........................................................................... 44 v 5.3.1 Qualitative description of flow behavior ........................................................................ 44 5.3.2 Synchronization ........................................................................................................................ 46 5.3.3 Additional measurements ..................................................................................................... 46 5.3.4 Quantitative analysis ............................................................................................................... 47 5.4 Results for tests with steep flow front ......................................................................... 51 5.4.1 Qualitative description of flow behavior ........................................................................ 51 5.4.2 Synchronization ........................................................................................................................ 52 5.4.3 Additional measurements ..................................................................................................... 52 5.4.4 Quantitative analysis ............................................................................................................... 53 6 Validation of the numeric model .............................................................................. 57 6.1 Model sensitivity analysis ................................................................................................ 62 7 Back-analysis of full scale testing of flexible barriers ...................................... 65 7.1 Resolution of DAN-Barrier total force ......................................................................... 65 7.1.1 Transverse cables – internal load transfer .................................................................... 66 7.1.2 Upslope retaining cables – external stability ................................................................ 69 7.2 USGS flume tests .................................................................................................................. 71 7.2.1 Field measurements ................................................................................................................ 72 7.2.2 Model setup and calibration ................................................................................................. 74 7.2.3 Calculated total force and cable analyses ....................................................................... 75 7.2.4 Comparison to observed values ......................................................................................... 77 7.3 Open hillslope debris avalanche tests at Veltheim, Switzerland. ...................... 78 7.3.1 Field measurements ................................................................................................................ 79 7.3.2 Model setup and calibration ................................................................................................. 82 7.3.3 Calculated total force and cable analyses ....................................................................... 83 7.3.4 Comparison to observed values ......................................................................................... 85 8 Conclusions and recommendations ........................................................................ 87 8.1 Summary of work completed ......................................................................................... 87 8.2 Summary of results ............................................................................................................ 88 8.3 Other considerations ......................................................................................................... 90 8.4 Conclusions ........................................................................................................................... 92 References ................................................................................................................................ 93 Appendices ............................................................................................................................. 100 Appendix A1: Test setup summary tables .................................................................. 101 vi Appendix A2: Results summary tables ........................................................................ 102 Appendix B1: Thin flow front video observations; flexible barrier with sand and gravel ............................................................................................................................... 103 Appendix B2: Thin flow front video observations; rigid barrier with sand and gravel ....................................................................................................................................... 111 Appendix C1: Thin flow front test results; flexible barrier with sand and gravel .................................................................................................................................................... 115 Appendix C2: Thin flow front test results; rigid barrier with sand and gravel .................................................................................................................................................... 120 Appendix D: Thin flow front test impacts at time of maximum fill height ...... 123 Appendix E1: Steep flow front video observations and dan-barrier time series; flexible barrier with sand ................................................................................................. 124 Appendix E2: Steep flow front video observations and dan-barrier time series; flexible barrier with gravel ........................................................................................................ 138 Appendix E3: Steep flow front video observations and dan-barrier time series; rigid barrier with sand ...................................................................................................... 142 Appendix F1: Steep flow front test results compared to dan-barrier results; flexible barrier with sand ................................................................................................. 146 Appendix F2: Steep flow front test results compared to dan-barrier results; flexible barrier with gravel .............................................................................................. 153 Appendix F3: Steep flow front test results compared to dan-barrier results; rigid barrier with sand ...................................................................................................... 156 Appendix G: Steep flow front tests at time of maximum force ............................ 159 Appendix H1: Cable force calculations for USGS flume test 2 - debris flow against a single bay flexible barrier .............................................................................. 161 Appendix H2: Cable force calculations for Veltheim, Switzerland field test 7.1 - debris avalanche against three bay flexible barrier ............................................... 162   vii LIST OF TABLES Table 1. Scaling factors as a function of the flow width to barrier width ratio (b/w) for a barrier with a deformed shape characterized by a symmetric parabola ....................................... 29 Table 2. Example output for BART.DAT, actual file does not include column titles. ................. 30 Table 3. Summary of test materials and bulk properties tested. ....................................................... 37 Table 4. Observed forces for thin flow front test results compared to calculated forces using dynamic impact pressure approach (Kwan and Cheung 2012) and Coulomb active lateral earth pressure (Budhu 2011). Values obtained using dynamic impact pressure approach are all overestimates, values using lateral earth pressure all underestimate actual values. ......... 49 Table 5. Input parameters for DAN-Barrier models of concentrated flow front tests. ............. 59 Table 6. Barrier and flow observations for USGS flume Test 2........................................................... 72 Table 7. Rheology and modeling parameters used along varying longitudinal spans of the USGS flume model. ................................................................................................................................................ 75 Table 8. Comparison of observed velocities and velocities from the numerical model used during calibration. Average velocities were calculated by noting the amount of time required for the flow front to pass identifiable positions, except for barrier impact velocity, which was measured from the video............................................................................................................. 75 Table 9. DAN-Barrier calculations of total force, deflection and fill height using different barrier stiffness. ..................................................................................................................................................... 76 Table 10. Summary of results for back analysis of USGS debris flow flume, Test 2 against a flexible barrier (DeNatale et al. 1999). Calculated values are direct outputs from DAN-Barrier or are calculated from the prediction of total force. ............................................................... 77 Table 11. Observations of travel distance, time and average velocity from field compared to velocity from numerical model used for calibration. .............................................................................. 82 Table 12. Summary of results for back analysis of Veltheim debris avalanche site, Test 7.1 against a three bay flexible barrier. Calculated values are direct outputs from DAN-Barrier or are calculated from the prediction of total force. ............................................................................... 85    viii LIST OF FIGURES Figure 1. (a) Ring net style debris flow breaker installed in a channel of Mount Yakedake, Japan and (b) same barrier after successfully retaining material in an event on July 18, 2004, see person in photo (b) for scale (Suwa et al. 2009). ................................................................................ 7 Figure 2. Rockfall protection barrier filled with 750 m3 of material after a debris flow event in Aobandani, Japan in 1998 (Roth et al. 2004). .......................................................................................... 8 Figure 3. Installation of a debris flow barrier in a torrent channel in Switzerland (Geobrugg 2009). Note that the fence does not extend to the base of the channel allowing for flow under normal hydrologic conditions. ............................................................................................................ 10 Figure 4. Typical debris flow barrier components (Geobrugg 2009). ............................................. 11 Figure 5. Assumed filling process for the calculation of dynamic and static loads on a barrier. Initial impact (a) imparts a dynamic load only followed by progressively larger static loads, (b) and (c), ending in overtopping where static and shear forces dominate. .............................. 14 Figure 6. Schematic of the pile-up mechanism (top) and run-up mechanism (bottom) as described by Sun and Law (2011) for the calculation of energy to be dissipated during impact with a flexible barrier. .......................................................................................................................... 15 Figure 7. Concept of equivalent fluid, after Hungr (1995). The complex two-phase (or possible three-phase) flow can be modeled as a single material with uniform bulk material properties. Image from (Hungr 1995). Reprinted with permission. ................................................ 21 Figure 8. Summary of the physical properties and forces experienced by boundary elements in DAN model for (a) normal elements and (b) vertical elements. Image from (Mancarella and Hungr 2010). Reprinted with permission. ......................................................................................... 21 Figure 9. Depiction of the mesh in Lagrangian curvilinear coordinates. Mass is discretized into boundary blocks, i = 1 to n, and mass blocks, j = 1 to n - 1. Image from (Mancarella and Hungr 2010). Reprinted with permission. .................................................................................................. 23 Figure 10. Total force generated by the barrier is assumed to be a function of barrier maximum deflection, varying linearly with the coefficient K, barrier stiffness, which is unique to each barrier configuration. ........................................................................................................... 25 Figure 11. Depiction of flow front passing the plane of the undeformed barrier in DAN-Barrier and how the different components of the volume are calculated. The leading element is taken as a triangular prism with the incremental volumes of remaining elements  calculated as trapezoidal prisms. .................................................................................................................... 26 ix Figure 12. Example tangential transverse cross section through a deflected barrier showing the undeformed plane (top line), deflected shape (bottom curved line) and approximate area where material is in contact with the barrier. ................................................................................. 28 Figure 13. Comparison of tangential transverse cross section of an actual barrier with pinned constraints at ends and DAN model with pseudo 2D configuration. Areas shown are from the undeformed plane to maximum deflection of the barrier. Sketch is not to scale. ... 29 Figure 14. Screen shot of barrier tab in options menu of DAN where user can specify barrier location, stiffness and force distribution algorithm. ............................................................................... 30 Figure 15. Schematic of the flume apparatus. The hopper at the top of the chute is attached to  tower frames. The chute pivots on a lower tower. The terminus of the chute is a barrier and carriage assembly capable of transmitting total impact forces into a single load cell parallel to the direction of flow. ...................................................................................................................... 32 Figure 16. Flume setup fit with rigid barrier. Photo shows the position of the lights, cameras (only a single side camera in this case), pivot hinge, data logger and computer. ....................... 33 Figure 17. Front view of hopper loaded prior to testing. Material includes gravel front followed by sand. Hopper trap door opens with lever on left of photo and rises in less than 0.10 s. .......................................................................................................................................................................... 33 Figure 18. Model of the barrier and cart assembly detached from the chute body. Includes rails that are mounted to the side of the chute, sliding cart and barrier platform with interchangeable barrier (model prepared in Google Sketchup). ....................................................... 34 Figure 19. Example impact with flexible barrier. Photo shows the flexible barrier assemblage with rubber barrier and clamps, longitudinal stiffening rods as well as the grid transparency used for image analysis........................................................................................................... 35 Figure 20. Photo of the underside of the flume chute showing where the sliding cart is tethered through the load cell. All impacting force is transmitting from the barrier to the load cell in a single direction. ........................................................................................................................... 36 Figure 21. Thin flow front observed as only a few grains thick with extensive saltation when granular material was released from the hopper and allowed to accelerated under gravitational conditions over the length of the chute. ........................................................................... 39 Figure 22. Alternate test setup to obtain concentrated flow front and dynamic loading of barrier. A temporary tear-away face was placed in proximity to flexible barrier to promote thicker flows. ........................................................................................................................................................... 40 x Figure 23. Example release for concentrated flow front tests. Material is accelerated from behind across the width of the flow then removed when flow front approaches barrier face. Observations under gravitational forces only begin at t = 0 s, shown here, corresponding to when external force is removed. ..................................................................................................................... 40 Figure 24. Calibration data showing the applied load to the cell and measured force using Equation [29]. Includes data points for calibration with load cell suspended vertically and attached to test apparatus with chute inclined at 34°. ........................................................................... 42 Figure 25. Measurements of velocity over time at different points within the release mass as output from Tracker software. The highlighted point corresponds to time of release from the video analysis and is comparable along the length of the mass. ................................................ 44 Figure 26. Example results for thin flow front tests impacting a rigid barrier (left) and flexible barrier (right). Data for total force taken from load cell, black line, where the amplitude of natural oscillation acts as an approximation of error. Red line represents fill height at plane of the undeformed barrier, red line the maximum deflection beyond plane measured only for flexible barriers. Both values measured from video analysis. ...................... 45 Figure 27. Example of measurements made for thin flow front tests at time of maximum fill height. Angle of backfill measured from horizontal and fill height measured at plane of undeformed barrier. ............................................................................................................................................. 47 Figure 28. Geometry for calculating Coulomb's lateral earth pressure for active state with inclined backfill and wall friction. ................................................................................................................... 48 Figure 29. Comparison of force to fill height relationship of thin flow front tests, see legend for symbology for tests versus calculated values using Coulomb lateral earth pressure relationships. Solid lines represent active earth pressure scenario for a range for backfill angles from 14° to 26°. Dashed lines show same range but using passive lateral earth pressures. .................................................................................................................................................................. 50 Figure 30. Two example results for steep flow front tests impacting a flexible barrier. Notes are the same as Figure 26................................................................................................................................... 51 Figure 31. Example of measurements made for steep flow front tests at time of maximum force. Two measurements of height were made, the higher is maximum height, the lower is an approximation of the impacting body height neglecting minor material runup along the face of the barrier. ................................................................................................................................................. 53 Figure 32. Results from steep flow tests presented as a function of velocity and flow height as commonly done for flow-type landslides (Sovilla et al. 2008; Bugnion et al. 2011; xi Brighenti et al. 2013). Four heights used for h on the abscissa axis, showing the subjectivity of height in the calculation: (a) height at release, (b) ½ height at release, (c) height at impact, and (d) assumed height of the impacting body. Dashed lines are calculated values of force using the abscissa value and typical dynamic scaling coefficients. ....................................... 54 Figure 33. Chart showing maximum observed fill height compared to impact velocity for steep flow front tests. Distinction is made for flexible and rigid barrier tests. ............................ 55 Figure 34. Example of input file created for DAN-Barrier simulation. Outer box is drawn as 1 m x 1 m and is used for scaling within the program. Flow profile was taken from screenshot at t = 0, corresponding to when accelerating force was removed. .................................................... 57 Figure 35. Chart showing force as a function of deflection for all flexible barrier tests. Slope of the linear fit line would be anticipated stiffness value for barrier configuration in DAN-Barrier model. ......................................................................................................................................................... 58 Figure 36. Value of the stiffness coefficient, K, needed to calibrate each model in DAN-Barrier plotted against kinetic energy at time of release for concentrated flow front tests. . 60 Figure 37. Results for test S1 of the concentrated flow front tests comparing total force, fill height, and deflection of the observed test with those predicted by DAN-Barrier. ................... 61 Figure 38. Sensitivity analysis showing effect of model stiffness on force, left, deflection and height, right. Three models with varying initial conditions, mass and release velocity combined as kinetic energy were tested. Circles represent actual values needed to calibrate each model to observed values. ....................................................................................................................... 63 Figure 39. Sensitivity analysis showing effect of release velocity on force, left, deflection and height, right. Three models with varying initial conditions, mass and release velocity combined as kinetic energy were tested. Circles represent actual values needed to calibrate each model to observed values. ....................................................................................................................... 63 Figure 40. Total force of the incoming flow is divided evenly between all transverse cables. This force is converted to a uniform line load acting over each cable. ............................................ 66 Figure 41. Catenary curve with line load q, and resulting constant horizontal force, H and a changing tensile load, T, at different locations along the curve. ........................................................ 68 Figure 42. Illustration of influence width as the front of the landslide with width, b, interacts with a flexible barrier containing multiple posts. The pressure across each influence width contributes to a force applied to each post. ................................................................................................ 69 Figure 43. Force diagram applied to individual post. Moments were summed about the base of the post. ................................................................................................................................................................ 70 xii Figure 44. Schematic profile and plan of the USGS test flume and barrier location used in back-analysis. .......................................................................................................................................................... 71 Figure 45. Photo of the USGS flume constructed in Oregon, USA (Iverson 1997). ..................... 72 Figure 46. Screenshot from Test 2 video at maximum material height. All dimensions are in meters. Blue line is height of the undeformed net used as reference, red lines are measurements of deformed net height and material run-up height. ............................................... 73 Figure 47. Screenshot from Test video at maximum deflection. Blue line is a reference distance of 2 m. Red lines show measurements of approximate impact width, barrier mesh deflection and cable rope deflection. ............................................................................................................. 73 Figure 48. Rope forces in right lateral anchor and right tie-back anchor measured during Test 2 of USGS flume tests using load cell attached to cable (DeNatale et al. 1999). ................ 74 Figure 49. Geometry of USGS test flume and input model used for DAN-Barrier. ..................... 75 Figure 50. Total force, fill height and deflection over time for USGS flume Test 2 predicted by DAN-Barrier. ............................................................................................................................................................ 76 Figure 51. Schematic profile and plan of the Veltheim test site including 3 panel barrier and location of instrumentation used for back-analysis. ............................................................................... 78 Figure 52. Overview of the Veltheim test site with the release basin at the top of the site, instrumented runout area and three panel flexible barrier (photo provided by Geobrugg and WSL). ........................................................................................................................................................................... 79 Figure 53. Dimensions of the filled barrier after Test 7.1 (figure provided by Geobrugg and WSL). ........................................................................................................................................................................... 80 Figure 54. Screenshot from the side camera at time of maximum deflection (t = 5.9 s) showing reference distance in blue and measurements of maximum deflection and fill height in red. ............................................................................................................................................................ 81 Figure 55. Rope forces in various cables during Test 7.1 (data provided by Geobrugg and WSL). ........................................................................................................................................................................... 81 Figure 56. Geometry of Veltheim test site and input model used for DAN-Barrier ................... 82 Figure 57. Calculations of total force, fill height and deflection over time for Veltheim Test 7.1 using DAN-Barrier. ........................................................................................................................................ 83 Figure 58. Estimated impact width and height of flow during peak force (upper image), and distribution of pressure for half the flow to designated posts, the influence width (bottom image). ........................................................................................................................................................................ 84 xiii ACKNOWLEDGMENTS I would like to take this opportunity to thank my supervisor Professor Oldrich Hungr. It was a pleasure to work with him, and to learn from such a knowledgeable and experienced engineer and academic. I would also like to thank Jorn Unger of the Earth and Ocean Science department machine shop for his assistance in constructing the test flume used throughout this work, as well as David Jones of the computer staff for writing the data acquisition code that made experimentation possible. Finally, I would like to thank my wife Yoko, for her patience and support throughout this work.  1 1 INTRODUCTION Landslides, along with many natural phenomena, can have a significant adverse impact on communities and civil infrastructure. However, they remain an extremely important landscape-forming process. They create broad geomorphologic features, and provide a means of transporting in-situ material down a slope and into the fluvial system (Petley 2010). Regardless of their morphological merit, landslides can pose great hazard and effort is placed on abating this by constructing mitigation measures. The focus of this thesis is the design practice of one very promising means of mitigation for a particular subset of landslides. As the use of flexible barriers for debris flow and debris avalanche mitigation expands, the methodology presented here will hopefully gain more widespread consideration. Between 2004 and 2010 there was an average of over 4,600 fatalities per year directly contributed to landslides (Petley 2012). This number continues to rise as reporting improves, but also as people migrate into more hazard prone environments at the base of steep slopes or adjacent to steep drainage channels. It is in these environments that extremely rapid (velocities greater than 5 m/s) flow-like landslides typically occur (Hungr et al. 2001). This subset of landslides includes a wide range of phenomena such as rock avalanches, flow slides, debris flows and debris avalanches. These vary in flow velocity up to 20 m/s, and can include tens to hundreds million m3 of material in the case of catastrophic rock avalanches (Hungr 2006). Great effort has been made in understanding the mechanics of such phenomena for engineering design of mitigation measures. As a result of these efforts, installations of earth fill and rigid reinforced structures have been successful at stopping or diverting reasonably sized flow-like landslides (less than 10,000 m3), typically debris flows or debris avalanches (e.g. Di Pietro and Tinti 2008). These technologies are quite material and labor intensive. In addition, extensive site access is needed during construction and after for general operation and maintenance. Recently, within the past few decades, the use of flexible barriers has addressed some of these limitations (Roth et al. 2004). The barriers are made of interconnected steel meshes and cables that yield as the landslide material is decelerated and retained. The result is an extended impulse that reduces forces in the fence components. In addition, the open construction allows for dewatering of the landslide debris being retained, reducing mobility (Volkwein et al. 2011). Construction is limited to the installation of rock bolts or soil anchors followed by the assembly of a prefabricated system. The installation process is simple enough for use in difficult to access locations.  2 As this is a relatively new technology, the design approach is still under development. Various approaches have been suggested for quantifying the pressure exerted by a landslide on a flexible barrier, each with benefits and limitations. Current practice relies solely on the fluid behavior of the landslide and does not take into an account the flexibility of the structure. This seems erroneous, as the benefit of the flexible barrier system is its structural reaction during loading.  1.1 Thesis objectives This thesis addresses the disconnect between the physical properties of landslides and the structural reaction of flexible barriers when dimensioning impact pressure. A simple numerical model has been developed that predicts the total force generated by a landslide during impact, by considering the deflection of the flexible barrier. The model was coded using Visual Basic into a previously validated numerical code for the analysis of flow-like landslides, called DAN-W (Hungr 1995). The result is an easy to use program, referred to as DAN-Barrier, where the user specifies material properties of the flow and a generalized stiffness of the barrier. The model predicts the landslide motion over a user defined flow path while taking into account changes in internal strength, basal resistance and geometry. Once the flow interacts with the barrier, the total force, material fill height behind the barrier, and barrier deflection are recorded. DAN-Barrier is intended to be an easy to use design tool for preliminary prediction of flexible barrier fence capacity and geometry. However, there are limitations to the applicability of the tool in regards to the filling process that occurs as landslide material interacts with a barrier. This thesis strives to quantify when the tool is appropriate, and what the alternatives are when it is not. 1.2 Layout of thesis After an introduction to flexible barriers in Chaper 2, the numerical basis of DAN-W and DAN-Barrier are presented in Chapter 0. In an effort to validate the model, a series of controlled laboratory experiments were conducted. This work constitutes a significant portion of the thesis. Setup of the apparatus, the testing process and results for two categories of tests are summarized in Chapters 0 and 5. Chapter 6 addresses the effectiveness of the numerical solution in predicting the total force, fill height and barrier deflection at the laboratory scale. To assess the ability of the model to predict larger scale flow-structure interactions, two back-analyses are performed in Chapter 7. The predicted total force from DAN-Barrier was divided it into component loads using two analytical approaches, the results are compared to data obtained from instrumented full-scale tests. Finally, conclusions and suggestions for future work are presented in Chapter 0.  3 2 BACKGROUND The discussion of landslides is facilitated by the development and refinement of classifications of different landslide types. The system, that is the most widely used, was developed by Varnes (1954, 1978), and has been continually refined as our knowledge improved and needs changed for example by Cruden and Varnes (1996) and most recently by Hungr et al. (2012). This type of system allows landslide practitioners to distinguish between materials involved and transportation mechanisms when referring to a mass movement event. Within the various categories, there exists room for continual review and refinement (Goodman and Bray 1976; Phillips and Davies 1991; Hungr et al. 2001; Hungr and Evans 2006; Stead et al. 2012), resulting in a nomenclature that is sufficiently narrow while not limiting. One particular subset of landslides, flow-like movements, is of particular interest to the protection of human life and infrastructure. This mechanism describes movement where a lack of internal shear stress allows mixtures of solids, liquids and gas to travel as a fluid. This is a broad category that encompasses slow intermittent landslides such as earth flows travelling as little as a few meters per year (Keefer and Johnson 1984), to the opposite end of the spectrum, with extremely rapid debris flows and debris avalanches capable of velocities in excess of 20 m/s (Costa 1984; Davies et al. 1992). The mobility of debris flows and avalanches coupled with their capability to transport large concentrations of material has placed them among the most damaging and catastrophic of natural events (Takahashi 2007). It is understandable that great effort has been placed on the mitigation of risk associated with them. This is the focus of the research described here. 2.1 Debris flows and debris avalanches As the name implies debris flows and debris avalanches involve the flow-like transport of debris. This is a mixture of fine to coarse-grained materials including cobbles and boulders, along with trace amounts of clay and organic material. The mélange is typically the result of natural geomorphic phenomena (e.g. weather, mass transport, glaciation) but can also be generated through anthropogenic processes (e.g. waste dumps and landfills). Water content plays a significant role in the initiation and mobility of such landslides and will often change throughout displacement as more material and water is entrained or deposited (Hungr et al. 2012). While both phenomena include debris and varying levels of saturation, the significant difference between debris flows and debris avalanches is the presence of confinement. Debris flows are 4 restricted to an established path, typically gullies and first or second order drainage channels. As a result of this channel specific behavior debris flows are often periodic as material accumulates in the channel until a perturbation triggers subsequent failure. Then the cycle repeats itself in the same path. These periodic events will form well-defined deposit zones referred to as fans. In comparison, debris avalanches are not confined to a specific channel and can involve partially saturated or fully saturated material. Often referred to as open-hillslope failures, they typically involve the failure of a thin veneer of residual soil or colluvium on steep slopes and morphologically resemble snow avalanches. The likelihood of subsequent failures occurring in an exact location is limited, however broad slopes prone to debris avalanches pose a significant threat in terms of the extent and unpredictability of the impact and deposit zone. Debris flows and avalanches typically begin in times of rapid infiltration and runoff of water and involve a slip of soil during the first stage of failure. The exact mechanism of the initial failure is not fully understood (Costa 1984), though current research is looking at reproducing such instances by subjecting slopes to excessive infiltration (Akca et al. 2011). The release of material causes reworking of the particles and may involve a dramatic rise in the pore pressure resulting is a loss of shear strength, a process known as liquefaction (Terzaghi and Peck 1967). This transition from a cohesive body of material to a viscous fluid can also be accomplished by an impulse in the form of rockfall or rock slide (Lacerda 2007). Accounts have also been made of debris flows being initiated spontaneously from oversaturation of gully bed material, or even excessive erosion of the channel banks. Once the process has initiated, the flow propagates due to undrained loading (Sassa and Wang 2005). The mobilized material overrides saturated bed material (or partially saturated in the case of some debris avalanches). This causes either compaction of the grains or an increase in pore pressure due to increased total stress, resulting in further loss of shear strength as pore pressure rises. The newly liquefied material becomes entrained in the flow and the landslide rapidly progresses. The majority of material may be contributed by the entrainment process as opposed to the initial failure (Hungr et al. 2012). This highlights the importance of available bed material in controlling the magnitude of debris flows and empirical relationships exist describing this (McDougall and Hungr 2005). Often the flow path widens downslope. A concept referred to as apex angle is described for debris avalanches (Guadagno et al. 2005) where the angle at which the flow widens as it progressively entrains material downslope is controlled by the characteristics of the soil veneer involved. 5 A particularly devastating characteristic of debris flows is the development of surge fronts. During the course of travel down a steep gradient, larger boulders tend to be accumulated at the front of the flow. This has been explained using various theories. Two competing thoughts on which are dispersive pressure where larger particles are driven up to the top of a flow, and dynamic sieving where finer grained particles settle the base of the flow (Takahashi 2007). Regardless of the mechanism, the larger components are transported toward the front of the flow due to strong vertical velocity gradients, resulting in a bulking of material at the snout (Pierson 1986; Iverson 1997). In this manner it has been noted that the peak discharge of a debris flow can be in excess of 40 times that of an extreme flood in the same channel (VanDine 1985). Often a portion of the flow front will become lodged in the channel creating a temporary dam and accumulation of material. When this releases additional surges of material are developed extending the duration of the debris flow event (Costa 1984). Surge or wave fronts are not completely dependent on damming however. Davies et al. (1992) described recurrent waves in a more dispersed muddy debris flow with waved spaced exactly 50 seconds apart. The surge front is responsible for the bulk or erosion and damage during a debris flow, and the occurrence of multiple waves increases the potential for disaster throughout an event. The existence of a developed surge front is not documented for debris avalanches. However, other issues associated with these types of flows that make them worthy of concern. One is the unpredictability of the point of initiation. On a wide planar slope it is difficult to pinpoint a single hazard which leads to mitigation measures spanning entire slopes (Geobrugg 2010). Sometimes it is not a single event that occurs. There are incidents where torrential rain or earthquakes cause widespread debris avalanches throughout a region. This has been referred to as Multiple-Occurrence Regional Landslide Events (MORLEs). These pose a significant threat in the regolith soils of northern New Zealand where as many as 100 landslides could occur in a single square kilometer (Crozier 2005). Recently, over 3,500 landslides occurred within two days following 48 hours of heavy rainfall outside of Rio de Janeiro (Avelar et al. 2011). Cumulatively these events killed over 1,500 people and caused widespread damage to infrastructure. Another characteristic of debris avalanches that is relevant to the design of protective measures is that some of the material involved may remain partially coherent, either because it is not completely saturated, or because it is bound by vegetation roots. 6 2.2 Protective structures Approaches to landslide risk mitigation can be broken into two broad categories, passive and active. The earlier includes avoidance measures such as relocating an entity at risk or stabilization of a potential hazard prior to mobilization (e.g. rock bolting or snow fences). While often efficient and cost effective, such approaches are not always achievable even after a hazard has been identified (e.g. Nicol et al. 2013). In this situation an active approach is requisite. This typically entails the construction of a berm or barrier with the intent of diverting or stopping a hazard prior to interacting with anything of value. The concept of constructing protective measures has been around for centuries and thus encompasses various designs. Examples include dykes and berms for diversion, terminal barriers as means of retention, or permeable check dams to separate large clasts from a developed surge. It is outside the scope of this research to discuss all mitigation measures in detail. Instead focus is on flexible barriers, which are a relatively new means of protection. 2.2.1 FLEXIBLE BARRIERS A description of these barriers and their use in conjunction with debris flows, and more recently debris avalanches, is best accomplished through a chronological review of the technology. Early flexible structures constructed within a channel were referred to as debris flow breakers. Testing of breakers began in Japan in the 1970s. The nets consisted of relatively light gauge steel wires strung across a torrent channel with a suspended net (Figure 1) designed to entrain large clasts similar to rigid permeable check dams. Their lightweight construction limited their effectiveness to low energy flows, or to use in combination with conventional check dams (Tabata et al. 2004; Suwa et al. 2009). There were also reported issues with corrosion of the components. Recent improvements in corrosion protection and a move towards more substantial components, including ring net mesh, have increased effectiveness. Successful case studies have been reported for Tateyama-Daishiwara valley (Tabata et al. 2004) and Mount Yakedake (Suwa et al. 2009).  Debris flow breakers rely on a widely spaced mesh pattern to retain only the largest clasts in a flow, breaking the surge front of the debris flow. The flexibility of the steel cables and mesh are enough to withstand impact. These are contrasted to debris flow barriers, which are intended to withhold a larger proportion of the landslide material by limiting the mesh spacing. More material captured results in greater forces transferred to components, and energy-dissipating elements are introduced to help accommodate this. 7    Figure 1. (a) Ring net style debris flow breaker installed in a channel of Mount Yakedake, Japan and (b) same barrier after successfully retaining material in an event on July 18, 2004, see person in photo (b) for scale (Suwa et al. 2009). Packaged debris flow barriers currently available for installation by manufacturers like Geobrugg or Trumer Schutzbauten have evolved from flexible rockfall barriers. Widespread installation of rockfall fences began in the 1980s throughout North America, Europe and Japan. The concept behind the barrier is the “soft catch,” where momentum of the moving block is dissipated over a longer contact period due to the barrier’ flexibility, reducing the observed forces throughout the system. Contact is further extended by the introduction of brake elements that yield plastically at predetermined loads extending the length of the structural wire ropes. The systems are designed based on energy absorption capacity, verified by full-scale tests adhering to various standards for testing (Higgins 2003; SAEFL & WSL 2006; EOTA 2008; Austrian Standards Institute 2013). Such standards initially ensure that barriers function appropriately at a given energy level and provide a threshold for implementation. They also require a level of serviceability to be proven during multiple impacts. For example, ETAG 027 (EOTA 2008) requires that a barrier impacted twice with a reduced energy (1/3 the maximum design energy) must maintain a residual useful height of 70% its initial height. Over time, rockfall barriers were accidentally impacted by various types of debris flows, debris avalanches and snow avalanches, demonstrating their effectiveness at retaining large amounts of material (Roth et al. 2004). A particularly enlightening event occurred at Aobandani Tateyama Sabo in Japan where a debris flow carrying 750 m3 impacted a 1,500 kJ rockfall barrier installed to protect construction work, Figure 2. The brake elements yielded between 20 and 80 % and all anchorage remained competent while the barrier mesh expanded over 3 m. Back analysis of the event suggested that 3,900 kJ of impact energy may have been imparted by the flow and successfully retained. 8  Figure 2. Rockfall protection barrier filled with 750 m3 of material after a debris flow event in Aobandani, Japan in 1998 (Roth et al. 2004). By the late 1990s, research had begun around the world investigating the effectiveness of these barriers at mitigating debris flows. To evaluate the effect of mesh configuration on debris retention, six full scale flume tests were tested utilizing a 95 m test flume in Oregon, USA constructed by the U.S. Geological Survey to study the mechanics of debris flows (Iverson 1997). 10 m3 of saturated debris flow material was released and filled various mesh configurations. Hexagonal meshes with 150, 200 and 300 mm openings as well as 300 mm diameter ring net meshes were tested. The greatest retention was accomplished by the ring net mesh lined with chain link wire mesh (DeNatale et al. 1999), which soon became the industry standard for implementing debris flow barriers.  The versatility of the barriers was demonstrated in another controlled experiment performed by Wartmann and Salzmann (2002). Flexible ring net barriers were impacted with wood debris ranging from single large trees up to mixed wood debris totaling 25 m3. The ring net material performed well when impacted by the punching load of the trees and elastically transmitted the force to the lateral anchorage with little damage. Following the proof and preliminary testing of debris flow retention barriers, a series of debris flow specific barriers were installed in the hills outside of San Bernardino, CA in the summer of 2004 following a devastating wildfire season (Rorem et al. 2013). Under the direction of CalTrans, six different designs were implemented at ten sites and have subsequently been impacted by multiple debris flows. After each event, the barriers were deconstructed and cleaned in anticipation of subsequent impacts and design alterations were made to facilitate easier operation and maintenance requirements. As the popularity of the solution spread, similar systems were reported throughout Europe and Asia and used in conjunction with embankments to provide a far reaching protection solution (e.g. Di Pietro and Tinti 2008). 9 To aid in the further refinement of the technology, several performance monitoring sites were established and continue to function. The longest running and most effective in terms of data delivered, is the Illgraben torrent site in Switzerland, implemented and monitored by the Swiss Federal Institute for Forest, Snow and Landscape Research (WSL) (Wendeler et al. 2006; Wendeler et al. 2007; Bartelt et al. 2009). Since the initial installation in 2005, several iterations of the barrier design have been constructed and impacted with debris flows ranging from 10,000 to 75,000 m3. The site is fully instrumented with strain gauges on the barrier, geophones to measure micro-seismicity, cameras, laser flow depth gauges, and pressure plates in the channel walls and floor. This suite of data has allowed for the progress of the design practice and the development of a new approach to dimensioning the impact forces of debris flows on flexible barriers developed by Wendeler (Wendeler et al. 2007; Wendeler 2008), which will be discussed later. A standardization of the design approach has led to the proliferation of flexible barriers as debris flow mitigation measures. Barriers have been implemented throughout Europe (Wendeler et al. 2008; Pederzani et al. 2009), New Zealand (Hind and McArdell 2010), and British Columbia (Bichler et al. 2012). The use of these barriers has also been extended to tiered installations in larger torrents, stiffened barriers to act as flow front breakers similar to the original Japanese design, and culvert protection (Geobrugg 2009). Most recently, the use of flexible barriers has extended to the mitigation of debris avalanches. This type of implementation required greater coverage because of the unspecified initiation point of the landslide. Therefore lighter, more cost effective meshes were used. Closely spaced posts, coupled with soil nailing at the base of the mesh, facilitate load transfer to the ground as opposed to lateral anchors in typical debris flow or rock fence design (Volkwein 2009). Testing of this concept began in 2006 with the construction of a full scale open hillslope landslide facility in Veltheim, Switzerland (Bugnion and Wendeler 2010; Bugnion et al. 2011). 50 m3 of saturated material was released down a 30° slope 41 m long and 8 m wide. The debris impacted a 3.5 m high three-panel barrier with the majority of debris concentrated in the central 5 m span. Instrumented support cables provided an understanding of the generated forces during an impact. In addition to the fence instrumentation, pressure plates were constructed within the flow path perpendicular to the direction of the travel. These plates were used to back calculate proportionality coefficients to estimate impact pressure when designing barriers for the mitigation of debris avalanches (Bugnion et al. 2011), as described in the following section. 10 2.3 Flexible barrier components Extensive full-scale testing and iterative design has resulted in the barrier configuration shown in Figure 3. A wire mesh is suspended across the channel width using steel cables with additional cables at mid span (vertically) for additional load distribution to the channel walls. The bottom of the barrier does not extend to the channel base to allow for unimpeded flow and sediment movement during normal hydrologic conditions. This type of barrier can be constructed up to 25 m wide, 6 m high, and retain approximately 1,000 m3 of debris material (Wendeler et al. 2010).  Figure 3. Installation of a debris flow barrier in a torrent channel in Switzerland (Geobrugg 2009). Note that the fence does not extend to the base of the channel allowing for flow under normal hydrologic conditions. The various components of the flexible barrier system are highlighted in Figure 4. The steel wire ring nets are responsible for entraining the material. A high capacity wire mesh could also be used as the primary mesh. A secondary wire mesh, typically chain link, can be added to increase retention of finer particles. The load is transferred from the mesh to the lateral transmission cables and mid span as well as the support ropes at the top and bottom of the barrier. The addition of break elements along the cable allows for extension that dissipates energy during expansion and also reduces the forces generated within the cable. This load is then transferred to the rope anchors, which may be bolted directly into competent rock at the walls of the torrent or are incorporated into poured concrete foundations. The top support rope is protected by angled steel against abrasion in the case of overflowing. For larger spans the addition of steel posts is necessary to ensure adequate vertical coverage across the channel. Roth et al. (2004) suggested that the load on these posts is not critical and that they should be able to withstand direct impact. However, Kwan et al. (2014) recently investigated a site where a rockfall barrier was impacted by a shallow hillslope failure and the posts suffered catastrophic damage. The overall barrier was still effective 11 as the anchors did not fail, but the posts were fully deformed. Debris avalanche barriers utilize similar components with the modifications mentioned earlier.  Figure 4. Typical debris flow barrier components (Geobrugg 2009). Corrosion is of particular concern with debris flow and debris avalanche barriers. All elements are galvanized using standard hot-dip methods. In addition, some companies use a special zinc/aluminum coating to further protect the ring net mesh and steel cables . 2.4 Current approaches to the determination of impact forces Fundamental to the dimensioning of any protective structure is an understanding of the flow behavior. The relationship between induced internal stresses and shear strain rates and flow velocities is referred to as rheology. The rheology of flow-like slides exists somewhere between elastic solids and viscous liquids (Brighenti et al. 2013). Motion can be described using first principles focusing on conservation of mass, energy and momentum. Models have been developed based on varying levels of simplification ranging from 2-D heterogeneous fluids to complex 3-D flows incorporating three phase interactions. An initial model for the design of flexible debris flow barriers was based on an energy approach and was first presented by Wartmann and Salzmann (2002) and further refined by Roth et al. (2004) and Wendeler et al. (2006). The approach assumed that the barrier must stop a certain body of 12 material with mass M, traveling with an average velocity v, such that the kinetic energy is defined by standard dynamics. [1]     ⁄     Once contained, this mass will stop subsequent flow arriving at the barrier. The difficulty was defining the quantity of material that interacts with the barrier. It was suggested that the mass of material be taken as [2]            where ρd is the density of the debris flow, typically between 1,800 kg/m3 and 2,300 kg/m3 based on field observations (Wendeler et al. 2006), Qp is the peak discharge, and Timp is the impact duration. Wartmann and Salzmann (2002) suggested an impact time of 4 seconds be used. The peak discharge can be derived from empirical equations for granular flow as [3]                  and for muddy debris flows [4]                   where VDF is the design debris flow volume (Wendeler et al. 2006). With the peak discharge, flow velocity can be estimated through an additional empirical relationship outlined by Rickenmann (1999). [5]                   with S being the local slope gradient. Roth et al. (2004) suggested this value be cross referenced with the Manning Stickler equation and the more conservative estimate be used, [6]                Using Equation [6], the pseudo Manning value, nd, is taken between 0.05 and 0.18 s/m1/3, with granular debris flows favoring the higher end of the range. This approach introduces the need to further approximate the flow depth, h. Wendeler et al. (2006) suggested calculating this from the peak discharge and average channel width, b, such that 13 [7]         Roth et al. (2004) cautioned that the energy derived using this approach was not the same as the energy ratings of flexible rockfall barriers that were established through full scale testing. As verification, it was encouraged that numerical modeling be used to better the understanding of the forces generated within the barrier. This was performed at the WSL institute in Switzerland through modifying a discrete element code used to model flexible rockfall barriers called FARO (Volkwein 2005). The debris flow load was distributed to a series of nodes making up the barrier mesh, and transferred to longitudinal support ropes. Results of the numeric tests were compared to results from the instrumented Illgraben torrent with appreciable variation (16 to 20% difference in cable forces) (Wendeler et al. 2006). However, adaptations to the code, and the application to other events resulted in better fit results with the error limited to 6% (Wendeler et al. 2008). The energy model described is dependent on impact time during a filling event. For events with a more gradual filling the entrained mass and therefore energy of the flow is drastically overestimated. This is the case for muddy debris flows which are reminiscent of heavily sediment laden floods, also referred to as hyperconcetrated flows (Hungr et al. 2001). The surging behavior is less pronounced and barriers will slowly fill, sometimes never exhibiting a change in discharge. To accommodate the lack of versatility in the energy approach, Wendeler et al. (2007) suggested a force approach based on conservation of momentum. The approach assumes that the debris flow material arrives in surges imparting a dynamic pressure on the barrier, similar to that considered in fluid dynamics. The load is evaluated from the momentum equation, assuming that all the momentum flux approaching the barrier is balanced by the impulse of the resisting force, per unit of time.  This is an approach that has commonly been used for the analysis of rigid barriers. Once a certain amount of material comes to rest, the force will transition to a static load as the arrival of a new front imparts additional dynamic force. The equation can be simplified to a function of dynamic density, ρd, which may vary from the static density once the particles are in motion relative to one another (Hungr 2008), and velocity, v. [8]          A dynamic coefficient, α, is included to account for the added thrust of the debris due to shock loading. The coefficient can vary between 1.5 and 5.0 (Canelli et al. 2012), but is commonly accepted as 2.0 when the barrier is flexible and drained (Kwan and Cheung 2012). 14 After the initial dynamic impact it as assumed that the material comes to rest and imparts a static pressure normal to the barrier. This can be calculated using lateral earth pressure across the depth of the deposited flow, (b) in Figure 5. [9]           Figure 5. Assumed filling process for the calculation of dynamic and static loads on a barrier. Initial impact (a) imparts a dynamic load only followed by progressively larger static loads, (b) and (c), ending in overtopping where static and shear forces dominate. It has been suggested that an earth pressure coefficient, K, of 1.0 be used in these calculations (Kwan and Cheung 2012). The depth, d in Equation [9] is measured vertically down from the free surface, ρs is the static density of the material, and g is gravity. In practice this value is assumed equal to the dynamic density in Equation [8]. This relationship for estimating the dynamic pressure has been adopted by guidelines for the construction of mitigation measures in Switzerland and Hong Kong (Egli 2005; Kwan and Cheung 2012). While commonly used for saturated debris flows (Bartelt et al. 2009; Brighenti et al. 2013), the approach has also been extended to the analysis of shallow hillslope failures and debris avalanches. However Bugnion et al. (2011) observed through back analysis of full scale tests that 15 the value of α is reduced to between 0.3 and 0.8. Similar velocity dependent pressures have also been observed in experiments with wet and dry snow avalanches (Sovilla et al. 2008; Thibert et al. 2008) and similarly have been adopted into EU standards for design of avalanche mitigation structures (Barbolini et al. 2009). A modified energy approach was suggested by Sun and Law (2011) that depends on the filling mechanism when debris first contacts the barrier, Figure 6. While initially quite promising as a means of dimensioning flexible barriers, the approach has been de-emphasized in recent reports on the design of flexible barriers in Hong Kong (Kwan and Cheung 2012), instead favoring the force approach described.   Figure 6. Schematic of the pile-up mechanism (top) and run-up mechanism (bottom) as described by Sun and Law (2011) for the calculation of energy to be dissipated during impact with a flexible barrier. The work still holds utility in the description of the filling mechanism, which can be summarized as either pile-up or run-up depending on the behavior of this material at contact with the barrier. This qualification arose from flume experiments performed by Law (2008). These initial tests were performed with dry and partially saturated granular mixtures against rigid barriers. The barrier was supported by springs and allowed to depress slightly as material accumulated at the face. The deflection of the plate was used to calculate the total force. Law (2008) focused on qualitative description of the force histories of different materials during impact. He noted the largest variable 16 was the time from initial impact to maximum force. This affected the rate of change of momentum, and the observed force. It was observed that dry granular materials had a prolonged fill time and therefore a lower force compared to partially saturated materials (water content less than 30%). The tests were modeled using Itasca’s Particle Flow Code (PFC). The granular material was modeled in 3-D using spheres with a diameter of 21 mm, which impacted a rigid plate supported by larger elastic spring particles. The filling mechanism nomenclature shown in Figure 6 was suggested by Sun and Law (2011). They used similar 3-D PFC modeling to Law (2008), but replaced the rigid plate with elastic barrier particles. Running various iterations they were able to identify two unique filling processes. The pile-up mechanism was described as a thin jet of material riding up the face of the barrier. This material was then impacted from behind as additional material arrives. The pile-up mechanism was the result of viscous particle damping applied between particles that resulted in faster moving flows. Alternatively, when a frictional relationship was specified between particles in the numerical model, slower flow was observed and impact resulted in the run-up mechanism. Here, the material would come to rest forming a wedge behind the barrier. This served as a ramp for additional material to override and make further contact with the barrier before coming to rest and forming a new wedge. This behavior is similar to the surge behavior used in the force approach. It was emphasized that these processes were not unique and that an impact could initially start with the pile-up mechanism but would be followed by subsequent flow resembling the run-up mechanism. Other numerical models have been used to describe the impact of debris flows with flexible barriers. The force approach is used to describe landslide pressure as input to the discrete element code FARO mentioned earlier. The pressure is evenly distributed to the face of the barrier as a static pressure and the reaction within the barrier is analyzed. While this is an improvement on previous attempts at numerical modeling, it does not take into account dynamic behavior of the fluid – structure interaction during initial impact and shock loading. More recently efforts have been made to combine fluid behavior of the flow with structural performance of the barrier (Boetticher et al. 2011a; Boetticher et al. 2011b). The debris flow material is modeled as a homogeneous fluid using computational fluid dynamics software. A 3D deformable mesh is generated at the contact between the flow and the barrier generating values for flow parameters such as density, water content, head and velocity. These then become input parameters for FARO. After each time step deformation of the barrier net and change in forces is applied back to the fluid and the system repeats. 17 This is a robust method capable of detailed analysis of the fluid – structure interaction. However, there is significant limitation in the ease of use and time it takes to run models. Also, the material is assumed to be a fluid, with no internal shear strength. To the authors knowledge there are no simple models that account for both the behavior of the flow and the general structural behavior of the flexible barrier.   18 3 NUMERICAL MODEL FOR THE DETERMINATION OF THE TOTAL IMPACT FORCE OF A LANDSLIDE ON A FLEXIBLE BARRIER Current approaches to dimensioning flexible barriers and the resulting component loads solely focus on flow characteristics to determine impact and static pressures. As described in Chapter 2, the industry standard considers the dynamic pressure of a landslide, using empirically derived coefficients. It has been suggested that barrier configuration (rigid or flexible) has an effect on the way material accumulates behind the barrier, and that should be considered when choosing the dynamic pressure coefficient (Canelli et al. 2012). However, considering the many barrier configurations available, it is clear that different designs will react differently if subjected to the same loading event. Unique barrier arrangements may experience varying internal stresses when subjected to a constant load if components are allowed to yield to some extent during loading, as is the case when fences by different manufacturers are impacted with similar test loads (Gerber and Böll 2002; Gerber and Böll 2006). It is therefore necessary to take into account both the fluid behavior of the landslide imparting the load as well as the barrier's reaction during force dissipation. In this manner, a more complete understanding of the forces generated during the landslide mitigation process can be obtained. The tool described here, referred to as DAN-Barrier, is an initial attempt at combining landslide and structural forces during a loading event. The goal was an easy to use design tool used for the dimensioning of flexible barriers, both in terms of geometry and capacity. The current version of DAN-Barrier, developed and coded as part of this thesis, is still working towards this goal. At this point in time it serves as a proof of the concept, and with future development and optimization should prove useful in application. The tool is an adaptation to an existing numeric model for unsteady flow developed by Hungr (1995) called DAN-W (“dynamic analysis”), which is an independently verified and validated model for the analysis of rapid landslides (Hungr 1995, 2008; Mancarella and Hungr 2010). Previous work pertaining to DAN-W is first described in this chapter. This is followed by a description of the numerical foundation of DAN-Barrier and how it was implemented into the existing program. All work regarding DAN-Barrier is new, and presented for the first time in this thesis. The coding using Visual Basic is a collaborative effort between the author and Dr. Oldrich Hungr. 19 3.1 The original dynamic model, DAN-W The original model called DAN-W, was developed by Hungr (1995) with the intent of modeling the dynamic behavior of rapid flow-like landslides. It is founded in continuum mechanics and is comparable to the shallow-flow analysis of turbulent water flow, which are typically implementations of the St. Venant and Navier-Stokes equations (e.g. Strelkoff 1970). In both cases the governing conservation equations can be reduced to the bed parallel direction by assuming vertical, or bed-normal, velocity gradients to be zero. This is commonly referred to as a depth averaged or depth integrated solution. Such conditions are often considered 1-D in hydraulics, however for clarity this will be referred to as 2-D as it is capable of approximating the 2-D profile of the flow. One of the first models to implement shallow flow assumptions for the purpose of granular flows was developed by Savage and Hutter (1989). Their 2-D equation of motion is based on conservation of momentum and references a moving Lagrangian coordinate system, Equation [10]. Here ρ is flow density, h the bed-normal depth of flow, v velocity, t time, g gravity, α the local slope angle, k a proportionality ratio of the bed-parallel (longitudinal stress) to bed-normal stress commonly used in soil mechanics (further described in Equation [14]), σ is the bed-normal stress within the flow taken at the basal surface, s the local bed-parallel direction, and τb is the basal shear stress. [10]                          By nature of the shallow flow analysis the bed-normal stress at the base of the flow is given by [11]     (        ) where the term ac is acceleration due to centrifugal force along vertical curvature in the path such that [12]        with R being the local radius of the path. The coefficient k is a pressure term defined as the ratio between bed-normal and bed-parallel stresses within the flowing mass, comparable to lateral earth pressure coefficients in geotechnical analyses (Terzaghi and Peck 1967). This coefficient is commonly taken to be equal to 1.0 in hydraulic settings where the fluid is hydrostatic (Chow 1959). Savage and Hutter (1989) based their term on Rankine stress state where the value varies between active and passive conditions depending on whether the flow is expanding or compressing. 20 The key assumption of the Savage-Hutter model, as adopted by Hungr (1995) is that the rheology of the basal sliding zone, as used in Equation [13], is different from the character of the interior of the sliding body, which is frictional and controlled by a constant internal friction angle. This assumption is justified in many natural landslides, where the basal sliding zone is lubricated by relatively high saturation and by entrainment of weak material from the path. The resisting shear stress at the base of the flow, τb in Equation [10], was assumed by Savage and Hutter (1989) to be a function of dry Newtonian friction such that [13]            with the basal friction ϕb a focal point in the relationship. This model, as with many shallow flow models, neglects internal shear stress. While greatly simplifying the computations, this may contribute to an overestimate of flow runout or mobility. However, studies have shown excellent agreement between lab tests and numeric analyses using this relationship (Gray et al. 1999; Denlinger and Iverson 2004; McDougall 2006; Mancarella and Hungr 2010). Landslides, as opposed to water or dry granular flows, are often complex heterogeneous systems of water, soil, boulders and other components. Hungr (1995) used the concept of an equivalent fluid, Figure 7, to allow the simplified 2-D Savage and Hutter model (referred to as SH model) to be applied to such a complex system. In this scenario bulk properties are applied to a uniform flow. These properties cannot be explicitly determined, but instead must be approximated through back analysis of real cases by matching flow shape and velocity to the best of the numeric model’s capability. With a uniform assumption of the landslide mass and material properties, Equation [10] can be applied as a simple dynamic balance of forces on a discrete mass within the flow as shown in Figure 8. The left hand side of the equation is Newton’s second law of motion defining the acceleration of the mass. The right side is a summation of forces including gravity, basal resistance, and differential pressure on either side of the defined mass in the direction of flow, which is the difference in the area of the two shaded triangles below. Depending on the situation this term may be a driving or resisting force. 21  Figure 7. Concept of equivalent fluid, after Hungr (1995). The complex two-phase (or possible three-phase) flow can be modeled as a single material with uniform bulk material properties. Image from (Hungr 1995). Reprinted with permission.  Figure 8. Summary of the physical properties and forces experienced by boundary elements in DAN model for (a) normal elements and (b) vertical elements. Image from (Mancarella and Hungr 2010). Reprinted with permission. The initial pressure term, k, derived by Savage and Hutter (1989) was modified by Hungr (2008) to account for thinning (spreading) flow behavior. When this occurs the magnitude of the pressure differential, ΔP, becomes significant relative to gravitational forces due to a depth gradient (    ⁄ ) 22 in the direction of flow. This results in additional shear stresses that cause rotation of the principal stress direction beyond that described by Savage and Hutter (1989). More importantly a curvature develops in the flow lines and this causes a general failure of the shallow flow assumption. Applying a fraction of the additional shear stress can approximate the effect upon basal shear stress. This results in the pressure term [14]           [  √        (           )      ]    where ϕi is the internal friction angle of the material and ϕb,mod is the modified basal friction angle based on the basal friction angle, ϕb, such that [15]                  (    ) The plus sign in Equation [14] corresponds to the passive state, bed-parallel compression, and the minus to the active, bed-parallel spreading. The effect of Equation [15] is transforming the basal shear stress, τb, in Equation [10] to a modified value, τb,mod. However, a direct substitution of Equation [15] into the original equation of motion is not possible, this is done with the modifications made in [14]. The fraction of the additional shear stress due to the depth gradient was determined empirically by Hungr (2008) to be 0.333 and is termed λ in [15]. This value may be material dependent but validation exercises show good agreement using 0.333 (McKinnon 2010). This modification tends to be most significant in flows dominated by lateral spreading. The force balance described is implemented in DAN-W using a finite difference approach suggested by Potter (1972). The sliding mass is discretized as an extended lumped mass model with n infinitesimally thin boundary elements, separated by n–1 mass blocks of constant volume. These elements are oriented along a Lagrangian curvilinear coordinate system, Figure 9. The solution is found explicitly at each time step beginning with the rear of the flow and progressing to the front. Initially, velocities for each boundary block, vi, are updated according to Equation [10]. Next the curvilinear displacement of each block, Si, is determined for the time step. This is a measured along the path from the initial toe of the sliding mass and is stored for each element independently per time step. The thickness of the mass blocks, hj, is calculated at the center according to the volume of the block and the width between the two adjacent boundary elements: 23 [16]       (       )(       ) where Bi is a user-defined width at that location. The mass block heights are then used to calculate heights of the boundary elements, Hi, as the average of two mass block heights. Height for the first and last boundary element is taken to be one half the height of the first or last mass block resulting in trapezoidal shaped mass elements at the front and rear of the flow.  Figure 9. Depiction of the mesh in Lagrangian curvilinear coordinates. Mass is discretized into boundary blocks, i = 1 to n, and mass blocks, j = 1 to n - 1. Image from (Mancarella and Hungr 2010). Reprinted with permission. The ability to choose the appropriate rheology is essential in accurately modeling landslide behavior (Rickenmann 2005). A unique feature of the DAN-W tool is a built in open rheological kernel that allows the user to choose the basal resistance term, τb. The various functions include: plastic flow, friction flow, Newtonian laminar flow, turbulent flow, Bingham flow, Coulomb viscous flow, and Voellmy fluid flow. See Hungr (1995) for a complete description of these terms. The rheology and associated flow parameters are unique to each event although research suggests typical criteria that are appropriate for landslide categories. The Voellmy model is often used for modeling debris flows (Ayotte and Hungr 2000; McKinnon et al. 2008; McKinnon 2010) and rock avalanches (Hungr and Evans 1996) while a dry frictional model is more appropriate for many debris avalanches (Ayotte and Hungr 2000). In rare cases where the mass movement involves fine particulate material, the Bingham model may be appropriate (Geertsema et al. 2006). These represent only a few examples as the body of literature on the subject of landslide runout modeling continues to expand. The modeling process described can be performed with slices oriented vertically as opposed to perpendicular as shown on the right of Figure 8. This is particularly useful where rapid changes of the base topography could cause instability due to normal elements overlapping. Equation [10] in this context becomes 24 [17]                               (        )     where h is measured vertically from the base to top of flow. With the vertical slices it is necessary to assume that horizontal unbalanced pressures are transmitted to the base slice. This would cause the bed-normal stress, σ, acting at the base of the flow to become [18]         (        )             (        ) The process for solving the system remains the same, as does the calculation of the pressure term and basal resistance. The simplicity of DAN-W makes it an ideal tool for modeling the mobility of rapid mass movements. It can also accommodate the addition of general structural parameters to create a fast and versatile tool for modeling fluid – structure interactions. This is described in detail in the section that follows. 3.2 Introduction of DAN-Barrier The utility of a barrier module built into a previously validated and calibrated model is that the dynamics of the flow are already well described. Velocity, depth and distribution of mass are known at each time step leading up to an impact event, and can be used throughout the interaction with a barrier to describe the forces generated. This is the concept behind the program presented here, called DAN-Barrier. By quantifying structural properties of the flexible barrier into a universal empirical factor, a more rigorous analysis of the flow – structure interaction has been developed. For the purpose of validating the DAN-Barrier model, a flume apparatus with a square cross section was used to generate small scale, easy to model flows against a barrier. As suggested by Mancarella and Hungr (2010) the side friction imparted by the plexiglass walls of the flume may be appreciable in areas of high normal stress, such as when material begins to accumulate behind the barrier. For this reason a side friction force was included in the summation of forces equal to [19]            (   )    This accounts for friction from both walls and assumes that the pressure coefficient perpendicular to the walls is equal to the coefficient in the direction of flow. The friction angle between the plexiglass and sand used during experimentation was measured to be 15°. 25 3.2.1 GENERAL APPROACH Fundamental to the DAN-Barrier analysis is the concept of barrier stiffness. This stiffness term is a generic feature for each system encompassing the barrier's ability to retard flow. As a first approximation, it is assumed that the total barrier force is a linear function of the deflection in the barrier, Equation [20] and Figure 10.  Figure 10. Total force generated by the barrier is assumed to be a function of barrier maximum deflection, varying linearly with the coefficient K, barrier stiffness, which is unique to each barrier configuration. The total force, Ftotal, is taken to be the cumulative force of the flowing mass imparted on the barrier and conversely the retarding force generated by the barrier.  [20]            In this case the stiffness coefficient, K, is a linear stiffness with units kN/m. Deflection, d, is measured along the curvilinear path as the difference between the leading boundary element and the position of the undeformed barrier [21]               It was considered that the total force might be a function of retained volume behind the barrier making K a volumetric stiffness with units kN/m3. However, this approach is limited in that the deformed shape DAN-Barrier deviates considerably from what is observed in experiments and field tests. It was decided that longitudinal deflection was easier to correlate. However, the volume of material retained by the barrier is still recorded by the software for use in determining the deceleration of the elements in contact with the barrier (Figure 11). Deflection, d Total dynamic landslide force, Ftotal Barrier stiffness, K 26  Figure 11. Depiction of flow front passing the plane of the undeformed barrier in DAN-Barrier and how the different components of the volume are calculated. The leading element is taken as a triangular prism with the incremental volumes of remaining elements  calculated as trapezoidal prisms. This concept is implemented in DAN by introducing an observation point along the path associated with a user-defined stiffness. At the beginning of each time step the boundary elements are investigated from the rear of the flow to the front. From the time the leading boundary element passes the barrier location the volume of the mass blocks passing through the observation point (the barrier plane) are determined individually and accumulated, in addition to measuring the displacement of the leading element beyond the barrier. Parameters used here are similar to those previously described. For the case where only portion of the mass block is beyond the barrier the incremental volume is taken as  [22]      (           ) (            ) (            ) where Hbarrier is the height of the flow at the plane of the observation point obtained by linear interpolation between Hi and Hi-1 [23]             (       )(           )(       ) Volumes of the remaining mass blocks beyond the barrier are calculated similarly to Equation [22] with heights of the preceding boundary element used as opposed to those of the barrier.  Vi bave Sbarrier Sn Vbarrier    Vn   27 The total volume is simply the sum of these incremental volumes [24]          ∑                 At each time step, the total force acting on the barrier is calculated according to [20]. The effect of this unbalanced force is a uniform deceleration that is applied to all elements that have passed beyond the plane of the barrier. [25]                      This deceleration is added (or subtracted depending on the direction of motion) to the boundary element as the program updates the position and velocity at the end of each time step. It is assumed that Ftotal only affects those elements where            , although it is probable that material behind the barrier is affected as well. It was also considered that the force is not distributed uniformly but instead leading elements of the flow would experience proportionally higher fraction of the total force. However, as a first approximation of this approach it is the opinion of the author that these assumptions are valid and the results are reasonable. 3.3 Correlating deformed shape  Net deflection is typically an easy value to report when monitoring the performance of flexible barriers. The point of maximum deflection can be taken from video observation of either the side or top of the barrier, resulting in a single point along a parabolic shaped curve. Comparatively, the pseudo 3-D nature of DAN-W assumes that flow will fill the entire user-defined width. This results in a rectangular section when cut parallel to the bed, which means that maximum deflection is actually a line at the leading boundary element. In order to better correlate the deflection predicted in DAN-Barrier with what is observed in lab tests or back analysis, a correlation factor, S, is needed. This is accomplished by first characterizing the shape of an actual deformed barrier as a parabola, Figure 12.  Any position on the outside edge is given by a quadratic equation, [26]            The constants A, B, and C can be solved for using the width between barrier posts, w, and the maximum deflection, dmax, at a point between. These form a set of (x,y) coordinates that can be solved as a system of equations. By integrating the resulting curve over the width where the 28 material is in contact with the barrier, bflow, an approximation for the actual cross sectional area is obtained. This area, Aactual, is a bed-parallel plane at the height of maximum deflection and shown as the shaded area in Figure 12. This is particularly useful for examples where observations are made from above the barrier, which is often the case in instrumented flume tests (DeNatale et al. 1999; Yang et al. 2011; Bugnion et al. 2011).  Figure 12. Example tangential transverse cross section through a deflected barrier showing the undeformed plane (top line), deflected shape (bottom curved line) and approximate area where material is in contact with the barrier. As previously mentioned, the cross sectional area in DAN-Barrier along a similar plane would be a rectangle with width, b. It is assumed that the cross-sectional area of the actual shape and the deformed shape in DAN-Barrier are constant. This is used as a point of correlation, and it is possible to solve for the deflection in the DAN-Barrier model necessary to ensure that area is conserved. [27]                     It is also assumed that the width, b, in DAN is the same as the observed width, bflow. During laboratory experiments the impacting flow would typically deflect the barrier to its maximum prior to significant material loss or lateral expansion. Therefore it is reasonable to assume that the width of the flow leading up the barrier will remain constant up to the point of maximum deflection.  At this point two values are obtained, the actual deflection, dmax, and the deflection required in the model to conserve area, dDAN. By taking the ratio of these two values the correlation factor is obtained. [28]            This concept is presented graphically in Figure 13. The area of the green dashed rectangle is equated to the blue shaded area of the actual deformed shape. The scaling factor can be used to correlate the deflection reported in DAN-Barrier to what is observed in the field. w   dmax bflow 29  Figure 13. Comparison of tangential transverse cross section of an actual barrier with pinned constraints at ends and DAN model with pseudo 2D configuration. Areas shown are from the undeformed plane to maximum deflection of the barrier. Sketch is not to scale. The value S is dependent on the ratio of the width of the flow to the width of the barrier (i.e. total width of the parabola), b/w. For incidents where the width of the impacting flow is small relative to the total barrier width the deflection calculated by DAN will be close to the observed deflection. This may be expected for shallow open hillslope failures where a smaller mass is mobilized relative to the total width of the barrier. As the impacting flow widens relative to the width of the posts, dDAN will reduce and a smaller scaling factor is obtained. This is the case for debris flow barriers where a net spans the channel width and the flow is expected to make full contact. A set of scaling factors is presented in Table 1, generated for a symmetric parabola. These values assume that the flow impacts the center of the barrier, which is the case in controlled experiments and lab tests however, may not be valid for all scenarios (e.g. Akca et al. 2011). Eccentric loadings such as this are not considered at this time. These scaling factors are not built into the DAN-Barrier model but are presented separately for reference and use in back analysis. Table 1. Scaling factors as a function of the flow width to barrier width ratio (b/w) for a barrier with a deformed shape characterized by a symmetric parabola b/w S 0.3 0.95 0.4 0.94 0.5 0.91 0.6 0.87 0.7 0.83 0.8 0.78 0.9 0.73 1.0 0.67   3.4 Implementation of DAN-Barrier The tool is accessed in DAN-W through the options menu, Figure 14. An additional tab has been coded where the user can specify whether a barrier is present, its location along the x-axis in m, and stiffness in kN/m.  dDAN = Sdmax   ADAN = Aactual dmax   30  Figure 14. Screen shot of barrier tab in options menu of DAN where user can specify barrier location, stiffness and force distribution algorithm. During runtime of the analysis a display window reports the current total force in kN, barrier volume in m3, deflection as observed in DAN in m and the maximum height, hmax. The height is measured as the maximum flow thickness (normal height) at any point situated between the barrier plane and flow front in m. When the analysis reaches a stable condition the analysis terminates and these values are reported in a message box. In addition, they are included in the report that is generated at the termination of a run and available for export. When the radio button for flexible barrier is toggled on, the software will also generate an additional ASCII file containing barrier-specific data for use in plotting. Variables as a function of time are output in BART.DAT, an example of which is included in Table 2 describing the column data. These values can be used to construct time series plots of various parameters. Table 2. Example output for BART.DAT, actual file does not include column titles. Time (s) Ftotal (kN) Deflection (m) hmax (m) xmax (m) Volume (m3) 0.14 0 0 0 0 0 0.15 0 0 0 0 0 0.16 0.0179 0.00186 0.00085 0.75186 1.00E-06 0.17 0.4339 0.00548 0.00815 0.75153 1.30E-05 0.18 1.2127 0.00885 0.0134 0.75321 3.50E-05 0.19 2.2881 0.01306 0.01761 0.75056 6.70E-05 ect.         31 4 PHYSICAL TESTS – UBC TEST FLUME A significant portion of the research conducted as part of this this thesis involved validation of the numerical model using laboratory experiments. A distinction is made between validation and calibration in the context of numerical models. The first deals with known properties of simple materials in controlled environments. If a model is capable of reproducing similar results to experiments under a range of boundary conditions it is considered validated and capable reproducing physical results. The latter involves calibration through back analysis of case studies or experiments with the goal of deriving input parameters for use in future analyses. In an attempt to validate models for the mobility of flow-type landslides, many researchers have conducted tests with clean dry sand (Savage and Hutter 1989; Gray et al. 1999; Denlinger and Iverson 2004; Iverson et al. 2004). Similarly, the original DAN-W code underwent extensive review using laboratory sand experiments in 2-D (Hungr 1995; Hungr 2008; Mancarella and Hungr 2010), and 3-D (McDougall and Hungr 2004; McDougall 2006). Expanding on the laboratory validation of DAN-W, a laboratory exercise was designed and constructed to investigate the behavior of clean dry sand and gravel impacting both rigid and flexible barriers at the terminus of an inclined flume. The apparatus was not designed to simulate any conventional form of landslide, only to provide means of impacting a barrier with a simple material. This reduces concern of scale effects that are encountered when attempting to extrapolate similar exercises to actual events (Munson et al. 2006). By measuring the mechanical properties of these granular materials independently, the validity of the model was assessed. The results of the experiments presented in Chapter 5 are promising for the early stages of this numerical model (validation in Chapter 0). 4.1 Apparatus design and setup An experimental apparatus, Figure 15, was designed to impart a dynamic force onto a barrier resulting in shock loading. It was comprised of two general components, each including various functional parts. The first was a flume capable of rapidly releasing material down a channel. The second component was a barrier constructed perpendicular to the direction of flow that was capable of measuring the total force imparted by the flow as a function of time. A series of constraints were identified to ensure adequate results from the setup. These included: rapid release of the material from a near frictionless initial condition, adjustable flume incline, multiple barrier configurations (e.g. flexible and rigid interface), a singular point of force aggregation. 32  Figure 15. Schematic of the flume apparatus. The hopper at the top of the chute is attached to  tower frames. The chute pivots on a lower tower. The terminus of the chute is a barrier and carriage assembly capable of transmitting total impact forces into a single load cell parallel to the direction of flow. The flume portion of the apparatus consisted of a hopper used to load the material and a chute to channel the flow into the barrier. The chute was 317 cm long from the face of the hopper to the end of the plexiglass sidewalls that abutted the barrier. The walls were 31 cm tall, one lined with black paper the other fitted with gridded transparencies to allow for video analysis, Figure 16. The chute width was 30.5 cm. The base was constructed of plywood lined with zinc-coated sheet metal, which extended 1.0 cm beyond the terminus of the chute to allow for overlapping with the barrier platform. The chute was attached to a framed tower with a hinged connection approximately 80 cm from the end of the chute allowing for the entire apparatus to pivot. Tests were conducted on a variety of inclines ranging from 22° to 34°. The upper end of the chute was connected to the release hopper and was bolted in place to provide a continuous path for material to travel without a break in slope angle, Figure 17. A frame was constructed on the base of the hopper to adjust the angle of the base to match that of the chute. The walls were constructed of finely sanded plywood to reduce friction effects and were separated 34.0 cm. This posed a minor constriction as the material left the hopper and entered the chute, however this had little effect on the behavior of the flow. The inclined base of the hopper was 96.5 cm long with a sloping rear wall that rose 50.0 cm perpendicular to the hopper base to meet the sidewalls. The unit was capable of holding approximately 0.2 m3 of material, though this large a 33 flow was never tested as it would have overwhelmed the barrier. The gate, or trap door, was constructed of plexiglass sliding in shallow channels on either side of the frame. Tension was applied with large rubber cords attached to the top of the frame. The door was lined at the base with foam to provide a tight seal and fixed in place when fully extended with a pin immediately above the top of the hopper box. This pin was released with a lever allowing the door to rise in a fraction of a second with little effect on the material behind the door.  Figure 16. Flume setup fit with rigid barrier. Photo shows the position of the lights, cameras (only a single side camera in this case), pivot hinge, data logger and computer.  Figure 17. Front view of hopper loaded prior to testing. Material includes gravel front followed by sand. Hopper trap door opens with lever on left of photo and rises in less than 0.10 s. 34 The ultimate goal of the apparatus was to test the total force of the granular flow impacting a barrier. To do this a sliding cart was constructed that limited the range of motion to a single degree of freedom in the direction of flow (see Figure 16 and schematic model in Figure 18). Two independent rails were mounted to the base of the chute near its terminus. Sitting atop the rails was a rectangular cart made of 1” angle iron. The cart was fitted with ball bearings mounted on small adjustable steel plates to ensure a snug fit. Four wheels were situated at the corners to sit on the rails, as well as two sets of lateral wheels directed out to limit rotation or racking of the cart. Finally, two wheels were fitted in the rear of the cart that applied pressure vertically up to the bottom of the rails to limit rotation in longitudinal direction during impact.  Figure 18. Model of the barrier and cart assembly detached from the chute body. Includes rails that are mounted to the side of the chute, sliding cart and barrier platform with interchangeable barrier (model prepared in Google Sketchup). The front of the cart was fitted with a platform that abutted the end of the chute sitting below the overlap of sheet metal extending from the chute. A frame of ½” angle iron was constructed to support multiple barrier configurations, Figure 19. In this manner the barrier could be represented by a rigid wall of plywood faced with sheet metal, or a flexible rubber membrane. Aluminum brackets were bolted to the face of the frame to hold the barrier in place and apply tension for the flexible arrangement. Threaded bracing bars were added to the upstream side of the barrier attached to the cart beneath the flume. These acted as longitudinal stiffening rods to minimize rotation of the barrier. The total cart mass including the flexible barrier and all removable parts was 14.9 kg. The displacement of the cart was insignificant during the tests, less than 1 mm, therefore the inertial forces of cart mass being accelerated were ignored throughout the analyses. 35  Figure 19. Example impact with flexible barrier. Photo shows the flexible barrier assemblage with rubber barrier and clamps, longitudinal stiffening rods as well as the grid transparency used for image analysis. The barrier flume interface allowed for 100% retention of material with the rigid barrier, however significant material loss occurred during flexible barrier impacts, as there was no means of retaining the flow laterally as the barrier extended. Fortunately, it was determined that this was not significant as the maximum deflection and recorded force occurred before appreciable material escaped. Loss of material from below the membrane was limited by reinforcing the lower margin of the rubber membrane by a steel cable glued within an overlap of the rubber. The cable was clamped  taut between the brackets and provided a guide for fixing the rubber membrane. In this manner the variability in the overall stiffness of the system could be limited. The ability to readily change the barrier configuration between rigid and flexible meant that the effect of increased contact time during impulses, the so-called “soft catch” phenomenon of flexible barriers, could be directly compared to typical rigid barriers. With the movement of the cart fully constrained except for in the direction of flow a single load cell could be tethered from the rear of the cart to the base of the flume, Figure 20. In this manner all momentum from the sliding mass would be converted to an impulse from a single total force impacting the barrier as predicted by the DAN-Barrier model. The load cell used was an Omega Engineering 1000 lb capacity S style strain gauge, model LCCA-1K. The load cell was connected to an analog to digital USB data acquisition devise (DAQ) capable or recording at 500 kHz. The DAQ was connected to a laboratory computer utilizing LabVIEW (TM, National Instruments) to display and store results. Data acquisition settings varied between 5000 and 6000 Hz. 36  Figure 20. Photo of the underside of the flume chute showing where the sliding cart is tethered through the load cell. All impacting force is transmitting from the barrier to the load cell in a single direction. The approach velocity of the flow, depth profile and barrier deflection (for flexible barrier only) were essential parameters needed for validation. These variables were determined through post processing of videos for each test run. Two cameras were placed adjacent to the flume on independent tripods to limit vibration. One camera was directed at the side of the flume immediately above the barrier, a second above the barrier looking obliquely at the base of the chute. Resolution of the videos ranged between 800 x 480 to 1920 x 1080 pixels, and 30 to 120 frames per second. A detailed log of the camera and data acquisition settings, flume geometry and material setup is included in Appendix A1. 4.2 Test materials Two test materials were used throughout the experiments. One was the same quartz sand used by Hungr (2008) and Mancarella and Hungr (2010), the other was common pea gravel used in landscaping. The sand consisted of rounded grains ranging from 0.5 to 1.0 mm, and the gravel included sub-angular to rounded grains ranging from 3.0 to 8.0 mm. The gravel contained trace amounts of rock dust but it was determined that this would not have any effect on the material properties. Combinations of these materials were used in either a 1:1 or 2:1 mixture of sand to gravel and loaded in the front of the hopper followed with a secondary filling of sand. The dynamic internal friction angle, basal friction and density of the four test materials were tested independently, Table 3. 37 Table 3. Summary of test materials and bulk properties tested. Material Dynamic internal friction angle, ϕi (deg.) Basal friction angle, ϕb (deg.) Density (Mg/m3) quartz sand 31.0 21.5 1.70 pea gravel 35.0 21.5 1.56 1:1 mixture 33.0 21.5 1.78 2:1 mixture 31.0 21.5 2.33     The friction angle for a loose granular material varies depending on whether the material is in a static or dynamic state. The static condition, or the angle of repose, can be reduced by a few degrees to the dynamic internal friction angle, ϕi, as a result of oversteepening of the face or other perturbation such as vibration. In this scenario, a shallow landslide would occur at the face and the dynamic internal friction angle would control the geometry of the deposition. This reduction in the bulk property is a result of a slightly less dense than critical grain structure that allows for continual grain movement throughout the mass (Hungr, 2008). Since the experiments of granular material impacting a barrier involved the constant movement of material it was clear that the dynamic friction angle should be used throughout. The process of testing the dynamic internal friction angle using tilt tests was initially outlined by Hungr (2008). The results for quartz sand were verified, and results for pea gravel and both sand-gravel mixtures were also obtained. The process of testing ϕi was done in the flume, lined with a large sheet of sandpaper to reduce the amount of basal sliding. Starting with the flume horizontal the granular material was piled at the angle of repose across the width of the flume to a height of approximately 0.3 m. The angle of the flume was then raised incrementally with minor agitation between each increment. The dynamic friction angle was measured as the angle the face of the pile makes with the horizontal when a steady stream of grains roughly 1 cm thick is flowing. Previous tests indicated ϕi to be 30.9° for sand (Hungr 2008). The current testing was only accurate to ± 0.5°, and a value of 31.0° was obtained. Gravel was observed to have the highest ϕi at 35.0°, and the mixtures had values between these two extremes with friction angles approaching sand as the concentration of sand over gravel increased. The basal friction angle was taken as the angle at which the entire mass began to slide on its substrate, assuming little to no internal deformation. This parameter, ϕb, was tested similarly to the internal friction angle using the flume while it is free to pivot. Material was piled approximately 50 mm high over a 1 m length of unlined flume. The flume was then raised incrementally with small agitations between. The basal friction was recorded as the angle of the flume at which the entire 38 mass began sliding after agitation. This value was tested for all four granular materials with variations of ± 0.5°. It was therefore assumed that the basal friction was constant for all materials and equal to 21.5° as previously documented. The frictional rheology in DAN-W is only dependent on three parameters, the internal and basal friction angles as described, as well as the material density. Density was measured for the materials being tested by simply measuring the mass of a sample and its volume using a standard laboratory beaker. The mixed materials were first prepared by measuring the intended ratio by mass. The sand and gravel was mixed until well blended then gently poured into a beaker to avoid compaction, then densities were measured as normal. A range of densities from 1.56 to 2.55 Mg/m3 were obtained as shown in Table 3. 4.3 Test procedure Initial runs were conducted at a 34° incline against a rigid barrier. A finite volume of gravel was placed immediately behind the plexiglass trap door followed by a larger volume of sand. The intention of this setup was to concentrate a larger mass of material at the front of the flow. While this is similar to well-developed stony debris flows where larger boulders migrate to the front of the flow (Takahashi 2007), the setup was not intended to mimic this behavior. Instead, the goal was to provide more mass to the flow front by taking advantage of longitudinal and vertical sorting that occurs in granular flows with varying particle size (Bagnold 1954). It was anticipated that the initial collision would cause a dynamic spike in the observed total force prior to settling to a more predictable static level. After loading the hopper, the side and top cameras were turned on followed by the data acquisition apparatus. The sand was released and allowed to impact the barrier after accelerating under gravitational forces. Over the length of the chute the grains spread considerably, as frictional materials do, to the point where the flow was only a few grains deep. There was some observable sorting, longitudinally and laterally as described by others (Pouliquen and Vallance 1999; Johnson et al. 2012), and considerable particle saltation. The result was an extremely chaotic, dispersed flow front, Figure 21. 39  Figure 21. Thin flow front observed as only a few grains thick with extensive saltation when granular material was released from the hopper and allowed to accelerated under gravitational conditions over the length of the chute. The forces observed in these types of tests for both rigid and flexible barriers were static in nature. The force would gradually rise as the sand and gravel fills in behind the barrier until reaching a maximum force where it would remain constant, except in the case where material raveled from the sides of the barrier. The results from these tests, referred to as thin flow front tests, did prove useful and conclusions have been drawn, see results in Chapter 5.3. However, this was not a desired result to verify a dynamic impact model and alterations were necessary. The expectation of a dynamic force was that it would exceed the force imparted by the same amount of material resting statically behind the barrier. It was anticipated that a thicker flow would be capable of imparting such a force. In an attempt to increase the flow depth at the time of impact various modifications were made to the test material and apparatus. Initially, more angular gravel was used; this resulted in similar thinning flow behavior. Many chute inclines were tested as well as basal frictions, all with similar results. It was not until the modification to the test setup shown in Figure 22, that a mass of sand or gravel impacted the barrier with thickness significant enough to cause a dynamic spike, or shock loading. This series of tests were labeled as steep flow front tests. The steep flow front tests utilized a temporary tear-away barrier placed 40 to 60 cm from the impact barrier. The chute angle was lowered to 22.2°, just above the basal friction angle to limit the rate at which material raveled at the front of the flow. The mass of sand or gravel was manually accelerated from behind using a paddle with the same dimensions as the chute, Figure 23. Initially, the material would bulk as it compressed between the paddle and the temporary barrier. As the temporary barrier was removed, the mass was allowed to accelerate under gravitational forces before impacting the barrier. 40  Figure 22. Alternate test setup to obtain concentrated flow front and dynamic loading of barrier. A temporary tear-away face was placed in proximity to flexible barrier to promote thicker flows.  Figure 23. Example release for concentrated flow front tests. Material is accelerated from behind across the width of the flow then removed when flow front approaches barrier face. Observations under gravitational forces only begin at t = 0 s, shown here, corresponding to when external force is removed. Great effort has been made to ensure that the initial conditions such as release velocity and mass shape were well documented. It is the opinion of the author that the consistency of the results obtained offset the unconventional nature of the process.   41 5 RESULTS As the process of collecting and synthesizing the data was quite complex, an overview is presented as well as the results from the thin flow front and steep flow front tests. This includes calibration, as well as measurement procedures that were common to all tests. Thin flow front refers to tests where material arriving at the barrier remained shallow (fill height less than 1 cm) throughout barrier impulse. Steep flow front references the wedge shape at the front of the flowing material mass that went from only a few grains deep to More than of 10 cm over 30 cm of longitudinal distance along the chute. 5.1 Calibration Two simple calibration tests were performed to ensure that the load cell was recording forces correctly. First was a vertical test where the cell was suspended from a rigid table and mass was added incrementally. The second involved attaching a similar mass to the end of the barrier cart, while the chute was inclined at 34°. For each test an initial measurement was taken without applied load to obtain a zeroing voltage. After each mass was added measurements were taken for one to two seconds at 5000 Hz and the recorded voltage was taken as the average over the time period. Measured force from the load cell was calculated based on constants provided by the manufacturer. [29]                          Here Vmeasured is the output from the load cell, Fmax is the maximum rating of the cell which was 1000 lbs (4.45 kN), C is a conversion factor provided from the manufacturer equal to 3.004 mV/V and Vapplied is the excitation voltage which was 5 V for all tests. Figure 24 shows the results of the calibration exercises. As additional mass was applied the load cell adjusted uniformly for the vertical test and by a constant 0.56 times the applied weight for the inclined test. This value is the proportion of the force in line with the flume apparatus, sin(34°) = 0.56. The consistency of the slope indicates that the carriage was capable of transferring the load to the longitudinal direction of the chute without loss. All measurements made throughout the experiments were concerned with the total longitudinal force of the landslide and therefore no additional conversions were necessary to the reported load cell reported value. 42  Figure 24. Calibration data showing the applied load to the cell and measured force using Equation [29]. Includes data points for calibration with load cell suspended vertically and attached to test apparatus with chute inclined at 34°. 5.2 Measurement and data At the completion of each test, the total force was calculated from the load cell data using Equation [29]. All other requisite values for analysis were obtained from post processing of videos. This was accomplished using a simple video analysis tool called Tracker (Brown 2009). To aid this process, a 1 x 1 cm grid placed on the distal end of the chute and on the barrier platform allowed for calibration of a ruler within the software. A coordinate system was superimposed with x parallel to the chute base and y tracing the undeformed face of the barrier perpendicular to the chute at x = 0. For the overhead camera the x-axis traced the width of the platform and y was the longitudinal direction of flow. The extent of the flexible barrier or the top of the flow were traced at each time step to obtain the maximum deflection of the flexible barrier from the overhead camera, and fill height at the barrier face from the side camera. In addition, identifiable features within the flow were traced. This allowed for the measurement of velocity by recording the relative displacement between time steps (a feature built into the software). 5.2.1 TIME SERIES Observations of force, fill height and deflection are plotted against time as continuous lines for all tests (Appendices C, E and F). They are actually comprised of observation points, the number of which depends on the frame rate of the camera (between 30 and 120 fps) and the sampling rate of the data acquisition apparatus (between 5000 and 6000 Hz). This resulted in too many data points to plot individually, and for the sake of clarity the data were condensed to single time series lines. It was estimated based on the resolution of the imagery that the precision for barrier deflection observation was 2 mm and 5 mm for measurements of fill height. These ranges are not shown on 43 the plots. Error in the force measurement was estimated to be ±0.001 kN. This value comes from the amplitude of the noise oscillations in the tests. It appears greater for the tests where a lower maximum force was obtained however the same magnitude was observed throughout the tests. The time series were synchronized for plotting. This was accomplished for deflection and fill height by noting a distinguishable feature of the flow (e.g. darker grain of sand) that was common to both the overhead camera used to measure deflection, and the side camera used to measure fill height. Time was matched for the two series as this feature passed an identifiable component of the flume (e.g. side bracket). The force time series was then matched to these by adding or subtracting an equal amount of time to all observation points. The initial rise in recorded force was matched to that of fill height as best as possible, though some error inevitably exists. 5.2.2 VELOCITY Different measurements of velocity were necessary depending on the test setup, either thin flow front or steep flow front. Both setups required the measurement of an approach velocity as the flow neared the barrier. It was observed that velocities at the center of the flow slightly exceeded those at the side, due to the added friction of the sidewall. To accommodate this, measurements were made for various flow lines and the velocity taken as the average of these values, and a uniform velocity was assumed across the width of the flow. Two values were taken from the side camera where the velocity was lower, and two were taken from the top camera where maximum velocity occurred. The steep flow front tests required an additional measurement for the release velocity after the accelerating force was removed. The point of release, t = 0, was set when the forward motion of the paddle stopped, signifying the time where flow travelled freely. Particles were traced at the front, middle and rear of the mass for frames before and after release and an average of these values was taken as the release velocity of the entire mass. Figure 25 shows plots of velocity during the acceleration process and through release at different points along the length of the flowing mass for test S8. The highlighted point in the charts corresponds to the time of release and has comparable values from the front of the flow to the rear. These types of observations were made for most tests, showing similar correspondence between velocities. It was therefore assumed that the average value was uniform along the length as well as across the width of the flow at the time of release. 44     Figure 25. Measurements of velocity over time at different points within the release mass as output from Tracker software. The highlighted point corresponds to time of release from the video analysis and is comparable along the length of the mass. 5.3 Results for tests with thin flow front As previously mentioned, the tests have been grouped into two categories, thin and steep flow front. Each of these included tests on flexible and rigid barriers. Observations from the different categories are presented separately as the flow behavior varied, and different conclusions can be drawn. 5.3.1 QUALITATIVE DESCRIPTION OF FLOW BEHAVIOR During impact with the rigid and flexible barriers for the thin flow front tests (see Appendix A2 for full details of test setup and observed parameters), material was initially observed to deflect upwards, creating a thin layer on the face of the barrier. This diverted mass was then impacted from behind causing material to accumulate upstream without any further change in fill height adjacent to the barrier, accompanied by a gradual rise in force. This behavior was particularly noticeable in flexible tests S2 and S3 (Appendix B1) and rigid test R2 (Appendix B2). The behavior was similar to the pile-up mechanism described by Sun and Law (2011). At a certain point, material flowed over the top of the existing deposits, resulting in a second wave making contact with the barrier. The arrival of the second front did not form a jet of material flowing up the face of the barrier as was observed with the first wave of material. Instead, the depth of material at the face of the barrier, which included the height of the previously deposited material, gradually increased. This type of behavior was far more reminiscent of the run-up mechanism. Sun and Law (2011) also noted the possibility of a two-phase filling process after running numerical models of debris impacting a flexible barrier in the Particle Flow Code. In terms of analytical methods used to dimension the landslide force, this observation would make it hard to justify the use of one particular mechanism- based approach. Instead a more holistic solution is necessary. 45 As a result of the two-phase filling process, the time series for force and fill height appeared as stepwise functions. Initially there was a steep rise in force, followed by a decrease in the slope of the curve and a final steep rise prior to static conditions (both charts in Figure 26 exemplify this behavior). In most cases, two distinct waves were present, though it could be argued that less pronounced fluctuations also represent the arrival of additional waves of material.    Figure 26. Example results for thin flow front tests impacting a rigid barrier (left) and flexible barrier (right). Data for total force taken from load cell, black line, where the amplitude of natural oscillation acts as an approximation of error. Red line represents fill height at plane of the undeformed barrier, red line the maximum deflection beyond plane measured only for flexible barriers. Both values measured from video analysis. Fill height (red line) and total force (black line) both exhibit a discontinuous rise for both the rigid barrier test shown (left side of Figure 26) and the flexible barrier test shown (right side of Figure 26). However, it appears that the depth of material at the barrier remained constant for a short period of time, while the force continued to rise but at a decreased rate. Results of the remaining thin flow front tests (shown in Appendix C1 and C2), also reflect this behavior with varying levels of intensity. During this time, material was continuing to accumulate upstream of the barrier. It appears that momentum of the arriving material was transferred to the barrier through the stationary wedge for both the rigid and flexible barrier tests. The decrease in slope of the force curve during this period shows that the stationary wedge buffered the force to a certain degree. It is possible that the stationary material was being compacted during this phase, increasing the overall stress state within the mass. At a specific time in the filling process the stationary wedge acts as a ramp, allowing for the arrival of new material to override and impact the barrier directly. The time at which this occurs is approximately when the upstream end of the wedge is approximately at the same height as the 46 material accumulated adjacent to the barrier (fill height at the barrier face). At this point there is no additional energy needed for the flow to run up and over the stationary wedge and can freely flow horizontally to make contact with the barrier. In terms of actual barrier design, this observation is a valid argument for placing a barrier in an area of decreased slope or channel gradient. This would encourage more material to accumulate upstream of the barrier as opposed to increasing the fill height adjacent to the barrier adding to the total force. Flexible barrier tests had the added observation of deflection. A slight change in the slope of the curve can be noted corresponding to plateaus in the fill height and force curves. An example of this can be seen between t = 0.6 and t = 0.7 in the chart on the right of Figure 26. The deflection continued to rise during this period but at a slower rate as material accumulated up the flume chute but continued to accumulate force on the barrier. As the static wedge was overridden, the deflection jumped once again. The thin flow front tests experienced a relatively long time of filling. The time of first registered force to the approximate maximum was between 0.8 and 1.0 s for all tests, both rigid and flexible 5.3.2 SYNCHRONIZATION Overall, it was noted that the three parameters were roughly in phase with maximum values occurring at nearly the same time. Observations for height and deflection were easily correlated using video as the flow front approached the barrier. Matching the front arrival to onset of the force curve was more subjective because of noise in the data and vibrations in the flume as material traveled down the chute. The time of the first significant rise in the force was set equal to the arrival of the flow front in the fill height and deflection curves giving an approximate synchronization. 5.3.3 ADDITIONAL MEASUREMENTS In addition to measurements of force, fill height, barrier displacement and velocity, snapshots were taken from the video at the time when maximum height was first observed. This was typically closely correlated to the time when total force reached its peak. The fill height and angle of backfill (measured to the horizontal) were recorded for each test to be used in quantitative analysis, an example of the measurement is shown in Figure 27. 47  Figure 27. Example of measurements made for thin flow front tests at time of maximum fill height. Angle of backfill measured from horizontal and fill height measured at plane of undeformed barrier. 5.3.4 QUANTITATIVE ANALYSIS Two separate approaches were used to calculate the total force acting on the barrier to compare to observed values at maximum fill height. The first was the dynamic pressure approach that is industry standard for design. Equation [8] in Chapter 2.4 was used to calculate the dynamic portion of the force, and Equation [9] for the static. The height of the dynamic impact, ho, was taken to be the difference between the maximum observed fill height and the height of the most pronounced intermediate filling (most prominent plateau in the fill height time series). The remaining material was assumed to be imparting a static lateral earth pressure. A pressure coefficient of K = 1.0 was used as suggested in the Hong Kong guidelines (Kwan and Cheung 2012). The total lateral earth pressure was also calculated using only lateral earth pressure theory (Budhu 2011). It was observed that as material filled behind the barrier there was little motion within the deposition, this was accompanied by a smooth rise in the force. It is therefore reasonable to assume that the material never imparted a dynamic load to the barrier. With this assumption the total force was calculated as [30]          ( )  with K being the pressure coefficient, γ the unit weight of material, hv(t) the fill height at the barrier measured vertically as a function of time, and b the width of the flume. A distinction is made between the flow depth measured at the barrier, h(t), which is measured parallel to the face and the where flow depth used for calculating static pressure, hv(t). [31]   ( )        ( ) 48 The barrier was constructed perpendicular to the chute base, which allows for the chute incline, α, to be used to adjust flow depth adjacent to the barrier. The original Coulomb limit equilibrium approach was modified by Poncelet (1840) to account for wall friction, δ, an inclined wall, α, and sloping backfill, β. The resulting coefficients for lateral earth pressure in the active and passive states are [32]         (   )        (   )[  {   (   )    (   )   (   )    (   )}   ]  [33]         (   )        (   )[  {   (   )    (   )   (   )    (   )}   ]  The variables in equations [32] and [33] are presented graphically in Figure 28. The friction angle between the sand and rubber was not measured so the more conservative value for sand on sheet metal, 21.7°, was used. Even though mixtures of sand and gravel were used during these tests the friction angle, φ, was dominated by that of the sand and a value of 30.9° was used. The angle of δ relative to the normal of the wall shown in Figure 28 is typical of an active case. The idea is that the wall moves away from the edge causing the material to move downwards relative to the wall. The directions here would be reversed for the passive state where overall compressive forces cause the wedge to move upwards relative to the wall.  Figure 28. Geometry for calculating Coulomb's lateral earth pressure for active state with inclined backfill and wall friction. 49 A total force was calculated for both active and passive conditions. Considering material continuously impacts the rear of the deposition, it was anticipated that a passive condition would dominate as the material between the barrier and arriving front was compacted. Surprisingly the passive earth coefficients overestimated the total forces by two to three times. Even by taking into account reduction factors for a curved slip plane as suggested by Caquot and Kerisel (1948) the passive condition was not a justifiable solution. However, the active state reasonably predicted the loads. Roth et al. (2004) briefly alluded to this condition when discussing the calculation of static pressure behind a flexible barrier after the arrival of a dynamic front and research conducted here agrees. Results from both approaches to calculating total force are compared to observed value in Table 4. Table 4. Observed forces for thin flow front test results compared to calculated forces using dynamic impact pressure approach (Kwan and Cheung 2012) and Coulomb active lateral earth pressure (Budhu 2011). Values obtained using dynamic impact pressure approach are all overestimates, values using lateral earth pressure all underestimate actual values. Test Observed Force (kN) Calculated Force, Dynamic Impact Pressure (kN), Equation [8] % Error Calculated Active Lateral Earth Pressure Coefficient, Equation [32] Calculated Force, Lateral Earth Pressure (kN), Equation [30] % Error S1 0.0986 0.855 767% 1.00 0.0749 24% S2 0.117 0.560 378% 1.03 0.0813 31% S3 0.140 0.832 494% 1.00 0.0930 34% S4 0.143 0.944 560% 0.95 0.0931 35% S5 0.00664 0.0796 1099% 1.10 0.0079 18% S6 0.0574 0.284 395% 1.16 0.0381 34% S7 0.0353 n/a n/a 1.02 0.0171 52% R1 0.207 0.406 96% 0.97 0.165 20% R2 0.115 0.185 61% 1.00 0.0825 28% R3 0.141 0.273 93% 1.20 0.125 11%        The dynamic impact pressure approach significantly overestimated the force, up to an entire order of magnitude. The tests showing the least amount of error are the rigid tests R1 through R3. This is a unique observation as the dynamic pressure approach is based on conservation of momentum and was initially developed for rigid retaining structures and has only recently been extrapolated to flexible barriers. Using active lateral earth pressure theory reduced the percentage error in total force. The average error went down to 29% with consistent values for both the rigid and flexible barriers. All of these values underestimated the actual force. It is also of interest to note that the active pressure 50 coefficient, Ka, confirms the suggestions of Kwan and Cheung (2012) that a generic value of 1.0 is appropriate. Knowing the fill height throughout the filling process would make it possible to calculate a time history of the static force using this approach. However, the investigations here are limited to the maximum total force occurring at the peak fill height. These values are shown in Figure 29 for the ten tests that were considered thin flow front impacts. Also plotted are curves showing calculated total force as a function of fill height measured parallel to the barrier face. Sets are presented for the active and passive state with upper and lower bounds of observed backfill angles, 14° to 26°. It is obvious that there was a trend in the observed values with the tests more accurately following the active state conditions.  Figure 29. Comparison of force to fill height relationship of thin flow front tests, see legend for symbology for tests versus calculated values using Coulomb lateral earth pressure relationships. Solid lines represent active earth pressure scenario for a range for backfill angles from 14° to 26°. Dashed lines show same range but using passive lateral earth pressures. The observed values trend towards the maximum of the predicted range. This may be contributed to a variety of issues not limited to: error in the method, overconsolidation during the filling process, natural variability in the face friction and backfill angle, or the presence of lateral walls contributing additional stress accumulation towards the center of the flow. 51 5.4 Results for tests with steep flow front The steep flow front test was designed to impart a shock load to the barrier that remained within the elastic regime of the system. This set of tests included twelve with sand against a flexible barrier, three with gravel against the same barrier and three with sand impacting a rigid barrier. The steep flow front tests resulted in a rise to peak force followed by a drop in load to a stable level. The stable level was comparable to force calculated using static earth pressure theory, therefore the force in excess of this value was taken to be the dynamic force imparted by the arriving flow. 5.4.1 QUALITATIVE DESCRIPTION OF FLOW BEHAVIOR During the steep flow front tests, no unique filling process was identified like that described for the thin flow front tests. Some material raveled from the front of the body of the flow resulting in a wedge shape with a steep face relative to the slope of the chute. The mass travelled with constant velocity throughout impact with the barrier. Initially, a small amount of material was deflected upwards but this was negligible as a constant supply of material resulted in a steady rise in all observations. In most cases the force rose to a single transient peak, which was followed by a reduction in force to a static condition, as shown on the left chart in Figure 30. It was observed in the load history of some tests that the flow may have been arriving in a surging manner, for example the step at t = 0.16 in right chart in Figure 30, however this behavior was difficult to distinguish in the video analysis and unnoticeable in fill height and deflection curves.    Figure 30. Two example results for steep flow front tests impacting a flexible barrier. Notes are the same as Figure 26. 52 Considerable shearing was observed within the body until the point of maximum deflection. At this point, material immediately behind the barrier became stationary as accumulation in the bed-normal direction continued. It would appear that this increase had no effect on the deflection or total force at the final stages of deposition. However, it is anticipated that any effect that increasing flow depth had was overcome by rebound in the other observations. This includes a transition from a dynamic impulse to a static force, as well as an elastic rebound in the barrier. The time from when force first began to rise until the maximum, varied between 0.10 s and 0.15 s for rigid barrier impacts, and between 0.18 s and 0.25 s for flexible barrier impacts. The steep flow front tests occurred significantly faster than the thin flow front tests as the material was concentrated and had relatively higher kinetic energy. It appears that the presence of a flexible barrier increased the impulse time for these higher energy impacts, which is the intention of flexible barriers. Additional tests would need to be conducted to make any conclusions on the effect this has on the total force. 5.4.2 SYNCHRONIZATION As with the thin flow front tests, fill height and barrier deflection were easy to synchronize using video recordings. The times in each series were then adjusted to 0 when release of the applied force was observed. Finally the force time series was adjusted to match these curves. During this process a time delay was observed. First, force would rise to its peak. The mass would continue to deflect the barrier while increasing in fill height until the maximum deflection was observed. Finally, the maximum fill height would be achieved at which time the force would have settled to a static condition. The static earth pressure calculation described in the previous section was used to calculate the load at the max height. Values were comparable to the final static state of the load history, which was below the observed maximum load.  5.4.3 ADDITIONAL MEASUREMENTS A particular parameter of interest throughout these tests was flow depth. This value is used in all quantitative method of calculating force, but changes rapidly and is difficult to predict. For each experiment flow depth was recorded at time of release as well as the shape of the overall mass (see Appendices E1 through E3). Screenshots were taken at the time of maximum force. Two values of fill height were identified, the actual recordable height, and an approximated impact height representing the thrusting body of the 53 flow, Figure 31. These values were used to calculate the total force using the standard dynamic pressure approach as described in the following section.  Figure 31. Example of measurements made for steep flow front tests at time of maximum force. Two measurements of height were made, the higher is maximum height, the lower is an approximation of the impacting body height neglecting minor material runup along the face of the barrier. 5.4.4 QUANTITATIVE ANALYSIS When calculating the dynamic pressure using Equation [8] Kwan and Cheung (2012) suggested using an average value for height and width. Given the tapered front observed in the steep flow front tests, the average height would have simply been half the observed height at time of release. This is contrasted to Figure 31, where two distinct heights were identified. This illustrates the difficulty in choosing the correct value for flow height. The subjectivity of height when calculating total force is shown in Figure 32. Four charts represent calculation of total force using different choices of fill height. Symbols are actual measurements of force plotted against the calculated value      . The top row represents the release heights, and the bottom row the impact heights. Included are lines showing calculated force using a range of heights, the average velocity from all tests, and a selection of dynamic scaling factors, α. A linear relationship exists for the test data without significant scatter. This confirms that the dynamic pressure approach based on conservation of momentum is a reasonable approximation of the physics of the phenomenon. However, depending on the height used, the observed values trend along a line with a slope between α = 1.0 and α = 2.0. 54  Figure 32. Results from steep flow tests presented as a function of velocity and flow height as commonly done for flow-type landslides (Sovilla et al. 2008; Bugnion et al. 2011; Brighenti et al. 2013). Four heights used for h on the abscissa axis, showing the subjectivity of height in the calculation: (a) height at release, (b) ½ height at release, (c) height at impact, and (d) assumed height of the impacting body. Dashed lines are calculated values of force using the abscissa value and typical dynamic scaling coefficients. When the full height was used, chart (a) and (c), results followed the lower α = 1 value. This is similar to values of the dynamic coefficient reported by Bugnion et al. (2011) that were back calculated from impacts of saturated debris avalanches against rigid vertical pressure plates. If the average height was used, chart (b), the trend was better fit by the α = 2 value as suggested in the Hong Kong design guidelines (Kwan and Cheung 2012) and other lab experiments using saturated flows (Canelli et al. 2012). In between were the resulting using the thrusting height of the flow, chart (d). A similar coefficient of 1.5 was suggested as a safety factors when calculating impulse loading of a debris flow on rigid structures (Hungr et al. 1984). While this chart shows significant variability in the chosen parameters, the conservative route would be to use a higher dynamic coefficient and an average height over the duration of the flow to incorporate a greater factor of safety. 55 The results in Figure 32 show no appreciable difference in the force recorded for rigid versus flexible barrier. Considering only one configuration of flexible barrier was tested it is not permissible to make any conclusions about the effectiveness of flexible barriers in terms of total force. Additional barriers, with varying stiffness, should be tested in a similar manner to see if varying results are observed. One clear benefit of the flexible barrier can be seen though when looking at the maximum observed fill height relative to the approach velocity, Figure 33. Although the trend includes significant scatter it can be seen that material tended to travel higher up the rigid barrier, which is to be expected as all momentum is immediately transferred vertically at the face of the barrier. Therefor, flexible barriers are ideal as they have a smaller construction profile in the longitudinal direction, and it may be possible to assume that they could be diminutive in the vertical direction as well.  Figure 33. Chart showing maximum observed fill height compared to impact velocity for steep flow front tests. Distinction is made for flexible and rigid barrier tests. There is a possibility that overly flexible barriers may result in a larger total force. Material accumulated immediately behind the barrier assists in stopping the arrival of new flow, which could be part of a single event, or the arrival of a later surge. When a barrier is highly flexible, a greater amount of material initially interacts with the barrier, and a larger force is exerted. This is contrasted to a rigid barrier, which limits the amount of material that can interact with the barrier and exert a static or dynamic pressure. It is anticipated that there is an optimum flexibility for deformable landslide barriers that allows for some force reduction by extending the time over which an impulse occurs through barrier flexibility, while still minimizing the amount of material that must be directly stopped by the barrier. This consideration does not matter in the design of 56 flexible barriers for use in rockfall mitigation. Rockfall involves a discrete mass that must be retarded regardless of the amount of deflection in a barrier. It is therefore advantageous to make barriers as flexible as possible, and to add brake elements that further extend the time over which the impulse is dissipated. It is possible that this concept is already applied in the design of flexible barriers, however no literature currently exists that supports or refutes it.   57 6 VALIDATION OF THE NUMERIC MODEL The concentrated flow front tests served as the body of data used to validate the DAN-Barrier model. Simulations were prepared using the measured material properties and ran for each test. The results were compared to observations to determine whether the model is in fact capable of predicting behavior.  Figure 34. Example of input file created for DAN-Barrier simulation. Outer box is drawn as 1 m x 1 m and is used for scaling within the program. Flow profile was taken from screenshot at t = 0, corresponding to when accelerating force was removed. Scaled images were drafted for each of the tests, depicting the flow profile at time of release and the initial velocities as observed from the videos, Figure 34. The distance 0 m on the Lagrangian scale represents the position of the barrier and corresponds to x = 0.75 m on the Cartesian coordinates. The only other material properties necessary were those previously described in Table 3. It was necessary to quantify the overall stiffness of the barrier comprised of the rubber membrane and the steel cable fixed at the base. It was initially assumed that this would be a linear elastic relationship between deflection and total force. A line was fit to the results of a force versus deflection plot considering all tests, as shown in Figure 35. The slope is taken as the stiffness, K, in Equation [20], and was used as a starting point for calibrating individual models. This is not to be confused with the overall intention of the flume exercise, which was validation of the numerical model. Calibrating the individual models was a requisite step in the validation process. 58  Figure 35. Chart showing force as a function of deflection for all flexible barrier tests. Slope of the linear fit line would be anticipated stiffness value for barrier configuration in DAN-Barrier model. Each test was initially run in DAN-Barrier using the K value shown in Figure 35. The slope of the force curve and the value of maximum total force were used to evaluate the accuracy of the model. It was observed that the value K = 1.7 kN/m provided reasonable results for some tests, however others exhibited significant error. It was decided that each model would require some additional calibration to obtain accurate results. The release velocity and material properties were measured quantities for each test and were therefore input directly to the model. The stiffness coefficient was the only variable that remained available for calibration and was therefore adjusted for each test. When reasonable results for force were obtained the model was considered calibrated and the fill height at the barrier and deflection were recorded. Considering the actual stiffness of the barrier was not directly measured and may have been more complex than a simple linear relationship, this approach was considered sufficient in evaluating the effectiveness of the DAN-Barrier model in predicting fluid-structure interaction. A summary of test release data and required calibrated stiffness is shown in Table 5.   59 Table 5. Input parameters for DAN-Barrier models of concentrated flow front tests. Test Mass (kg) Velocity (m/s) Kinetic Energy (kJ), KE = ½ mv2 Calibrated Stiffness, K (kN/m) S1 18.1 1.12 1.13E-02 1.6 S2 20.1 0.93 8.70E-03 1.6 S3 18.4 1.09 1.09E-02 1.6 S4 21.8 1.39 2.11E-02 1.5 S5 12.4 1.14 8.09E-03 1.6 S6 15.6 0.75 4.05E-03 1.5 S7 18.4 0.89 7.27E-03 1.4 S8 22.9 1.39 2.21E-02 4.3 S9 26.1 1.37 2.45E-02 3.4 S10 16.5 1.58 2.06E-02 3.4 S11 16.5 1.40 1.48E-02 3.1 S12 16.2 0.96 7.48E-03 1.5 G1 14.8 0.92 6.28E-03 1.3 G2 18.5 1.12 1.16E-02 2.0 G3 12.1 0.66 2.64E-03 1.8      Plotting the calibrated stiffness values for each test against the release kinetic energy (Figure 36) gives insight into the complexity of barrier stiffness. The flat dashed line in Figure 36 is a representation of the assumed linear elastic stiffness shown in Figure 35. If the barriers reaction to applied stress was elastic, K for all tests should follow this line. However, we see that tests where the release was of higher initial kinetic energy (either through larger mass or greater velocity), a larger value of K was necessary to calibrate the model. This can be explained by the actual stress – strain curve of the rubber used for the flexible barrier. Rubber is a viscoelastic material that exhibits a non-linear stress-strain relationship with a degree of hysteresis between loading and unloading (Tomita et al. 2008). Furthermore, there is a degree of strain rate dependence, with faster loading rates resulting in a stiffer response. If we assume that release kinetic energy can be correlated to the rate at which the barrier deflects (strain rate), the non-linear rise in stiffness with increasing kinetic energy is to be expected. The non-linear stress –strain relationship also explains the additional scatter in data points at higher deflections in Figure 35. The fact that the current version of DAN-Barrier does not accurately reflect the stress – strain relationship of the rubber membrane does not detract from the validity of the numerical model. The stress – strain curve of rubber does not deviate significantly from linear (Tomita et al. 2008), and the strain rate dependence was overcome by calibrating each model individually. A similar exercise would need to be done for future validation if using a similar material. However, to use DAN-Barrier as a predictive tool the linear elastic behavior currently in the program must be substituted with the stress – strain behavior of the barrier material. For the rubber membrane the viscoelastic 60 behavior must be quantified. For application to actual flexible barriers, a different model would be required. Due to the presence of the brake elements that begin yielding at a specific tensile load, an elastic-plastic relationship is likely to dominate. Quantifying this behavior would require describing the elastic response of the mesh and cables during the initial elastic deformation, as well as the plastic response of the brake elements at higher strain. This task is not within the scope of this thesis, however is a task that would be of value to move fluid – structure modeling of flexible barriers forward.  Figure 36. Value of the stiffness coefficient, K, needed to calibrate each model in DAN-Barrier plotted against kinetic energy at time of release for concentrated flow front tests. The results from each calibrated model were plotted against time, an example of which can be seen in Figure 37. Charts comparing model results to observations for all tests are included in Appendices F1 through F3. The comparisons show good correspondence between the observed and predicted values. While the peak forces in the models were calibrated to the test observations, the slopes of the curves, the maximum fill heights and to a certain degree the deflections were all comparable. It was not anticipated that the model would predict the residual force; instead this could be calculated using the fill height and the static active lateral earth pressure as previously discussed. Some tests did show considerable deviation in the deflection profile. The values reported are for the rectangular 61 longitudinal profile predicted by DAN-Barrier. By applying the scaling factor as described in Chapter 3.4 a better estimate is obtained, however this parameter was left out of the code for simplicity.  Figure 37. Results for test S1 of the concentrated flow front tests comparing total force, fill height, and deflection of the observed test with those predicted by DAN-Barrier. The model tends to deviate in two ways. First is the slope of the fill height curve with the model predicting a dramatically faster rise than what was observed. The second is the shape of the deposition profile (Appendices E1 through E3). It is likely that these two deviations are linked. Initially, a thin jet of material will flow to the maximum fill height immediately following the leading elements contact with the barrier, hence the rapid rise in the height curve. Eventually, the model will result in a concentration of material in proximity to the barrier at appropriate heights and a much thinner tail at the distal end. Test observations show a more gradual decrease in flow height from the barrier face to the tail. This bunching of material at the barrier in the model is more pronounced for higher energy tests, those with either faster release velocities or larger masses. While the final prediction of the fill height is quite accurate the process is not fully represented at this time. A possible explanation for this behavior lies in the foundation of the DAN-W model and the shallow flow assumption. At the front of the flow, when the initial boundary elements make contact with the barrier, the addition of a retarding force causes a rapid increase in the depth of the flow. This 62 represents a transfer of the longitudinal momentum in the bed-normal direction, creating vertical velocity gradient. This is not accommodated in the shallow flow assumption that assumes all flow is parallel to the bed, and therefore no resistance is considered in the vertical direction. This allows a rapid growth in flow height and may explain the steep slope of the fill height versus time curves observed. Another result of assuming that flow lines are parallel to the bed is that shear stress is neglected on all planes perpendicular to the direction of flow. A rise in the flow front bends the flow lines and would create extensive internal shearing. This would propagate upstream of the flow acting as an additional retarding force for all elements. However, no inter-slice shearing is present in the DAN-W model, which may account for the deviation in filling profile where more material is concentrated at the front of the deposition. Adaptations to the original DAN-W model were made by Mancarella and Hungr (2010) to accommodate shock behavior similar to what is described here. The velocity of each element was adjusted taking into account the velocities of adjacent elements, one upstream and one downstream. In this manner numeric instabilities were smoothed over three elements and better results were obtained. It is possible that shock to the flow induced by the introduction of a barrier outweighs these adjustments. Further modification will be considered for future iterations of the model and perhaps smoothing extended to five elements when considering barrier interactions. 6.1 Model sensitivity analysis A sensitivity analysis was performed to assess the effect of the controlling input parameters. Three tests were chosen to represent a range of release kinetic energies. The effect on force, deflection and fill height were measured by incrementally changing the model stiffness, Figure 38, and release velocity, Figure 39. The three colored lines represent the different tests. Black circles positioned on each line show the actual values for barrier stiffness required to calibrate each simulation, or the release velocity measured from the video analysis. This serves as a reference as stiffness or velocity was increased or decreased. There appears to be only a moderate range of stiffness values that control the trends, with the effects tapering off above 6 kN/m. While this value is unique to this scale of test performed, it is expected that similar trends would exist for larger models only with a different upper limit of the effective stiffness. The calibrated value for all three tests exists on the downward trend of the force curves. Slightly more flexible barriers result in greater forces, and stiffer ones cause a fall in force 63 until a local minimum occurs between 3 and 5 kN/m. This is a reasonable result when considering how flexible barriers stop landslides. There is a finite amount of material that can interact with the barrier, which once restrained results in a plug that will help to dampen the impact of subsequent debris. Too soft a barrier will increase the amount of material that the barrier must initially stop, adding to the load on the barrier elements. Above certain stiffness no additional benefit is derived and the barrier may need to do appreciable work to stop a mass over a shorter distance. This relationship will most likely change if material behind the barrier plane contributed to the total force, and should be revisited with subsequent alternations to the model.  Figure 38. Sensitivity analysis showing effect of model stiffness on force, left, deflection and height, right. Three models with varying initial conditions, mass and release velocity combined as kinetic energy were tested. Circles represent actual values needed to calibrate each model to observed values.  Figure 39. Sensitivity analysis showing effect of release velocity on force, left, deflection and height, right. Three models with varying initial conditions, mass and release velocity combined as kinetic energy were tested. Circles represent actual values needed to calibrate each model to observed values. 64 The effect of stiffness on linear measurements is seen on the right side of Figure 38. The deflection curves are clear exponential decay curves with deflection directly related to stiffness. This behavior is not surprising. The fill height measurements show more complex behavior similar to force curves. There is a local maximum in the curve near the calibrated value. Significantly less material is accumulated in the bed-normal direction for lesser values of K and slightly less for larger values. There appears to be a correlation in the fill height versus stiffness and total force versus stiffness curves that may have an implication on the design of flexible barriers. Low values for stiffness resulted in small fill height and total force, however such values may not be feasible in terms of actual barrier design and construction. A slightly stiffer barrier (the 3 to 5 kN/m range shown here), represents a “sweet spot” for performance where both the fill height and force are a local minimum and could be feasibly constructed. Whether this behavior exists in full-scale barriers that are significantly more complex is yet to be determined. The testing of additional types of barriers in the flume would lend insight into this hypothesis. Tests on a thinner and thicker gauge rubber would give a spectrum of barrier stiffness to help in the optimization of barrier design. The release velocity was not an assumed value in the models but is included in the sensitivity analysis. Velocity holds a non-linear position in the kinematic energy relationship as well as the conservation of momentum based approach for dimensioning dynamic pressure and was expected to have a controlling affect on model results. As seen in Figure 39 the curves appear quadratic with non-linear rise in force and deflection connected to increasing velocity, but more linear for the height curves (dashed lines on the right chart). It is assumed that the jog in the curves for Test S9 (solid green lines) is numeric instability as is the decrease in fill height for Tests S1 and S7 (dashed pink and blue lines on the right). The model appears to represent the behavior of the flume tests reasonably well. The comparison of total force, deflection and fill height between DAN-Barrier and the observed values is consistent with only a few outliers, most notable were for gravel tests. It was identified that the linear elastic assumption for barrier stiffness was not valid and a more complex relationship controls the response. This was overcome in the current model by calibrating the stiffness for each model, but would need to be addressed if the model were to be used for predictive purposes. The sensitivity analysis confirms reasonable behavior of the model and gives insight into the complex nature of the fluid-structure interactions and highlights essential areas of additional research particularly the testing of multiple barrier configurations.  65 7 BACK-ANALYSIS OF FULL SCALE TESTING OF FLEXIBLE BARRIERS Comparisons of DAN-Barrier results to two full-scale tests are presented to assess the effectiveness of the numerical model at predicting the total impact force of a flow-like landslide. A model was prepared for each of two full-scale tests on flexible barriers. The model captured the release of debris material from a stationary position, runout along a channel and impact with the flexible barrier. The result was a material velocity and flow depth at time of impact, as well as total force, fill height and deflection of the barrier. These values could be compared to observed values from the field tests to assess the validity of DAN-Barrier. Instrumented full-scale tests of flexible barriers typically record cable tensile loads. Therefore, it was necessary to resolve the total force obtained from DAN-Barrier into tensile loads experienced by individual cables. The approach used to resolve the forces will initially be described, followed by a description of the tests and results for the individual back-analyses. As previously discussed, the linear elastic relationship that was assumed in DAN-Barrier for calculating the total force may not be appropriate for actual implementations of flexible barriers. However, the two tests analyzed here reported little to no deformation in brake elements attached to the barrier cables. This observation suggests that the tests remained within the elastic range of the barrier, assuming significant yielding of the barrier mesh and cables did not occur. If this is true, the results from DAN-Barrier should produce reasonable results. 7.1 Resolution of DAN-Barrier total force The total force predicted by the DAN-Barrier numerical model was compared to measured forces using two separate analyses. First, it was assumed that the total force would induce a tensile load in the transverse cables (perpendicular to flow). This was treated as an internal force, independent of the overall stability of the fence system, as the vector is roughly perpendicular to the direction of the applied landslide total force. The second analysis looked at the upslope retaining ropes (in the direction of flow). An influence area was specified for each post in the system and moments are summed about the base of the post to resolve the total force into a tensile load. The two analyses were treated as independent. However, this is a simplifying assumption. The distinct cable systems (transverse and upslope) do influence one another. In addition, the flexibility of the mesh would dissipate energy of the landslide, as would the brake elements attached to individual cables. To assess the stability of the system as a whole, and the distribution of forces to various components, a more rigorous structural model would be necessary, which is outside of the 66 scope of this work. The simple analytical approach used here shows that results of the numerical model previously described provide reasonably accurate results. Prior to resolving the forces into tensile loads, flow models of the tests were prepared utilizing velocity and flow height data observed from the full-scale tests. A barrier was introduced in the DAN-Barrier numerical model and the stiffness, K, was adjusted until reasonable approximations of deflection and fill height were obtained. The resulting total force was then compared to measured values of tension in the transverse cables and upslope retaining cables. 7.1.1 TRANSVERSE CABLES – INTERNAL LOAD TRANSFER A line load was applied over the initial length of the transverse cables that were in contact with the mesh. It was assumed that this line load, q, would induce a tensile load in the cable comparable to a catenary cable under uniform load (similar to self-weight). A solution for the tensile load, T, was determined analytically and compared to the observed tensile loads reported in the transverse cables during the full-scale tests.  The line load, q, was calculated by splitting the total force, Ftotal, equally between the n transverse cables, Figure 40. For both of the back-analyses performed, there were only two transverse cables present. It was assumed the mesh was first to deform during impact. As the mesh deflected it applied a force evenly to the upper and lower transverse cables. If intermediate transverse cables were present it may not be appropriate to assume an even distribution between all cables and an influence diagram would be necessary.  Figure 40. Total force of the incoming flow is divided evenly between all transverse cables. This force is converted to a uniform line load acting over each cable. As the total force was transferred from the mesh to the transverse cables a line load was applied to each. This load was taken as uniform across the initial length of the cable that was in contact with the mesh, referred to as lo. This was assumed to be the same length as the post spacing, w. It should 67 be noted that this measurement is separate from the width of the flow, b. The applied line load for each cable was calculated as [34]           Flow interacted directly with two inner posts during the Veltheim tests. For this case the total force was reduced, assuming that all pressure on the posts was transferred directly to the upslope retaining cables. Pressure at the face of the flow was determined to be  [35]            where b is the width of the flow and h its height. This was then transformed back to force acting on the area of the post in contact with the flow [36]                     and the total force was reduced by [37]                 with n being the number of posts in contact with the flow. This correction was quite small relative to the magnitude of the total force, reducing the 450 kN force by 7.5 kN per post. The initial and final cable lengths were measured for the Veltheim test. Individual measurements were made for the three sections of cable between the four posts. The total of these three was taken as the initial and final length. Values of initial and final cable length had to be calculated for the USGS test. This was accomplished by making measurements of the cable deflection from videos of the test. It was assumed that the deformed cable had a symmetric parabolic shape. The horizontal width of the cable, w, was known from documentation of the tests (DeNatale et al. 1999), and the deformation was measured. This was treated as sag in a catenary curve, f. The initial length and final deformed length of cable were calculated as lengths of a parabola (Kern and Bland 1948) by  [38]   ((  ⁄  )     )    (  ⁄ )         (  (  ⁄ )) A load applied to a length of the cable and the resulting parabolic shape is shown in Figure 41. The induced tensile load in the cable, T, varied depending on the position along the parabola. 68  Figure 41. Catenary curve with line load q, and resulting constant horizontal force, H and a changing tensile load, T, at different locations along the curve. The tensile load at the endpoints of the cable was calculated by determining the horizontal component, which remained constant across the span of the cable. Wendeler (2008) described the relationship between the cable line load and the induced horizontal force as [39]        (      )       ∫      where E is the modulus of elasticity for the steel cable, A is its cross sectional area of steel and the integral at the right side of the equation represents the distribution of the load across the cable. Considering the load was applied evenly across the length of the cable, the integral of the line load over the length becomes [40] ∫             If more than one panel was present, as with the Veltheim tests, the quantity in Equation [40] was calculated separately for each panel. The length, lo, was then the initial length of cable for only that panel, and the line load, q, uniform across all panels. The initial and final length of cable on the left hand side of Equation [39] would be the sum of the individual panel lengths. Equation [39] must be solved iteratively to get a solution for the horizontal force. This was accomplished by setting up the equation in Excel and using "goal seek". The total force was finally determined from vector addition of the horizontal component and half the line load, the magnitude of which is [41]   (   (    ) )    It was suggested by Brighenti et al. (2013) that H may be a good approximation of T for cases where deflection is small. This was the case for the GeoBrugg tests where the support cables were 69 constrained at intermediate posts limiting the amount of deflection in the cables. Therefore, equation [41] was not used. The approach described neglects the 3-D nature of the deforming cable. The longitudinal load is applied to the cable in the direction of flow. The resulting internal stresses were calculated based on observable deformation that was assumed to be in the same direction of loading. The actual process was more complex, involving extension of the support cables in various planes, and also involved loads on support posts, dissipation of energy through expansion of the mesh, as well as many other minor complexities. The intent of this comparison was not to fully understand all the interactions that were occurring during an impact, but instead provide a check to see if the numerical model produces results that are in the vicinity of observed values. 7.1.2 UPSLOPE RETAINING CABLES – EXTERNAL STABILITY In a separate analysis, the total force of the landslide was converted to a pressure at the time of maximum force, as described by Equation [35]. It was assumed that this pressure was applied to the mesh and distributed to separate posts along the width the fence based on an influence width, winf,. The sum of all influence widths must equal the flow width, b, different from the width of the fence panels. This concept is illustrated in Figure 42 with the colored section representing the width of the flow and the dashed line representing the deform shape of the flexible barrier. The height of the applied pressure, hflow, was assumed constant across the width of the flow and is illustrated in Figure 43.  Figure 42. Illustration of influence width as the front of the landslide with width, b, interacts with a flexible barrier containing multiple posts. The pressure across each influence width contributes to a force applied to each post. Figure 43 is a section through a post with an upslope retaining rope. The applied pressure due to the flow is the only destabilizing force. The tension in the upslope retaining cable, T, is the only force stabilizing the system. These forces were taken to be in equilibrium at the time of maximum 70 force, ensuring stability of the post against rotation around the base (the bending stiffness of the post is neglected) .  Figure 43. Force diagram applied to individual post. Moments were summed about the base of the post. The tensile load in the upslope cables was recorded during the full-scale tests. The moment of this load about the base of the post was calculated as [42]               This was compared to the moment induced by the applied pressure, which was a function of the total force predicted from DAN-Barrier. This moment was calculated as [43]                      To provide a second check of the accuracy of the prediction total force the moments in Equations [42] and [43] were assumed to be equal. The tensile force, T, resulting from a total force and landslide pressure, pflow, could then be calculated and compared to observed value. Transverse support ropes would be attached to the top, bottom, and possibly at intermediate points along the height of the post in an actual installation of a flexible barrier. In regards to overall stability of the fence system, the transverse cable tension can be thought of as a fully internal load assuming there is no rotation in the post. In this case, the cable connection to the lateral anchors would remain perpendicular to the direction of flow. However, the posts are typically hinged and 71 allowed to rotate, which results in a longitudinal component of the transverse cable tension. These forces are disregarded in the current analysis for simplicity. 7.2 USGS flume tests The first back-analysis is of a test performed by the USGS, where debris flow material was released down an 80 m concrete chute (DeNatale et al. 1999). It was one of six tests performed to assess the effectiveness of different mesh configurations. A single flexible barrier panel was impacted at the end of the chute (Figure 44 and Figure 45). Data was collected from the published report as well as analysis of public domain videos of the tests.  Figure 44. Schematic profile and plan of the USGS test flume and barrier location used in back-analysis. The intent of the USGS debris flow barrier tests was to determine the effectiveness of different mesh configurations at retaining material. 10 m3 of saturated gravelly sand was released down a 100 m long, 2 m wide concrete flume. The barrier was positioned approximately 3.5 m beyond the end of the flume. The barriers were 9.1 m wide and 2.4 m high, suspended between hinged posts of equal height. 1.9 cm diameter cables were used for transverse cables (support the mesh) as well as upslope cables (support the posts). There were two transverse cables, and upper and lower, as well as two upslope cables, one at each post. Several cables were instrumented with strain gauges during the experiments to measure tensile loads transmitted to the anchors. When performing rope force calculations, only the extent of the transverse cable between the posts was considered, because little deformation in the cable occurred in the outer flanks. 72  Figure 45. Photo of the USGS flume constructed in Oregon, USA (Iverson 1997). 7.2.1 FIELD MEASUREMENTS Only Test 2 of the six debris flow impacts provided appropriate data. The geometric parameters summarized in Table 6 were obtained by video analysis. These, in combination with total force obtained from DAN-Barrier were sufficient in providing an estimate of the tensile load in the upper suspension cable, from here on referred to as Tmodel. Table 6. Barrier and flow observations for USGS flume Test 2. Parameter Symbol Value Barrier height, m h 2.4 Barrier width, m w 9.1 Initial sag, m fo 0.1 Final sag, m ff 1.1 Max. fill height, m hmax 1.3 Max. barrier deflection, m d 1.5 Debris impact width, m wi 4.5    Figure 46 and Figure 47 are screenshots taken from the Test 2 video depicting the values reported in Table 6. The first shows a significant amount of material diverted up the face of the barrier, reminiscent of the pile-up mechanism described by Sun and Law (2011). The material behavior was quite chaotic and not well represented by the DAN-Barrier model. This figure also shows a vertical deflection of 0.8 m in the upper support rope.  73  Figure 46. Screenshot from Test 2 video at maximum material height. All dimensions are in meters. Blue line is height of the undeformed net used as reference, red lines are measurements of deformed net height and material run-up height.  Figure 47. Screenshot from Test video at maximum deflection. Blue line is a reference distance of 2 m. Red lines show measurements of approximate impact width, barrier mesh deflection and cable rope deflection. The second screenshot was taken at the point of maximum deflection that was recorded as 1.5 m. The impact width was approximated at 4.7 m, and the horizontal deflection of the upper cable was 0.7 m. The vertical and horizontal deflections of the cable were added vectorialy for a total of 1.1 m. This value was used as the sag to calculate parabolic length, Equation [38]. A spreadsheet with this data as well as rope force calculations is included in Appendix H1. 74 The cable tensile loads reported by DeNatale et al. (1999) are shown in Figure 48. Only the right upslope cable force was recorded, the maximum of which occurred around 21 s and was roughly 40 kN.  Figure 48. Rope forces in right lateral anchor and right tie-back anchor measured during Test 2 of USGS flume tests using load cell attached to cable (DeNatale et al. 1999). 7.2.2 MODEL SETUP AND CALIBRATION The USGS test flume was input to DAN-Barrier according to the geometry in Figure 49. The shape of the start volume was set such that 10 m3 was contained in the 2 m width of the flume. This width was held constant until the end of the flume which corresponded with x = 103.1 m. The width was changed gradually to 4.5 m by x = 106.5 m, where the barrier observation point was placed. In order to best mimic the flow behavior observed in Test 2 three different rheologies were applied to the flume base as described in Table 7. The initial frictional resistance allowed for greater acceleration of the material. A Voellmy resistance with a relatively high turbulence coefficient was used to accumulate material in a thicker flow front. The final section utilized the Voellmy basal resistance with a higher frictional coefficient to slow the flow and further concentrate the material as it travelled through the elbow of the flume. 75  Figure 49. Geometry of USGS test flume and input model used for DAN-Barrier. Table 7. Rheology and modeling parameters used along varying longitudinal spans of the USGS flume model. Material Flume Span (m) Rheology Friction Angle (deg.) Pore-pressure Coeff. Friction Coeff. Turbulence Coeff. Internal Friction 1 0 - 51 frictional 28 0.75 n/a n/a 39 2 51 - 78 Voellmy n/a n/a 0.13 1100 39 3 78 - 100 Voellmy n/a n/a 0.24 600 39         The result of this was model configuration was higher velocities in the upper reaches of the flume where the flow was thin and spreading. As the material traveled down the flume and approached the curve, the flow height thickened and slowed. A comparison of the observed values to those recorded in the numerical model is included in Table 8. The most important value, the velocity at time of impact, was similar, though the DAN model slightly underestimated this value. Depth of flow during runout was not reported and could not be used for calibration. Table 8. Comparison of observed velocities and velocities from the numerical model used during calibration. Average velocities were calculated by noting the amount of time required for the flow front to pass identifiable positions, except for barrier impact velocity, which was measured from the video.   Release Post 1 Post 2 Barrier x (m) 0 32.0 66.0 86.0 t (s) 0 3.0 5.5 7.5 ave. v (m/s) 0 10.7 12.0 8.0* DAN v (m/s) 0 16.5 14.4 7.4 *actual value measured from video        7.2.3 CALCULATED TOTAL FORCE AND CABLE ANALYSES A series of different values for barrier stiffness were tested in DAN-Barrier with little difference in the resulting total force, Table 9. In all cases the fill height at the barrier was significantly lower than what was observed in the videos. However, this is not concerning, considering that a large 76 amount of material piled up on the face of the barrier and was not believed to significantly contribute to the loads transmitted to the anchors. Table 9. DAN-Barrier calculations of total force, deflection and fill height using different barrier stiffness. Barrier Stiffness (kN/m) Maximum Values Force (kN) Deflection (m) Fill Height* (m) Fill Height (m) 60 74 1.2 0.4 0.5 120 76 0.6 0.4 0.6 180 77 0.4 0.3 0.6 *measured at time of maximum total force, not maximum fill height      A barrier stiffness of 60 kN/m was selected to use in the rope force calculation because it produced the most realistic deflection. Either of the other values could have been used without any major effect on results, as only a 3 kN variance existed between all three tests. Figure 50 shows the calculated total force, deflection and fill height over time obtained from the numerical model. A peak total force of 74 kN was obtained 0.5 s after material first arrived at the barrier.  Figure 50. Total force, fill height and deflection over time for USGS flume Test 2 predicted by DAN-Barrier. The total force of 74 kN was used to calculate a line load in the upper transverse cable using Equation [34], by assuming the total force was split evenly between the upper and lower transverse cables. A value of 4.1 kN/m was obtained. Calculation of the horizontal component of the tensile 77 load was determined to be 38 kN using Equations [38] and [39]. When this was combined the longitudinal component of the tensile force (vertical load in Figure 41) a total tensile load, Tmodel, of 42 kN was obtained (Equation [41]).  The pressure on the mesh resulting from the total force was calculated to be 13.1 kN/m2 using Equation [35]. It was assumed that this pressure would be divided evenly between the two posts. This generated a moment about the base of each post as illustrated in Figure 43. The disturbing moment due to the landslide was calculated using Equation [43] to be 22 kNm, which can be used to calculate a tension in the upslope retaining cable of 12 kN. 7.2.4 COMPARISON TO OBSERVED VALUES Only the upper transverse cable and one upslope retaining cable were instrumented during the USGS tests. The maximum forces observed in these cables are reported in Table 10 along with the calculated values using DAN-Barrier to obtain a total force and decomposing that into component loads. Table 10. Summary of results for back analysis of USGS debris flow flume, Test 2 against a flexible barrier (DeNatale et al. 1999). Calculated values are direct outputs from DAN-Barrier or are calculated from the prediction of total force.   Calculated Observed Deviation (%) Landslide Total Force (kN) 74 -- -- Landslide Pressure (kN/m2) 13.1 -- -- Impact Line Load (kN/m) 4.1 -- -- Transverse Cable Tension (kN) 42 40 5 Upslope Cable Tension (kN) 12 16 -25 Maximum Fill Height (m) 0.5 1.2 -58 Maximum Deflection (m) 1.2 1.5 -20 Flow Approach Velocity (m/s) 7.4 8.0 -8     The tension in the upper transverse cable was calculated with great accuracy, resulting in only 5% error. However, tension in the upslope retaining cable showed slightly more error, although not unreasonable amounts. As previously mentioned, it is possible that the transverse cables also supplied a disturbing moment about the base of the post as the mesh deflected and the posts rotated downstream. This could account for a low estimate of the disturbing moment due to landslide pressure, and an underestimate of the tensile load. This discrepancy could also be contributed to the slight underestimate of velocity as the flow impacted the barrier underestimating the total force. While the calculated forces showed optimistic results, the fill height appears to be considerably underestimated in this analysis. The observed value of 1.2 m was a measured maximum that 78 occurred as material first impacted the barrier. There was an obvious jet of material that piled up immediately behind the barrier. It is likely that this behavior is not captured within the model. Accumulation of force occurred much more rapidly in the numerical model than what was observed in the USGS test. This was consistent with what was previously noted for back analysis of flume tests (Chapter 5). Figure 48 above shows roughly a 3 s delay between the arrival of material and the maximum observed force. This is compared to only 0.5 s in the model. The model did correctly predict the lag between maximum deflections and fill height. The maximum fill height was observed to occur 0.3 s after the maximum deflection in both the numerical model and the actual test. Overall, the results from the DAN-Barrier analysis of the USGS test compare quite well with the observed values.  7.3 Open hillslope debris avalanche tests at Veltheim, Switzerland.  The second back-analysis is one of many tests performed by the WSL and GeoBrugg at the Veltheim test site in Switzerland. A broad channel with a three panel flexible barrier at the end (Figure 51) was used to simulate the interaction of open hillslope failures with flexible barriers (Bugnion et al. 2011). Data was provided through the WSL with permission from GeoBrugg. Both of the experiments were previously described in Chapter 2.2.  Figure 51. Schematic profile and plan of the Veltheim test site including 3 panel barrier and location of instrumentation used for back-analysis. Figure 52 shows an aerial view of the test site immediately before impact. Two vertical pressure plates were installed within the flow channel. The chaotic flow upstream of the barrier is due to material impacting these plates. 79  Figure 52. Overview of the Veltheim test site with the release basin at the top of the site, instrumented runout area and three panel flexible barrier (photo provided by Geobrugg and WSL). The use of flexible barriers in mitigating open hillslope failures has brought about new design challenges. The barriers must be constructed over broader areas and provide greater retention. The design adaptations that have accompanied this were described in Chapter 2.1. A test site in Veltheim, Switzerland has focused on these adaptations and the implication on dimensioning techniques.  The site layout and testing process was described by Bugnion et al. (2011). Saturated volumes up to 50 m3 are released from the reservoir at the top of the slope. The material accelerates down a 41 m long, 8 m wide channel with an average slope of 30°. Material was confined laterally by 1 m high berms, and some transverse velocity gradients were observed. The material does impact a barrier over a wide area (8 to 9 m before lateral spreading), and therefor is reminiscent of debris avalanches. The barriers tested were 3.5 m high, spanning 15 m over 3 panels. All cables were 22 mm diameter steel cables. These included top and bottom transverse cables that were continuous between all posts with 2 brake elements, and upslope retaining cables extending from each of the four posts. During impact the flow directly interacted with 2 of the 4 posts. When calculating the cable forces it was assumed that the pressure exerted on the post was directly transferred to the upslope anchors.  7.3.1 FIELD MEASUREMENTS Numerous tests were performed at Veltheim including multiple impacts on a single barrier. The Swiss Federal Institute for Forest, Snow and Landscape Research (WSL) provided data for three tests with permission by Geobrugg who has been responsible for the fence design and construction. 80 Only one test, Test 7.1, included video observation and has been analyzed here for comparison with DAN-Barrier. Figure 53 shows measurement made before and after Test 7.1. The initial cable length was assumed to be the width between the posts shown at the top of the figure. As with the USGS tests, the length of the cable on the outer flanks was not considered. The deformed length of the upper and lower support cables were taken as equal to the measurement shown in the middle image.   Figure 53. Dimensions of the filled barrier after Test 7.1 (figure provided by Geobrugg and WSL). A deformation of 1.3 m at mid span was reported as the net deflection in the figure above. However, this was measured after material had settled. Video analysis was used estimate of the dynamic deflection. The screenshot in Figure 55 shows the 1.3 m as reference, and a dynamic deflection of 1.5 m. Also, the impact height of 2.2 m was estimated, though it is obvious that most of this is spray. Rope forces in the upper and lower support cables were observed to be quite similar, Figure 55. A peak force of about 85 kN was recorded for both. The upper support cable had an additional deflection of 2 cm due to elongation of the break element. This was added to the measured deformed length reported in Figure 53. Brake elements were not engaged for the bottom support cable. Retaining cable #3 (green line) references the inner right post retaining cable, and #4 (cyan line) the outer right retaining cable. It is realistic that the observed force in cable #3 was higher 81 than #4 as it had the added force of the debris impacting the post directly. The retaining cable forces were not used in the numerical model comparison.  Figure 54. Screenshot from the side camera at time of maximum deflection (t = 5.9 s) showing reference distance in blue and measurements of maximum deflection and fill height in red.  Figure 55. Rope forces in various cables during Test 7.1 (data provided by Geobrugg and WSL). The flow did not begin to spread laterally until after the peak force. Therefore, it was assumed that the impact width was slightly wider than the channel width. A value of 9 m was used in calculation of rope forces.   82 7.3.2 MODEL SETUP AND CALIBRATION The geometry of the Veltheim test that was used as input to the numerical model was quite simple, Figure 56. The width was held constant at 8 m until just before the barrier where it widened to 9 m between x = 43 m and x = 44 m.  Figure 56. Geometry of Veltheim test site and input model used for DAN-Barrier Only a single video of the impact from the side was provided and reviewed as part of this comparison study. Therefore, observations of velocity were limited to those reported in Table 11. Given the lack of data, a single basal rheology was used to represent the basal resistance term in numerical model. The Voellmy model was used with unit weight of 17.3 kN/m3 (provided in WSL/Geobrugg report), friction coefficient of 0.06, turbulence coefficient of 1000, and internal friction angle of 3° was used to simulate the saturated and fluidized nature of the observed flow. This resulted in velocities, which are included in Table 11. Velocities are close with the best match occurring at the barrier. Table 11. Observations of travel distance, time and average velocity from field compared to velocity from numerical model used for calibration.   Release Post 1 Post 2 Post 3 Barrier x (m) 0 11 21 31 41 t (s) 0 1.3 2.3 3.2 4.3 ave. v (m/s) 0 8.5 9.1 11.1 11.1 DAN v (m/s) 0 9.3 10.3 10.9 11.2         83 7.3.3 CALCULATED TOTAL FORCE AND CABLE ANALYSES Upon running the model and plotting results, the calculated values of total force, barrier deflection and material fill height exhibited numerical instability in the form of oscillations in the recorded values. The results, shown in Figure 57, are truncated at the time when maximum fill height at the barrier is first observed.  Figure 57. Calculations of total force, fill height and deflection over time for Veltheim Test 7.1 using DAN-Barrier. A stiffness of 400 kN/m appeared to provide the best results in terms of barrier behavior. The total force was calculated to be 515 kN. At this time, the force corresponds to a deflection of 1.3 m and a fill height of 0.8 m. The maximum fill height was calculated to be 2.3 m. The total force of 515 kN was used to calculate the resulting tensile loads in the transverse cables. The total force was divided equally between the top and bottom cable. Taking into account the small reduction in total force due to material impacting the posts directly (Equation [37]), the resulting line load applied to each cable was calculated to be 14.9 kN/m using Equation [34]. The rope force equation was modified to accommodate the initial and final cable length of each panel separately, Equation [44]. [44]        (      )       (                             ) 84 The subscripts 1 through 3 represent the three separate panels of the barrier fence. Brake elongation in the top support cable was added to the final length on the left side of the equation. Solving the equation resulted in a horizontal force of 95 kN in the top cable and 98 kN in the bottom. The difference was due to elongation of brake elements in the top transverse cable but not in the bottom. These values were used as approximations of the tensile load in the cable because deflections in each bay were quite small and the longitudinal component of the tensile vector would be insignificant.  The longitudinal moment stability analysis for the Veltheim back-analysis required an assumption for influence width of each post because the flow impacted multiple panels across the width of the barrier. Figure 58 shows the impact area estimated as a rectangle in the upper image. This was used to approximate the impact pressure. Stability analysis was performed for one outer and one inner post as these were the only instrumented upslope cables. The bottom image in Figure 58 shows the width of the impact pressure that was assumed to influence the stability of the outer post, highlighted blue, and the width influencing the inner post, highlighted orange.   Figure 58. Estimated impact width and height of flow during peak force (upper image), and distribution of pressure for half the flow to designated posts, the influence width (bottom image). The landslide pressure was calculated using Equation [35] to be 26 kN/m2. Using the assumptions for influence width, a moment balance was performed for the two posts and tensions were calculated for the two upslope retaining cables. The moment about the base of the inner post due to the calculated landslide pressure was 214 kNm, and 76 kNm for the outside post. These translate to tensile loads of 66 kN and 23 kN.   85 7.3.4 COMPARISON TO OBSERVED VALUES The observed values for the upper and lower transverse cable tensions, as well as upslope retaining cables for one middle post and one outer post are compared to calculated values in Table 12. Table 12. Summary of results for back analysis of Veltheim debris avalanche site, Test 7.1 against a three bay flexible barrier. Calculated values are direct outputs from DAN-Barrier or are calculated from the prediction of total force.   Calculated Observed Deviation (%) Landslide Total Force (kN) 515 -- -- Landslide Pressure (kN/m2) 26 -- -- Impact Line Load (kN/m) 17 -- -- Transverse Cable Tension, Upper (kN) 108 83 30 Transverse Cable Tension, Lower (kN) 111 85 31 Upslope Cable Tension, Middle Post (kN) 66 60 10 Upslope Cable Tension, Outside Post (kN) 23 40 -43 Maximum Fill Height (m) 2.3 2.2 5 Maximum Deflection (m) 1.3 1.5 -13 Flow Approach Velocity (m/s) 11.2 11.1 1     The top and bottom transverse cable tensions were observed to both be roughly 85 kN during the full scale test. This is slightly less than the calculated values of 108 and 111 kN. A secondary chain link mesh was used in all of the Veltheim tests to increase material retention. This mesh was pinned upslope with shallow soil anchors and shackled to the main mesh in proximity to the lower transverse cable. It is anticipated that these anchors shed some of the total load that was imparted on the barrier system by the arriving material. It is likely that a greater proportion of the landslide total force was felt by the lower cable, and that much of that load was immediately shed to the ground. It is therefore difficult to assess the effectiveness of this analysis. The recorded tensile load in the upslope retaining cables was reported to be 60 and 40 kN for the cables attached to the inner and outer posts. The calculated values for the cables using the moment balance analysis were 66 and 23 kN. The force in the cable attached to the inner post, which was in direct contact with the flow, was quite accurate in the analysis. The prediction for the outer support cable showed considerably more error. It is possible that the influence areas were not estimated correctly, and the outer post would support additional flow width. This would reduce the force for the inner post cable and increase the force for the outer post cable. This would still result in an underestimate of the forces, as was the case with the USGS test for this type of analysis. As mentioned previously, it is possible that this discrepancy is a result of disregarding the effect of the 86 transverse cables. It is also possible that the barrier was too stiff in the model and the total force was overpredicted. Predicted values of barrier deflection and material fill height were quite accurate in this analysis. While these values, as well as calculated values of force, are accurate in magnitude, the time at which they occured deviated from observation. Figure 55 shows that the time from first impact to peak force in the field observations was approximately 1 s. This is compared to a time of only 0.4 s for the calculated values using DAN-Barrier as shown in Figure 57. A time series for the other parameters was not obtained from the video analysis. The error observed regarding the peak values of DAN-Barrier predictions suggests that further validation is necessary. The model worked well for frictional material against a barrier approximated by a linear elastic load model. However, this does not mean that it can be extrapolated to all situations. Experimentation with more cohesive landslide materials, and numerical studies of different barrier force models should be considered to further expand the validation process.   87 8 CONCLUSIONS AND RECOMMENDATIONS The need for easily constructed and robust mitigation measures is essential in protecting human life and infrastructure from landslides, particularly of flow-type. Due to site constraints, it is often not possible to construct massive earth fill or concrete structures. This has led to the proliferation of flexible barriers that rely on the yielding of the barrier mesh and specific brake elements to dissipate the force imparted by the landslide. Current approaches to dimensioning the forces generated by the arriving landslide mass are lacking in that they do not take into account the flexibility of the structure. The accepted means of calculating a dynamic impact pressure for a flexible barrier is the same as what has been used for rigid structures. Consequently it was anticipated that the predicted anchorage forces could be conservative. 8.1 Summary of work completed A new numerical model has been proposed that accounts for both flow and structural behavior. The flow parameters are predicted by the previously validated numerical model DAN-W (Hungr 1995). Material is characterized as a homogeneous fluid capable of travelling over user specified terrain. Built in is the capability of simulating various flow rheologies. The new model, DAN-Barrier, allows for a structure to be placed in the model that intersects the flow. The total force of the landslide imparted to the barrier is a function of barrier deflection. A linear proportionality constant between force and displacement is utilized at this time, referred to as stiffness, K. This value describes the overall structural behavior of the barrier and must be quantified separately. A series of controlled laboratory tests have been used as means of validating the model. A barrier was erected at the end of a chute with the ability to adjust the incline of the entire apparatus. The barrier was attached to a sliding cart with all range of motion limited, except for in the longitudinal direction of flow. In this manor all momentum from the arriving landslide would be transferred to the barrier and recorded as a single force using a strain gauge attached to the sliding cart. It was anticipated that the total force observed during a dynamic impact would exceed the force imparted by a similar amount of material existing behind the barrier in a static state. The testing resulted in two categories of flow behavior, each with separate results. The first, referred to as thin flow front tests, were the result of the granular material being released from the top of the chute and allowed to accelerate under gravitational forces. This type of test was not successful in generating a dynamic force, due to the small thickness of the flow front approaching the barrier. It was possible to use these results to verify that the force imparted on the barrier, 88 regardless of whether it was rigid or flexible, was comparable to the static load calculated using active lateral earth pressure theory. The second category of tests was referred to as steep flow front tests. The name signifies that the arriving landslide mass (granular material) retained a wedge shaped front, but had appreciable thickness near the front of the mass that resulted in a steep face. These tests were capable of producing a dynamic spike in the observed total force. Results from this group of tests were used for validating the numerical model. By calibrating the stiffness of the barrier, satisfactory results were obtained in terms of total force, material fill height at the face of the barrier, and to a lesser degree, barrier deflection. Similar values of total force were also calculated using the standard approach for dimensioning flexible barriers. However, this was only possible by knowing the exact depth of material interacting with the barrier. In an attempt to extrapolate the numerical model to true flexible barriers, results were compared to instrumented full-scale debris flow and debris avalanche test barriers. The total force from DAN-Barrier was transformed to cable tensile forces using two separate analytical approaches. The results were compared to those observed in upper and lower transverse cables and upslope retaining cables attached to barrier posts. In full-scale field tests these cables were instrumented with strain gauges giving insight into the tensile loads experienced in various fence components. 8.2 Summary of results Based on the results of the numerical model for the thick flow front tests it is reasonable to say that the DAN-Barrier model is capable of simulating the total force of a flow-like landslide impacting a flexible barrier. The values observed for total force, fill height and deflection in the numerical model were comparable to those recorded during laboratory tests for sand impacting a flexible barrier. For a dynamic impact of granular material against a flexible membrane reasonably approximated by the linear elastic load model, error was limited to less than 5% for total force and fill height. These two values are considered to be most significant in the dimensioning of a flexible barrier, and therefore the results are optimistic. Further validation with additional materials and barrier configurations is still necessary. The behavior of the stiffness between the various models was reminiscent of strain rate dependent behavior of rubber the membrane. More energetic impacts were considered to load the barrier at a faster rate. For these tests a stiffer barrier was necessary in the DAN-Barrier model to obtain accurate results. Even though this behavior was not built into the numerical, the process of 89 adjusting stiffness on a model basis was able to capture this complex behavior of the chosen rubber barrier. It is therefore possible to say that validation was accomplished. It would be beneficial to expand the amount of tests, and include greater variability in flow and barrier parameters for further validation under different circumstances. It was determined through the laboratory experiments, and the validation process, that the numerical model was not appropriate for all types of landslides. Good results were obtained for steep flow front tests that imparted a dynamic peak force that exceeded the static force. These tests were reminiscent of a boulder fronted debris flow, where a concentrated mass at the front of the flow makes initial contact with the barrier. In this scenario, the DAN-Barrier model would be appropriate for predicting total force derived from the landslide. However, for thinner flows, such as mudflows or hyper-concentrated floods, the tool developed here is not necessary. Instead, it was shown that lateral earth pressure theory, using active state conditions and accounting for wall friction, was enough to predict the total force on the barrier. This observation was significant in that the force could be calculated regardless of whether the barrier was flexible or rigid. Lateral earth pressure theory was enough to predict the total force for both rigid and flexible barriers during thin flow front tests. This suggests that barrier flexibility may not have been an issue with these types of flows. It was not until more energetic flows impact the barrier that any effect of flexibility was observed. A benefit was seen in the fill height behind the barrier, where the flexible barrier capable of reducing the height of accumulated material behind the barrier. It is anticipated that flexibility may be a hindrance for highly energetic flows in terms of the total force that the barrier must dissipate. It is possible that with too much deflection, the barrier interacts with an increased amount of material. By limiting flexibility, the benefits of an extended impulse is maintained while limiting the amount of material that the barrier must initial stop and allowing this stationary mass to stop subsequent flow. Additional testing against barriers of difference stiffness is necessary to justify this theory. The result would be a force versus stiffness diagram. The results from the back-analysis of full-scale debris flow and debris avalanche tests showed reasonable results. Using analytical approaches to resolve the DAN-Barrier total force into cable tensions, error was limited to 30% for the USGS debris flow test, and 43% for the Veltheim debris avalanche test. While these errors may appear large, they are still optimistic. The approach used was limiting in the fact that is treated the different fence components, transverse cables and 90 upslope cables, as independent systems that did not share the load of the impacting landslide. It is likely that some load in the transverse cables was shed to the upslope anchors, particularly when the posts are allowed to rotate downslope changing the trajectory of the transverse tension vector on the flanks of the barrier. To accurately account for this behavior a more rigorous tool is necessary, which defeats the purpose of the DAN-Barrier model. Therefore, the results were considered successful in that a first order approximation of the total force and cable tensile forces were derived. While results were obtained for full-scale tests, the numerical model as it currently exists is not considered complete and accurate for design purposes. Some numeric instability was observed, and should be further investigated. The model was capable of predicting fill height accurately in various circumstances. For gradual and rapid filling processes against both rigid and flexible barriers, DAN-Barrier was able to model the fill height within 10% of observed values. Therefore the tool could assist in the dimensioning the geometry of a flexible barrier in a debris flow channel. Hopefully, with continued refinement and additional testing to further validate material interaction with the barrier and structural response to loading, the tool could prove useful in the design of flexible barriers for flow-type landslides. A list of additional considerations is included in the following section to highlight areas of attention. Not all of these are necessary to obtain a working design tool, but are worthy of consideration. 8.3 Other considerations This research has been useful in showing the potential for simplified flow – structure interactions. The numerical model, as presented here, warrants refinement to better simulate the coupled system. Additionally, further laboratory testing could help to answer questions about the numerical model and the applicability of flexible barriers in general. A list of recommendations follows:  It is anticipated that the model's inability to accurately predict the shape of the deposited material behind the barrier is due to a lack of internal shear stresses. As material rapidly rises at the barrier face, shear stress would be generated between adjacent elements. Taking the relative motion of adjacent elements may be a feasible way of simulating this effect.  The rate at which the fill height increases in the model is of concern. As noted in the results chapter, fill height rose to proper levels, however this occurred much faster than what was 91 observed in the experiments. It is possible that this is also due to the lack of internal shear stress.  This research has confirmed that once the material reaches a static state the total force can be approximated using active lateral earth pressure. This could be programmed into the model to show a drop from dynamic and static force.  Some rebound in total force and barrier deflection was observed in the numerical model resulting in a local maximum. The nature of this is not currently understood and should be further investigated.  There is no explicit shock capturing calculation in this model. The development of a shock wave at impact with a barrier may result in pressure differentials and loss in energy. This could be considered in future iterations.  Further testing must be performed to conclude the effect of barrier flexibility on the observed total force. Tests performed in this research were limited to rigid and a single flexible barrier. Future tests should include multiple barrier configurations to create a force versus flexibility relationship similar to what is presented theoretically in Figure 38. This data would provide insight in the effective range of flexibility for the barriers under question.  Future tests should find a better way of imparting a concentrated flow front. The technique used here, with a mass accelerated manually, limits reproducibility. Possibilities include accelerating the granular material before it travels through an elbow that would concentrate the grains, or introduce a form of cohesion.  During testing with the concentrated flow front it was assumed that the mass had a uniform longitudinal velocity. Given the level of instrumentation, this was considered reasonable. With more cameras along the length of the flume a velocity gradient could be mapped and applied as an initial condition in the numerical model to more accurately simulate the flow.  More data points would be useful to fill the data. Particularly, tests that provide a high initial kinetic energy prior to impact (either more mass or greater velocity).  It would be of interest to do a direct comparison of the total force predicted by DAN-Barrier to the pressure predicted by the standard conservation of momentum approach (Equation [8]). This could be accomplished by using both approaches as input to a finite element software capable of accurately modeling a barriers internal distribution of stress, such as FARO. 92  To make this tool practical for predictive purposes a better understanding of barrier stiffness would be necessary. This would require quantifying an overall stiffness of various barrier configurations. It is anticipated that this is not a linear relationship as proposed in the current model, and may require revision to obtain a total force as a function of deflection. 8.4 Conclusions A numerical model has been developed that is capable of estimating the total force imparted by flow-like landslide on flexible barriers. The model has been initially validated at the laboratory scale, and provides reasonable solutions when compared to full-scale tests if combined with methods of discretizing the total force. It was not intended for this numerical model to be used as a tool for design of flexible barriers, but instead act as a proof of concept. Similar efforts are currently being made to model the flow – structure interaction that occurs during impact. However, they utilize a suite of complex numerical models that hinder their use in common engineering practice. 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J Mt Sci 8:109–116. doi: 10.1007/s11629-011-2083-x   100 APPENDICES   101 APPENDIX A1: TEST SETUP SUMMARY TABLES GRAVITATIONAL – THIN FLOW FRONT Test Flume Inclination (deg) Barrier Configuration Material Type Release Mass Locationa Load Cell Setting (Hz) Side Camera Type / Setting Top Camera Type / Setting S1 34 flexible 2:1 sand:gravel mix at front with sand behind flume hopper 2000 GoPro Hero 2 / WVGA-120fps Canon IXY / WVGA-120fps S2 34 flexible 1:1 sand:gravel mix at front with sand behind flume hopper 2000 GoPro Hero 2 / 720p-60fps Canon IXY / WVGA-120fps S3 34 flexible 1:1 sand:gravel mix at front with sand behind flume hopper 2000 GoPro Hero 2 / 720p-60fps Canon IXY / WVGA-120fps S4 34 flexible 1:1 sand:gravel mix at front with sand behind flume hopper 2000 GoPro Hero 2 / 720p-60fps Canon IXY / WVGA-120fps S5 28 flexible sand flume hopper 2000 GoPro Hero 2 / 720p-60fps Canon IXY / WVGA-120fps S6 28 flexible 2:1 sand:gravel mix at front with sand behind flume hopper 2000 GoPro Hero 2 / 720p-60fps Canon IXY / WVGA-120fps S7 28 flexible 2:1 sand:gravel mix at front with sand behind flume hopper 2000 GoPro Hero 2 / 720p-60fps Canon IXY / WVGA-120fps R1 34 rigid gravel front with sand behind flume hopper 2000 GoPro Hero 2 / 720p-60fps n/a R2 34 rigid gravel front with sand behind flume hopper 2000 GoPro Hero 2 / 720p-60fps n/a R3 34 rigid 2:1 sand:gravel mix at front with sand behind flume hopper 2000 GoPro Hero 2 / WVGA-120fps n/a aMeasured as distance from barrier in meters      ACCELERATED MASS – CONCENTRATED FLOW FRONT Test Flume Inclination (deg) Barrier Configuration Material Type Release Mass Locationa Load Cell Setting (Hz) Side Camera Type / Setting Top Camera Type / Setting S1 22.2 flexible sand between 0.30 and 1.02 m 6000 GoPro Hero 2 / 960p-48fps Canon IXY / WVGA-120fps S2 22.2 flexible sand between 0.30 and 0.97 m 6000 GoPro Hero 2 / 960p-48fps Canon IXY / WVGA-120fps S3 22.2 flexible sand between 0.30 and 1.02 m 6000 GoPro Hero 2 / 960p-48fps Canon IXY / WVGA-120fps S4 22.2 flexible sand between 0.40 and 1.20 m 6000 Sony Handycam / 1080p-60fps Canon IXY / WVGA-120fps S5 22.2 flexible sand between 0.41 and 1.16 m 6000 Sony Handycam / 1080p-60fps Canon IXY / WVGA-120fps S6 22.2 flexible sand between 0.41 and 1.13 m 6000 Sony Handycam / 1080p-60fps Canon IXY / WVGA-120fps S7 22.2 flexible sand between 0.40 and 1.22 m 6000 Sony Handycam / 1080p-60fps Canon IXY / WVGA-120fps S8 22.2 flexible sand between 0.40 and 1.12 m 6000 Sony Handycam / 1080p-60fps Canon IXY / WVGA-120fps S9 22.2 flexible sand between 0.40 and 1.23 m 6000 Sony Handycam / 1080p-60fps Canon IXY / WVGA-120fps S10 22.2 flexible sand between 0.40 and 1.06 m 6000 Sony Handycam / 1080p-60fps Canon IXY / WVGA-120fps S11 22.2 flexible sand between 0.40 and 1.08 m 6000 Sony Handycam / 1080p-60fps Canon IXY / WVGA-120fps S12 22.2 flexible sand between 0.40 and 1.08 m 6000 Sony Handycam / 1080p-60fps Canon IXY / WVGA-120fps G1 22.2 flexible gravel between 0.60 and 1.10 m 5000 GoPro Hero 2 / 960p-48fps Canon IXY / WVGA-120fps G2 22.2 flexible gravel between 0.60 and 1.45 m 5000 GoPro Hero 2 / 960p-48fps Canon IXY / WVGA-120fps G3 22.2 flexible gravel between 0.40 and 1.08 m 6000 Sony Handycam / 1080p-60fps Canon IXY / WVGA-120fps R1 22.2 rigid sand between 0.40 and 1.14 m 6000 Sony Handycam / 1080p-60fps Canon IXY / WVGA-120fps R2 22.2 rigid sand between 0.40 and 1.03 m 6000 Sony Handycam / 1080p-60fps Canon IXY / WVGA-120fps R3 22.2 rigid sand between 0.40 and 1.12 m 6000 Sony Handycam / 1080p-60fps Canon IXY / WVGA-120fps aMeasured as distance from barrier in meters        102 APPENDIX A2: RESULTS SUMMARY TABLES GRAVITATIONAL – THIN FLOW FRONT Test Initial Vel. (m/s) Ave. Frontal Vel. at Impact (m/s) Max. Load (kN) Fill Height at Max. Load (m) Approx. Impact Depth (m) Angle of Backfill at Max Load (deg) Time From First Impact to Max. Deflection (s) Max. Deflection (cm) Fill Height at Max. Deflection (cm) Max Fill Height (cm) S1 n/a 3.10 0.099 n/a n/a 16.7 1.56 10.15 20.2 20.2 S2 n/a 3.22 0.140 n/a n/a 16.7 1.23 9.91 21.0 22.5 S3 n/a 2.63 0.117 n/a n/a 17.5 1.48 9.00 20.2 20.8 S4 n/a 2.63 0.143 n/a n/a 14.8 1.25 9.68 21.1 23.1 S5 n/a 1.37 0.0066 n/a n/a 25.5 1.41 2.63 5.8 6.0 S6 n/a 1.91 0.0574 n/a n/a 26.5 1.33 5.93 12.3 11.0 S7 n/a 2.06 0.0353 n/a n/a 23.6 1.03 4.60 11.3 9.0 R1 n/a 3.59 0.207 n/a n/a 14.6 1.12 n/a n/a 31.1 R2 n/a 3.50 0.115 n/a n/a 16.7 1.18 n/a n/a 21.2 R3 n/a 3.58 0.141 n/a n/a 22.2 1.02 n/a n/a 20.9  ACCELERATED MASS – CONCENTRATED FLOW FRONT Test Initial Vel. (m/s) Ave. Frontal Vel. at Impact (m/s) Max. Load (kN) Fill Height at Max. Load (m) Approx. Impact Depth (m) Angle of Backfill at Max Load (deg) Time From First Impact to Max. Deflection (s) Max. Deflection (cm) Fill Height at Max. Deflection (cm) Max Fill Height (cm) S1 1.12 1.79 0.0953 0.131 0.115 19.9 0.25 6.91 14.8 17.2 S2 0.93 1.69 0.0749 0.116 0.100 22.7 0.27 5.54 13.9 15.7 S3 1.09 1.59 0.0885 0.134 0.125 14.6 0.30 6.99 14.9 17.1 S4 1.39 1.97 0.1760 0.138 0.128 18.9 0.23 10.68 16.4 21.6 S5 1.14 2.00 0.0482 0.058 0.050 19.0 0.13 4.24 8.9 10.8 S6 0.72 1.09 0.0267 0.084 0.084 7.9 0.38 3.08 8.9 9.7 S7 0.89 1.59 0.0636 0.120 0.100 7.4 0.22 5.33 12.6 14.5 S8 1.39 1.84 0.1330 0.111 0.115 21.7 0.23 9.08 15.2 20.7 S9 1.37 1.67 0.1480 0.137 0.125 19.2 0.26 9.61 16.3 21.5 S10 1.58 2.49 0.1550 0.106 0.105 14.1 0.14 8.36 13.6 20.8 S11 1.34 2.20 0.1310 0.112 0.105 20.5 0.18 7.72 12.7 19.6 S12 0.96 1.46 0.0611 0.091 0.070 20.7 0.22 5.05 10.9 14.5 G1 0.92 1.20 0.0301 0.078 0.078 11.1 0.27 3.16 8.5 9.3 G2 1.12 1.56 0.0635 0.068 0.068 18.7 0.27 4.93 11.2 14.4 G3 0.66 0.71 0.0137 0.042 0.042 24.4 0.26 1.55 4.3 4.6 R1 1.33 1.50 0.0838 0.124 0.098 20.9 0.28 n/a n/a 20.8 R2 1.48 1.79 0.1110 0.129 0.102 18.5 0.16 n/a n/a 22.6 R3 0.93 1.24 0.0404 0.112 0.100 4.1 0.28 n/a n/a 14.1   103 APPENDIX B1: THIN FLOW FRONT VIDEO OBSERVATIONS; FLEXIBLE BARRIER WITH SAND AND GRAVEL  Material released from hopper down chute at varying inclinations.  Angle of flume incline varies between tests, see summary table in Appendix A1 for details.  104 TEST S1: VAVE. = 3.10 M/S   105 TEST S2: VAVE. = 2.63 M/S   106 TEST S3: VAVE. = 3.22 M/S   107 TEST S4: VAVE. = 2.63 M/S   108 TEST S5: VAVE. = 1.37 M/S   109 TEST S6: VAVE. = 1.91 M/S   110 TEST S7: VAVE. = 2.06 M/S  111 APPENDIX B2: THIN FLOW FRONT VIDEO OBSERVATIONS; RIGID BARRIER WITH SAND AND GRAVEL  112 TEST R1: VAVE. = 3.59 M/S   113 TEST R2: VAVE. = 3.50 M/S   114 TEST R3: VAVE. = 3.58 M/S  115 APPENDIX C1: THIN FLOW FRONT TEST RESULTS; FLEXIBLE BARRIER WITH SAND AND GRAVEL  Test force taken from load cell at a sampling rate of either 5 or 6 kHz, see test setup in Appendix A1 for details.  Apparent thickness of force line is indicative of error in recorded value. This is roughly 0.001 kN for all tests, however natural oscillation (noise in the data) appears greater for tests with a smaller ultimate force, or smaller overall span.  Fill height and deflection measured from videos at regular time intervals. Data is presented as a line for clarity. Error for fill height is approximately ±0.005 m, and ±0.002 m for deflection.  No data is presented from DAN-Barrier as this was not used for thin flow front tests, see Chapters 5 and 6 for discussion.   116 TEST S1   TEST S2   117 TEST S3   TEST S4   118 TEST S5   TEST S6   119 TEST S7    120 APPENDIX C2: THIN FLOW FRONT TEST RESULTS; RIGID BARRIER WITH SAND AND GRAVEL   121 TEST R1   TEST R2   122 TEST R3    123 APPENDIX D: THIN FLOW FRONT TEST IMPACTS AT TIME OF MAXIMUM FILL HEIGHT  Material released from hopper at top of test flume and allowed to accelerate under gravitational forces.  Angle of flume incline varies between tests, see summary table in Appendix A1 for details.  All heights measured at time of maximum fill height for use in earth pressure calculations.  Backfill angle measured as average slope relative to horizontal.   124 APPENDIX E1: STEEP FLOW FRONT VIDEO OBSERVATIONS AND DAN-BARRIER TIME SERIES; FLEXIBLE BARRIER WITH SAND  Material accelerated manually starting between 40 and 80 cm upstream of barrier.  Initial velocity recorded at time when external force is removed, trelease = 0.00s.  DAN-Barrier model used observed shape of flow and initial velocity from time of release as initial conditions.  Barrier stiffness for each DAN-Barrier model, as described in Section 3.2.1 and Chaoter 6 is calibrated to observed maximum force for test.  125 TEST S1: VINITIAL = 1.12 M/S, KCALIBRATED = 1.6 KN/M   126 TEST S2: VINITIAL = 0.93 M/S, KCALIBRATED = 1.6 KN/M   127 TEST S3: VINITIAL = 1.09 M/S, KCALIBRATED = 1.6 KN/M   128 TEST S4: VINITIAL = 1.39 M/S, KCALIBRATED = 1.5 KN/M   129 TEST S5: VINITIAL = 1.14 M/S, KCALIBRATED = 1.6 KN/M   130 TEST S6: VINITIAL = 0.75 M/S, KCALIBRATED = 1.5 KN/M    131 TEST S7: VINITIAL = 0.89 M/S, KCALIBRATED = 1.4 KN/M  132   133 TEST S8: VINITIAL = 1.39 M/S, KCALIBRATED = 4.3 KN/M   134 TEST S9: VINITIAL = 1.37 M/S, KCALIBRATED = 3.4 KN/M   135 TEST S10: VINITIAL = 1.58 M/S, KCALIBRATED = 3.4 KN/M   136 TEST S11: VINITIAL = 1.40 M/S, KCALIBRATED = 3.1 KN/M   137 TEST S12: VINITIAL = 0.96 M/S, KCALIBRATED = 1.5 KN/M  138 APPENDIX E2: STEEP FLOW FRONT VIDEO OBSERVATIONS AND DAN-BARRIER TIME SERIES; FLEXIBLE BARRIER WITH GRAVEL   139 TEST G1: VINITIAL = 0.92 M/S, KCALIBRATED = 1.3 KN/M   140 TEST G2: VINITIAL = 1.12 M/S, KCALIBRATED = 2.0 KN/M   141 TEST G3: VINITIAL = 0.66 M/S, KCALIBRATED = 1.8 KN/M  142 APPENDIX E3: STEEP FLOW FRONT VIDEO OBSERVATIONS AND DAN-BARRIER TIME SERIES; RIGID BARRIER WITH SAND   143 TEST R1: VINITIAL = 1.33 M/S   144 TEST R2: VINITIAL = 1.48 M/S   145 TEST R3: VINITIAL = 0.93 M/S  146 APPENDIX F1: STEEP FLOW FRONT TEST RESULTS COMPARED TO DAN-BARRIER RESULTS; FLEXIBLE BARRIER WITH SAND  Test force taken from load cell at a sampling rate of 6 kHz, see test setup in Appendix A1 for details.  Apparent thickness of force line is indicative of error in recorded value. This is roughly 0.001 kN for all tests, however natural oscillation (noise in the data) appears greater for tests with a smaller ultimate force, or smaller overall span.  Fill height and deflection measured from videos at regular time intervals. Data is presented as a line for clarity. Error for fill height is approximately ±0.005 m, and ±0.002 m for deflection.  Barrier stiffness for each DAN-Barrier model, as described in Section 3.2.1 and Chapter 6, is calibrated to observed maximum force for test and reported for each test result at the top of the chart.  Fill height measured in DAN-Barrier as max height of any boundary element between initial barrier position and furthest forward boundary element.  Deflection measured in DAN-Barrier as the distance between barrier position and further forward boundary element.   147 TEST S1   TEST S2   148 TEST S3   TEST S4   149 TEST S5   TEST S6  150 TEST S7   TEST S8   151 TEST S9   TEST S10   152 TEST S11   TEST S12   153 APPENDIX F2: STEEP FLOW FRONT TEST RESULTS COMPARED TO DAN-BARRIER RESULTS; FLEXIBLE BARRIER WITH GRAVEL  154 TEST G1   TEST G2   155 TEST G3    156 APPENDIX F3: STEEP FLOW FRONT TEST RESULTS COMPARED TO DAN-BARRIER RESULTS; RIGID BARRIER WITH SAND  Test total force taken from load cell.  Fill height measured from at face of rigid barrier.  DAN-Barrier used to predict flow thickness at barrier location.  Predicted fill height used to calculate force according to static earth pressure calculations presented in Section 5.3.4.   157 TEST R1   TEST R2    158 TEST R3    159 APPENDIX G: STEEP FLOW FRONT TESTS AT TIME OF MAXIMUM FORCE  Material accelerated manually, initial velocity recorded at time when external force is removed.  All heights measured at time of maximum force prior to maximum deflection or fill height was observed.  Larger measurement noted is observed fill height, smaller measurement is approximate impact height of flow front neglecting any minor pile-up on barrier face.  A single measurement is shown where both values were equal.  160    161 APPENDIX H1: CABLE FORCE CALCULATIONS FOR USGS FLUME TEST 2 - DEBRIS FLOW AGAINST A SINGLE BAY FLEXIBLE BARRIER  Applied Force  Rope and Fence Geometries Parameter Value Unit  Parameter Value Unit Total force, Ft 74 kN  No. of ropes, n 2   Deflection, d 1.2 m  Rope cross-sectional area, A 1.43E-04 m2 Flow height, h 1.2 m  Elasticity modulus, E 1.28E+11 N/m2 Assumed width, b 4.5 m  Post spacing, w 9.1 m Pressure over impact area, pimact 13.7 kN/m2  Post height, h 2.4 m Pressure over entire mesh, pmesh 3.5 kN/m2  Initial cable height (above ground) 2.3 m Force per unit length per rope in contact with mesh (divided equally), q 4.1 kN/m  Final cable height (above ground) 1.3 m     Initial sag, fo 0.1 m Top Rope Force Calculation      Final sag, ff 1.1 m Parameter Value Unit  Total initial rope length, l 9.1 m No. brakes 2    Total parabolic rope length, l' 9.4 m Deformation per brake 0.00 m     Total rope length, so 9.44 m  User input cell =    EA 1.83E+04 kN  Spreadsheet output cell =     a = EA (1 - l / so) 6.59E+02 kN     b = EA / 2 so 9.69E+02 kN/m     Q1 = q2 l13 / 12 1038.5 kN2m     left side: H3 + a H2 1006481.5 kN3     right side: b Q1 1006481.5 kN3     H 38.0 kN   T 42.3 kN               162 APPENDIX H2: CABLE FORCE CALCULATIONS FOR VELTHEIM, SWITZERLAND FIELD TEST 7.1 - DEBRIS AVALANCHE AGAINST THREE BAY FLEXIBLE BARRIER  Applied Force  Rope and Fence Geometries   Parameter Value Unit  Parameter Value Unit   Total force, Ft 515 kN  No. of ropes 2   Deflection, d 1.5 m  Rope cross-sectional area, A 2.56E-04 m2  Flow height, h 2.3 m  Elasticity modulus, E 1.28E+11 N/m2  Assumed width, b 9.0 m  Bay 1 2 3 Pressure over impact area, pimact 24.9 kN/m2  Measured initial rope length 5.0 4.7 4.9 Pressure over entire mesh, pmesh 11.8 kN/m2  Measured parabolic rope length 5.1 4.8 5.0 Number of posts 2   Initial rope length (in contact with mesh), lo 14.6 m  Post width 0.15 m  Parabolic rope length (in contact with mesh), lo' 14.9 m  Force reduction per post 8.6 kN  Fence height 3.5 m  Force per unit length per rope in contact with lesh (divided equally), q 17.0 kN/m  Deformed fence height 3.0 m           Top Rope Force Calculation  Bottom Rope Force Calculation  Parameter Value Unit  Parameter Value Unit  No. brakes 2   No. brakes  2   Deformation per brake 0.01 m  Deformation per brake 0.00 m  Total rope length, so 14.91 m  Total rope length, so 14.89   EA 3.28E+04 kN  EA 3.28E+04 kN  a = EA (1 - l / so) 6.86E+02 kN  a = EA (1 - l / so) 6.43E+02 kN  b = EA / 2 so 1.10E+03 kN/m  b = EA / 2 so 1.10E+03 kN/m  Q1 = q2 l13 / 12 3027.8 kN2m  Q1 = q2 l13 / 12 3027.8 kN2m  Q2 = q2 l23 / 12 2514.9 kN2m  Q2 = q2 l23 / 12 2514.9 kN2m  Q3 = q2 l33 / 12 2849.8 kN2m  Q3 = q2 l33 / 12 2849.8 kN2m  left side: H3 + a H2 9220897.3 kN3  left side: H3 + a H2 9233280.9 kN3  right side:  b (Q1 + Q2 + Q3) 9220897.3 kN3  right side:  b (Q1 + Q2 + Q3) 9233280.9 kN3  H 107.8 kN  H 110.7 kN               User input cell =          Spreadsheet output cell =      

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