Stress-deformation analysis of Denis-Perron dam: verification andvalidation for better prediction of rockfill responsebyBoris Nikolaev KolevBEng, The University of Edinburgh, 2014A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Civil Engineering)The University of British Columbia(Vancouver)April 2017c© Boris Nikolaev Kolev, 2017AbstractRockfill dams present a challenge for engineers due to the many uncertainties revolving aroundthe behaviour of rockfill. A governing factor in the behaviour of rockfill is the particle breakagedue to change of moisture, which was observed in laboratory and field conditions. Alonso andOldecop have proposed a rockfill model (RM), where the suction inside the cracks of the rockfillis a state variable that controls the breakage mechanism. This research focuses on verification andvalidation of stress-deformation analysis methodologies, for better prediction of rockfill response.It involves application of the RM in numerical simulation of a benchmark case study on the wellinstrumented Denis-Perron dam (SM3). Denis-Perron dam is a rockfill dam with a central till core,171 metres high and 378 metres long, located on the Sainte-Marquerite river in northern Quebec,Canada. The instrumentation data was made available by Hydro-Que´bec, for a period of six yearsof construction, impoundment, and operation of the dam. Numerical simulations are conducted us-ing Code Bright – a fully coupled three phase finite element program for unsaturated porous media.A validation stage was first carried out through modelling of Beliche dam – a well studied case byAlonso et al. The numerical model of the SM3 dam captures the staged construction, reservoir im-poundment and rainfall history recorded. Model parameters for the till core and rockfill shoulderswere either calibrated using limited available laboratory and field data, adopted from literature, orassumed with some rationale. Deformations measured by the inclinometers during constructionand impoundment, both upstream and downstream, are simulated successfully. Piezometer andpressure cell measurements are replicated to a very good extent. Post-construction deformationsare reproduced with reasonable success, given the limited data for detailed characterization of thevarious zones in the dam. Some important challenges around characterization of the rockfill com-pressibility and the related scaling issues for model calibration are presented and discussed. Anattempt is made to quantify the amount of scaling observed through a back analysis of field mea-surements. Finally, the effect of permeability on rockfill in the development of deformations isdiscussed.iiPrefaceEarly in 2015, Hydro-Que´bec invited the UBC Theoretical & Applied Geomechanics group to par-ticipate in a numerical analysis workshop that was to be held in parallel to the Sixty Eight CanadianGeotechnical Conference, in September 2015 in Que´bec, QC, Canada. The workshop was aimedto evaluate the state of the art on constitutive and numerical modeling of rockfill dams, and pro-vide means for Verification & Validation of the numerical tools for better predictions. Contributingto this workshop shaped the beginning of this research project. The project was then continuedbeyond the workshop with interest and support from Hydro-Que´bec and the Natural Sciences &Engineering Research Council of Canada (NSERC).The research was lead by my supervisor Professor Mahdi Taiebat. I, Boris Nikolaev Kolev, amthe principle contributor to all seven chapters and two appendices of this thesis. My contributionto different elements of the project that lead to this thesis included i) studying the background in-formation about the SM3 dam, ii) including the reports and data provided by Hydro-Que´bec, iii)learning about the fundamental aspects of response in rockfill materials, iv) getting familiar withthe state of the art of constitutive modelling of rockfill material and numerical modelling of rockfilldams accounting for various stages of construction, reservoir impoundment, and rainfall history, v)verification of my modelling methodology by comparing my simulation of Beliche dam with theprevious study by the group of Alonso at UPC in Spain, vi) detailed simulation of SM3 for variousstages of construction and operation, vii) fine tuning the numerical model and material parametercalibration, viii) detailed comparison of the numerical results with the instrumentation data pro-vided by Hydro-Que´bec, ix) sensitivity analyses on rockfill compressibility and permeability, andx) packaging and reporting the research outcomes.Some outcomes of my thesis are published in form of a conference paper in Kolev et al. (2016).A more extensive journal paper is now in preparation covering various outcomes of this thesis.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Thesis structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Denis-Perron Dam – case description . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Project background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Field instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 Inclinometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.2 Pressure cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.3 Observation terminals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.4 Piezometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 Laboratory data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.1 Central till core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.2 Rockfill shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17iv2.4 Previous Denis-Perron dam analyses . . . . . . . . . . . . . . . . . . . . . . . . . 192.4.1 Pre-construction FE analysis using a hyperbolic model (1990) . . . . . . . 192.4.2 FE analysis using the Rockfill Model (2012) . . . . . . . . . . . . . . . . 223 Mechanical and hydraulic models used in the analysis of Denis-Perron . . . . . . . . 233.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 Mechanical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.1 Barcelona basic model (BBM) . . . . . . . . . . . . . . . . . . . . . . . . 243.2.2 Rockfill compressibility model (RM) . . . . . . . . . . . . . . . . . . . . 303.3 Hydraulic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.3.1 Van Genuchten hydraulic model . . . . . . . . . . . . . . . . . . . . . . . 383.3.2 Liquid phase relative permeability . . . . . . . . . . . . . . . . . . . . . . 394 Description of the numerical model . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.1 Finite element software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.2 Geometry and zoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.2.1 Geometry and model layers . . . . . . . . . . . . . . . . . . . . . . . . . 424.2.2 Constitutive models assigned to material zones . . . . . . . . . . . . . . . 424.3 Material parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.3.1 Till core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3.2 Rockfill material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.3.3 Drain, filter and alluvial foundation . . . . . . . . . . . . . . . . . . . . . 534.3.4 Bedrock, concrete and water . . . . . . . . . . . . . . . . . . . . . . . . . 574.4 Initial and boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.4.1 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.4.2 Initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.5 Time intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.5.1 Construction stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.5.2 Impoundment stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.5.3 Rainfall stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.6 FE mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.6.1 Mesh description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.6.2 Mesh quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.7 Solution scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69v5 Base case simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.2 Pore water pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.2.1 General results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.2.2 Comparison with instrument data . . . . . . . . . . . . . . . . . . . . . . 755.3 Degree of saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.3.1 General results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.4 Vertical total stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805.4.1 General results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805.4.2 Comparison with instrument data . . . . . . . . . . . . . . . . . . . . . . 825.5 Vertical displacements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.5.1 General results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.5.2 Comparison with instrument data . . . . . . . . . . . . . . . . . . . . . . 845.6 Horizontal displacements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.6.1 General results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.6.2 Comparison with instrument data . . . . . . . . . . . . . . . . . . . . . . 885.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 886 Complementary simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 906.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 906.2 Sensitivity analysis on rockfill compressibility . . . . . . . . . . . . . . . . . . . . 906.2.1 Effect of particle scale on rockfill compressibility . . . . . . . . . . . . . . 916.2.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 916.2.3 Quantification of size effect . . . . . . . . . . . . . . . . . . . . . . . . . 946.3 Sensitivity analysis on rockfill permeability . . . . . . . . . . . . . . . . . . . . . 986.3.1 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 987 Summary and future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027.1 Summary of research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027.2 Recommendations for future research . . . . . . . . . . . . . . . . . . . . . . . . 103Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105viA Validation Problem – Beliche dam simulation . . . . . . . . . . . . . . . . . . . . . . 108A.1 Problem information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108A.2 Simulation results comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112A.3 Simulation method differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114B Rockfill mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115B.1 Field and laboratory observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 115B.2 Particle breakage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119B.3 Testing apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124viiList of TablesTable 2.1 Available instruments along the whole body of the dam(Hammamjil, 2003). . . 8Table 2.2 Till core dry density measurements (Pe´loquin, 2015). . . . . . . . . . . . . . . 17Table 2.3 Results of triaxial permeability tests (Lafleur, 1998). . . . . . . . . . . . . . . . 17Table 2.4 Hyperbolic model material parameters for all dam zones. . . . . . . . . . . . . 20Table 3.1 Summary of BBM parameters and calibration methods. . . . . . . . . . . . . . 29Table 3.2 Basic relationships for BBM and RM*. Table adopted from Alonso et al. (2005). 36Table 3.3 Summary of RM parameters and calibration methods. . . . . . . . . . . . . . . 37Table 4.1 Assigned constitutive models to dam zones. . . . . . . . . . . . . . . . . . . . 43Table 4.2 Comparison of H-06 glacial till material physical characteristics with SM3 glacialtill material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Table 4.3 Hydraulic parameters for the till core. . . . . . . . . . . . . . . . . . . . . . . . 46Table 4.4 Mechanical parameters for the till core. . . . . . . . . . . . . . . . . . . . . . . 49Table 4.5 Hydraulic parameters for the rockfill shells. . . . . . . . . . . . . . . . . . . . . 51Table 4.6 Mechanical parameters for the rockfill shells. . . . . . . . . . . . . . . . . . . . 54Table 4.7 Hydraulic parameters for the drain, filter and the alluvial foundation. . . . . . . 55Table 4.8 Mechanical parameters for drain, filter and alluvial foundation. . . . . . . . . . 56Table 4.9 Hydraulic parameters for bedrock, concrete and water. . . . . . . . . . . . . . . 58Table 4.10 Mechanical properties for bedrock, concrete and water. . . . . . . . . . . . . . 59Table 4.11 Description of time intervals details and impoundment boundary condition as-sociated with each interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Table 4.12 Solution scheme data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Table A.1 Mechanical parameters for rockfill. . . . . . . . . . . . . . . . . . . . . . . . . 110viiiTable A.2 Mechanical parameters for the till core. . . . . . . . . . . . . . . . . . . . . . . 111Table A.3 Hydraulic parameters for rockfill, till core and foundation . . . . . . . . . . . . 112ixList of FiguresFigure 1.1 Deformations durign operation of multiple rockfill dams. The numbers inbrackets represent the height of the respective dam. Data obtained from Olde-cop and Alonso (2013a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Figure 2.1 Location of Denis-Perron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Figure 2.2 Aerial view of Denis-Perron Dam (Pe´loquin, 2015) . . . . . . . . . . . . . . . 6Figure 2.3 Analyzed cross section A-A of Denis-Perron dam (Pe´loquin, 2015). . . . . . . 7Figure 2.4 Analyzed cross section A-A visualized in 2D. . . . . . . . . . . . . . . . . . . 7Figure 2.5 Locations of upstream and downstream inclinometers INB1 and INB5, respec-tively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Figure 2.6 Vertical settlement measurement for INB1 and INB5 during construction forend of time intervals [A] to [C]. . . . . . . . . . . . . . . . . . . . . . . . . . 10Figure 2.7 Vertical settlement measurement for INB1 and INB5 after construction for endof time intervals [D] to [F]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Figure 2.8 Location of total pressure cells CPB 251 and CPB 255. . . . . . . . . . . . . . 12Figure 2.9 Total pressure cell measurements of CPB 251 and CPB 255, . . . . . . . . . . 12Figure 2.10 Downstream horitonztal displacement gauges measurements of B0-28, B0-9and B0-5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Figure 2.11 Downstream vertical displacement gauges measurements of B0-28, B0-9 andB0-5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Figure 2.12 Location of piezometer cells PPB 272, 302, 342 and 381. . . . . . . . . . . . . 14Figure 2.13 Piezometer cells measurements for PPB 272, 302, 342 and 381. . . . . . . . . 15Figure 2.14 Grain size distribtuion of the Denis-Perron till core material (Hammamjil (2003))and the grain size distribution of a till sample from Northern Que´bec (dashedred line) (Watabe et al., 2000). . . . . . . . . . . . . . . . . . . . . . . . . . . 16xFigure 2.15 Oedometer rockfill data for dry and saturated samples (Errecalde, 2012). . . . . 18Figure 2.16 (a) Grain size distribution of inner shell (b) Grain size distribution of outershell (Hammamjil, 2003). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Figure 2.17 Contour plots of the simulation results for (a) Vertical displacements [m] (b)Horizontal displacements [m] (c) Vertical total stress [tonne/m2] (d) Horizontaltotal stress [tonne/m2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Figure 2.18 Vertical displacements at (a) Upstream inclinometer INB1 (b) Downstream in-clinometer INB5 for different dates. Adapted from Errecalde (2012). . . . . . . 22Figure 3.1 Strains assosiated with loading and suction changes in BBM. . . . . . . . . . . 25Figure 3.2 The dimensional view of the BBM yield surfaces in (p,q,s) space. Adaptedfrom Alonso et al. (1990). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 3.3 (a) Representation of the S.I. and L.C. curve in (s,p) space (b) Compressioncurves in ν ,s, p space (c) Compression curves for saturated and unsaturatedsoils in ν , p space (d) Compression curves in ν ,s space for BBM (Alonso et al.,1990). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Figure 3.4 (a) Idealized model response for different stress paths (b) Yield surface (L.C.curve) for different values of p∗0 for RM. . . . . . . . . . . . . . . . . . . . . . 31Figure 3.5 The dimensional view of the yield surfaces in (p,q,s) space for RM. . . . . . . 32Figure 3.6 Water retetion curves with varying P0 and λvan parameters. . . . . . . . . . . . 38Figure 3.7 Varying relative permeability for clay and rockfill materials (Alonso et al., 2005). 40Figure 4.1 Construction sequence of dam for model calculations. . . . . . . . . . . . . . 42Figure 4.2 Denis-Perron dam material zones. . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 4.3 (a) Standard Proctor compaction curve for all samples tested (b) Hydraulicconductivity as a function of the compaction degree of saturation. Figuresmodified from Watabe et al. (2000). . . . . . . . . . . . . . . . . . . . . . . . 44Figure 4.4 (a) Soil characteristic curves for till samples in Watabe et al. (2000). Red lineshows an average curve. (b) Fitted curve (blue) to averaged soil characteristiccurve using van Genuchten (1980). . . . . . . . . . . . . . . . . . . . . . . . . 46Figure 4.5 Oedometer test on compacted till from Northern Quebec, sample H-06 (Watabeet al., 2000). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 4.6 Water retention curves for rockfill material: Beliche Dam (Alonso et al. (2005)),Lechago Dam (Alonso et al. (2012)) and Denis-Perron Dam (Errecalde (2012)). 50xiFigure 4.7 Oedometer test data and model results for wet (Sr = 100%) and dry (Sr = 30%)rockfill samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Figure 4.8 Calibration of parameters µ and β c based on data from Figure B.8 (a). . . . . . 53Figure 4.9 Mechanical and hydrauilic boundary conditions. . . . . . . . . . . . . . . . . 60Figure 4.10 Initial suction values for the material zones. . . . . . . . . . . . . . . . . . . . 60Figure 4.11 Initial porosity values for the material zones. . . . . . . . . . . . . . . . . . . 61Figure 4.12 Construction sequence of the dam between 1996 and 1998 according to Pe´loquin(2015). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Figure 4.13 Dam construction and impoundment sequence in real life and the numericalmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Figure 4.14 The average and standard deviation of critical parameters . . . . . . . . . . . 63Figure 4.15 Precipitation data recorded in the field. Data digitized from Hammamjil (2003). 65Figure 4.16 Finite element mesh of Denis-Perron dam. . . . . . . . . . . . . . . . . . . . . 67Figure 4.17 (a) Shape quality (b) Maximum edge cumulative distrobution. . . . . . . . . . 68Figure 5.1 Summary of instruments and selected monitoring points used in analysis ofsimulation results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Figure 5.2 Evolution of: (a) Construction and impoundment sequence (b) Water pressurefor upstream points B0-28, 1 and 2; (c) Water pressure for downstream pointsB0-9, 3 and 4: Base case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 5.3 (a) Porosity-Mean net stress (b) Suction-Mean net stress for rockfill shells. . . 75Figure 5.4 Pore water pressures in the till core of the dam: comparison of measured andcalculated values for base case. . . . . . . . . . . . . . . . . . . . . . . . . . . 76Figure 5.5 (a) Construction and impoundment sequence. Evolution of degree of saturationfor (b) upstream points A, 1 and 2; (c) downstream points C, 3 and 4: Base case. 78Figure 5.6 Contour plots for degree saturation at (a) end of time [A] (b) end of time [C](c) end of time [E] (d) end of time [F]. . . . . . . . . . . . . . . . . . . . . . . 79Figure 5.7 Vertical stresses during construction and impoundment on a horizontal planeat elevation 60 m above the bottom boundary of till core for Times [A] to [F]. . 80Figure 5.8 Contour plots for vertical total stress in MPa at (a) end of time [A] (b) end oftime [C] (c) end of time [E] (d) end of time [F]. . . . . . . . . . . . . . . . . . 81Figure 5.9 Vertical stress in MPa at the bottom of the till core for points CPB 251 andCPB 255: comparison of measured and calculated values for base case. . . . . 82xiiFigure 5.10 Contour plots for vertical displacements (settlement) at (a) end of time [A] (b)end of time [C] (c) end of time [E] (d) end of time [F]. . . . . . . . . . . . . . 83Figure 5.11 Calculated and measured vertical settlement for inclinometers INB1 and INB5after construction for stages [A] to [D]: base case. Elevation 260 correspondsto bottom of the rockfill shell. . . . . . . . . . . . . . . . . . . . . . . . . . . 85Figure 5.12 Calculated and measured vertical settlement for inclinometers INB1 and INB5after construction for stages [E] to [G]: base case. Elevation 260 correspondsto bottom of the rockfill shell. . . . . . . . . . . . . . . . . . . . . . . . . . . 85Figure 5.13 Vertical displacements for points B0-28, B0-9 and B0-5 along the dam crest:comparison of measured and calculated values for base case. . . . . . . . . . . 86Figure 5.14 Contour plots for horizontal displacements in metres at (a) end of time [A] (b)end of time [C] (c) end of time [E] (d) end of time [F]. . . . . . . . . . . . . . 87Figure 5.15 Horizontal displacements for points B0-28, B0-9 and B0-5 along the dam crest:comparison of measured and calculated values for base case. . . . . . . . . . . 88Figure 6.1 Calculated and measured vertical displacements for INB1 and INB5 at Time[B] for four differen values for λ d0 . . . . . . . . . . . . . . . . . . . . . . . . . 92Figure 6.2 Calculated and measured vertical displacements for INB1 and INB5 at Time[C] for four differen values for λ d0 . . . . . . . . . . . . . . . . . . . . . . . . . 93Figure 6.3 Calculated and measured vertical displacements for INB1 and INB5 at Time[E] for four differen values for λ d0 . . . . . . . . . . . . . . . . . . . . . . . . . 93Figure 6.4 Calculated and measured vertical displacements for INB1 and INB5 at Time[F] for four differen values for λ d0 . . . . . . . . . . . . . . . . . . . . . . . . . 94Figure 6.5 Variation of compressibility parameter λ d for different αscaling values. . . . . . 95Figure 6.6 (a) Compressibility for samples with different maximum particle size at twodifferent void ratios (b) Corrected compressibility of limestone material to ac-count for scale effect. Modified from Oldecop and Alonso (2013a). . . . . . . 96Figure 6.7 Variability of parameter αscaling based on void ratio for laboratory data. Datafrom Oldecop and Alonso (2013a) and simulation results of Denis-Perron andBeliche Dam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Figure 6.8 (a) Construction sequence (b) Water pressure for upstream points (c) Waterpressure for downstream points. . . . . . . . . . . . . . . . . . . . . . . . . . 99Figure 6.9 Vertical displacements for markers B0-28, B0-9 and B0-5 for the Base case,Low Permeability and High permeability cases. . . . . . . . . . . . . . . . . . 100xiiiFigure 6.10 Horizontal displacements for markers B0-28, B0-9 and B0-5 for the Base case,Low Permeability and High permeability cases. . . . . . . . . . . . . . . . . . 101Figure A.1 (a) Simulation layers and (b) Mesh from (Alonso et al., 2005) . . . . . . . . . 109Figure A.2 (a) Simulation layers and (b) Mesh from validation problem . . . . . . . . . . 109Figure A.3 Vertical displacements at position for extensometers (a) I1, (b) I3 and (c) I6for construction stages [A] to [E]. Validation simulation results and computedresults from Alonso et al. (2005) . . . . . . . . . . . . . . . . . . . . . . . . . 112Figure A.4 Validation simulation and Alonso et al. (2005) simulation of vertical stressesfor stages [A], [B] and [E] on a horizontal plane at elevation 13 m above bound-ary of clay core. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Figure B.1 (a) Particles of an unsaturated low-plasticity soil, adopted from Oldecop andAlonso (2004) (b) Rockfill particle with a crack (pore), modified from Oldecopand Alonso (2001). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Figure B.2 Sketch of a simplified volume of rockfill and a rockfill particle containing acrack that eventually propagates and causes particle breakage. Modified fromOldecop and Alonso (2013a). . . . . . . . . . . . . . . . . . . . . . . . . . . 117Figure B.3 Typical stress intensity curve. Modified from Oldecop and Alonso (2007). . . . 118Figure B.4 (a) Water vapour entering an idealised crack, modified from Oldecop and Alonso(2013b) (b) Reaction between a water molecule and a strained silicium dioxidemolecule. Modified from Michalske and Freiman (1982). . . . . . . . . . . . . 119Figure B.5 Rockfill particle with contact crushing zone and a single fracture surface, Alonsoet al. (2013). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120Figure B.6 Rockfill particle with contact crushing zone and a single fracture surface, Alonsoet al. (2013). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Figure B.7 Variation of breakage index with change of the coefficient of uniformity, adaptedfrom Cristian (2011). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Figure B.8 (a) Time-dependent compressibility index against applied stress for differentconstant suction values (b) Correlation between time-dependent compressibil-ity index and compressibility index for tested rockfill. Adopted from Oldecopand Alonso (2007). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Figure B.9 Relative humidity (RH) controlled oedometer test and water transport schemecirculation inside rockfill particle, adopted from Oldecop and Alonso (2004). . 126xivAcknowledgementsI offer my sincerest gratitude to my supervisor, Professor Mahdi Taiebat, who has supported mewith his guidance throughout my research. His encouragement and high level of competence in-spired me to explore the subject. I am truly indebted and thankful to him for the time he devoted todiscussions on the subject matter and for his moral support. His comments helped me to becomea better researcher. My sincere thanks are extended to Dr. Arcesio Lizcano and Professor Ali Pakfor providing technical support during various stages of this research project, giving me the mo-mentum to keep going, and providing feedback on the final manuscript. I would also like to thankDr. Nuria Pinyol for assisting with the use of the finite element software, and Dr. Ruth Derksen forpatiently helping me improve my technical writing skills, and Annick Bigras, E´ric Pe´loquin, andDaniel Verret of Hydro-Que´bec for providing technical insight to the instrumentation data.I would like to thank my girlfriend Cecillya Sumono for always being patient, supportive andloving. Her positivity and love helped me go through the tough times and gave me strength andenergy to persevere. Thanks will not be enough for my parents, Violeta and Nikolay Kolevi, withoutwhose support none of my accomplishments would be possible. Even with a long distance betweenus, their support remains as strong as ever.Financial support for the project was provided in part by the Natural Sciences & EngineeringResearch Council of Canada (NSERC).xvChapter 1Introduction1.1 MotivationRockfill has gradually become a significant part of the construction industry since the beginningof the nineteenth century. Some of the first larger construction projects were mining dams in Cal-ifornia (Oldecop and Alonso, 2001). An understanding of rockfill behaviour has been a challengedue to difficulties of constructing large scale testing devices. Another source of information forrockfill, is records of already existing structures as presented on Figure 1.1. The long term defor-mations of the structures can be seen on Figure 1.1, where the crest settlement of a number of damsis presented over the span of five to thirty years.The purpose of the design of earth and rockfill structures is to ensure the stability and op-erational requirements of the structure throughout its entire life-span. In the case of dams, theupstream and downstream slopes must be stable during construction and impoundment as well asin the long term operation of the dam (Cardoso and Alonso, 2010). Another consideration is reduc-tion of settlement or creating compatible compressibility between the shells and core in order toavoid cracking of the core (Parkin, 1977). A key factor for concrete-faced compacted rockfill damsis the determination of deformations induced during construction and impoundment (Saboya Jr.and Byrne, 1993). Some other rockfill structures that support railways need detailed prediction oflong term settlements due to an operation criterion of the facilities (Oldecop and Alonso, 2001).10 5 10 15 20 25 30Time [years]1.61.41.210.80.60.40.20Crest Settlement [% of height over foundation]Denis-Perron DamCRFD/ dumped rockfillCRFD/ compacted rockfillCentral core/rockfill shellsCentral core/gravel shellsBeliche (54)Dix River (84)Mackintosh (75)Exchequer (150)Nanthala (80)El Infiernillo (146)Rivera de Gata (60)Chocon (90)Alicura (130)Murchison (94)Cethana (110)Alto Anchicaya (140)Foz do Areia (160)Figure 1.1: Deformations durign operation of multiple rockfill dams. The numbers in brack-ets represent the height of the respective dam. Data obtained from Oldecop and Alonso(2013a).Oldecop and Alonso (2001) have tackled the complex behavioural patterns of rockfill responsein the framework of continuum mechanics by introducing an elasto-plastic constitutive model usingthe concept of “compressibility despite the fact that rockfills usually consist of very large discreteparticles. Obtaining the model parameters presents a challenge due to having particles in the fieldwith sizes as large as 2 m, whereas laboratory tests are limited to samples with much smaller size ofup to 0.2 m (Saboya Jr. and Byrne, 1993). Another way of exploring the behaviour of rockfill is byobservation of already existing structures and analysing field measurements, such as the analysisof Beliche dam described in the work of Alonso et al. (2005).21.2 GoalsAlthough a lot of studies have been conducted in the area of rockfill mechanics, no comprehensiveguide and methodology for modelling of rockfill structures has been provided. Therefore, one of themajor goals of the current thesis is to address this deficit and create a framework for the analysis ofrockfill dams. A numerical study on the well instrumented Denis-Perron dam is conducted usingthe constitutive model developed by Oldecop and Alonso (2001). The dam consists of rockfillshoulders and a central clay core, and has experienced settlement due to impoundment and rainfallas seen on Figure 1.1. The instrumentation data provide an excellent opportunity to examine thestate-of-the-art modelling techniques for settlement response of rockfill dams. The simulation ofthe stage construction and impoundment phase is conducted using the above model in Code Bright(2015), which is a fully coupled three-phase finite element program for unsaturated porous media.The second goal is to explore the theory of rockfill behaviour and test it against a comprehen-sive set of field measurements like settlements, displacements, water pressures and stresses via anumerical simulation. Environmental effects like rainfall are explored as well as some microscopicones like particle size and “creep” effects. An interesting outcome of the work is to quantify theparticle size effect based on the available field measurement. Such quantification via a large scalenumerical simulation potentially opens doors for researchers to explore other existing dams in thesame way and further investigate this effect.1.3 Thesis structureThis thesis is separated in multiple different Chapters. Chapter 2 describes the Denis-Perron dam indetail. It includes the background of the project, available field instrumentation data and laboratorytests carried out on the different materials.Chapter 3 explores the different constitutive models used to capture the behaviour of the dammaterials. Higher attention is placed on the constitutive model for the rockfill in particular.Chapter 4 describes the process of creating the Finite Element model. This includes a detaileddescription of calibration of the material parameters for each zone of the dam. Initial and boundaryconditions are also explored. Finally, information regarding the finite element mesh is included.Following the numerical model description, Chapter 5 explores the outcomes of the simulationfrom Chapter 4. This is considered the “base case” and is later used for sensitivity analysis pur-poses. Simulation results of the base case are compared with available field measurements such asvertical and horizontal displacements, total stresses and water pressures.Chapter 6 builds on top of the base case by exploring different aspects of the rockfill behaviour.3The first half of the chapter aims to quantify the effect of particle size on rockfill compressibility.The second half explores the effect of rockfill permeability on the response.The thesis leads to a summary and conclusions of the findings and recommendations for futureresearch.Appendix A summarizes a validation stage conducted prior to the analysis of the Denis-PerronDam. It has been completed through reproducing the results of Alonso et al. (2005). Explorationof the key factors influencing the rockfill behaviour are presented in Appendix B.4Chapter 2Denis-Perron Dam – case description2.1 Project backgroundThe Denis-Perron Dam is a rockfill embankment dam spanning the Sainte-Marguerite River, partof the lower Saint Lawrence River, in eastern Que´bec, Canada. The geographical location of thedam can be seen on Figure 2.1 and the cross section on Figure 2.2. The dam is the second highestin Que´bec and the hydraulic head of its power plant is also the largest in the province.6/28/2016 50°47'25.0"N 66°47'31.0"W Google Mapshttps://www.google.ca/maps/place/50%C2%B047'25.0%22N+66%C2%B047'31.0%22W/@49.0909999,73.8646105,6z/data=!4m5!3m4!1s0x0:0x0!8m2!3d50.790... 1/1Map data ©2016 Google 100 km 50°47'25.0"N 66°47'31.0"W50°47'25.0"N 66°47'31.0"WFigure 2.1: Location of Denis-PerronConstruction on the dam began in 1994. Prior to dam construction, a 19 m high co er-damwas built to direct the river through a tunnel west of the site according to Hydro-Que´bec (1999).The dam began to impound water in 1998 and finally reached full capacity in 2001. The dam5Figure 2.2: Aerial view of Denis-Perron Dam (Pe´loquin, 2015)and reservoir lies in a very remote region, and a 86 km long access road was built to facilitatetransportation to the construction site (Pe´loquin, 2015).Project completion occurred in 2002 and the cost is estimated to be around CA$2.4 billion.This makes the dam one of the most significant 21st century hydroelectric developments in NorthAmerica. As of 2003, the dam was projected to generate about 2.73 TWh of electricity per year, oran average output of just over 310 megawatts (MW) (Hydro-Que´bec, 1999).The dam impounds a 140 km long, 253 km2 reservoir with a capacity of about 12.5 km3.Excess water is released through a set of outlets at the base of the dam, with a capacity of 1,440m3/s, and an emergency spillway about 1 km north-west of the dam. Standing 171 meters (561ft) high and 378 meters (1,240 ft) long, the dam is the primary component of Hydro-Que´bec’sSainte-Marguerite 3 hydroelectric project (Pe´loquin, 2015). The dam has a central till core, filtersand transitions that rest on concrete. The rockfill shoulders of the river portion are built on alluvialdeposit. On the abutments, the entire dam section rests on bedrock. The crest level is at 410 m andits width is 10 m. Downstream slope of the dam is approximately 1.65H : 1V and the upstreamslope is 1.75H : 1V (Bigras and Tournier, 2000). The dam is analysed in 2D and the chosen section6Call for proposal - Workshop on Numerical Analysis for Embankment and Rockfill Dams Verification & Validation for better Prediction GEOQuébec2015 8 SCG/CGS Table 1 – Fill Placement and Compaction As-built for SM-3 Zone Material Layer thickness Passes Compactor Core Zone 1 0 - 300 mm 450 mm ≥ 4, max 8 50 t pneumatic or 50 t off road truck Filter Zone 2A 0 - 80 mm 450 mm ≥ 4 ≥ 10 t vib. Transition Zone 3A 0 - 150 mm 450 mm 1-2 ≥ 10 t vib. Inner Rockfill Zone 3B 0 - 450 mm 450 mm 1-2 ≥ 10 t vib. Inner Rockfill Zone 3C 0 - 900 mm 900 mm 4 ≥ 10 t vib Outer Rockfill Zone 3D 0 - 1 800 mm 1 800 mm 4 ≥ 10 t vib 3.5 Material properties 3.5.1 Foundations Some portion of both U/S and D/S shells of the dam in the river and river banks area are founded on alluvial and colluvial deposits as shown on the next figure. The narrow valley filled with concrete under internal footprint is shown in pink. The grey portion corresponds to the stripped rock foundation. Figure 7 –Geological mapping of SM-3 dam foundation A APM 1+235Figure 2.3: Analyzed cross section A-A of Denis-Perron dam (Pe´loquin, 2015).for the analysis is shown in Figure 2.3 annotated with PM 1+235.The simplified geometry in 2D is shown on Figure 2.4 and the dam materials are markedappropriately.0 50200250Rockfill3DRockfill3DBedrockCrushed StoneFilterRockfill 3BRockfill3CRockfill3CCoreConcreteWater100 150 200 250 300 350 400 450-50-100-150-200-250-300-350-400-450Alluvial300350400Figure 2.4: Analyzed cross section A-A visualized in 2D.72.2 Field instrumentsThe Denis-Perron Dam has several types of auscultation devices to monitor its behaviour. Theinstruments mainly aim to measure pore pressures, infiltration rates and deformation. A total of238 instruments were installed to monitor the dam. For the analysis of the dam, only instrumentswith proximity to the analysed cross section and instruments that were not reported to be defectedare used. All of the instruments available and the ones chosen for the analysis are summarized inTable 2.1. More details about each instrument are presented in the next sub-sections of this chapter.Table 2.1: Available instruments along the whole body of the dam(Hammamjil, 2003).Type of instrumentsNumber of instruments Instruments usedin analysisTotal DefectElectrical piezometers 56 5 —Open tube piezometers 3 2 —Pneumatic piezometers 23 1PPB272; PPB302;PPB342; PPB381;Total pressure cells 4 — CPB251; CPB255;Relative settlement gauges 13 13 —Total settlement gauges 3 3 —Inclined inclinometers 6 1 INB1Vertical inclinometers 3 1 INB5Horizontal inclinometers 2 1 —Individual thermometers 27 8 —Chain thermometers 40 10 —Observation terminals 33 —BO-28; BO-9;BO-5Settlement marks uphill 17 17 —Weirs 6 — —Accelerometers 2 — —Some of the instrumentation data is presented in terms of a simulation time interval, correlatingsimulation time with real time. The time intervals are presented bellow.8A Construction to elevation 320 mt = 0−400 daysB Construction to elevation 360 m; Impounding of the reservoir to elevation 292 mt = 400−610 daysC Completion of construction to elevation 410 m; Impounding of the reservoir to elevation 343mt = 610−760 daysD Impounding of the reservoir to elevation 350 mt = 760−980 daysE Impounding of the reservoir to elevation 382 mt = 980−1500 daysF Completion of reservoir impoundment to elevation 405 mt = 1500−2320 days2.2.1 InclinometersDam deformations are measured by vertical, inclined and horizontal inclinometers and by surveysof observation terminals. A cut in the centre of the river is instrumented by a few inclinometers: twovertical inclinometers, located in upstream recharge areas; an inclined inclinometer in the down-stream filter and a horizontal inclinometer in the downstream shell. The inclinometer installed inthe upstream shell aims to detect of rockfill subsidence when impoundment occurs. Two more cutsare equipped with inclinometers inclined in the downstream filter only. The vertical and inclinedinclinometers are anchored in the rock end to create a reference point. Terminals are the standardtype used by Hydro-Que´bec. The movements of these benchmarks are measured two to four timesper year from the reference points in the riverbanks.Figure 2.5: Locations of upstream and downstream inclinometers INB1 and INB5, respec-tively.9The inclinometers used in this study are INB1 and INB5, shown on Figure 2.5. INB1 is locatedin the upstream side of the dam, where the rockfill gets gradually impounded. This inclinometeraims to capture the effect of the impoundment and provide valuable information about the occur-ring settlements. INB5 is located downstream, where the rockfill does not get flooded due to thecore action. This inclinometer helps to capture the “dry” behaviour of rockfill and allows for re-calibration of the material parameters. Both INB1 and INB5 measurements used are relevant to theend of the construction phase. Figure 2.6 shows the field measurements of both inclinometers forthree different points in time during construction. For INB1, the black line represents constructionup to elevation 325m with no impoundment; the green line represents construction up to 360mand partial impoundment to elevation 293m (blue line shows reservoir level); and the orange lineshows the end of construction with partial impoundment to elevation 334m (blue line shows reser-voir level). For INB5, the dates of measurement are chosen to be as close as possible to the ones ofINB1 for consistency purposes.0 -250 -500 -750 -1000 -1250 -1500 -1750Settlement during construction (mm)INB-1 USBR260270280290300310320330340350360370380390400410Elevation (m)Time A - MeasurementTime B - MeasurementTime C - MeasurementReservoir Level0 -250 -500 -750 -1000 -1250 -1500 -1750Settlement during construction (mm)INB-5 USBR260270280290300310320330340350360370380390400410Elevation (m)Time A - MeasurementTime B - MeasurementTime C - MeasurementFigure 2.6: Vertical settlement measurement for INB1 and INB5 during construction for endof time intervals [A] to [C].Data for settlements of INB1 and INB5 after construction is provided as well. Initial data show10large settlements of both inclinometers at elevation 260 m, where they attach to the bedrock. Thereason for such settlements are unclear. The data has been processed by subtracting the settle-ments of elevation 260 m to every data point, making elevation 260 m as the reference point. Thisapproach could yield the data unusable due to the unclear circumstances which lead to high set-tlements (in the range of 0.5 m) close to the bedrock. The processed data is shown on Figure 2.7.From the plot of INB1, it can be seen that at the already impounded area, little settlements occuras expected. From the plot of INB5, settlements occur at all elevations due to creep effects andrainfall.-0 -100 -200 -300 -400 -500Settlement after construction (mm)INB-1260270280290300310320330340350360370380390400410Elevation (m)Time D - MeasurementTime E - MeasurementTime F - Measurement0 -50 -100 -150 -200 -250 -300 -350 -400 -450 -500Settlement after construction (mm)INB-5260270280290300310320330340350360370380390400410Elevation (m)Time D - MeasurementTime E - MeasurementTime F - MeasurementFigure 2.7: Vertical settlement measurement for INB1 and INB5 after construction for end oftime intervals [D] to [F].2.2.2 Pressure cellsFour pressure cells have been placed on the concrete surface at the bottom of the till core to mon-itor the development of vertical stresses and detect the magnitude of the arching effect. Theseinstruments are very sensitive to variations in compressibility of the backfill around them. Theyare located near the piezometers in order to calculate effective stresses. Only two pressure cells are11used for the analysis: one in both ends of the core as seen on Figure 2.8.Figure 2.8: Location of total pressure cells CPB 251 and CPB 255.The plotted pressure readings can be seen on Figure 2.9. The top X axis shows the measurementdates. The bottom X axis shows the corresponding time in days, where time “0 days” represents8/27/1996. The reason for showing this axis is to relate the numerical simulation time to real lifetime. Those X axes are used in the plots of observation terminals and piezometers data as well0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days]0300600900120015001800210024002700300033003600Vertical Total Stress [kPa]0300600900120015001800210024002700300033003600CPB 251 - MeasurementCPB 255 - Measurement8/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/02Figure 2.9: Total pressure cell measurements of CPB 251 and CPB 255,122.2.3 Observation terminalsThe observation terminals are concrete buildings with a total length of 2 m, partially inserted in theembankment. The survey has a total of 33 observation terminals in the whole dam (BO-1 to BO-33) which periodically measure cumulative horizontal and vertical displacements. Three stationsare selected that are in proximity to the cross section PM 1+235 and are labelled BO-28, BO-9 andBO-5.0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days]0100200300400500600700Horizontal Displacement, Dy [mm]0100200300400500600700B0-28 - MeasurementB0-09 - MeasurementB0-05 - Measurement8/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/02Figure 2.10: Downstream horitonztal displacement gauges measurements of B0-28, B0-9 andB0-5.0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days]-1100-1000-900-800-700-600-500-400-300-200-1000100Vertical Displacement, Dz [mm]-1100-1000-900-800-700-600-500-400-300-200-1000100B0-28 - MeasurementB0-09 - MeasurementB0-05 - Measurement8/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/02Figure 2.11: Downstream vertical displacement gauges measurements of B0-28, B0-9 andB0-5.13The cumulative horizontal displacements are plotted on Figure 2.10 and show the developmentof horizontal movement with time. Similarly, cumulative vertical displacements are presented onFigure 2.11.It has to be noted the top of inclinometer INB1 matches the location of that observation terminalB0-28. The measurement for INB1 at end of construction and impoundment is around 500 mm andthe measurement for B0-28 for the same date is 1000 mm, which introduces a big discrepancy inthe results. It was discussed that INB1 had some unknown issues regarding its post-constructionmeasurements (stages [D] to [F]), therefore its results could be considered unreliable. Results arecompared to the post-construction measurements of INB1 for consistency purposes.2.2.4 PiezometersFive pneumatic piezometers have been installed in the till core, the locations of which are shownin Figure 2.12. The apparatus consists of a metallic body housing a porous ceramic filter, a cellfilled with distilled water and a diaphragm. A rate of gas (nitrogen) under pressure is supplied tothe diaphragm via tubing input. The gas pressure is applied gradually to avoid sudden detachmentof the diaphragm. The pressure causes separation and is equivalent to the piezometric pressureexerted on the diaphragm.Figure 2.12: Location of piezometer cells PPB 272, 302, 342 and 381.Frequently observed variations in readings are often explained by the sensitivity of the di-aphragm and the difficulty to control the gas pressure applied on the diaphragm. An effective useof the device involves a prolonged and sufficient reading time in order to allow the diaphragm toreturn to its initial position. An insufficient length of reading stabilization could cause erroneousreadings. Excessive length of the inlet pipe also causes loss of pressure applied to the end of thetubing in contact with the diaphragm. That said, the pneumatic piezometers are considered lessaccurate than electric piezometers. However, they are simple to build, reliable and not prone to14electrical disturbances. Readings of pressures were performed using PR-20 indicator. The positionallows rapid filling of tubes and direct reading of the pressure measured by the sensor according toHammamjil (2003).Data was provided in the form of piezometer levels and was transformed into readings of porepressures usingNP = Cote+0.10197×Reading (2.1)where “NP” is the piezometric level (m), “Cote” is the installation level of the piezometer (m), thefactor “0.10197” is a conversion factor for the specific device, transforming from kPa to meters(m/kPa), and the “Reading” is the field measurement of pore pressures (kPa). The measurementsare plotted on Figure 2.13 and are later used to compare simulation pore pressures. The measure-ment at point PPB 251 has strange variations and is reported to be broken. Instruments PPB 272,302, 342 and 381 are sufficient for comparison purposes.0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days]00.20.40.60.8Water Pressure [MPa]-0.200.20.40.60.8PPB 272 - MeasurementPPB 302 - MeasurementPPB 342 - MeasurementPPB 381 - Measurement8/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/02Figure 2.13: Piezometer cells measurements for PPB 272, 302, 342 and 381.2.3 Laboratory data2.3.1 Central till coreA major component of the dam that needs appropriate attention during analysis is the core. Labo-ratory tests have been performed to determine key characteristics of the behaviour of the glacial till15core. The angle of internal friction is reported to vary between 38◦ and 40◦. Triaxial-permeabilitytests have been performed on the core to establish the major hydraulic properties. Based on thetriaxial test results the hydraulic conductivity is reported to vary between 1× 10−5 and 1× 10−8cm/s (Pe´loquin, 2015). Grain size distribution and dry density measurements are available as well.The grain size distribution of the till material can be seen on Figure 2.14. The red line representsthe grain size distribution of a similar sample from Northern Que´bec. The sample has very similarcharacteristics as the one used for the till core of Denis-Perron and has undergone more testing,which will aid the calibration of the mechanical parameters in the analysis.0.001 0.01 0.1 1 10 100Diameter, D [mm]020406080100Percentage Passing0.001 0.01 0.1 1 10 100020406080100SM3 20mm PassSM3 5mm PassWatabe, 2000Figure 2.14: Grain size distribtuion of the Denis-Perron till core material (Hammamjil(2003)) and the grain size distribution of a till sample from Northern Que´bec (dashedred line) (Watabe et al., 2000).Table 2.2 shows all the Dry density measurements of the till core material using Standardproctor or Nuclear device.Table 2.3 shows the characteristics of three samples from the core 2660-D, 2741-O and 3708-O.Triaxial tests have been performed and a coefficient of permeability has been determined for eachof the samples. Unknown properties of the material, due to limited laboratory data is taken fromliterature. Laboratory tests on a similar material from Northern Que´bec are available in Watabeet al. (2000), but this is discussed in detail in Chapter 4.16Table 2.2: Till core dry density measurements (Pe´loquin, 2015).In place Dry Density(nuclear device)Maximum Dry Density(Standard Proctor)Number of Tests 256 250Average 2113 kg/m3 2137 kg/m3Standard Deviation 53 kg/m3 53 kg/m3Minimum 1960 kg/m3 2002 kg/m3Maximum 2232 kg/m3 2284 kg/m3Table 2.3: Results of triaxial permeability tests (Lafleur, 1998).CompactionPreconsolidationPressure Water Void Dry density SaturationFinal watercontentHydraulicconductivityσ ′3 content w0[%] ratio e0 ρdry Sr w f [%] k [cm/s]Sample 2660-D500 7.9 0.29 2130 75 9.8 9.8E-61000 7.8 0.30 2116 72 10 1.3E-51500 7.7 0.32 2099 66 10 1.2E-5Sample 2741-O500 8.8 0.24 2215 99 7.3 1.1E-81000 8.6 0.25 2193 93 7.0 8.3E-91500 9.0 0.24 2209 99 6.7 1.1E-8Sample 3708-O500 8.0 0.31 2100 71 9.7 4.4E-51000 8.0 0.3 2111 73 10.1 4.0E-51500 7.9 0.29 2132 75 9.7 2.0E-52.3.2 Rockfill shellsOedometer tests have been performed on dry and saturated material with a reported scaled grainsize distribution, where the coefficient of uniformity, Cu, of the oedometer and the field materialhas been preserved. The results can be seen on Figure 2.15.17-1 0 1 2 3Vertical Stress, [MPa]86420Vertical Strain, [%]InterpretationMeasurementFlooded Sample0 1 2 3Vertical Stress, [MPa]543210Vertical Strain, [%]InterpretationMeasurementDry SampleFigure 2.15: Oedometer rockfill data for dry and saturated samples (Errecalde, 2012).The black line is the idealized measurement because the data is adopted from figures in Er-recalde (2012). It is reported that at the beginning of the loading stage, the testing head got stuck.This resulted in measuring unrealistically low vertical strain. At higher stresses, the head gotreleased and caused high collapse. Therefore, determining of the mechanical properties of the ma-terial is done in accordance with the dashed red line (Interpretation) according to Errecalde (2012).The grain size distributions of inner and outer shells of the dam are shown on Figures 2.16(a)and 2.16(b) respectively. The particle size specification curves were provided from the designteam of SM3. These plots are the only laboratory data available for the rockfill material.Therefore,missing parameters are obtained from literature and a sensitivity analysis on a few of them isdescribed out in Chapter 6.181 10 100 1000Diameter, D [mm](a)020406080100Percentage Passing1 10 100 1000020406080100Particle Size SpecificationSample 170-O1 10 100 1000 10000Diameter, D [mm](b)0204060801001 10 100 1000 10000020406080100Percentage PassingParticle Size SpecificationAverage Particle Size CurveFigure 2.16: (a) Grain size distribution of inner shell (b) Grain size distribution of outer shell(Hammamjil, 2003).2.4 Previous Denis-Perron dam analysesTwo analyses of Denis-Perron were previously performed. The first one was conducted in 1990prior to construction of the dam. The purpose of this analysis was to aid the design and constructionstages of the dam. The analysis used a hyperbolic model. The second analysis, was administeredin 2012, at the Polytechnic University of Catalonia in Barcelona. The aim of this analysis was tocapture the behaviour of rockfill based on current understanding of its unsaturated behaviour.2.4.1 Pre-construction FE analysis using a hyperbolic model (1990)Prior to construction of the Denis-Perron dam, a finite element analysis has been performed in orderto determine the expected overall behaviour of the structure and guide the design. The informationhas been used to adjust the widths of different zones, geometry of the dam, specification control-ling the establishment and compaction of the materials. The dam has been simulated only duringconstruction. Impoundment has not been included, which is proven to cause the highest amountof settlement in rockfill. Therefore, the simulation results are expected to have more qualitative,rather than quantitative meaning. The figures and information are extracted from a technical reportprovided for Hydro Que´bec by Hydro-Que´bec (1990).The dam is modelled in 2D at a cross section at the maximum height of the dam. The analysishas been performed in a finite element code called FEADAM Duncan et al. (1980), developed at the19University of California, Berkeley. FEADAM has an implemented hyperbolic model, developed byDuncan and Chang (1970). The model utilises 8 parameters that are used to establish the tangentmodulus, unloading and re-loading modulus and the bulk modulus through equations 2.2, 2.3 and2.4 respectively.Et =(R f (1− sin(φ)(σ1−σ3)2)2ccos(φ)+2σ3 sin(φ))2KPa(σ3Pa)n(2.2)Eur = KurPa(σ3/Pa)n (2.3)B = KbPa(σ3/Pa)m (2.4)Since no laboratory tests had been conducted at that point, the parameters for the materials ofthe foundation and embankment have been identified in literature for similar materials. Therefore,the parameters used for the simulation have been derived based on the LG4 dam (1979) Duncanet al. (1979). The parameters are summarized in Table 2.4 for one of the cases examined in thereport.Table 2.4: Hyperbolic model material parameters for all dam zones.Material Descriptionγ(g/cm3)c(kPa)φ(◦)K(kPa)nKur(kPa)Kb(kPa)m RfAlluvion 1.88 0 34 1250 0.4 1500 600 0.2 0.7Transition 2.2 0 38 600 0.4 800 240 0.2 0.7Core 2.1 0 37 600 0.6 800 200 0.2 0.7Filter 2 0 35 300 0.4 400 120 0.2 0.7Rockfill 2.2 0 45 600 0.4 1000 240 0.2 0.7Concrete 2.3 2000 5 60000 0.5 70000 3000 0.1 0.7γ – densityc – cohesionφ – angle of frictionK – compressibility modulusn – exponent of the compressibility modulusKur – unloading deformation modulusKb – volumetric deformation modulusRf – failure ratioSix cases were used to examine different material properties. Table 2.4 shows the parameters20for the first case. Contour plots are provided only for this case and are shown on Figure 2.17.Figures 2.17 (a) and (b) exhibit the vertical and horizontal deformations.Figure 2.17: Contour plots of the simulation results for (a) Vertical displacements [m] (b)Horizontal displacements [m] (c) Vertical total stress [tonne/m2] (d) Horizontal totalstress [tonne/m2].21Larger settlements are present in the rockfill and reach up to 0.8 m. Horizontal deformationsare symmetrical. As mentioned in the previous chapter, more deformations are expected to occurduring the reservoir impoundment. Figures 2.17 (c) and (d) convey the vertical and horizontalstresses in the dam. The expected stress transition between the rockfill, transitions and core arealso observed.2.4.2 FE analysis using the Rockfill Model (2012)Errecalde (2012) conducted a more recent study on the Denis-Perron Dam with an attempt tocapture the unsaturated behaviour of rockfill. The simulation has been completed using a 2D threephase finite element platform called Code Bright, which has an implemented advanced constitutivemodel with the capability of capturing the rockfill behaviour. Current research uses a more recentversion of the same software and the same constitutive models. Therefore, a detailed descriptionof the constitutive models, modelling procedures and material parameters are provided in the nextchapters of the thesis to avoid redundancy. For details, refer to Errecalde (2012)Due to technical issues and non–convergence of the code, the simulation of Errecalde (2012)manages to successfully represent only construction of the dam up to the elevation of 360 m andpartial reservoir impoundment. Comparison of the partial simulation results with field measure-ments of two inclinometers in the upstream (INB1) and downstream (INB5) are presented in Figure2.18.Figure 2.18: Vertical displacements at (a) Upstream inclinometer INB1 (b) Downstream in-clinometer INB5 for different dates. Adapted from Errecalde (2012).22Chapter 3Mechanical and hydraulic models usedin the analysis of Denis-Perron3.1 IntroductionThis chapter introduces the advanced mechanical constitutive models and hydraulic models usedto simulate the materials within the body of the dam. The linear elastic model used to simulate therest of the materials, such as bedrock, is not presented due to its simplicity.A constitutive model is a mathematical formulation of the stress and strain response of a ma-terial. Generally, constitutive models are a simplification of the real material behaviour, but canvary in the level to which they simplify the response. In order to accomplish an adequate simula-tion of a boundary value problem, it is important to have a necessary level of sophistication in theconstitutive models.In the recent decades, a number of models of different complexity have been developed. Thehyperbolic model of Duncan and Chang (1970) was used to simulate Denis-Perron. The modelrequires two separate analysis for dry and saturated conditions, missing the transition of the par-tially saturated state of the dam. Another more recent elasto-plastic critical state model was usedby Naylor et al. (1997) to back analyse Beliche Dam. This model requires two different set ofparameters for dry and saturated conditions and it manages to capture the collapse mechanism ofrockfill, but does not incorporate the important time dependent deformation of rockfill.The first section in this chapter examines an advanced elasto-plastic three phase constitutivemodel used for modelling of unsaturated soils called the Barcelona Basic Model. The second23section studies the mechanical behaviour of rockfill. Following is a description of the RockfillModel (RM) constitutive model based on the principles of BBM and incorporating the observedmechanisms discussed prior to that. Finally, the last two sections discuss the hydraulic constitutivemodels used in the simulations.3.2 Mechanical models3.2.1 Barcelona basic model (BBM)The Barcelona basic model has been developed at the Polytechnic University of Catalonia inBarcelona, Spain in the works of Alonso et al. (1990). BBM is intended for modelling of slightlyto moderately expansive partially saturated soils such as silts, clayey sands, sandy clays and lowplasticity clays.The model is formulated in the framework of hardening plasticity and becomes a conventionalcritical state model (Modified Cam Clay) upon reaching full saturation. BBM is defined by two setsof stress variables. The first one is the mean net stress defined as p = (σ1+2σ3)/3−ua, where pis net mean stress, σ1 is vertical total stress, σ3 is horizontal total stress and ua is air pressure. Thesecond variable is the suction, defined as s = ua−uw, where s is suction and uw is water pressure.The deviatoric stress is defined in a conventional way as q = σ1−σ3.The strains associated with the model are split into the conventional volumetric and deviatoricstrains, notated with v and q as a subscript respectively. Each of them is obtained due to change ofstress (loading/unloading) or change of suction, notated with with l and s as a superscript respec-tively. The strains induced based on changes of stress or suction are either elastic or plastic and arenotated with e and p as a superscript respectively. A visual break down of the strains is presentedin Figure 3.1. The changes of stress and suction form two yield surfaces in (p,q,s) space and areshown on Figure 3.2 in (p,q,s) space24𝑑𝜀𝑣𝑙,𝑒 =κν𝑑𝑝𝑝𝑑𝜀𝑣𝑙,𝑝=< 𝐿 >𝜕𝑔𝜕𝑝𝑑𝜀𝑣𝑠,𝑒 =κ𝑠ν𝑑𝑠(𝑠 + 𝑝𝑎𝑡𝑚)𝑑𝜀𝑣𝑠,𝑝=λ𝑠 − κ𝑠ν𝑑𝑠0(𝑠0 + 𝑝𝑎𝑡𝑚)𝑑𝜀𝑞𝑙,𝑒 =13𝐺𝑑𝑞𝑑𝜀𝑞𝑙,𝑝=< 𝐿 >𝜕𝑔𝜕𝑞𝑑𝜀𝑞𝑠,𝑒 = 0𝑑𝜀𝑞𝑠,𝑝= 0Figure 3.1: Strains assosiated with loading and suction changes in BBM.Figure 3.2: The dimensional view of the BBM yield surfaces in (p,q,s) space. Adapted fromAlonso et al. (1990).25Yield surfacesThe first yield surface, f1, is called the L.C. (loading-collapse) yield surface, which defines theincrease in pre-consolidation pressure with increasing suction and also the collapse phenomenaobserved during wetting. At full saturation (s = 0), the yield surface is defined as the ModifiedCam Clay (M.C.C). The surface in (p,q,s) space is defined asf1(p,q,s, p∗0) = q2−M2[p+ ps(s)] [p0(s)− p] = 0 (3.1)where ps(s) = kss is a shear strength parameter, linearly increasing with suction and M is thecritical state line slope defined in a conventional way as M = 6sinφ/(3− sinφ). The loading-collapse curve (LC) defines the set of p0(s) values for each associate suction. It can be consideredas a set of yield curves in (p,s) space. The LC curve is as follows:p0(s) = pc(p∗0pc)λ (0)−κλ (s)−κ (3.2)where pc is a reference stress, p∗0 is pre-consolidation stress for saturated conditions, λ (0) is acompressibility parameter for saturated conditions, κ is an elastic stiffness parameter and λ (s) isthe change of the compressibility parameter with suction defined byλ (s) = λ (0) [(1− r)exp(−β s)+ r] (3.3)where β controls the rate of increase of stiffness with suction and r is a parameter that defines themaximum soil stiffness.The second yield surface, f2, is associated with the suction increase locus (SI). The s0 variableis the maximum past suction experienced. When suction is increased, s0 bounds the transition fromthe elastic state to the virgin range. The yield surface is represented by Equation 3.4 and can bevisualized on Figure 3.3 (a).f2(s,s0) = s− s0 = 0 (3.4)26νκλ λ λ λνλκνλ λκλFigure 3.3: (a) Representation of the S.I. and L.C. curve in (s,p) space (b) Compression curvesin ν ,s, p space (c) Compression curves for saturated and unsaturated soils in ν , p space(d) Compression curves in ν ,s space for BBM (Alonso et al., 1990).The effect of suction change on the compressibility and size of p0(s) are illustrated on Figure3.3 (c). The three curves shown, from black to red, represent values for λ (s) at different suctions.With the increase of suction, the compressibility of the soil decreases and the yield surface p0(s)increases in size as seen on Figure 3.3 (a). The parameters λs and κs are fixed as a constant forthe sake of simplicity and therefore experience no change in value due to suction changes. This isreflected in Figures 3.3 (b) and (d).Flow rulesThe plastic strain increments (flow rule) associated with yield surface f1 are dε pvp (volumetric plas-tic increment associated with the LC curve) and dε pq (deviatoric plastic increment associated withthe LC curve) are defined asdε pvpdε pq=2qαM2(2p+ ps− p0) (3.5)27where α is a non-associativity parameter defined. Assuming zero elastic deviatoric strain incrementand K0 stress conditions, α is defined byα =M(M−9)(M−3)9(6−M)11− κλ (0)(3.6)The flow rule associated with f2 is (dε pvs,0), defined asdε pqdε pvs= 0 (3.7)where dε pvs is the volumetric plastic strain increment for the S.I. locus.Hardening lawsThe hardening law for the loading yield surface, f1, is controlled by the hardening parameter p∗0,which evolves as Equation 3.8 suggestsd p∗0 =(1+ e)p∗0λ (0)−κ dεpv (3.8)The hardening law governing yield surface f2 is controlled by the evolution of the hardeningparameter s0. Its evolution depends on dε pv (total plastic volumetric strain) and is defined asds0 =(1+ e)(s0+ patm)λs−κs dεpv (3.9)ElasticityThe volumetric and deviatoric elastic strains associated with changes in loading and suction are asfollows:dεev =κvd pp+κsvds(s+ patm)(3.10)dεeq =13Gdq =2(1+ν)3Edq (3.11)where κ is the elastic stiffness parameter associated with changes of stress and κs is the elasticstiffness parameter associated with changes of suction. A summary of the parameters required forthe BBM and the way of calibrating them, are presented in Table 3.1.28Table 3.1: Summary of BBM parameters and calibration methods.Parameter definition Symbol Units Calibration methodElastic parametersElastic stiffness parameter during loading/unloading κ MPa−1 Suction controlled oedometer testPoisson’s ratio ν – Suction controlled oedometer testElastic stiffness parameter for changes in suction κs MPa−1 Drying-wetting test cycle at a given net mean stressYield surfaceCritical state slope M – Direct shear testPre-consolidation pressure p∗0 MPa ICD triaxial or oedometer testReference stress pc MPa Suction controlled ICU triaxial or oedometerParameter in the LC curve β MPa−1 Suction controlled ICU triaxial or oedometerParameter in the LC curve r – Suction controlled ICU triaxial or oedometerStiffness parameter during suction changes λs MPa−1 Drying-wetting test cycle at a given net mean stressPlastic potentialNon-associativity parameter α – From M, κ , ν and λ (0)Hardening lawVirgin compressibility for saturated conditions λ (0) MPa−1 Oedometer test293.2.2 Rockfill compressibility model (RM)The model used to simulate the rockfill response is an viscoplastic constitutive model based onthe main principles of the Barcelona Basic Model (BBM) (Alonso et al., 1990). The stress vari-ables for the RM are defined in the same manner as in BBM. The model captures the volumetricdeformation behaviour of the rockfill that is based on a fracture propagation mechanism. This de-formation mechanism is able to give a qualitative physical explanation of time-dependent strainsand collapse strains of rockfill, and of their simultaneous dependence on stress and water action.Prior to description of the constitutive model, the main factors affecting the behaviour of rockfillare examined.The Rockfill Model (Oldecop and Alonso, 2001) considers a linear relationship for the stress-strain response for both instantaneous and time dependent deformation of the material based onexperimental data. The model is based on isotropic compressibility, elastic behaviour, yield stressfunction with a volumetric hardening law, critical state and has an extension for triaxial stressconditions with a yield and plastic potential functions.Isotropic compressibilityThe volumetric compressibility is assumed to be governed by two components. Under a thresholdstress value, py, only the first mechanism occurs. It is called particle re-arrangement and involvesslip and rotation of the particles in relation to their neighbours. The second mechanism is ac-tive beyond that threshold stress value and controls particle breakage. Isotropic compressibility isdescribed as follows:dεv = λ id p p≤ py (3.12)dεv = λ id p+λ d(s)d p p > py (3.13)where dεv is the incremental volumetric strain, p is the total mean net stress and λ i is a com-pressibility parameter that governs the particle re-arrangement mechanism, where the superscript istands for instantaneous deformation. The compressibility parameter λ d(s) represents the particlebreakage mechanism, which is dependent on the total suction and captures some of the macro-scopic phenomena observed in laboratory testing. The compressibility λ d(s) increases when therockfill is wetted (decrease of suction). The superscript d shows the delayed nature of the particlebreakage mechanism. Equation 3.14 appropriately captures this behaviour30λ d(s) = λ d0 −αs ln(s+ patmpatm)(3.14)where λ d0 is rockfill compressibility at full saturation and αs controls the rate of increase of rockfillstiffness due to suction increase. A visual representation of Equations 3.12 and 3.13 for differentstress paths can be seen on Figure 3.4 (a).𝜀𝑣λ𝑖λ𝑖λ𝑖 + λ𝑑(𝑠)κ𝑝0∗ < 𝑝𝑦𝑝0∗ 𝑝𝑝𝑝𝑦𝑝𝑦𝑝0∗> 𝑝0∗>> 𝑝0∗>>>Figure 3.4: (a) Idealized model response for different stress paths (b) Yield surface (L.C.curve) for different values of p∗0 for RM.Yield surfaceRockfill behaves in an non-associated manner and the yield function based on BBM is modified toobtain the potential function G. Both functions are shown belowF(p,q,s) = q2−M2(s) [p+ ps(s)] [p0(s)− p] = 0G(p,q,s) = q2−αM2(s) [p+ ps(s)] [p0(s)− p] = 0(3.15)31where α is a non-associativity parameter, ps(s) = kss is a shear strength parameter, linearly increas-ing with suction. M(s) shows the effect of the suction on the critical state slope, varying betweentwo extreme values: Mdry for very high values of suction and Msat for s = 0, presented in Equation3.16. The loading-collapse curve (LC) defines the set of p0(s) values for each associate suction.It can be considered as a set of yield curves in (p,s) space. The LC curve is defined in Equations3.17 and 3.18.M(s) = Mdry− (Mdry−Msat)(MsatMdry)s/patm(3.16)p0(s) = p∗0 p∗0 ≤ py (3.17)p0(s) = py+(λ i−κ)(p∗0− py)λ i+λ d(s)−κ p∗0 > py (3.18)where p∗0 is the yield stress for the very dry rockfill material. Under the threshold value py, thebehaviour does not depend on water content. This could be seen on Figure 3.4 (b), where the L.C.curve is shown in (s,p) space for different values of p∗0. The yield surface is also represented in(p,q,s) space on Figure 3.5.𝑝𝑝𝑦𝑞𝑠𝑝0∗𝑝𝑠Figure 3.5: The dimensional view of the yield surfaces in (p,q,s) space for RM.32Flow ruleThe constitutive model proposed in Oldecop and Alonso, 2001 is extended and a viscoplastic for-mulation is added in Alonso et al., 2005. Adding viscoplasticity to the model offers computationaladvantages because collapse behaviour can be viewed as a softening process and could result innumerical problems. Such instabilities happen because collapse concentrates in isolated elementswhile adjacent elements experience stress relaxation resulting in elastic behaviour. The viscoplasticapproach homogenizes the spatial distribution of the collapse strains and prevents this numericalinstability. The total strain is decomposed into elastic and viscoplastic in Equation 3.19. Equation3.20 calculates the viscoplastic strain.ε˙ = ε˙e+ ε˙vp (3.19)ε˙vp = Γ〈φ(F)〉∂G∂σ(3.20)where Γ is the fluidity parameter and 〈φ(F)〉 is a flow function defined as〈φ(F)〉= φ(F) F > 0 (3.21)〈φ(F)〉= 0 F ≤ 0 (3.22)φ(F) =(FF0)N(3.23)To achieve a solution close to the real elastoplastic solution, the fluidity parameter Γ must beincreased sufficiently. Typical values are Γ= 100 and N = 5.Hardening lawThe model follows a volumetric hardening law that describes the evolution of p∗0:d p∗0 =dε pvλi−κ (3.24)where the volumetric plastic strain dε pv = dεv−dεev .33ElasticityThe volumetric elastic strain of rockfill is dependent on the two compressibility coefficients κ andκs and the Poisson’s ratio, ν . The swelling index κs is negligible in non-expansive materials andthus ignored here. The parameter κs is defined as follows:dεev = κd p =d pE3(1−2ν) (3.25)dεesv = κsdss+ patm≈ 0 (3.26)CreepThere is an extra feature in RM which simulates the long term behaviour of rockfill. The volumetriccomponent of the “creep” behaviour is based on experimental data and is expressed asε˙cv =dεcvdt=λt(p,s)t=1ηv(s, t)p (3.27)where ηv(s, t) is a viscosity coefficient dependent on suction and time. It is expressed as1ηv(s, t)=µt[1−β cln(s+ patmpatm)](3.28)where µ and β c are constitutive parameters. To account for the deviatoric part of the “creep” strain,a tentative expression, which is not based on data, has been established asε˙cd =dεcddt=13ηd(s, t)q (3.29)where ηd = aηv and a is usually taken as 0.1. The total creep strain is calculated via the viscoelasticequationε˙c =12ηd(σ − pI)+ 13ηvpI (3.30)The formulation for the time dependent compressibility manages to capture its reliance on stressand suction observed in laboratory settings.34Differences with BBMThere are several differences between the BBM and the RM model. The first one is that compress-ibility relations for the rockfill are described by linear functions between stress and strain. Thevalue of py (threshold stress) has no equivalent value for unsaturated soils. Another significantdifference is the definition of the suction, s. In unsaturated soils s has a mechanical meaning anddescribes the capillary or matric component of suction. The role of suction in rockfill is to controlthe velocity of crack propagation within the particles. Therefore, s is used as a state variable thatis externally controlled by boundary conditions and flow phenomena. The velocity of crack propa-gation depends on the relative humidity, or by the total suction. In the case of dams, the distinctionbetween both definitions of suction is not significant because the chemical composition of water isnot a relevant variable. The chemical composition of water governs the osmotic component of thetotal suction, but when it is not present this effect disappears and total and matric suction becomeidentical.For both BBM and RM constitutive models, the suction variable s is controlled by the flowphenomena and the assigned boundary conditions. This is done through using a unique waterretention curve for each material, relating s with the current saturation, Sr, of the material. In thecase of rockfill, however, the Sr refers to relative humidity that is inside the particle cracks and not,as in the standard definition of Sr, the amount of water in the pore space between the particles.A summary of the constitutive model equations for BBM and RM are presented in Table 3.2for comparison purposes. The parameters required by RM are summarized in Table 3.3 and a shortdescription of the calibration methods is included.35Table 3.2: Basic relationships for BBM and RM*. Table adopted from Alonso et al. (2005).Barcelona Basic Model (BBM)(Alonso et al., 1990)Rockfill Model (RM)(Compressibility part described inOldecop & Alonso, 2001)Isotropic elastoplasticvolumetricdeformationdεv = λ (s)(1+e)d ppdεv = λ id p p≤ pydεv = λ id p+λ d(s)d p p > pyλ (s) = λ (0) [(1− r)exp(−β s)+ r]λi+λ d(s)λ d(s) = λ d0 −αsln(s+patmpatm)Volumetriccompressibility indexd p∗0 =(1+e)p∗0λ (0)−κ dεpv d p∗0 =dε pvλi−κHardening lawp0(s) = pc(p∗0pc) λ (0)−κλ (s)−κ p0(s) = p∗0 p∗0 ≤ pyp0(s) = py+(λ i−κ)(p∗0−py)λ i+λ d(s)−κ p∗0 > pyLoadingcollapse curve(LC)Shear strength critical-state parameterM(s) = M M(s) = Mdry− (Mdry−Msat)(MsatMdry)s/patmps = kssTensile strengthparameterF = 3J2D−M2(s)9(J1+3kss) [3p0(s)− J1] = 0G = 3J2D− αM2(s)9(J1+3kss) [3p0(s)− J1] = 0Yield surface(triaxial)Plastic potential(triaxial)Creep straindεcvdt=1ηv(s, t)pdεcddt=13ηd(s, t)q1ηv(s, t)=µt[1−β cln(s+ patmpatm)]ηd = aηv* A common notation was used for equivalent parameters. Material parameter values are different for the rockfill and soil36Table 3.3: Summary of RM parameters and calibration methods.Parameter definition Symbol Units Calibration methodElastic parametersYoung’s modulus E MPa Unloading stage – oedometer testPoisson’s ratio ν – Material propertyPlastic behaviourPlastic virgin instantaneous compressibility λ i−κ MPa−1 Loading stage under dry conditionsat low stress – oedometer testVirgin clastic compressibility for saturated conditions λ d0 MPa−1 Loading stage under saturatedconditions – oedometer testParameter describing the rate of change of compressibility with suction αs – Flooding of dry sample under constant stressSlope of critical-state strength envelope for dry conditions Mdry – Friction angle of dry material, φdry – DSSSlope of critical-state strength envelope for saturated conditions Msat – Friction angle of saturated material, φsat – DSSParameter that controls the increase in cohesion with suction ks –From the cohesive intercept –ICU triaxial/oedometer testThreshold yield mean stress for the onset of clastic phenomena py MPaFlooding of dry sample under constant stress(collapse strain); Flooding of dry sample underlow stress (expansion strain);ICU triaxial/oedometer testParameter that defines the non-associativeness of plastic potential α – Material parameterCreepCreep coefficient for saturated conditions µ MPa−1Suction controlled oedometer test underconstant stressParameter that controls the influence of suction on creep rate β c –Suction controlled oedometer test underconstant stress373.3 Hydraulic models3.3.1 Van Genuchten hydraulic modelThe water retention curve shows the relation between capillary pressure (suction) and degree ofsaturation (Sr) of various materials. Typically, it is used in unsaturated soils with high plasticityand the suction variable refers to the suction within the pores between the particles. In the case ofrockfill, however, the suction is found within the cracks of the particle, instead of in between thepores of the particles. Also, the saturation in rockfill refers to the relative humidity located, again,inside the particle cracks. One model in particular seems to capture well the shape of those curvesand it is the model described in van Genuchten (1980). The Van-Genuchten equation implementedin Code Bright (2015) isSr =Sl−SlrSls−Slr =[1+(ua−uwP)1/(1−λvan)]−λvan(3.31)where Sr is the degree of saturation (cm3/cm3), which varies between 0 and 1, Sl is equivalent sat-uration ratio, P = σP0/σ0, σ0 is surface tension at temperature at which P0 was measured (usually0.072N/m), P0 is the air entry value of the material, λvan is an exponent parameter, Sls is maximumsaturation and Slr is residual saturation. By definition, the suction s = ua−uw. An example of fourwater retention curves is presented in Figure 3.6 to show the effect of the most dominant parametersin this equations, which are P0 and λvan.0.001 0.01 0.1 1 10 100 1000Matric suction, s [MPa]00.20.40.60.81Saturation, Sr [%]0.001 0.01 0.1 1 10 100 100000.20.40.60.81P0 = 0.1 MPa; = 0.3P0 = 0.1 MPa; = 0.6P0 = 0.01 MPa; = 0.3P0 = 0.01 MPa; = 0.6Figure 3.6: Water retetion curves with varying P0 and λvan parameters.38Typically, for rockfill, the value for P0 is lower than 0.01 MPa and for clay/till materials, P0could go as high as 0.5 MPa. Values for λvan are typically 0.6 for rockfill and 0.3 for clay.3.3.2 Liquid phase relative permeabilityThe relative permeability introduces the effect of partial saturation on intrinsic permeability. Thefunction is notated with Kr(Sr) and varies between 0, for dry soil, and 1 for fully saturated soil.The function acts as a multiplier to the intrinsic permeability asK = kρwgµwKr(Sr) (3.32)where K is the hydraulic conductivity (m/s), k is the intrinsic permeability (m2), g is the gravita-tional constant (m/s2) and µw is the dynamic viscosity of the water (kg/m.s) and ρw is the densityof water (kg/m3). There are different simple laws that express the reduction of permeability withdecrease of saturation. In the present work, a power law is selected asKr(Sr) = ASmr (3.33)where A is a constant, usually taken as 1, m is the exponent, usually taken as 10 for rockfill and3 for clay core. In the case of rockfill, having a higher exponent results in Kr(Sr) becoming 0 fordegree of saturation more than 0.3. This equates to water freely percolating within the saturatedrockfill pores. Visual representation of the power law can be seen on Figure 3.7, adopted fromAlonso et al. (2005).39Figure 3.7: Varying relative permeability for clay and rockfill materials (Alonso et al., 2005).40Chapter 4Description of the numerical model4.1 Finite element softwareThe numerical simulation is set up in a finite element platform called Code Bright, developed atthe Polytechnic University of Catalonia (Code Bright, 2015). This is a two dimensional FEM soft-ware for coupled Thermo-Hydro-Mechanical analysis in geological media. The theory consists ofa set of governing equations and a set of constitutive laws. The code is developed in FORTRANand consists of multiple subroutines. Code Bright uses GiD as pre and post-processing tool (Collet al., 2016). GiD is an interactive graphical user interface that is used to prepare the numericalmodel of the dam for analysis. The data defined in GiD includes setting up the geometry, materialparameters used by Code Bright, initial and boundary conditions, solution information, time inter-vals and time step definition. Meshing of the model is done after introducing all of the describeddata. Constitutive laws in GiD are defined by entering a combination of material parameters. Forexample, to use the Rockfill compressibility model, material parameters have to be filled for LinearElasticity, Viscoplastic General Parameters 1,2 and 3 in the “Mechanical Parameters 1” section ofthe software. In the next sections, the constitutive models that are used for modelling the dam, areexplored in depth, including an explanation of the parameters involved.4.2 Geometry and zoningThe model of the dam has been built layer by layer in accordance with real life construction andimpoundment stages. The whole simulation captures the construction and full impoundment of thedam reservoir, lasting for 5 years. The geometry has been exported from Hydro Quebec’s DXF file41in GiD 12.0.7. The height of the dam is 171 m and it reaches to an elevation of 410 m. A localcoordinate system is placed with its X origin to be along the centre of the till core. The next twosubsections show the numerical model layer discretization and the constitutive models assigned forthe different materials.4.2.1 Geometry and model layersThe geometry of the dam is divided into multiple layers with depth of around 20 m as shown inFigure 4.1.0 50200250100 150 200 250 300 350 400 450-50-100-150-200-250-300-350-400-450300350400Figure 4.1: Construction sequence of dam for model calculations.The layer discretization has been obtained from the provided DXF file, assuring that the layersare constructed exactly as in the field. This process guarantees a more accurate representation of theconstruction sequence than simulating idealized horizontal layers. Construction has been simulatedby adding layers to an initial geometry of the alluvial foundation and bedrock. The weight of eachlayer has been applied in a ramp manner in order for the layer to reach full weight at the end ofthe construction time interval. Detailed information regarding the time intervals, construction andimpoundment are provided in Section 4.5.4.2.2 Constitutive models assigned to material zonesFigure 4.2 describes all the material zones.420 50200250Rockfill3DRockfill3DBedrockCrushed StoneFilterRockfill 3BRockfill3CRockfill3CCoreConcreteWater100 150 200 250 300 350 400 450-50-100-150-200-250-300-350-400-450Alluvial300350400Figure 4.2: Denis-Perron dam material zones.Table 4.1 exhibits the respective constitutive model assigned to the material zones.Table 4.1: Assigned constitutive models to dam zones.Dam Zones Constitutive ModelRockfill Shells (3C, 3D) RMTransition (Rockfill 3B) RMDrain and Filter BBMTill Core BBMAlluvial Foundation BBMBedrock LEConcrete LEWater LE4.3 Material parametersEach of the material zones requires a set of parameters in order to solve the stress equilibriumand flow equations. Generally, a set of mechanical parameters to describe the LE, BBM or RMmodels are needed. Each of these three constitutive models require different parameters as shownin Chapter 3.Another set of parameters needed are the hydraulic parameters. They include the definition ofa water retention curve and intrinsic permeability. The final set of parameters for each material isthe initial values for porosity and suction. Subsections 4.3.1 to 4.3.4 investigate the calibration of43the parameters for the materials in Table 4.1.4.3.1 Till coreThe core is constructed out of a glacial till material. A suitable constitutive model for this typeof material is the BBM. To use the BBM in Code Bright, a combination of linear elasticity andviscoplasticity for unsaturated soils is used. The laboratory and field data provided are not sufficientto derive all necessary material parameters for the numerical simulation. A similar glacial tillmaterial from Northern Quebec has been thoroughly examined in the work of Watabe et al. (2000).Twelve samples, H-01 to H-12, under different compaction and saturation conditions have beentested. Figures 4.3a and 4.3b show the compaction curves and the hydraulic conductivities for thetwelve samples respectively.(a) (b)Figure 4.3: (a) Standard Proctor compaction curve for all samples tested (b) Hydraulic con-ductivity as a function of the compaction degree of saturation. Figures modified fromWatabe et al. (2000).Sample H-06 has suitable physical characteristics and is chosen based on a few criteria de-scribed in Table 4.2, exhibiting similarities with the SM3 glacial till material. Hydraulic parametersare derived based on hydraulic conductivity and water retention curve of that sample. Mechanicalparameters are derived based on an oedometer test performed on sample H-06. Derivation of thoseparameters is explored in the next subsections.44Table 4.2: Comparison of H-06 glacial till material physical characteristics with SM3 glacialtill material.Physical parameter/definitionValue and/or ReferenceH-06 Sample SM3 SampleSoil classification Glacial Till Glacial TillGrain size distribution Figure 2.14 Figure 2.14Maximum average dry density, ρd,max,average 2135 kg/m3 2137 kg/m3; Table 2.2Void ratio 0.25 0.24; Table 2.3Hydraulic conductivity, K 7×10−7 m/s; Figure 4.3b 1×10−7 – 1×10−10 m/sWater content after compaction, w f 7.5 % 7.3 %; Table 2.3Hydraulic parametersThe intrinsic permeability is calculated using Equation 4.1k = Kµwρwg(4.1)From the permeability tests it is established that K = 7× 10−7 m/s. Using Equation 4.1, k =7.2×10−14 m2. Permeability is assumed to be isotropic as no anisotropy has been reported.The water retention curve has been estimated from Watabe et al. (2000) for the till core material.The curve varies based on compaction conditions, thus an average was taken (thick red line) shownon Figure 4.4a. To capture the shape of the retention curve, the van Genuchten (1980) law is used.A plot of the water retention curve with the estimated parameters for Equation 3.31 is shown onFigure 4.4b with the thick blue line.Sample H-06’s saturation is reported as Sr = 0.76. Using the retention curve from Figure4.4b, a value for the initial suction is calculated as s = 0.01 MPa. The hydraulic parameters aresummarized in Table 4.3.45(a)0.0001 0.001 0.01 0.1 1 10Matric suction, s [MPa]020406080100Saturation, Sr [%]Derived WRC - VanGenuchtenWatabe, 20000.0001 0.001 0.01 0.1 1 10020406080100(b)Figure 4.4: (a) Soil characteristic curves for till samples in Watabe et al. (2000). Red lineshows an average curve. (b) Fitted curve (blue) to averaged soil characteristic curveusing van Genuchten (1980).Table 4.3: Hydraulic parameters for the till core.Definition of parameter Symbol Value UnitsIntrinsic Permeability k 7.2×10−14 m2Water Retention Curve (van Genuchten, 1980)Pressure at T = 20◦ P0 0.01 MPaMaximum Saturation Sls 1 –Residual Saturation Slr 0.075 -Curve Shape Defining Exponent λ 0.4 –Liquid phase relative permeabilityModel constant A 1 –Model exponent m 3 –Initial Suction (applied as an initial condition to model) s0 0.01 MPa46Mechanical parametersThe parameters for the BBM are calibrated based on oedometer data for sample H-06. The oe-dometer test is simulated in Code Bright with a 10× 10 mesh. The initial suction for the test iss0 = 0 MPa (Sr = 100%). The initial porosity is n = e/(1+ e) = 0.195. The initial suction andporosity are both applied as initial surface boundary conditions. The saturation level of the sampleis kept constant during the test by applying a constant liquid pressure equal to the suction levelcorresponding to the given saturation. Ramp loading is applied as a boundary condition on the topsurface of the oedometer. The results of the tests can be seen on Figure 4.5.10 100 1000 10000Vertical effective stress, sv [kPa]0.210.220.230.240.25Void ratio, eSample H-06 (Watabe et al. 2000)Model resultsFigure 4.5: Oedometer test on compacted till from Northern Quebec, sample H-06 (Watabeet al., 2000).The parameters calibrated with the test are:• Elastic parameters - E and ν using the unloading stage of the test• Virgin compressibility parameter using the data from the loading stage - λ (0)• Viscoplasticity parameters for the general shape of the loading stage - Γ and NThe model does not seem to capture the behaviour of the till at lower stresses in the range of 100to 300 kPa, experiencing less volume change than what the laboratory data is suggesting.47The slope of the critical state line is estimated based on the reported angle of friction, φ = 39(SNC-Shawinigan, 1996), using Equation 4.2.M =6sin(φ)3− sin(φ) (4.2)The non-associated parameter α is calculated based on Equation 4.3 (Vaunat, 2015).α =M(M−9)(M−3)9(6−M)11− κλ (0)(4.3)The parameters governing the LC curve could not be calibrated due to a lack of suction con-trolled experiments. The effect of suction on the compressibility is considered low for this materialdue to the high density. Suction values of the till material are in the low range (less than 0.05 MPa)due to the high initial saturation. Thus, the compressibility value is very close to the maximumvalue (when Sr = 100%). A summary of the mechanical parameters is shown in Table 4.4.4.3.2 Rockfill materialThree different rockfill material zones are considered in the analysis. The inner (Rockfill 3C)and outer shells (Rockfill 3D) of the dam have the most significant impact on the dam behaviour.Therefore, they will be the focus of this study. The transition zone (Rockfill 3B) is composed ofthe same material, but with smaller maximum particle diameter of 450 mm. All of the three zonesare modelled with the RM model. For the base case, the constitutive model parameters will be thesame for all three rockfill materials.According to Errecalde (2012) the rockfill particles are composed of biotite and anorthosite.Biotite is characterized by a foliated structure, which favours development of many microcracks.The higher the amount of microcracks in the particles, the more settlement is expected. Duringthe compaction process, the material has been placed without sluicing. The omission of sluicingcauses more collapse during the first impoundment due to the nature of rockfill response.Hydraulic parametersDue to a lack of provided data for rockfill, the hydraulic properties are established based on litera-ture. Previous research has shown that rockfill intrinsic permeability varies between k = 1×10−8m2 and k = 1×10−12 m2. In the case of Beliche dam (Alonso et al., 2005), the intrinsic permeabil-ity of the rockfill is kBeliche = 2×10−11 m2 for a rockfill with porosity of n = 0.35. In the case of48Table 4.4: Mechanical parameters for the till core.Definition of parameter Symbol Units ValueElastic behaviourElastic modulus E MPa 300Poissons ratio ν – 0.33Plastic behaviourVirgin compressibility for saturated conditions λ (0)−κ MPa−1 0.011Parameter that establishes the minimum value of the compressibility for high suction r – 0.7Parameter that controls the rate of increase in stiffness with suction β MPa−1 0.6Reference stress pc MPa 0.001Slope of critical-state strength line M – 1.6Parameter that controls the increase in cohesion with suction ks – 0Parameter that defines the non-associativeness of plastic potential α – 0.46ViscoplasticityFluidity parameter Γ s−1 1000Flow function exponent N - 649Lechago dam (Alonso et al., 2012), the intrinsic permeability of the rockfill is kLechago = 1×10−12m2 for a rockfill with porosity of n = 0.30. Examining the work of Konrad et al., 2011, rockfillintrinsic permeability could go as high as k = 1× 10−8 m2. It is safe to assume that the intrinsicpermeability for Denis-Perron is somewhere in the middle, kSM3 = 1×10−10 m2. A more detailedstudy regarding the sensitivity of the intrinsic permeability is carried out in Chapter 6.Data for the water retention characteristics of the rockfill is missing, therefore, a water reten-tion curve is estimated from literature. The model used to describe the curve is van Genuchten(1980). A suitable water retention curve is adopted from Errecalde (2012). Figure 4.6 conveys thewater retention curve used in the analysis of SM3 dam in blue. The Figure also exhibits the waterretention curves used for Beliche and Lechago dams for comparison purposes.1E-005 0.0001 0.001 0.01 0.1 1 10 100Matric suction, s [MPa]020406080100Saturation, Sr [%]1E-005 0.0001 0.001 0.01 0.1 1 10 100020406080100Errecalde 2012Beliche Dam, 2005Lechago Dam, 2012Figure 4.6: Water retention curves for rockfill material: Beliche Dam (Alonso et al. (2005)),Lechago Dam (Alonso et al. (2012)) and Denis-Perron Dam (Errecalde (2012)).It is very difficult to estimate initial saturation of the rockfill in the field and no information forthis is available. This value depends in the way the rockfill has been placed in the field. If therehas been sluicing involved, the initial saturation should be considered higher and therefore initialsuction is lower. If the rockfill has not been placed with sluicing, the initial saturation should beconsidered lower, which causes higher long term settlements. The oedometer test on the rockfill50material is carried out at a relative humidity of 30% (Sr = 30%). The initial saturation for thenumerical simulation is assumed to be the same due to no other information available. Using thewater retention curve from Figure 4.6, the initial suction is calculated to be s0 = 0.007 MPa. Thehydraulic parameters for the inner and outer shells are summarized in Table 4.5.Table 4.5: Hydraulic parameters for the rockfill shells.Definition of parameter Symbol UnitsRockfillInner Shell Outer ShellIntrinsic Permeability k m/s 1×10−10 1×10−10Water Retention Curve (Van Genuchten, 1980) –Pressure at T = 20◦ P0 MPa 0.01 0.01Maximum Saturation Sls – 1 1Residual Saturation Slr – 0 0Exponent Defining Curve Shape λ – 0.6 0.6Liquid phase relative permeabilityModel constant A – 1 1Model exponent m – 10 10Initial Suction (applied as an initial condition to model) s0 MPa 0.007 0.007Mechanical parametersOedometer tests have been performed on dry and saturated material with a reported scaled grainsize distribution, where the coefficient of uniformity, Cu, of the oedometer and the field materialis preserved. The oedometer device has a diameter of 300 mm; the maximum particle size forthe tested material is estimated to be 1/5th of that, i.e. about 60 mm. The mechanical parametersof the rockfill compressibility model are calibrated using oedometer data. Similar to the elementtest for the till material, the oedometer test is simulated in Code Bright with a 10× 10 mesh attwo different saturations: Sr = 30% for the dry sample and Sr = 100% for the flooded sample.The saturation levels of the sample is established by applying a constant liquid pressure equal tothe suction level corresponding to the given saturation: s = 0.007 MPa for Sr = 30% and s = 0MPa for Sr = 100%. In the case of rockfill Sr corresponds to the relative humidity of the material,meaning the saturation within the cracks of the particles, instead of the saturation in the pores51between the particles. The boundary condition is applied to the top and bottom boundaries of thesample. Results of the simulation are illustrated on Figure 4.7.The porosity of the sample is calculated from Equation 4.4 on a reported saturated unit weightof γsat = 22 kN/m3 and an assumed Gs = 2.7 (SNC-Shawinigan, 1996). The porosity is thencalculated as 0.27 and is applied as an initial surface boundary condition to the element test.γsat = (Gs(1−n)+n)γw (4.4)Figure 4.7: Oedometer test data and model results for wet (Sr = 100%) and dry (Sr = 30%)rockfill samples.Elasticity parameters, E and ν , are estimated based on the unloading. It seems like the un-loading slope of the two samples is influenced by the level of saturation. The compressibilityparameters λi and λ d0 are calibrated based on the loading slopes of the two tests. The rate of changeof compressibility parameter αs is also calibrated according to the oedometer test. Mdry and Msatare assumed to correspond to φmax = 45◦ and φmin = 42◦ respectively (SNC-Shawinigan, 1996).No increase in cohesion is reported and thus ks = 0. A low value for the threshold stress py isassumed because deformations are seen to occur nearly instantaneously. The mechanical parame-ters are summarized in Table 4.6, showing a comparison between the parameters used in BelicheDam’s inner rockfill shell. The rockfill material in SM3 has lower compressibility than the rockfillfrom Beliche due to the higher quality of the material used. The analysed experimental data are52not sufficient to discriminate with accuracy between different model parameters. Oedometer testsunder suction control are required for a precise determination of the parameters (λi−κ), λ d0 andαs.Calibration of the constitutive model parameters µ and βc could be obtained from a suctioncontrolled oedometer test, providing values for λ t at different suction. Such calibration has beencompleted for the quartzitic shale used in the analysis of Beliche dam (Alonso et al. (2005)) and avisual representation of the calibration procedure is shown on Figure 4.8.Figure 4.8: Calibration of parameters µ and β c based on data from Figure B.8 (a).The relation to “real time” is shown in the constitutive description of RM in equation 3.29.4.3.3 Drain, filter and alluvial foundationThe drain and filter are relatively small in size and do not affect the dam settlements significantly.For simplicity purposes and the lack of laboratory data, the two materials are modelled as one.The focus of this study is on the rockfill settlements during construction and impoundment,therefore a detailed examination of the foundation is not conducted. The rockill shoulders laypredominately on bedrock and thus the effect of this thin layer of alluvial material is considerednegligible.53Table 4.6: Mechanical parameters for the rockfill shells.Definition of Parameter Symbol UnitsRockfill ShouldersSM-3BelicheInner ShellElastic behaviourElastic Modulus E MPa 400 150Poisson’s ratio ν – 0.3 0.3Plastic behavioorPlastic virgin instantaneous compressibility λ i−κ MPa−1 0.010 0.025Virgin clastic compressibility for saturated conditions λ d0 MPa−1 0.009 0.028Parameter describing the rate of change of clastic compressibility with total suction αs – 0.02 0.01Slope of critical-state strength envelope for dry conditions Mdry – 1.85 1.75Slope of critical-state strength envelope for saturated conditions Msat – 1.7 1.3Parameter that controls the increase in cohesion with suction ks – 0 0Threshold yield mean stress for the onset of clastic phenomena py MPa 0.005 0.01Parameter that defines the non-associativeness of plastic potential α – 0.3 0.3CreepCreep coefficient for saturated conditions µ MPa−1 0.0012 0.0012Parameter that controls the influence of suction on creep rate β c – 0.083 0.083ViscoplasticityFluidity parameter Γ s−1 100 N/AFlow function exponent N – 5 N/A54Hydraulic parametersThe permeability of the drain and filter materials is assumed to be the same as the one for thetransition zone. The water retention curve of the material is considered the same as the one for thetill material. For more detailed and accurate representation of those zones, more experimental datais required.The hydraulic parameters for the alluvial foundation are taken from the work of Alonso et al.(2005). The hydraulic properties are summarized in Table 4.7Table 4.7: Hydraulic parameters for the drain, filter and the alluvial foundation.Definition of parameter Symbol UnitsValueDrain and Filter FoundationIntrinsic Permeability k m2 1×10−10 1×10−11Water Retention Curve (Van Genuchten, 1980)Pressure at T = 20◦ P0 MPa 0.01 0.1Maximum Saturation Sls – 1 1Residual Saturation Slr – 0 0Exponent Defining Curve Shape λ – 0.5 0.27Liquid phase relative permeabilityModel constant A – 10 10Model exponent m – 10 10Initial Suction (applied as an initial condition to model) s0 MPa 0.01 0.002Mechanical parametersThe drain and filter are considered to exhibit similar behaviour as the till core, but with decreasedstiffness and decreased compressibility. They are modelled with BBM and values for materialparameters are adopted from the work of Errecalde (2012). Data for the dry densities is availableand is used to calculate the porosity of the materials. The maximum average dry density of thetwo materials is ρdry,average = 2146 kg/m3. Assuming Gs = 2.7 and using Equation 4.5, the averageporosity of the material becomes n = 0.21.ρd = (1−n)Gsρw (4.5)55Table 4.8: Mechanical parameters for drain, filter and alluvial foundation.Definition of parameter Symbol UnitsMaterialsDrain Filter AlluvialElastic behaviourElastic modulus E MPa 100 100 400Poissons ratio ν – 0.3 0.3 0.3Plastic behaviourVirgin compressibility for saturated conditions λ (0)−κ MPa−1 0.006 0.006 0.038Parameter that establishes the minimum value ofthe compressibility, for high suctionr – 0.8 0.8 0.75Parameter that controls the rate of increase in stiffness with suction β MPa−1 0.4 0.4 0.4Reference stress pc MPa 0.001 0.001 0.01Slope of critical-state strength line M – 1.1 1.1 1.45Parameter that controls the increase in cohesion with suction ks – 0 0 0Parameter that defines the non-associativeness of plastic potential α – 0.3 0.3 0.3ViscoplasticityFluidity parameter Γ s−1 100 100 100Flow function exponent N – 5 5 556The alluvial foundation is modelled with the BBM and parameters are obtained from the work ofAlonso et al. (2005). The summarized material properties are presented in Table 4.84.3.4 Bedrock, concrete and waterThe bedrock, the concrete at the bottom of the core and the water material are modelled as linearelastic materials. The bedrock and concrete behave as very stiff materials and values taken for theirparameters are standard.The water is defined as a linear-elastic material in Code Bright Code Bright (2015). Instead ofapplying a hydrostatic pressure as most commercial codes handle hydro-mechanical problems, herethe water is considered as a highly porous and soft material that gets “filled up” with liquid as theimpoundment is happening. This method has been verified and validated as a good approximationof reality, both by the Code Bright creators and the author of current work. For validation of themethod, refer to Appendix A. This way of simulating the reservoir impoundment is a new featurein the software and brings a few advantages:• The first one is from a practical point of view. It drastically reduces the manual labour.The standard way of impounding is by calculating the pore pressures and the correspondingmechanical pressures (weight of water) for each of the depths and assigning it manually tothe upstream surfaces of the dam for each time interval. By using the new method, only onevalue has to be calculated per interval and only one boundary condition has to be applied pertime interval. Also, no mechanical pressures have to be calculated to simulate the weight ofthe water.• In addition, computation time is reduced. Applying only one boundary condition, comparedto multiple ones, reduces the computation time.• Lastly, rainfall impact with the reservoir surface can be simulated due to the presence of anavailable water surface. In standard numerical modelling, the water is artificially introducedand no actual water surface is present.57Hydraulic parametersThe hydraulic properties for the bedrock, concrete and water are presented in Table 4.9. The zerosuction for the bedrock and concrete translates to a saturation of 100 %. The assigned suctionof 0.1 MPa for the water simulates the atmospheric pressure. The water retention curves for thebedrock and concrete are not of importance, because those materials are under the water table leveland are fully saturated during the whole simulation. The water retention curve for the water isobtained from the tutorial examples in Code Bright (2015), showing how to use this new methodof simulating the reservoir rising.Table 4.9: Hydraulic parameters for bedrock, concrete and water.Definition of parameter Symbol UnitsValueBedrock Concrete WaterIntrinsic Permeability k m2 1×10−12 1×10−12 1×10−10Water Retention Curve (Van Genuchten, 1980)Pressure at T = 20◦ P0 MPa 0.1 0.1 0.001Maximum Saturation Sls – 1 1 1Residual Saturation Slr – 0 0 0Exponent Defining Curve Shape λ – 0.3 0.3 0.33Initial Suction (applied as an initial condition to model) s0 MPa 0 0 0.1Mechanical parametersThe values for E and ν for the bedrock and concrete are standard - very high values for E andsmaller ν . The used E = 5 MPa and ν = 0.49 for the water guarantees very high bulk modulusand low shear modulus. The high porosity and intrinsic permeability guarantees fast percolationof water within the material. The mechanical parameters for the three materials are summarized inTable 4.10.4.4 Initial and boundary conditionsFor the code to solve the hydro-mechanical equations, it needs initial and boundary conditions.Every boundary condition is assigned during the appropriate time interval. The time intervals areexplored in detail in Section 4.5.58Table 4.10: Mechanical properties for bedrock, concrete and water.Definition of parameter Symbol UnitsValueBedrock Concrete WaterYoung’s Modulus E MPa 1800 5000 5Poisson’s ratio ν – 0.15 0.15 0.49Porosity (applied as an initial condition to model) n – 0.18 0.18 0.94.4.1 Boundary conditionsThe necessary boundary conditions for the Denis-Perron dam are:• Mechanical boundary conditions - applied as line conditions– X and Y displacement constraints at the bottom boundary of the foundation (applied as0 displacement rate in the X and Y directions)– X displacement constraints at the side boundaries of the model (applied as 0 displace-ment rate in the X direction)• Hydraulic (flux) boundary conditions - applied as line conditions– Impermeable boundary conditions are applied at the bottom and sides of the model– The seepage boundary condition is applied on the face of the dam, allowing for waterto flow out– The atmospheric boundary condition is applied on the dam boundaries to simulate rain-fall– The nodal flow with prescribed pressure is assigned at the bottom of the “Water” mate-rial to simulate impoundment of the damThe assigned mechanical and hydraulic (flux) boundary conditions are shown on Figure 4.9.Details regarding the impoundment stages are discussed in subsection 4.5.2.59Impermeable boundary Seepage boundaryWater baseFigure 4.9: Mechanical and hydrauilic boundary conditions.4.4.2 Initial conditionsThe necessary initial conditions for the Denis-Perron dam are applied as surface conditions and arethe following:• Initial suction values assigned to the model internal surfaces to simulate the initial saturationof the materials• Initial porosity values assigned to the model internal surfacesFigure 4.10 illustrates the initial suction values that the software uses as a state variable in theconstitutive models. The values are assigned to dam surfaces as an “Initial unknown”. Suctionis defined as s = Pg−Pl , where Pg is gas pressure and Pl is liquid pressure. In the software Pg isassumed to be 0, therefore, Pl = −s0, where s0 is the initial value of suction calculated in Section4.3. For the water this value is 0.1 MPa, which represents the atmospheric pressure (1 atm).Figure 4.10: Initial suction values for the material zones.In Code Bright, porosity is assigned as an initial condition to the geometry’s surfaces. Thevalues for each material are calculated in Section 4.3 and the values assigned to the model are60shown in Figure 4.11. It must be noted that the initial conditions apply only for the initial activationof the given layer. For example, if the foundation is placed during Interval 1 with an applied initialporosity of 0.18, the porosity condition for Interval 2 would be calculated based on the equilibriumequations solved by the code. Even if an initial porosity is assigned for the same material in Interval2, this value is ignored.Figure 4.11: Initial porosity values for the material zones.4.5 Time intervalsThe intervals in Code Bright control the application of loading (i.e. construction stages) and ap-plication of boundary and initial conditions (i.e. reservoir impoundment). Each time interval has alength in units of time. In the case of SM3, the time intervals are defined in days.4.5.1 Construction stagesEach layer is constructed during a time interval with the length representing the time it took forconstruction of the layer in real life. Communicating the interval in which the given layer needsto be constructed (activated) is done through the “Construction Excavation” tab in the materialparameters. This construction process usually involves reduction in material stiffness, but due tolow initial pre-consolidation stress (p∗0 = 0.02 MPa) applied to the layers, there is no need for suchreduction (Alonso et al., 2005). The construction stages of the dam are illustrated in Figure 4.12.Visualization of the construction sequence from placement of foundation, to full constructionand impoundment of the dam, is presented on Figure 4.14. The construction stages and impound-ment are shown in Figure 4.13. The brown line represents the dam elevation with respect to timeand is obtained based on the construction sequence shown in Figure 4.12.61Figure 4.12: Construction sequence of the dam between 1996 and 1998 according to Pe´loquin(2015).The top X axis on Figure 4.13 shows the construction sequence in terms of dates, with a begin-ning date 8/27/96 and is chosen as t = 0 days in the simulation. The end date is 01/01/2003 whichis the end of the impoundment stage and is equivalent to t = 2320 days in the simulation, as shownon the bottom X axis. The solid blue line represents the reservoir level measured and the dashedred line is the equivalent simulation reservoir level. The impoundment is simulated as a hydraulic(flux) boundary condition in GiD and is described in the next subsection.0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days]260280300320340360380400420Elevation (m)260280300320340360380400420Dam LevelReservoir LevelReservoir Level Model8/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/02A B C D E FFigure 4.13: Dam construction and impoundment sequence in real life and the numericalmodel.620 50200250Rockfill3DRockfill3DBedrockDrainFilterTransitionRockfill3CCoreConcreteWater100 150 200 250 300 350 400 450-50-100-150-200-250-300-350-400-450Alluvial300350400Rockfill3C(a) Foundation construction.0 50200250Bedrock Concrete400100 150 200 250 300 350 400 450-50-100-150-250-300-350 -200-400-450300350WaterAlluvialDrainFilterTransitionNIV. 280 Rockfill3DRockfill3DRockfill3CCoreRockfill3C(b) 1996: Dam construction.0 50200250Bedrock ConcreteWater400100 150 200 250 300 350 400 450-50-100-150-250-300-350 -200-400-450300350Rockfill3DRockfill3DDrainFilterTransitionRockfill3CCoreAlluvialRockfill3CNIV. 360(c) Jun – Dec 1997: Dam construction.0 50200250Bedrock ConcreteWater400100 150 200 250 300 350 400 450-50-100-150-250-300-350 -200-400-450300350Rockfill3DRockfill3DDrainFilterTransitionRockfill3CCoreAlluvialRockfill3CNIV. 360NIV. 323(d) Mar – May 1998: Impoundment0 50 400200250Bedrock ConcreteWater-300-400 100 150 200 250 300 350 450-50-100-150-200-250-350-450300350400Rockfill3DRockfill3DDrainFilterRockfill3CCoreAlluvialRockfill3CTransitionNIV. 410.0NIV. 407.0(e) Jun 1998 – Jan 2003: ImpoundmentFigure 4.14: Visualization of construction sequence and impoundment simulated inCode Bright.634.5.2 Impoundment stagesThe water is modelled as a highly porous material, with high bulk modulus and low stiffness asdescribed earlier in the chapter. In order to simulate the impoundment, a hydraulic (flux) boundarycondition is applied at the base of the “Water” material (light blue line on Figure 4.9). For eachinterval a “Prescribed Liquid Pressure”, a “Prescribed Liquid Pressure Increment” and “Gamma forLiquid” are prescribed. The “Prescribed Liquid Pressure” (PLP for short) defines the starting waterpressure in the reservoir, i.e. uPLP = hreservoir×γw = 0.1 MPa for water height of 10 m. “PrescribedLiquid Pressure Increment” (PLPI for short) defines how much the liquid pressure during thatinterval will increase, i.e. uPLPI = hincrease× γw = 0.1 MPa for an additional impoundment of 10m. “Gamma for Liquid” controls the speed of impoundment and direction of flow, i.e. if it is anegative value, seepage occurs (red line on Figure 4.9) and if it is 0, the boundary is impermeable(dark blue line on Figure 4.9).The impoundment is the only boundary condition that varies with the time intervals. Theprescribed liquid pressures for each interval are shown in columns 5 and 6 in Table 4.11. Columns3 and 4 show the interval lengths in days and Column 2 shows the corresponding beginning datefor that interval. Columns 7 and 8 show the time steps associated with the intervals in order toreach convergence.4.5.3 Rainfall stagesIn the past, rainfall has been shown to affect the behaviour of rockfill dams. In some cases, partialwetting can have the same effect as full flooding. Such examples are the Beliche dam (Naylor et al.,1997) and the Martin Gonzalo Dam. Most computational models have not been able to capture thisbehaviour, but Code Bright in combination with the Rockfill Model have the capabilities to do that.Figure 4.15 shows precipitation values recorded at the Denis-Perron dam site in mm. Standardprecipitation data shows values in mm and is the measurement of water height in the span of 24hour increments.640 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300Time, t [days]01020304050Precipitation [mm]Precipitation measurement010203040508/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/02Figure 4.15: Precipitation data recorded in the field. Data digitized from Hammamjil (2003).Therefore, to obtain the proper units, mm/s, each data point from 4.15 is divided by 24×3600sec. The rainfall information is incorporated in the analysis through means of an “Name atm.dat”file placed in the simulation folder. The file is linked through an atmospheric boundary condition.The boundary condition is introduced on the current exposed surface of the dam geometry. It is thenremoved from the surface of a given layer as soon as a new layer is constructed. The precipitationdata is placed in the “Name atm.dat” file in units of mm/s and the time is in units of seconds. Therainfall flow is imposed as a function of time rather than dependent on the time intervals, the wayimpoundment is simulated.65Table 4.11: Description of time intervals details and impoundment boundary condition asso-ciated with each interval.Interval Start DateStart[Days]End[Days]Prescribed LiquidPressure [MPa]Prescribed LiquidPressure Incr. [MPa]Initial TimeStep [Days]Partial TimeStep [Days]1 1996-08-27 0 50 0.01 0.12 1996-10-16 50 100 0.01 0.013 1996-12-05 100 280 1 0.014 1997-06-03 280 310 1.00E-08 0.015 1997-07-03 310 340 1.00E-08 0.16 1997-08-02 340 370 0.01 0.17 1997-09-01 370 400 0.01 0.018 1997-10-01 400 430 0.1 0.019 1997-10-31 430 460 0.001 0.0110 1997-11-30 460 490 0.01 0.0111 1997-12-30 490 508 0.01 0.00112 1998-01-17 508 526 0.001 0.0113 1998-02-04 526 544 0.001 0.0114 1998-02-22 544 562 0.001 0.0115 1998-03-12 562 580 0.001 0.0116 1998-03-30 580 640 0 0.374 0.001 0.0117 1998-05-29 640 670 0.374 0.0510 0.01 0.0118 1998-06-28 670 700 0.425 0.034 0.1 0.00119 1998-07-28 700 730 0.460 0.035 0.0001 0.00120 1998-08-27 730 760 0.495 0.034 0.01 0.00121 1998-09-26 760 810 0.529 0.057 0.01 0.0122 1998-11-15 810 980 0.587 0.040 0.01 0.0123 1999-05-04 980 1005 0.627 0.107 0.01 0.0124 1999-05-29 1005 1185 0.735 0.103 0.01 0.0125 1999-11-25 1185 1345 0.838 0.024 0.01 0.0126 2000-05-03 1345 1390 0.863 0.088 0.01 0.0127 2000-06-17 1390 1710 0.951 0.058 0.01 0.0128 2001-05-03 1710 1725 1.010 0.029 0.01 0.0129 2001-05-18 1725 2090 1.039 0.088 0.01 0.0130 2002-05-18 2090 2120 1.128 0.049 0.01 0.0131 2002-06-17 2120 2320 1.177 0.009 0.001 0.01664.6 FE mesh4.6.1 Mesh descriptionFor a 2D simulation, four element types are available for use:• Linear triangle. It is primarily used in flow problems. Those elements are not recommendedfor incompressible media• Linear quadrilateral with four integration points and a modified B matrix. This avoids lockingwhen the medium is highly incompressible.• Quadratic triangle with three integration points• Zero thickness elementFor the initial used of the code, linear triangular elements were used and provided satisfactoryresults. Using a higher degree of elements (quadrilateral) later on caused instability in the codeand convergence could not be achieved past time = 730 days. Therefore, due to time limitations,the research was continued using linear triangular elements. The usage of those elements in nearlyincompressible media could result in shear locking and some under-prediction of displacementstakes place. Results are compared between the simulations with the two meshes at time = 730 daysand the difference in the results is less than 5%, thus the results are considered reliable and thelinear triangular elements are used for the rest of the research.The finite element mesh is composed of 2968 3-node triangular elements as shown on Figure4.16. The nodes can have up to six degrees of freedom (ux, uy, uz, Pl , Pg, T ). In the case of SM3,only three degrees of freedom are used. Horizontal (uy) and vertical (uz) displacements and waterpressure (Pl). Even though the mesh is composed of linear triangle elements, the simulation timeis around 7-8 hours.Figure 4.16: Finite element mesh of Denis-Perron dam.674.6.2 Mesh qualityThe quality of mesh is determined based on a few different criterion. Two criterion are examined.The first one is “Shape quality”. The quality criterion measures the likeness of the element to thereference one. In the case of a triangular element, the reference element is a equilateral triangle.The value is 1 for a perfect element (the reference element), and it decreases as the element becomesworse. The value is defined by Equation 4.6q =4√3Area∑3i=1 l2i(4.6)where Area is the triangle area and li (i=1,2,3) are the triangle edges. The value becomes negativeif the element has a negative Jacobian matrix. Figure 4.17 (a) shows the cumulative plot for theShape quality of the FE mesh elements. Less than 10 elements have quality under 0.5 and all ofthe elements have quality above 0.177.Figure 4.17: (a) Shape quality (b) Maximum edge cumulative distrobution.The second criterion for mesh quality is based on element size. Figure 4.17 (b) shows thecumulative distribution of elements based on maximum edge size. All of the elements within thedam have maximum element edge less than 17 m. The elements with sizes between 17 and 27.5 mare in the foundation and/or water material. The element size is sufficiently small for the purposesof this research. In the case for the need of dynamic analysis, the mesh has to be refined in order tocapture the wave propagation correctly.684.7 Solution schemeAn important part of the description of the numerical model is showing the definition of the “Prob-lem Data” and the “Interval Data”. In the “Problem Data” menu, the first task is to assign the valuefor gravity which is−9.81 in the Z direction. The second step is to tell the software what equationsare desired to be solved. In the current model, the equations solved are the “The stress equilib-rium (unknown displacement u)” and the “Mass balance of water (unknown liquid pressure PL)”.The air pressure is assigned to be a constant value of Pg = 0 and the temperature to be constantT = 20◦. In this model, an Updated Lagrangian Method is not used due to the small magnitude ofdisplacements expected.The third step is to define the “Solution Strategy”. The Solver is assigned as “direct LU+Back3”;the Elemental relative permeability is computed from the average nodal degree of saturation; theconvergence criterion is “on nodal correction or residual”. The rest of the Solution Strategy param-eters are summarized in Table 4.12.69Table 4.12: Solution scheme data.Parameter Units Value CommentsEpsilon (Intermediatetime for nonlinear functions)– 1Position of intermediate time tk+εfor matrix evaluation, i.e. the point where the non-linear functions are computed. (usual values: 0.5, 1)Theta – 1Position of intermediate time tk+θ forvector evaluation i.e. the point where the equationis accomplishedTime step control – 7Controls time stepping by means of a prediction basedon the relative error deviation in the variables(relative error less than 0.001). Recommended value: 7Max number of iterationsper time step– 10Maximum number of Newton Raphson iterations pertime step. If the prescribed value is reached, time stepis reducedMax Absolute Displacement [m] 1E-4Maximum (absolute) displacement error tolerance.When correction of displacements (displacementdifference between two iterations) is lowerthan this value, convergence is achievedMax Nodal Balance Forces [MN] 1E-8Maximum nodal force balance error tolerance. If theresidual of forces in all nodes are lower than this value,convergence is achievedDisplacement Iteration Correction [m] 1E-1Maximum displacement correction per iteration(time increment is reduced if necessary)Max Abs. PI [MPa] 1E-3 Maximum (absolute) liquid pressure error toleranceMax Nodal Water Mass Balance [kg/s] 1E-8 Maximum nodal water mass balance error tolerancePI Iteration Correction [MPa] 1Maximum liquid pressure correction per iteration(time increment is reduced if necessary)70Chapter 5Base case simulation results5.1 IntroductionThe construction and impoundment of the Denis-Perron dam is simulated using the material pa-rameters summarized in Tables 4.3 to 4.10. This case represents the base case. Different aspects ofresponse like pore water pressure, degree of saturation, vertical stress, vertical and horizontal dis-placements are explored. The presented in this chapter are presented in this chapter in time series,contour plots or a spacial variation at a given snapshot in time.For each of the selected response, if available, comparison with field measurements is made.The aim of this is to give a qualitative and quantitative measurement of the model performanceand accuracy. The results are compared to the instruments investigated in Chapter 2. Other moregeneral results are explored as well.Figure 5.1 shows all the locations within the dam that are used for assessing the simulationresults. Points labelled PPB 381, PPB 342, PPB 302 and PPB 272 are used to compare simulationresults with field measurements of pore water pressures within the till core. Pressure cells measure-ments of vertical stress are compared at points CPB 251 and CPB 255. A horizontal cut through thedam is examined at chosen snapshots in time to explore the stress distribution. Inclinometer resultsduring and post construction are compared at lines labelled INB1 and INB5. The points labelledwith B0-28, B0-09 and B0-5 are used to compare simulation results with field measurements ofvertical and horizontal displacements. Additionally, B0-28 and B0-9 are also used in parallel withPoints 1 to 4 in order to investigate the progression of the degree of saturation and the pore waterpressures in the rockfill.71Figure 5.1: Summary of instruments and selected monitoring points used in analysis of sim-ulation results.The simulation time is divided into six intervals, as presented in Chapter 2, representing dif-ferent stages of construction and impoundment. When referring to a “Time [A]” when presentingresults, it refers to the end of time interval [A].A Construction to elevation 320mt = 0−400 daysB Construction to elevation 360m; Impounding of the reservoir to elevation 292mt = 400−610 daysC Completion of construction to elevation 410m; Impounding of the reservoir to elevation343mt = 610−760 daysD Impounding of the reservoir to elevation 350mt = 760−980 daysE Impounding of the reservoir to elevation 382mt = 980−1500 daysF Completion of reservoir impoundment to elevation 405mt = 1500−2320 days5.2 Pore water pressure5.2.1 General resultsThere are no available field measurements of the pore pressures within the rockfill zones. There-fore, simulation results are examined in order to understand the behaviour of the rockfill and the72occurring displacements. Figure 5.2 shows the evolution of pore water pressure for points in theupstream and downstream rockfill shells.0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](a)260280300320340360380400420Elevation (m)260280300320340360380400420Dam LevelReservoir LevelReservoir Level Model8/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/020 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](b)-0.400.40.81.2Water Pressure, [MPa]-0.400.40.81.2B0-28120 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](c)-0.2-0.16-0.12-0.08-0.040Water Pressure, [MPa]-0.2-0.16-0.12-0.08-0.040B0-934Figure 5.2: Evolution of: (a) Construction and impoundment sequence (b) Water pressure forupstream points B0-28, 1 and 2; (c) Water pressure for downstream points B0-9, 3 and4: Base case.73Referring to Figure 5.2 (b), point 1 initially starts at a small water pressure and graduallydecreases until day 650 due to drainage of the material. When a layer is constructed on top at day650 it causes a reduction in suction (increase of water pressure) due to higher saturation levels inlayer on top.The initial water pressure at B0-28 begins to drop down at a slower rate compared to points1 and 2 because of the less permeable materials underneath, restricting drainage. The pressuregradually increases when the reservoir begins impounding.Points B0-9, 3 and 4 are on the downstream side and are entirely in the rockfill material. Figure5.2 (c) shows that the rate of reduction of water pressure for points B0-9 and 3 is similar. Point 4experiences lesser reduction in water pressure due to its proximity to the less permeable and moresaturated transition zones.It is evident that suctions in the downstream are higher because of the lower saturation levels.This points to lesser settlements prevailing in this zone based on the RM formulation and theobserved mechanical behaviour of rockfill described in Appendix B.The calculated changes in porosity for two comparable points in the upstream and downstream(Points 2 and 4) are presented on Figure 5.3 (a). The purpose of this figure is to present the differ-ences between the changes of porosity for the upstream and downstream. Although the points arecomparable, the loading and wetting history are rather different for the two points due to the damscomplex layering. The decrease in porosity of the upstream shell due to raising of the reservoir levelis reflected in the plot as well. Full flooding at the observed location occurs in Time [C], notatedwith a red line. This could be also seen on Figure 5.3 (b), where the suction at the upstream sidedecreases to 0 during Time [C]. The complex behaviour of the small increase of porosity duringTime [C] is attributed to the simultaneous construction (increases in net stress) and impoundment(reduction in net stress). Construction finalizes at Time [C], but the impoundment continues all theway to end of Time [F]. This is reflected in the unloading on Figure 5.3 (a), notated with a dashedgreen line.The upstream experiences a variation in suction and mean net stress due to the rainfall history.This could easily be seen on Figure 5.3 (b). This change of suction causes “miniature” collapsesover time unlike the collapse seen for the upstream, where upon flooding porosity suddenly de-creases.After full saturation, mean net stresses become effective stresses and changes in the reservoirlevel are reflected in the changes of effective stress.74-0.2 0 0.2 0.4 0.6 0.8 1 1.2Mean net stress, p [MPa](a)0.260.2640.2680.272Porosity, n [-]Time [A]Time [B]Time [C]Time [D]Time [E,F]-0.2 0 0.2 0.4 0.6 0.8 1 1.2Mean net stress, p [MPa](b)00.040.080.120.16Suction, s [MPa]Point 2 (Upstream)Point 4 (Downstream)Figure 5.3: (a) Porosity-Mean net stress (b) Suction-Mean net stress for rockfill shells.5.2.2 Comparison with instrument dataIn addition to examining the pore water pressures in the rockfill zones, piezometer readings areavailable in the till core. Figure 5.4 exhibits the evolution of measured and calculated (model)water pressures compared at four different locations in the core. The till core is simulated with theBarcelona Basic Model, which incorporates the effects of suction. The pneumatic piezometer cellsdo not have the capability to measure the effect of suction. Therefore, before the reservoir levelreaching the elevation of the cell, zero pore pressures are recorded.750 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days]-0.200.20.40.60.811.2Water Pressure [MPa]-0.200.20.40.60.811.2PPB 272 - MeasurementPPB 272 - ModelPPB 302 - MeasurementPPB 302 - ModelPPB 342 - MeasurementPPB 342 - ModelPPB 381 - MeasurementPPB 381 - Model8/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/02Figure 5.4: Pore water pressures in the till core of the dam: comparison of measured andcalculated values for base case.At the beginning of the simulation, when the reservoir has not reached the level of the instru-ment points, the simulated pore pressures become negative and keep decreasing due to the increaseof suction in the material. This phenomenon is due to draining of water out of the material overtime, causing the saturation level to drop and therefore increase the suction based on the waterretention curve of the till core. Over time, when the water reaches the level the piezometer cells, itfully saturates the material and the prediction of the simulation matches the field measurements toa good extent. This provides confidence in the method of simulating reservoir impoundment andthe selection of appropriate hydraulic parameters for the till core.5.3 Degree of saturation5.3.1 General resultsAnother interesting aspect of the dam behaviour is the degree of saturation in the zones. It isdirectly tied to the pore water pressures through individual water retention curves for each materialzone. Examining the degree of saturation provides information of the proper (or wrong) simulationof impoundment stages of the dam.Figure 5.5 conveys the evolution of the degree of saturation for points in the upstream anddownstream rockfill shells. The “spikes” observed on the figures are attributed to the construction76of a new layer with an initial degree of saturation of around 30%, as the prescribed initial conditiondictates. At day 760, the construction of layers is completed and thus the water begins to drainfrom the rockfill. This is due to governing equations dictating flow equilibrium in the system andhigher permeability of the material.A better visualization of the impoundment stages can be seen with contour plots. The contourplots are shown at four different stages between time [A] to [F]. The dark red colour representsfully saturated material and dark blue, dry material. The levels of saturation for each of the stagesdisplays that the impoundment is simulated according to the sequence shown on Figure 5.5 (a). Asexpected, the downstream rockfill material has a low level of saturation, in the range of 3−15%770 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](a)260280300320340360380400420Elevation (m)260280300320340360380400420Dam LevelReservoir LevelReservoir Level Model0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](b)00.20.40.60.81Degree of Saturation, Sr [-]00.20.40.60.81B0-28120 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](c)00.10.20.30.4Degree of Saturation, Sr [-]00.10.20.30.4B0-9348/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/02Figure 5.5: (a) Construction and impoundment sequence. Evolution of degree of saturationfor (b) upstream points A, 1 and 2; (c) downstream points C, 3 and 4: Base case.78Figure 5.6: Contour plots for degree saturation at (a) end of time [A] (b) end of time [C] (c)end of time [E] (d) end of time [F].795.4 Vertical total stress5.4.1 General resultsThe calculated stress transfer phenomenon between the shells, transition and core is observed inFigure 5.7, where vertical stresses along a horizontal line, 60 m above the bottom of the till core(elevation 325 m), are represented. The stress distribution is explored at four stages between Time[A] and Time [F].Vertical stresses between the inner shell, transition and the core reflect the collapse calculatedfor the rockfill. Moving from Time [B] to Time [E], the initial symmetrical distribution of stressesbecomes non-symmetrical as a result of the impoundment, which induces rockfill collapse.100 125 150 175 200 225 250 275 300 325 350 375 400 425 450Y Coordinate [m]-0-0.2-0.4-0.6-0.8-1-1.2-1.4-1.6-1.8-2Vertical total stress, Syy [MPa] End of time [A]End of time [B]End of time [E]End of time [F]Outer rockfillOuter rockfillInner rockfillInner rockfill CoreTransitionFigure 5.7: Vertical stresses during construction and impoundment on a horizontal plane atelevation 60 m above the bottom boundary of till core for Times [A] to [F].Contour plots are produced for the vertical total stress Syy for the same four dates as the contourplots for the degree of saturation. They can be seen on Figure 5.8, where dark blue colour representsstresses of 3.46 MPa and dark red stresses of 0 MPa The Figures show a gradual progression of thestresses as the dam is constructed and impounded. Figure 5.8 (b) represents end of constructionand impoundment of half of the reservoir. As the reservoir is fully impounded, it can be seen thatthe stress in the upstream shell has increased due to the water weight and some stress redistributionhas taken place towards the downstream. Shifting of stresses are better seen when comparingsimulation results with measurements from pressure cells.80Figure 5.8: Contour plots for vertical total stress in MPa at (a) end of time [A] (b) end of time[C] (c) end of time [E] (d) end of time [F].815.4.2 Comparison with instrument dataVertical total pressures are compared to measured values in Figure 5.9. The simulation results areagreeable with the measured field value for point CPB 251. Field observations show a reduction ofthe total stress over time, due to horizontal displacement and shifting of the material towards thedownstream. The observation from the pressure cell at point CPB 255 shows an increase in stress,which confirms shifting of the material towards the downstream. The model seems to capturethis shifting behaviour and produces an agreeable qualitative result, but seems to under-predictthe stress at point CPB 255. The soil column above point CPB 255 is predominantly transitionmaterial. The under-prediction of the stress could come from the choice of inaccurate materialproperties for the transition zones, such as porosity, Gs, intrinsic permeability or even the initialdegree of saturation.0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days]0300600900120015001800210024002700300033003600Vertical Total Stress [kPa]0300600900120015001800210024002700300033003600CPB 251 - MeasurementCPB 251 - ModelCPB 255 - MeasurementCPB 255 - Model8/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/02Figure 5.9: Vertical stress in MPa at the bottom of the till core for points CPB 251 and CPB255: comparison of measured and calculated values for base case.5.5 Vertical displacements5.5.1 General resultsThe vertical displacements (settlements) are one of the key criterion for the safety operation of adam. Figure 5.10 shows the contour plots of settlement for different stages of the dam construc-tion and impoundment. In Figures 5.10 (a) and (b), settlements are generally uniform due to thesymmetrical geometry of the dam.82Figure 5.10: Contour plots for vertical displacements (settlement) at (a) end of time [A] (b)end of time [C] (c) end of time [E] (d) end of time [F].Once impoundment commences, settlements begin to generate more in the upstream. In Figure5.10 (c), the reservoir is halfway filled and displacements are generated more in the upstream shelf.835.10 (d) represents full impoundment of the dam and exhibits higher amount of settlements in theupstream shelf compared to the downstream one. Due to the highly dense and compacted core,much less settlements take place.5.5.2 Comparison with instrument dataInclinometersThe evolution of calculated vertical displacements with depth at inclinometers INB1 and INB5 areshown during construction and initial impoundment on Figure 5.11 and after construction and finalimpoundment on Figure 5.12.The agreement is good for the downstream inclinometer INB5 during the construction pe-riod. The reservoir impoundment does not affect the downstream, therefore, the particle breakagemechanism does not play a significant role due to the low level of saturation, making the particlere-arrangement mechanism more dominant.The same inclinometer, INB5, after the construction of the dam, has a very good agreementwith field measurements as observed on Figure 5.12. Calculated displacements are underestimatedfor inclinometer INB1 during the construction of the dam as seen on Figure 5.11. The cause is lowercompressibility of the saturated material than in reality. The under-prediction of the compressibilitystems from the attempt to simulate rockfill with particle sizes of up to 1.8 m using laboratory dataof scaled down rockfill with particle sizes of up to 0.06 m. This discrepancy between laboratoryand field compressibility values is due to the effect of particle size. In Chapter 6, the effect ofparticle size on the particle breakage mechanism is examined thoroughly.Long term settlements in the upstream shell (INB1) are shown on Figure 5.12. The settlementtrend is approximated to an extent. Settlements at elevations 260 to 320 m are low because collapsein those zones already occurred during initial construction and impoundment. Post-constructionsettlements are measured with reference date 09/10/1998, when reservoir level has reached 320 m.The settlements at elevations greater than 320 m, are prone to gradually increase due to the slowimpoundment of the reservoir until finally reaching 400 m in the year 2003. It has to be notedthat the post construction inclinometer measurements for INB1 could not be considered reliable,as mentioned in Chapter 2.840 -250 -500 -750 -1000 -1250 -1500 -1750Settlement during construction (mm)INB-1 USBR260270280290300310320330340350360370380390400410Elevation (m)Time A - MeasurementTime A - ModelTime B - MeasurementTime B - ModelTime C - MeasurementTime C - ModelReservoir Level0 -250 -500 -750 -1000 -1250 -1500 -1750Settlement during construction (mm)INB-5 USBR260270280290300310320330340350360370380390400410Elevation (m)Time A - MeasurementTime A - ModelTime B - MeasurementTime B - ModelTime C - MeasurementTime C - ModelFigure 5.11: Calculated and measured vertical settlement for inclinometers INB1 and INB5after construction for stages [A] to [D]: base case. Elevation 260 corresponds to bottomof the rockfill shell.100 0 -100 -200 -300 -400 -500 -600 -700 -800Settlement after construction (mm)INB-1260270280290300310320330340350360370380390400410Elevation (m)Time D - MeasurementTime D - ModelTime E - MeasurementTime E - ModelTime F - MeasurementTime F - Model0 -50 -100 -150 -200 -250 -300 -350 -400 -450 -500Settlement after construction (mm)INB-5260270280290300310320330340350360370380390400410Elevation (m)Time D - MeasurementTime D - ModelTime E - MeasurementTime E - ModelTime F - MeasurementTime F - ModelFigure 5.12: Calculated and measured vertical settlement for inclinometers INB1 and INB5after construction for stages [E] to [G]: base case. Elevation 260 corresponds to bottomof the rockfill shell.85Observation terminalVertical displacements are measured at the surface crest and downstream face during the wholeprocess of construction and impoundment at chosen locations. Simulation results are comparedwith the measurements as seen on Figure 5.13. Point B0-05 has very good approximation of thefield measurement. Points B0-28 and B0-9 have a good qualitative approximation of the settlementtrend, but are inaccurate by 20− 40%. This under-prediction is the result of a few factors. Thefirst one is, as discussed for inclinometer INB1, the particle size effect. This effect is thoroughlydiscussed in Chapter 6. There are other physical causes for the discrepancy between measurementsand simulations such as possible unreliable field measurements. Generally, there could be veryshallow surface displacements, which are not representative of the actual deformations in the area.This could cause the observation terminals to show higher displacements, when in reality they aresmaller. Another factor could be a reported shear crack on the crest of the dam. The crack presencecould lead to higher measured vertical and horizontal displacements.0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days]-1100-1000-900-800-700-600-500-400-300-200-1000100Vertical Displacement, Dz [mm]-1100-1000-900-800-700-600-500-400-300-200-1000100B0-28 MeasurementB0-28 ModelB0-9 MeasurementB0-9 ModelB0-5 MeasurementB0-5 Model8/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/02Figure 5.13: Vertical displacements for points B0-28, B0-9 and B0-5 along the dam crest:comparison of measured and calculated values for base case.5.6 Horizontal displacements5.6.1 General resultsContour plots of the horizontal displacements are shown on Figure 5.14. They help to visualize theforming shear planes within the dam and progression of material movement. The pre-impoundmentspatial distribution of horizontal displacements is seen on Figures 5.14 (a) and (b).86Figure 5.14: Contour plots for horizontal displacements in metres at (a) end of time [A] (b)end of time [C] (c) end of time [E] (d) end of time [F].87Once impoundment commences, downstream horizontal displacement rates increase towardsthe upstream side. Downstream horizontal displacements reach to 1.4 m and the upstream only to0.65 m.5.6.2 Comparison with instrument dataThe complete evolution of horizontal displacements at observation points B0-28, B0-9 and B0-5are shown on Figure 5.15. The horizontal displacements at point B0-28 are underestimated by afactor of two but follow the general trend. Point B0-9’s calculated horizontal displacements agreewith the observation. The horizontal displacements for point B0-5 are significantly overestimated,but follow the trend of the measured displacement curve to a good extent. The over-predictionof displacements occurs during the final stage of the construction process, ending at day 760. Asimilar phenomenon is observed in the analysis of Beliche dam by Alonso et al. (2005), wherehorizontal displacements from the mid section of the dam are over-predicted. This could probablybe due to the model formulation and generation of excessive deviatoric stresses in that zone.0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days]010020030040050060070080090010001100Horizontal Displacement, Dy [mm]010020030040050060070080090010001100B0-28 - MeasurementB0-28 ModelB0-9 MeasurementB0-9 ModelB0-5 MeasurementB0-5 Model8/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/02Figure 5.15: Horizontal displacements for points B0-28, B0-9 and B0-5 along the dam crest:comparison of measured and calculated values for base case.Some additional cases such as modifying rockfill compressibility, to account for scale effects,and exploring rockfill permeability variation are examined in Chapter 6.5.7 SummaryThe base case is defined based on the basis of material parameters estimated from laboratory testsand literature. Due to the complexity of the constitutive models used, the provided laboratory data88has limited capabilities of providing all of the necessary material parameters. The extensive lit-erature available provided a solid basis for assuming some of those parameters. Generally, thesimulation outcome is highly successful. The simulation results matched fairly well field measure-ments for few different responses.The piezometer measurements in the core matched qualitatively and quantitatively the simu-lation results with an error of less than 10%. Therefore, it gives confidence in the impoundmentstages simulated and the chosen hydraulic parameters for the zones.Simulation results for total stress at the bottom of the core approximate the general trend ofpressure cell measurements. Some interesting stress transfer phenomena is captured by the sim-ulation due to movement of material towards the downstream and the impoundment. The samephenomena is observed by the pressure cells. The discrepancy with the final measurements couldbe attributed to poor approximation of the transition zone material parameters.Simulations results for settlements during construction and initial impoundment for the up-stream and downstream shells, approximate the behaviour to a good extent as well. The resultsmatch qualitatively the inclinometer measurements, which confirms the correct implementation ofthe construction stages. The results also approximate well the response in a qualitative mannerwith an error of less than 20%.There are discrepancies between the long term displacement measurements and the simulationresults. Generally, the trend is approximated well, but the final simulated settlements are less thanthe one observed in the field. For clarification purposes, it has to be noted that material parametersfor the base were not adjusted to “match” instrument data.On another subject, it has to be appreciated that, even though the constitutive models are fairlycomplex and capture the behaviour of rockfill, simulating a massive structure like a dam is a diffi-cult task. Simplifying a large 3D structure and simulating it in 2D could lead to miss-representationof reality. Weather conditions, in particular rainfall, was simulated successfully but accounting forthe hard winter conditions was not done. Other sources of error could include faulty instrumentsor miss-representation of the actual construction process.89Chapter 6Complementary simulations6.1 IntroductionThe reference case, based on available laboratory results and literature, provides a satisfactorymodel response. However, discrepancies in measured upstream and downstream horizontal andvertical displacements remain.Several reasons for those discrepancies are proposed in this chapter. The validity of scaledsamples is a key issue. Compressibility is expected to increase with particle size, due to the sizeeffects of crack propagation. Also, two laboratory samples are hardly representative of the wholein-situ material in such a large structure. This effect has proven to be quite significant and thereforea more substantial portion of this chapter focuses on exploring this phenomenon. An attempt ismade to quantify the scaling effect.Rockfill hydraulic properties are estimated based on literature, but the actual in-situ values areunknown. Properties like the water retention curve, initial saturation and permeability are unknownand are derived based on similar rockfill material from other dams. Exploring the effect of differentwater retention curves is not a part of this research due to the complexity of the problem. Instead, aparameter such as intrinsic permeability, is examined because it provides a more clearer perspectiveof its effect.6.2 Sensitivity analysis on rockfill compressibilityThe objective of this section is to address the effect of particle size on the compressibility param-eters through a numerical simulation. First, based on previous research, the connection between90particle size and the compressibility of rockfill and other potential factors needs to be established.6.2.1 Effect of particle scale on rockfill compressibilityTests show that the external stress capable of breaking particles, (σext) f , depends on the particlesize and can be defined as(σext) f ∝ d−αscaling (6.1)where d is the average particle size and αscaling varies between 0.3 and 0.5 for the tested materials.For more information on the derivation, refer to Oldecop and Alonso (2013a). An explanation forthe phenomenon is that more defects, cracks and micro-cracks in a bigger particle than a smallerone provides more stress concentration zones and thus weakens the particle. Therefore the biggerthe particle, the more particle breakage occurs. Large oedometer tests are impractical and expensiveand the maximum grain size that can be tested is 150-200 mm (Oldecop and Alonso, 2013a).Most dams have a maximum particle size of 0.5-1 m, which is impossible to test in a laboratory.Grain size distributions may be scaled down in an attempt to preserve the behaviour of the sampledimensions. However, the scale effects still have to be addressed in the numerical simulation.Scaling up of λ d0 is necessary because it governs the particle breakage mechanism, which, asdiscussed before, depends on the particle size. The parameter λi on the other hand, governs theparticle re-arrangement mechanism, which is not reported to be dependent on the particle size.6.2.2 Simulation resultsTo evaluate the effect of scaling regarding the rockfill material from Denis-Perron, simulation re-sults with no scaling are examined and simulations results with scaling are explored as well.Comparison of the simulation results to the settlement measurements at INB1 and INB5 hasbeen done initially with using the λ d0 = 0.009 directly calibrated based on the oedometer test dataand no scaling applied. Three more simulations have been performed with λ d0 = 0.012; 0.015; 0.018.The results of those simulation are presented for four different time intervals. The first two timeintervals, [B] and [C], represent the response during construction and initial impoundment. Thelast two intervals, [E] and [F], represent the long term behaviour until the full impoundment of thedam.For base case where λ d0 = 0.009, results show under-prediction of the settlements recorded atINB1 in the zones where the rockfill has been exposed to the water action but good predictionsare otherwise for evident both inclinometers. Judging by the results from Figures 6.1 and 6.2, the91compressibility parameter λ d0 , responsible for the wet behaviour of rockfill, has to be increased, orin other words scaled up from the one calibrated based on the oedometer test. This is supportedalso by the background discussed regarding the effect of particle breakage in the previous section.Both inclinometers are predominantly within the inner shells of the dam. Therefore, the effectof the outer shell settlements cannot be captured by the inclinometers. Hence, the more representa-tive value λ d0 for the inner shell is estimated based on comparing the settlement from the numericalsimulations and the data of INB1 and INB5.Figure 6.1: Calculated and measured vertical displacements for INB1 and INB5 at Time [B]for four differen values for λ d0 .Furthermore, the best match of the settlements is achieved with scaling the λ d0 of the inner shellby a factor of 1.65 from the value of 0.009 obtained in the lab test, resulting in λ d0 = 0.015. Thehigher value of λ d0 = 0.018 over-predicts the settlements for end of time [B] for both INB1 andINB5 and also for end of time [C] for INB5. The scaling effect is less obvious in the post con-struction response of the dam. Figures 6.3 and 6.4 illustrate this and is evident that the differencein settlement between simulations with λ d0 = 0.012;0.015 and 0.018 is negligible. Generally, theresults illustrate that the scaled λ d0 provides an improved approximation of the field settlementswith better agreement with the field data, hence a better capturing the compressibility of large wetparticles.92Figure 6.2: Calculated and measured vertical displacements for INB1 and INB5 at Time [C]for four differen values for λ d0 .Figure 6.3: Calculated and measured vertical displacements for INB1 and INB5 at Time [E]for four differen values for λ d0 .93Figure 6.4: Calculated and measured vertical displacements for INB1 and INB5 at Time [F]for four differen values for λ d0 .6.2.3 Quantification of size effectTo asses and quantify the particle size effect, a scaling law has to be put in place. Assumingassemblies of uniform spherical particles and linear stress-strain relationship, a scaling law sim-ilar to Equation 6.1 is proposed by Oldecop and Alonso (2013a) for the delayed compressibilityparameterλ ∝ dαscaling (6.2)λ d = λ d0(dd0)αscaling(6.3)Equation 6.3 follows directly from Equation 6.2, where d is the maximum particle size of theprototype (field) material; d0 is the maximum particle size of the model (laboratory) material; λ dis the compressibility parameter of the prototype and λ d0 is the compressibility parameter of themodel. The exponent αscaling is a function of the density of the aggregate and the type of rockand governs the severity of scaling. In the work of Oldecop and Alonso (2013a) a limestonematerial has been presented, which has α values varying between 0.33 and 0.5 for dense andloose aggregates respectively. Based on Equation 6.3, a plot on Figure 6.5 is presented to show thevariation of λ d with different αscaling values, where SF = d/d0 is a scaling factor, relating prototype94dimensions to model dimensions.Figure 6.6 shows the scaling law from Equation 6.3 applied to laboratory data. The laboratorydata is related to the compressibility of two sets of samples, both with uniform particle sizes (40-30mm, 30-20 mm; 25-20 mm; 20-10 mm) but different densities (one loose with e = 0.947 and onedense with e = 0.5). The scaling law of Equation 6.3 is used by (Oldecop and Alonso, 2013a) toscale down the λ d of each sample to the corresponding λ d0 of the sample with the smallest particlesize.In this process it has been founded that “taking d0 as the minimum particle diameter tested,the size effect disappears, provided αscaling = 0.5 for the loose gravel and αscaling = 0.33 for thedense aggregate”. The conclusion from this process is that “the αscaling coefficient and, therefore,the intensity of scale effects depends on aggregate density”.10 20 30 40Scaling factor, SF = d/d0 [-]123456ld /ld 0 [-]a = 0.1a = 0.2a = 0.3a = 0.4a = 0.5Figure 6.5: Variation of compressibility parameter λ d for different αscaling values.9510 20 30 40 50Maximum initial particle size, [mm]b)0.0120.0160.020.0240.028Scaled compressibility parameter l / (d/d0)ae = 0.947, d0 = 20mme = 0.502, d0 = 25mma= 0.5a= 0.310 20 30 40 50Maximum initial particle size, [mm]a)0.010.0150.020.0250.030.0350.04Coefficient of compressibility, le = 0.947e = 0.502Figure 6.6: (a) Compressibility for samples with different maximum particle size at two dif-ferent void ratios (b) Corrected compressibility of limestone material to account forscale effect. Modified from Oldecop and Alonso (2013a).With reference to Figure 6.5, the parameter α for the rockfill material of the SM-3 dam can becalculated when the scaled λ d0 (presented above) and field to laboratory SF are known for the ma-terial. For the inner and outer shells, the values of SF could be calculated based on their maximumparticle sizes. Assuming the maximum particle size tested in the oedometer is about 60 mm theSF = d/d0 can be calculated, where d0 is the maximum particle size of the tested material and dis the Dmax of the material in the field. For the inner shell, SF = d/d0 = 900/60 = 15, and for theouter shell SF = d/d0 = 1800/60= 30. Based on this information and given the obtained factor of1.65 for scaling of the compressibility parameter of the inner shell, parameter αscaling is estimatedas 0.19 for the inner shell.Having no instrumentation within the upstream outer shell makes it impossible to explore thisscaling effect for this material. Therefore, it is assumed the inner and outer shells behave similarlyand share the same intensity of scaling parameter αscaling = 0.19. Earlier, it has been shown that theintensity of scaling parameter α depends on the density (void ratio) of the material. The presentstudy suggests αscaling = 0.19 for the case of Denis-Perron dam with an approximate void ratio of0.37 for the inner shell. This information in combination with the data from Figure 6.6 provides arelation between αscaling and e0 (initial void ratio).To take it one step further, an αscaling value can be determined for Beliche dam as well. In thepaper of Alonso et al. (2005) the scaling factor SF =D50, f ield/D50,lab = 100/18 and the compress-ibility index has been increased with 50%. This translates to 1.5 = (100/18)αscaling from Equation966.3, which yields αscaling,Beliche = 0.236. The reported initial void ratio for the rockfill shells inBeliche dam is 0.538. A plot of the relation between αscaling and void ratio can be seen on Figure6.7Figure 6.7: Variability of parameter αscaling based on void ratio for laboratory data. Data fromOldecop and Alonso (2013a) and simulation results of Denis-Perron and Beliche Dam.The data points provided on Figure 6.7 give an initial estimation of what the relation is betweenαscaling and the void ratio. In order to establish a more reliable correlation, the plot has to bepopulated with more data points. This could be done by including more laboratory data, otherlarge scale simulations or even results of a discrete element modelling of a large scale laboratorytest.The validity of determining the scaling effect needs to be addressed. Firstly, the compressibilityparameter that is affected by scaling has to be established. As discussed, this parameter is the oneresponsible for the particle breakage phenomenon and dictates the maximum compressibility ofthe particle at full saturation. Secondly, in order for the scaling methodology to be valid, theeffect of this parameter has to be isolated. The parameter is generally influenced by the level ofsaturation, the hydraulic properties of the material and the constitutive parameter of RM, αs andβ . At full saturation, the hydraulic properties of rockfill and the constitutive parameter becomeirrelevant, because λ d0 reaches its maximum value. Therefore, comparison of the result betweenthe simulations with applied parameter scaling and the field measurements is apparent for the fullysaturated areas, which are in INB1. The results for INB5 are presented for consistency purposes97and even though the effect of particle size is harder to isolate for the downstream zone, havingaccurate approximation of the settlements brings a level of confidence to the simulation approach.6.3 Sensitivity analysis on rockfill permeabilityAnother reason for discrepancies that could be omitted on first sight, is the effect of the hydraulicparameters in rockfill. In this section, the permeability is discussed in particular. The value of thepermeability for the rockfill is estimated based on available literature and deserves attention. Otherhydraulic properties, like the water retention curve and the change of permeability with saturation,affect the response in a unclear manner that would be difficult to quantify.A change in the rockfill permeability implies a change in the suction field. Lower water po-tential gradients are caused by increasing the rockfill permeability. This results in a more limitedreduction of initial suction. Therefore, less collapse in the rockfill should be expected.6.3.1 Simulation resultsTwo simulations are performed to examine the permeability effect of rockfill by increasing anddecreasing the value from the original one of krockfill = 1× 10−10 m2. The first one has a tenfoldreduction of rockfill permeability, krockfill = 1× 10−11 m2. The second, has a tenfold increase ofpermeability - krockfill = 1×10−9 m2.Comparison of the water pressure field and the displacements to the Base Case simulation andfield measurements (if available), are discussed in this section.6.3.2 DiscussionThe water pressure within the rockfill is affected by the permeability of the material. Figures 6.8 (a)and (b) exhibit this behaviour - lower permeability increases water pressure and higher permeabilityreduces it. This results in lower suction for the lower permeability and higher suction values forthe higher permeability cases.Displacements are generally consistent with the expectation. Figures 6.9 suggest that lowerpermeability case yields higher settlements and the higher permeability one yields lower settle-ments. However, the effect on the horizontal displacements are less clear as can be seen on Figure6.10. In locations B0-28 and B0-9, the higher permeability case yields more accumulated horizon-tal displacements than the lower permeability case.Chapter 7 presents a summary of the thesis findings and a direction for future research in thefield of rockfill mechanics.98Figure 6.8: (a) Construction sequence (b) Water pressure for upstream points (c) Water pres-sure for downstream points.990 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](b)-1000-900-800-700-600-500-400-300-200-1000Vertical Displacement, Dz [mm]-1000-900-800-700-600-500-400-300-200-1000Low PermeabilityHigh PermeabilityBase CaseMeasurement0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](c)-400-350-300-250-200-150-100-500Vertical Displacement, Dz [mm]-400-350-300-250-200-150-100-5000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](d)-550-500-450-400-350-300-250-200-150-100-500Vertical Displacement, Dz [mm]-500-450-400-350-300-250-200-150-100-500Low PermeabilityHigh PermeabilityBase CaseMeasurement0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](b)-1000100200300400500600700Horizontal Displacement, Dz [mm]-1000100200300400500600700Low PermeabilityHigh PermeabilityBase CaseMeasurement0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](c)-1000100200300400500600700800Horizontal Displacement, Dz [mm]-1000100200300400500600700800Low PermeabilityHigh PermeabilityBase CaseMeasurement0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](d-100010020030040050060070080090010001100Horizontal Displacement, Dz [mm]-100010020030040050060070080090010001100Low PermeabilityHigh PermeabilityBase CaseMeasurement0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](a)260280300320340360380400420Elevation (m)260280300320340360380400420Dam LevelReservoir LevelReservoir Level Model8/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/020 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](a)260280300320340360380400420Elevation (m)260280300320340360380400420Dam LevelReservoir LevelReservoir Level Model8/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/02B0-28B0-28B0-9B0-5B0-9B0-5Figure 6.9: Vertical displacements for markers B0-28, B0-9 and B0-5 for the Base case, LowPermeability and High permeability cases.1000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](b)-1000-900-800-700-600-500-400-300-200-1000Vertical Displacement, Dz [mm]-1000-900-800-700-600-500-400-300-200-1000Low PermeabilityHigh PermeabilityBase CaseMeasurement0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](c)-400-350-300-250-200-150-100-500Vertical Displacement, Dz [mm]-400-350-300-250-200-150-100-5000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](d)-550-500-450-400-350-300-250-200-150-100-500Vertical Displacement, Dz [mm]-500-450-400-350-300-250-200-150-100-500Low PermeabilityHigh PermeabilityBase CaseMeasurement0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](b)-1000100200300400500600700Horizontal Displacement, Dz [mm]-1000100200300400500600700Low PermeabilityHigh PermeabilityBase CaseMeasurement0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](c)-1000100200300400500600700800Horizontal Displacement, Dz [mm]-1000100200300400500600700800Low PermeabilityHigh PermeabilityBase CaseMeasurement0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](d-100010020030040050060070080090010001100Horizontal Displacement, Dz [mm]-100010020030040050060070080090010001100Low PermeabilityHigh PermeabilityBase CaseMeasurement0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](a)260280300320340360380400420Elevation (m)260280300320340360380400420Dam LevelReservoir LevelReservoir Level Model8/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/020 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Time, t [days](a)260280300320340360380400420Elevation (m)260280300320340360380400420Dam LevelReservoir LevelReservoir Level Model8/27/96 2/27/97 8/27/97 2/27/98 8/27/98 2/27/99 8/27/99 2/27/00 8/27/00 2/27/01 8/27/01 2/27/02 8/27/02B0-28B0-28B0-9B0-5B0-9B0-5Figure 6.10: Horizontal displacements for markers B0-28, B0-9 and B0-5 for the Base case,Low Permeability and High permeability cases.101Chapter 7Summary and future research7.1 Summary of researchThe response of rockfill dams presents a lot of challenges due to the uncertainties associated withrockfill behaviour. A fundamental variable governing rockfill behaviour is the effect of suctioncaused by the water action within the rockfill cracks. Some methodologies are already availablethat incorporate the role of suction, but are not based on physical phenomena and cannot takeinto account environmental factors, such as precipitation and/or evaporation. The thesis exploreda modelling technique that is based on fundamentals of fracture mechanics, which is achievedthrough an implemented set of constitutive models in a fully coupled three phase finite elementplatform called Code Bright (2015). The constitutive models used are the Barcelona Basic Modeland the Rockfill Model, which captures the unsaturated behaviour of soils and rockfill respectively.The research focuses on verification and validation of this particular modelling techniquethrough an application of the RM in a numerical simulation of the well instrumented Denis-Perronrockfill dam. Denis-Perron dam is a zoned earth dam with compacted glacial till core and rock-fill shoulders. Instrumentation data for a period of 6 years during construction, impoundment andoperation was provided by Hydro-Que´bec.Prior to modelling of Denis-Perron, a validation stage was carried out through simulating Be-liche dam, which has been previously analysed by Alonso et al. (2005). The numerical model ofDenis-Perron captures the construction stages, impoundment and the rainfall history recorded onsite. Limited laboratory data was used to characterize the materials and calibrate constitutive modelparameters. Ideally, the constitutive models require suction controlled tests to determine materialparameters. In the case of Denis-Perron, the glacial till core’s parameter calibration is carried out102based on a suction controlled oedometer tests from a very similar material described in Watabeet al. (2000). For the rockfill shoulders, two oedometer tests under flooded and dry conditions areused for calibration. The oedometer test data was not sufficient to determine all necessary param-eters, including the hydraulic ones. Therefore, some of them were estimated based on availableliterature.Despite the limitations posed by the methodology of determining model parameters and lack oflaboratory data, the general dam response has proven to be quite satisfactory. The accuracy of theresults for settlements, horizontal displacements, stresses and pore pressures is within an acceptablerange, considering all the uncertainties surrounding an analysis of such a large structure.One of the contributions of the author is the successful simulation of the construction, im-poundment and rainfall stages of the Denis-Perron dam. The current work can be used as a com-prehensive guide to modelling future rockfill structures. This includes the creation of the numericalmodel, calibration of material parameters using laboratory data and an in depth analysis of the re-sults. Another contribution of the author is the attempt to quantify the effect of particle size. It hasbeen shown in the past that the compressibility of coarse grained material in laboratory experimentsis reduced due to the smaller particle sizes tested. To account for this effect, the compressibility hasbeen corrected through a back analysis of field measurements by using the numerical simulation.The results show a relation between the amount of compressibility increase and the void ratio ofthe sample. Finally, the effect of rockfill permeability on the dam settlements is explored as well.7.2 Recommendations for future researchThe field measurement data for Denis-Perron is only available for the period between 1997 and2003. This does not allow assessing the performance of the numerical model regarding long termdeformations. Gaining access to records between 2003 and 2017 would give valuable informationand means compare long term simulation results to the field measurements.Another direction for future research is studying and quantifying the effect of particle size onrockfill compressibility, using the approach adopted in this thesis. Modeling rockfill structureswith available records of instrument measurements and laboratory data, could help establish evenfurther the relation between particle size and the void ratio of the material. The scale effect couldalso be examined through simulations of oedometer and triaxial tests, using the Discrete ElementMethod (DEM). Unlike large scale testing apparatus, DEM is not limited by the size of the particletested, even thought the level of complexity revolving around the model creation is very high.Finally, large scale oedometer and triaxial tests with existing or newly constructed laboratory103equipment could be performed, to continue the research on the different types of rockfill. Althoughrockfill’s collapse is governed by a crack propagation mechanism, it is highly dependent on thetype of minerals and structure of the rockfill. Therefore, it is necessary for future researchers tocarry on a comprehensive set of tests to characterize the different rockfill materials.104BibliographyAlonso, E. E., Gens, A. and Josa, A. (1990), ‘A constitutive model for partially saturated soils’,Ge´otechnique 40(3), 405–430.Alonso, E. E., Olivella, S. and Pinyol, N. M. (2005), ‘A review of beliche dam’, Ge´otechnique55(4), 267–285.Alonso, E. E., Olivella, S., Pinyol, N. M., Soriano, A. and Esteban, F. 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(2011), ‘Intrinsic permeability of materials ranging fromsand to rock-fill using natural air convection tests’, Canadian Geotechnial Journal 48, 679–690.Lafleur, J. (1998), Projet sainte-marquerite (site sm3) e´chantillons de matriaux utilise´s dans lenoyau du barrage (zone 1)., Technical report, Centre de de´veloppement technologique (C.D.T),E´cole Polytechnique de Montre´al, Montreal, Canada.Marachi, N. D., Chan, C. K., Seed, H. B. and Duncan, J. M. (1969), Strength and deformationcharacteristics of rockfill materials, Technical report, Department of Civil Engineering,University of California, Berkley, California, USA.106Michalske, T. and Freiman, S. (1982), ‘A molecular interpretation of stress corrosion in silica’,Nature 295, 511–512.Naylor, D. J., Maranha, J. R., Neves, E. M. and Pinto, A. A. (1997), ‘A back-analysis of belichedam’, Ge´otechnique 47(2), 221–233.Oldecop, L. A. and Alonso, E. (2007), ‘Theoretical investigation of the time-dependent behaviourof rockfill’, Ge´otechnique 57(3), 289–301.Oldecop, L. A. and Alonso, E. E. (2001), ‘A model for rockfill compressibility’, Ge´otechnique51(2), 127–139.Oldecop, L. A. and Alonso, E. E. (2004), ‘Testing rockfill under relative humidity control’,Geotechnical Testing Journal 27(3), 269–278.Oldecop, L. A. and Alonso, E. E. (2013a), Rockfill mechanics, in ‘Advances in UnsaturatedSoils’, Taylor & Francis Group, London, UK.Oldecop, L. A. and Alonso, E. E. (2013b), ‘Rockfill mechanics’, Presentation at FirstPan–American Conference on Unsaturated Soils (UNSAT2010). Cartagena de Indias,Colombia.Parkin, A. (1977), ‘The compression of rockfill’, Australian Geomechanics Journal G7(4), 33 –39.Pe´loquin, E. (2015), Call for proposalworkshop on numerical analysis for embankment androckfill dams; verification & validation for better prediction, Technical report, Hydro-Que´bec,Que´bec, Canada.Saboya Jr., F. and Byrne, P. (1993), ‘Parameters for stress and deformation analysis of rockfilldams’, Canadian Geotechnical Journal 30, 690–701.SNC-Shawinigan (1996), Ame´negament hydro-e´lecetrique sainte-marquerite-3 site sm-3: Barrageet travaux connexes, Rapport de conception, lot 3040, Hydro-Que´bec, Que´bec, QC, Canada.van Genuchten, M. T. (1980), ‘A closed-form equation for predicting the hydraulic conductivity ofunsaturated soils’, Soil science society of America journal 44(5), 892–898.Vaunat, J. (2015), ‘Mechanical constitutive laws, behaviour of unsaturated soils’, Short CourseNotes. Department of Geotechnical Engineering and Geosciences, UPC, Barcelona, Spain.Watabe, Y., Leroueil, S. and Le Bihan, J. P. (2000), ‘Influence of compaction conditions onpore-size distribution and saturated hydraulic conductivity of a glacial till’, CanadianGeotechnial Journal 37, 1184–1194.107Appendix AValidation Problem – Beliche damsimulationA.1 Problem informationThe problem chosen for validation of using Code Bright and the constitutive models successfullyis the Beliche Dam. The dam is 54 m high and has a standard design: central clay core and tworockfill shells. The size of the dam is significantly smaller compared to the Denis-Perron dam andthe geometry less complicated. The reason for choosing this dam is due to the numerous studiesconducted on it and, in specific, the work of Alonso et al. (2005). In the study, the dam wasmodelled using Code Bright and the implemented Rockfill Model (RM). The goal is to reproducethe simulation results by Alonso et al. (2005), using the calibrated material parameters from thepaper and the simulation methodology.Figure A.1 shows the layers and mesh of the performed simulation in 2005. In comparison,Figure A.2 shows the validation layers and mesh used. The material parameters used are extractedfrom the same paper and are summarized in Tables A.1, A.2 and A.3. The values in not availablein the study from 2005 and were estimated.108Figure A.1: (a) Simulation layers and (b) Mesh from (Alonso et al., 2005)Figure A.2: (a) Simulation layers and (b) Mesh from validation problem109Table A.1: Mechanical parameters for rockfill.Definition of Parameters Symbol UnitsRockfill ShouldersOuter Shell Inner ShellElastic behaviourElastic Modulus E MPa 180 150Poisson’s ratio ν – 0.3 0.3Plastic behaviourPlastic virgin instantaneous compressibility λ i−κ MPa−1 0.010 0.025Virgin clastic compressibility for saturated conditions λ d0 MPa−1 0.01 0.028Parameter describing the rate of change of clastic compressibility with total suction αs – 0.003 0.01Slope of critical-state strength envelope for dry conditions Mdry – 1.9 1.75Slope of critical-state strength envelope for saturated conditions Msat – 1.8 1.3Parameter that controls the increase in cohesion with suction ks – 0 0Threshold yield mean stress for the onset of clastic phenomena py MPa 0.01 0.01Parameter that defines the non-associativeness of plastic potential α – 0.3 0.3CreepCreep coefficient for saturated conditions µ MPa−1 0.0012 0.0012Parameter that controls the influence of suction on creep rate β c – 0.083 0.083ViscoplasticityFluidity parameter Γ s−1 100 100Flow function exponent N – 5 5110Table A.2: Mechanical parameters for the till core.Definition of parameter Symbol Units ValueElastic behaviourElastic modulus E MPa 100Poissons ratio ν – 0.4Plastic behaviourVirgin compressibility for saturated conditions λ (0)−κ MPa−1 0.02Parameter that establishes the minimum value of the compressibility coefficient for high values of suction r – 0.7Parameter that controls the rate of increase in stiffness with suction β MPa−1 1.2Reference stress pc MPa 0.02Slope of critical-state strength line M – 0.88Parameter that controls the increase in cohesion with suction ks – 0.1Parameter that defines the non-associativeness of plastic potential α – 0.3ViscoplasticityFluidity parameter Γ s−1 1000Flow function exponent N - 61110 -0.2 -0.4 -0.6 -0.8 -1 -1.2 -1.4Vertical Displacement, [m]Extensometer I1(a)0510152025303540455055Y Coordinate, [m]Time B - AlonsoTime C - AlonsoTime E - AlonsoTime B - SimulationTime C - SimulationTime E - Simulation0 -0.2 -0.4 -0.6 -0.8 -1 -1.2 -1.4Vertical Displacement, [m]Extensometer I3(a)0510152025303540455055Y Coordinate, [m]Time A - AlonsoTime C - AlonsoTime E - AlonsoTime A - SimulationTime C - SimulationTime E - Simulation0 -0.2 -0.4 -0.6 -0.8 -1 -1.2 -1.4Vertical Displacement, [m]Extensometer I6(a)0510152025303540455055Y Coordinate, [m]Time A - AlonsoTime C - AlonsoTime E - AlonsoTime A - SimulationTime C - SimulationTime E - SimulationFigure A.3: Vertical displacements at position for extensometers (a) I1, (b) I3 and (c) I6 forconstruction stages [A] to [E]. Validation simulation results and computed results fromAlonso et al. (2005)Table A.3: Hydraulic parameters for rockfill, till core and foundationDefinition of parameter Symbol UnitsValueRockfill Till Core FoundationIntrinsic Permeability k m2 2×10−11 8×10−15 3×10−12Water Retention Curve (Van Genuchten, 1980)Pressure at T = 20◦ P0 MPa 0.01 0.5 0.01Maximum Saturation Sls – 1 1 1Residual Saturation Slr – 0 0 0Exponent Defining Curve Shape λ – 0.6 0.27 0.3Initial Suction (applied as an initial condition to model) s0 MPa 20 0.5 0A.2 Simulation results comparisonTwo figures have been chosen to be reproduced from the paper of 2005. The first one is Figure20, showing vertical settlements for extensometers in the upstream rockfill (I1), the core (I3) andthe downstream rockfill (I6). The results are compared in Figure A.3. Time [A] to [E] are definedbelow.A Construction to elevation 29 m (t=0-180 days)B Construction to elevation 47 m (t=180-360 days)112C Impounding of the reservoir to elevation 29m (t=360-420 days)D Completion of construction to elevation 55 m (t=420-450 days)E Impounding of reservoir to elevation 49 m (t=450-1500 days)The results for extensometer I1 in the dry rockfill over-predicts the settlements for times [A] and[C]. This is probably due to the difference in the retention curves used, generating more compress-ibility of the rockfill in the impounding stage. At time [E], the two simulations match well becausethe rockfill material is fully saturated. At full saturation the compressibility is at its maximum,λi + λ d0 , because the suction s = 0 and the water retention curve does not have any effect. Forextensometer I3, the differences for times [A] and [C] probably come from the layer thickness’.The second figure chosen is Figure 22 (a) from the work of Alonso et al. (2005). It is chosenin order to monitor if the stress prediction of the two simulations match along a horizontal cut 13m above the boundary of the model. Figure 22 (a) reproduced for times [A], [B] and [E]. Thecomparison in results can be seen on Figure A.4.40 80 120 160 200 240Distance, [m]-0-0.1-0.2-0.3-0.4-0.5-0.6-0.7-0.8-0.9Vertical Stress, [MPa]Time A - AlonsoTime B - AlonsoTime E - AlonsoTime A - SimulationTime B - SimulationTime E - SimulationFigure A.4: Validation simulation and simulation results from Alonso et al. (2005) of verti-cal stresses for stages [A], [B] and [E] on a horizontal plane at elevation 13 m aboveboundary of clay core.The shape of the stress plot is illustrated effectively and the differences come from the dis-cretization and layering of the model. The abrupt transitions captured by the model come from the113change in materials and the collapse of the rockfill and are captured by the validation simulation.Generally, the results are satisfactory and bring a level of confidence in the use of the software andits features to begin modelling the response of the Denis-Perron dam.A.3 Simulation method differencesThere were a few differences in the simulation methodology that cause deviations in the results.These are listed below.• Geometry and layering differences. Precise CAD drawings or coordinates of the dam are notavailable and therefore are estimated. The numerical model layers in Alonso et al. (2005) aresmaller than the ones represented. This could cause a difference in the stress and thereforethe settlements. This can be seen from the comparison of Figures A.1 (a) and A.2 (a)• Reproducing the same mesh is not possible. The two meshes can be seen on Figures A.1 (b)and A.2 (b)• Way of simulating impoundment. In the current version of Code Bright, a simpler and moreeffective way of simulating reservoir filling is available. The method is by simulating thewater as a material with linear elastic properties. Details of this method can be found inChapter 4. In 2005, the way of simulating water impoundment is by applying the waterpressure variations on the surface of the dam.• Some missing material parameters. In particular, the exact parameters for the water retentioncurves for both the core and the rockfill are not available. The BBM and RM models are sen-sitive to the water retention curves, because they govern the liquid pressure determinations,which results in changes of the compressibility of the materials, especially in the rockfill.The water retention curves in the current problem are reproduced using the Van Genuchtenmodel and the water retention curves are approximated.• Some missing constitutive model parameters for the till core. In particular, the fluidity pa-rameter Γ for the till core is not available.114Appendix BRockfill mechanicsThis appendix aims to summarize some of the key components of rockfill response, that are incor-porated in the constitutive model following. The appendix begins with observations made exploringfield and laboratory data, followed by an analysis of the rockfill response from a fracture mechanicsperspective. After that, the key mechanism known as particle breakage and key factors affecting itare presented. Finally, testing apparatus and techniques used in laboratory setting are explored.B.1 Field and laboratory observationsDue to the rockfill’s “free draining” nature, it remains in an unsaturated or partially saturated stateunless fully submerged in water (Oldecop and Alonso, 2013a). Partial saturation can occur due tomultiple reasons with the most common being interaction with the atmosphere, i.e. rainfall. Wateraction has a significant effect on the behaviour of rockfill according to Parkin (1977),Atkinson andMeredith (1984) and Oldecop and Alonso (2004). However, the nature of the effect differs fromthe one in unsaturated soils. The influence of water on rockfill behaviour is physiochemical, ratherthan purely mechanical (Oldecop and Alonso, 2013a).To establish the differences between rockfill and unsaturated soils, first the definition of suctionhas to be defined. For unsaturated soils, the suction, s, has a definite mechanical meaning and isidentified with the matric component of suction. In the case of rockfill, suction is identified withthe total suction, which governs the speed of crack propagation (Alonso et al., 2005). The cleardistinction between the two definitions can be seen in Figure B.1. Figure B.1 (a) conveys a particleof a low-plasticity soil, where the suction acts in the inter-particle space; whereas Figure B.1 (b)shows a rockfill particle with a crack, where the suction acts at the tip of the crack of the particle.115The terms relative humidity and suction have been used interchangeably in the body of this thesis.Figure B.1: (a) Particles of an unsaturated low-plasticity soil, adopted from Oldecop andAlonso (2004) (b) Rockfill particle with a crack (pore), modified from Oldecop andAlonso (2001).They are related through a psychrometric relationship defined by Oldecop and Alonso (2004) asRT Ln(RH) =−vs (B.1)where R is the gas constant, T is the absolute temperature, v is the molar volume of water and s isthe total suction. Figure B.2 shows an idealised particle with a crack in the middle. Each rockfillparticle hosts multiple defects of different size and orientation, such as the one showed. Whenapplying stress to a particle, the crack tip acts as a stress concentration zone and could begin topropagate due to different factors. Oldecop and Alonso (2013a) provides an insight from a fracturemechanics point of view and interprets existing laboratory data based on this.116σσ σ2aσPσ∗PFigure B.2: Sketch of a simplified volume of rockfill and a rockfill particle containing a crackthat eventually propagates and causes particle breakage. Modified from Oldecop andAlonso (2013a).A crack develops under a uniform tensile stress field of magnitude σ∗ and propagates at a highspeed, when the stress intensity factor K reaches a threshold value known as the fracture toughnessof the material Kc. Linear elastic fracture mechanics applies for this type of failure and thereforecould be defined asK = Kc = σ∗β√pia (B.2)where β depends on the particle geometry and a a is the crack length. Figure B.3 presents a plotof crack propagation velocity varying with both relative humidity and the stress intensity factor.Figure B.3 is divided into three regions. In region three, the K > Kc causes immediate breakageof the particle in a catastrophic manner. This region is responsible for deformations occurringright after load applications. Cracks in region two grow simultaneously due to increase in relativehumidity and increase in the cracks length.117over 20%). Moreover, experimental data presented byFreiman (1984) suggest that V in zone 1 increases with theRH in an almost linear manner. V0 in equation (4) thereforeincludes the effect of relative humidity or total suction.A unique K value could theoretically be assigned to allcracks existing in a given particle arrangement under stress,and therefore they will form an ordered series along the Kaxis in Fig. 9(a). Every time a stress increment is applied,the series of cracks will move towards higher K values. Thereverse will occur upon unloading. All cracks falling withinregion III will immediately break after load application.Cracks in region II will propagate, V being the initialvelocity of propagation given by the stress corrosion curve.The time-dependent component of strain arises from thebreakage of cracks lying in region II. Since, in region II, thevelocity of crack propagation depends on the RH, the time-dependent strains of rockfill will also depend on the RH, asobserved in experiments.SUBCRITICAL PROPAGATION OF A SINGLE CRACKThe propagation of a single crack contained in a rockparticle will now be considered, assuming that the appliedstress state and the prevailing RH remain constant. It willalso be assumed that no significant changes occur in theconfiguration of the particle assembly during propagation ofcrack i, so that !!i in equation (3) can also be taken as aconstant.KCRegion III(b)(a)13%30%30%28%Vacuum VacuumWaterWaterWaterWaterWaterWaterK K/ C1 10$ "91 10"8$1 10"7$1 10"6$1 10"5$1 10"4$1 10"3$1 10"2$1 10"1$V: m/sn15#n30#n60#n200#Tennessee Sandstone (Atkinson, 1984)Synthetic quartz (Atkinson, 1984)Westerly granite (Atkinson, 1984)Carrara Marble (Atkinson, 1984)Ralston Basalt (Atkinson, 1984)Soda-lime-silica glass (Wiederhorn , 1982)et al.Charles model, 0·1 m/sV0 #100%30%10%1%0·2%0·02%Tested in liquidTested in gasK0Region IIRegion ICrack propagation velocity,(log scale)VStress intensity factor, K100%RHorliquidwaterDryenvironment (vacuum)min( )K0Incr. RHZone 1Zone 2Zone 30·3 0·4 0·5 0·6 0·7 0·8 0·9 1·0Fig. 9. (a) Schematic stress corrosion curves and conceptual model by Oldecop & Alonso(2001); (b) stress corrosion experimental data from different rocks, quartz and glass, andplots of Charles model. Testing condition indicated next to each curve: immersed in liquidwater, environment with controlled relative humidity (in %) or vacuum294 OLDECOP AND ALONSOFigure B.3: Typical stress intensity curve. Modified from Oldecop and Alonso (2007).This region is usually referred to as “subcritical crack propagation” region. As the crack in-creases in size, it starts increasing the propagation velocity and begins approaching region three,where eventually the particle breaks. This breakage is responsible for the time dependent defor-mations in rockfill and is determined by relative humidity (or total suction) and the stress level.Increasing of moisture content under a constant rate would also increase the crack propagation ve-locity, hence it is responsibl for the “creep” effect in rockfill. More details for the “creep” effectare explored in Chapter 6. In region one, K < K0, no propagation occurs.The increase of crack propagation velocity has been established to depend on the relative hu-midity. The physiochemical phenomenon causing this effect is known as stress corrosion. Theprocess begins by a water molecule entering the tip of the crack in the form of vapour or liquid asshown on Figure B.4 (a).Then, water reacts with the strained silicium bond at the crack tip (Figure B.4 (b), 1). Afterthe reaction, the bond is weakened (Figure B.4 (b), 2) and under the applied load it finally breaks(Figure B.4 (b), 3).Water content and stress levels are the most significant factors affecting the breaking of parti-cles through a crack propagation mechanism. However, there are other factors that influence thebreaking of particles and they are explored in the next section.118Figure B.4: (a) Water vapour entering an idealised crack, modified from Oldecop andAlonso (2013b) (b) Reaction between a water molecule and a strained silicium diox-ide molecule. Modified from Michalske and Freiman (1982).B.2 Particle breakageCristian (2011) summarized all the factors affecting particle breakage. They are divided into threegeneral categories i) factors connected to the particles ii) factors connected to the particle assemblyiii) factors connected to conditions.Particle mineral compositionThe influence of the mineral composition is related to the strength of the particle and thus theamount of breakage. Researchers like Marachi et al. (1969) and Atkinson and Meredith (1984)have conducted tests on different geological materials. Atkinson and Meredith (1984) found thatsilicates’ particle breakage increases as their environment becomes depleted in hyroxyl species. Onthe other hand, quarts tends to experience low amount of cracking in basic environments and basaltexperiences higher cracking in moist air.119Particle shapeThe second factor related to the particles is the shape of the particles. Generally, angular particlesexperience higher amounts of breakage compared to rounded ones. This is because the angularedges serve as stress concentration zones and tend to break at contact. Figure B.5 shows a particlesplit in two with one failure surface and some crushing at the contact zones.CONTACT CRUSHINGFRACTURE SURFACEFigure B.5: Rockfill particle with contact crushing zone and a single fracture surface, Alonsoet al. (2013).Particle sizeThe final factor related to the particles is the size of the particle. This has been reported by Alonsoet al. (1977), among others. The reason for this effect lies in the statistical distribution of flawswithin the particle. Therefore, for the same material with a homogeneous distribution of flaws,particles with bigger diameters have more defects compared to smaller ones. This results in parti-cles breaking under lower tensile stress. Figure B.6 shows the reduction in failure stress σ f withthe increase of the particle size diameter dN for different materials tested. This phenomenon isexamined more thoroughly in Chapter 6.1201 0.5 (dN )(f)Figure B.6: Rockfill particle with contact crushing zone and a single fracture surface, Alonsoet al. (2013).GradationThe first factor related to the assembly of the particles is their gradation. Cristian (2011) summarizeshear strength data relating the coefficient of uniformity Cu = D60/D10 and the breakage factor Bdefined asB =12∫ DmDM| f0(D)− f f (D)|dD (B.3)where f0(D) and f f (D) are the initial and post-test retained mass for a given sieve of size D. Thefactor B is commonly used in soil mechanics practice for characterizing the amount of crushing ofgranular materials. The plot of Cu versus B is shown on Figure B.7 and exhibits lower amounts ofcrushing for higher values of Cu, or in other words for well graded soils. This could be explainedby observation of stress chains in the soils. Well graded soils have identical stress states and uponbreakage, the stress redistribution causes other particles with similar size to experience a higheramount of stress and thus cause additional breakage.121Figure B.7: Variation of breakage index with change of the coefficient of uniformity, adaptedfrom Cristian (2011).CompactionCompaction of particles with same diameters but different initial void ratios experience the sameamount of breakage but under different amounts of stress. Higher void ratios causes breakage undersmaller stresses and lower void ratios at higher stresses. According to Cristian (2011) eventually,after applying sufficient amount of stress, both samples tend to reach the same void ratios. An-other observation by Oldecop and Alonso (2013a) is that void ratio plays a part in determining theamount of compressibility experienced by larger particles. Quantification of this effect is exploredin Chapter 6.Water contentMoisture content (relative humidity) affects the speed of crack propagation and is one of the mostsignificant factors governing particle breakage, as already discussed.Stress levelNaturally, higher stress levels tend to increase the breakage of particles. The breakage coefficientB is observed to increase with higher stress levels as stated by Cristian (2011).122Time dependency and “creep”The two dominant mechanisms governing rockfill response are particle re-arrangement and particlebreakage. Particle re-arrangement occurs when particles roll and slide past each other, causingimmediate strain increments upon loading. Particle breakage, on the other hand, is a delayedmechanism. This time-dependency is a result the stress corrosion mechanism, which is observed bymany researchers to depend on time. In the works of Oldecop and Alonso (2007), data of long termoedometer tests performed under different suction and stress conditions confirm the observationsin the field.The “creep” in rockfill refers to the gradual propagation of cracks causing small strain incre-ments, which is considered as a long time dependent process. This behaviour is different from theconventional definition of creep, where water is expelled from the soil over a long period of timedue to higher permeability of soils.Researchers like Oldecop and Alonso (2007) suggest that the time dependent strain follows alinear relationship in logarithmic space. Those observations are based on field settlement recordsof multiple rockfill dams. In the constitutive formulation of the RM, an expression is suggestedto capture the behaviour observed in both the field and laboratory oedometer tests. The logarith-mic deformation equation suggests an indefinite accumulation of settlement of the rockfill. Suchbehaviour may seem odd from a physical point of view, but observing the data of rockfill damsettlements, shown on Figure 1.1 for more than forty years of operation, communicates the same.Due to the crack propagation nature of the “creep” mechanism, it is natural that the behaviour isdependent on the suction within the cracks. Therefore, the compressibility λ t associated with the“creep” strains is dependent on suction. Lower suction causes a faster rate of λ t increase withstress as suggested by Oldecop and Alonso (2013a).Figure B.8 (a) shows the dependency of the time dependent parameter λ t with suction andapplied stress for compacted gravel of a quartzitic shale.It has been also established that during the two stages of rockfill response, clastic yielding andclastic hardening, the parameter λ t is proportional to the conventional compressibility λ as shownbelowλ tλ∼= 1n(B.4)where n is parameter in Charles law (Charles, 1958) that describes the crack propagation veloc-ity associated with the stress corrosion effect. The test results from Figure B.8 (a) were re-plottedas λ t vs λ and two envelopes were plotted with higher bound for n= 20 and lower bound n= 200.123Figure B.8: (a) Time-dependent compressibility index against applied stress for different con-stant suction values (b) Correlation between time-dependent compressibility index andcompressibility index for tested rockfill. Adopted from Oldecop and Alonso (2007).Atkinson and Meredith (1984) summarize experimental data for variety of rocks, showing thechange of the subcritical crack growth index n and its variability with relative humidity. For thequartzitic shale, the best fit to the data is reached for n = 60 as seen on Figure B.8 (b). This iscongruent with the findings of Atkinson for this type of rock.As mentioned, the time dependent parameter λ t is dependent on time, applied pressure, com-pressibility of the material and suction. The parameter varies linearly with applied vertical stressup to stresses of 1 MPa. Additionally, there is a linear dependence of the parameter with suction innatural logarithmic space.B.3 Testing apparatusAs previously mentioned, relative humidity within the rockfill cracks is one of the governing factorsdictating the amount of breakage that occurs upon loading. Determination of rockfill responserequires three laboratory tests.The first test determines the relation between the relative humidity and the suction within thecracks. In unsaturated soils (and rockfill), this is known as a water retention curve and is a fun-damental material property. In the case of rockfill, determining this requires three different ap-124proaches depending on the level of suction. For high suctions, usually up to 250 MPa, a vapourequilibrium technique is used, and the rock sample is stored in an isolated container, where the rel-ative humidity (RH) is controlled by saturated saline solution. For the low-suction range, initiallya ceramic suction plate is used to apply a negative water pressure in the pores, also known as the“tensiometer technique”. After this, the final stage is the “axis translation technique”, where an airoverpressure is applied to the rock sample (Oldecop and Alonso, 2001). This water retention curveestablishes the basis of connecting the microscopic response to a global problem, such a dam.The second test is a RH controlled oedometer test, where the sample is compressed at differentlevels of relative humidity (suction). The device works in a similar way as the one for determiningthe water retention curve. An air flow with a controlled amount of relative humidity percolatesthrough the rockfill pores and different levels of stress is applied. The device can be seen on FigureB.9.The third tests is performed with the same suction controlled oedometer device, with the dif-ference that the volumetric strains are measured under a constant load over a period of 0 - 1000minutes to establish the time-dependent behaviour of the rockfill. This test is performed underdifferent levels of stress and different levels of relative humidity, because the “creep” effect isdependent on both stress and suction.125Figure B.9: Relative humidity (RH) controlled oedometer test and water transport schemecirculation inside rockfill particle, adopted from Oldecop and Alonso (2004).126
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Stress-deformation analysis of Denis-Perron dam : verification and validation for better prediction of… Kolev, Boris Nikolaev 2017
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Title | Stress-deformation analysis of Denis-Perron dam : verification and validation for better prediction of rockfill response |
Creator |
Kolev, Boris Nikolaev |
Publisher | University of British Columbia |
Date Issued | 2017 |
Description | Rockfill dams present a challenge for engineers due to the many uncertainties revolving around the behaviour of rockfill. A governing factor in the behaviour of rockfill is the particle breakage due to change of moisture, which was observed in laboratory and field conditions. Alonso and Oldecop have proposed a rockfill model (RM), where the suction inside the cracks of the rockfill is a state variable that controls the breakage mechanism. This research focuses on verification and validation of stress-deformation analysis methodologies, for better prediction of rockfill response. It involves application of the RM in numerical simulation of a benchmark case study on the well instrumented Denis-Perron dam (SM3). Denis-Perron dam is a rockfill dam with a central till core, 171 metres high and 378 metres long, located on the Sainte-Marquerite river in northern Quebec, Canada. The instrumentation data was made available by Hydro-Qu´ebec, for a period of six years of construction, impoundment, and operation of the dam. Numerical simulations are conducted using Code Bright – a fully coupled three phase finite element program for unsaturated porous media. A validation stage was first carried out through modelling of Beliche dam – a well studied case by Alonso et al. The numerical model of the SM3 dam captures the staged construction, reservoir impoundment and rainfall history recorded. Model parameters for the till core and rockfill shoulders were either calibrated using limited available laboratory and field data, adopted from literature, or assumed with some rationale. Deformations measured by the inclinometers during construction and impoundment, both upstream and downstream, are simulated successfully. Piezometer and pressure cell measurements are replicated to a very good extent. Post-construction deformations are reproduced with reasonable success, given the limited data for detailed characterization of the various zones in the dam. Some important challenges around characterization of the rockfill compressibility and the related scaling issues for model calibration are presented and discussed. An attempt is made to quantify the amount of scaling observed through a back analysis of field measurements. Finally, the effect of permeability on rockfill in the development of deformations is discussed. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2018-04-30 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NoDerivatives 4.0 International |
DOI | 10.14288/1.0345628 |
URI | http://hdl.handle.net/2429/61356 |
Degree |
Master of Applied Science - MASc |
Program |
Civil Engineering |
Affiliation |
Applied Science, Faculty of Civil Engineering, Department of |
Degree Grantor | University of British Columbia |
GraduationDate | 2017-05 |
Campus |
UBCV |
Scholarly Level | Graduate |
Rights URI | http://creativecommons.org/licenses/by-nd/4.0/ |
AggregatedSourceRepository | DSpace |
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