"Applied Science, Faculty of"@en . "Civil Engineering, Department of"@en . "DSpace"@en . "UBCV"@en . "Smyth, Kenneth Jeffrey"@en . "2010-07-21T18:13:28Z"@en . "1987"@en . "Master of Applied Science - MASc"@en . "University of British Columbia"@en . "The phenomenon of the debris torrent is explored by examining the mechanisms of initiation, particularly those of rainfall and deforestation.\r\nThe types of precipitation likely to contribute to instability are identified and data collection is reviewed.\r\nDebris torrents have characteristics unlike that of ordinary stream flow, and are capable of transporting massive quantities and sizes of material. Models to explain this transport capability are compared and contrasted. A theoretical analysis of the flow regime is carried out which is argued to be consistent with the observed turbulent nature of a debris torrent. This analysis is extended to the calculation of superelevation\r\nin bends and shows that current attempts to estimate velocities from super-elevation data may be very conservative.\r\nFurther application of the turbulent stress analysis is used to estimate the angle of spread of the debris torrent in the deposition zone, and this analysis may be useful in zoning the downstream area to safeguard construction."@en . "https://circle.library.ubc.ca/rest/handle/2429/26739?expand=metadata"@en . "DEBRIS TORRENT MECHANISMS by K.J. SMYTH B.Sc. Queen's U n i v e r s i t y of B e l f a s t , 1974 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of C i v i l Engineering We accept t h i s t h e s i s as conforming to the re q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA SEPTEMBER 1987 \u00C2\u00A9 K.J. SMYTH, 1987 In presenting this thesis in part ia l fulfil lment of the requirements for an advanced degree at the University of Br i t i sh Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of C i v i l Engineering The University of Br i t i sh Columbia 2075 Wesbrook Mall Vancouver, B.C. V6T 1W5 Date: September, 1987 ABSTRACT The phenomenon of the debris torrent is explored by examining the mechanisms of i n i t i a t i o n , part icularly those of r a i n f a l l and deforesta-t ion. The types of precipitation l ike ly to contribute to ins tab i l i ty are identif ied and data col lection is reviewed. Debris torrents have characteristics unlike that of ordinary stream flow, and are capable of transporting massive quantities and sizes of material. Models to explain this transport capability are compared and contrasted. A theoretical analysis of the flow regime is carried out which is argued to be consistent with the observed turbulent nature of a debris torrent. This analysis is extended to the calculation of super-elevation in bends and shows that current attempts to estimate velocit ies from super-elevation data may be very conservative. Further application of the turbulent stress analysis is used to estimate the angle of spread of the debris torrent in the deposition zone, and this analysis may be useful in zoning the downstream area to safeguard construction. - i i -TABLE OF CONTENTS Page ABSTRACT i i LIST OF TABLES iv LIST OF FIGURES v LIST OF SYMBOLS v i i ACKNOWLEDGEMENT v i i i CHAPTER 1. INTRODUCTION 1 2. INITIATION IN SOURCE AREA 4 2.1 Instability Due to Rainfall 4 2.2 Instability Due to Removal of Forest Cover 8 2.3 Instability from Other Causes 10 3. PRECIPITATION 17 3.1 Classification 17 3.1.1 Synoptic or Macroscale 17 3.1.2 Mesoscale 17 3.1.3 Microscale 17 3.2 Data Collection 18 3.3 Precipitation Network 23 3.4 Predicting Orographic Effects 24 4. DEBRIS TORRENT MOVEMENT 36 4.1 Massive Sediment Motion 36 4.2 Initiation of Movement in Torrent Stream 36 4.3 Suspension of Massive Material 38 4.4 Bagnold's Dilatant Fluid Model 39 4.5 Plastico-Viscous Rheological Models 41 4.6 Evaluation of Models 42 5. FLOW REGIME OF A DEBRIS TORRENT 45 5.1 Dilatant Flow 45 5.2 Flow Around Bends . . \u00E2\u0080\u00A2 48 5.3 Further Applications of Turbulent Flow 52 5.4 Turbulent Stress 53 6. CONCLUSIONS 61 REFERENCES 65 - i i i -LIST OF TABLES Page Table 3.1 Errors inherent in sparse gauging network 28 3.2 Data from Beaufort Range, Vancouver Island 28 3.3 Network specification recommended by WMO (1970) 29 3.A Precipitation network data for selected regions 1971 . . . 30 - iv -LIST OF FIGURES Page Figure 2.1 Characteristics of debris source area 12 2.2 Limiting slopes for s o i l s l ips , Santa Monica mountains 13 2.3 Diagram showing buildup of perched water table in co l luv ia l s o i l during heavy r a i n f a l l 14 2.4 Diagram showing z such that mz is the vert ica l height of ground water table above s l ip surface 15 2.5 Relation of fai lure in some typical soi ls to ground water content and slope angle 16 3.1 Comparison of hydrographcs from ten minute radar and equivalent hourly gauge data (after Bonser, 1982) 31 3.2 Relative distributions of land area, precipitation stations and snow courses by elevation intervals in B.C 32 3.3 Densities of precipitation networks by elevation interval in Switzerland, Norway and B.C 33 3.4 Simplified inflow and outflow wind profi les over a mountain barrier 34 3.5 Data from WMO (1973), p. 64 35 4.1 Characteristic shear-stress distributions 44 4.2 Cr i t er ia for occurence of various types of sediment transportation 44 5.1 Velocity/depth relationship applicable ot the peak of debris torrent surge (after Hungr et a l . , 1984) 57 5.2 Velocity/depth prof i les , comparing dilatant flow with laminar and turbulent flow (from mathematics) 58 5.3 Fluctuations of instantaneous velocity component with respect to time at a fixed point in steady flow 59 5.4 Normal distribution applied to lateral velocity fluctuation in turbulent flow 60 - v -LIST OF SYMBOLS A constant a constant B surface width of flow C cohesion/unit area c' cohesion intercept c^ grain concentration by volume in static debris bed D grain diameter g acceleration due to gravity h depth of flow h w porewater pressure k constant K constant m fraction of depth such that M is the vert ica l height of ground water table above s l ip surface (Fig. 2.4) p pressure due to weight of solids and water P dispersive pressure APj,AP 2 inflow, outflow pressure difference in mb hydraulic radius R radius of bend R^ radius of centreline of stream bend s standard deviation of normal distribution S 0 slope T shear stress t time u velocity of flow u time averaged part of velocity u u 1 momentary fluctuation of velocity u u^ c c r i t i c a l shear velocity V velocity for calculation of thrust force z vert ica l depth of s l ip surface - v i -LIST OF SYMBOLS (Continued) a dynamic angle of internal f r i c t ion B angle of flow to face of barrier X unit weight of solids r unit weight of water 8 slope angle u viscosity p density of water 6 density of grains a normal stress n T shearing resistance/unit area x y ie ld strength ' angle of shearing resistance A linear concentration of particles - v i i -ACKNOWLEDGEMENT I would l ike to take this opportunity to express my appreciation and thanks to my advisor Professor M.C. Quick for his advice and guid-ance during the research and the preparation of this thesis. - v i i i -1 CHAPTER 1 INTRODUCTION A debris torrent channel is often a re lat ive ly quiet mountain stream which under suitable conditions can become the transporter of massive material that has great destructive power. The physical processes which give rise to a debris torrent are reviewed. Logical ly, they are sub-divided into geologic, meteorologic, and part ic le and hydrodynamic processes. Some of the geologic para-meters are shown to be reasonably well defined. However, the r a i n f a l l necessary for the formation of a torrent is shown to be subject to considerable uncertainty, especially because of the lack of good data. The main emphasis of this thesis is on the part ic le and hydrodynamics of the debris movement. The physical interactions of the sol id and f lu id components are re-analyzed and i t is argued that peak velocit ies of debris movement may have been underestimated. A consequence of this underestimation would be a major revision of estimates of impact forces and possible damage to structures. The effects of debris torrents are manyfold, ranging from the disasters to property and l i f e , by the movement of large boulders, to the long term buildup of landforms by the formation of debris fans in the river valleys. Debris torrents contribute to the formation of a l luv ia l fans. The widespread, perhaps dominant, influence of this mechanism in the natural evolution of landforms has gone largely unrecognized owing to the long recurrent interval between events (Campbell, 1975). 2 A debris torrent can quickly f i l l basins behind small check dams rendering them ineffective in controlling subsequent surface runoff. The effects on small residential dwellings range from quiet inunda-tion to complete destruction. Flows of sufficient volume and momentum have smashed structures into pieces and move foundations, for example in Alberta Creek, Br i t i sh Columbia: \"Damages included total destruction of three houses and structural damage to one other house and carport . . . Five culverted road crossings were washed out and Highway 99 bridge was swept off i t s foundations.\" (Woods, 1983). In other instances, bu i ld -ings have had layers of muddy debris deposited inside them, commonly accompanied by l i t t l e structural damage. Apparently the debris was moving at re lat ive ly low velocit ies; the flows entered the dwellings through open doors or windows and quietly flooded the inter iors . It is also worth noting that the size of the boulders (and hence the destructive abi l i ty) depends on the character of the bedrock, i . e . volcanic rock w i l l contribute large boulders, whereas a weak sandstone w i l l only contribute clasts of pebble size. A debris torrent may cause the channel to shi f t , especially in the downstream depositional region. This channel shifting can be triggered by the 1) sediment load, which varies greatly with debris torrent surges. 2) local deposition during l u l l s in the storm, or between torrents, may f i l l the old channel and divert subsequent flow into a new one, or cause flooding of the fan remote from the pre-existing stream channel, 3) During deposition debris levees tend to form along the channel boundaries and these levees may channel or divert subsequent flows. 3 Channel bends are a particular hazard region, for example, in the Alberta Creek torrent of February 1983 the confines of the channel were unable to contain the torrent on the bend causing part of the debris to leave the channel and bury a recreational vehicle with subsequent loss of l i f e . The l i terature is f i l l e d with tragic case histories l ike that of Alberta Creek, but unfortunately these dangers are not always obvious, since the periodicity of debris torrents is irregular on any individual creek and long periods of dormancy often permit f u l l re-establishment of forest cover over affected areas. In the following chapters, the processes which give rise to a debris torrent w i l l be reviewed. In part icular , the precipitation necessary to in i t ia te a torrent w i l l be considered and the r a i n f a l l data network density needed to define the r a i n f a l l w i l l be considered. Consideration w i l l then be given to the dynamics of the sediment motion and Bagnold's dilatant f lu id model w i l l be compared with the plast ico-viscous rheological model. The Bagnold model is then used to analyze velocity distribution and special application is made to the flow in a bend. This analysis indicates that peak velocit ies of debris may be higher than previously estimated and therefore impact loads may be considerably higher. 4 CHAPTER 2 INITIATION IN SOURCE AREA 2.1 Instabi l i ty Due to Rainfal l In order for a debris torrent to be in i t ia ted there must be s u f f i -cient material in the form of mud, rocks, sand and branches combined with an amount of water available to the creek bed. This material is transported to the creek by land movements from what we w i l l c a l l debris source area of the creek (Fig. 2.1). The transport of material into a creek bed is t ied to the correla-tion between debris torrent act iv i ty and moderate to heavy r a i n f a l l . Once sufficient water makes i t unstable the source material moves in debris s l ides, avalanches or debris flows, making i t s way into the creek. This s l iding of material results from the interaction of i n f i l t r a -tion and downward percolation at depth, (Kesseli, 1943), where the former takes place at a rate greater than the lat ter , the water content of the top zone w i l l increase to a c r i t i c a l point at which s l iding w i l l originate. When i n f i l t r a t i o n through the regol i th 1 exceeds the trans-missive capacity of the rocks below, a temporary perched water table is formed (Campbell, 1975). The head w i l l continue to increase, with continued r a i n f a l l , unt i l a l l the sur f i c ia l zone is saturated, after which a l l the r a i n f a l l in excess of the transmissive capacity of the bedrock is distributed as surface runoff and downslope seepage. The xThe loose incoherent mantle of rock fragments and s o i l which rests upon the bedrock. 5 association of debris slides with rainstorms is clear evidence that slope-mantle materials that are stable under \"normal\" conditions become unstable during r a i n f a l l of sufficient duration and intensity. For any site i t is possible to establish l imiting slopes at which so i l s l ips are unlikely and an upper slope above which retention of a continuous mantle of colluvium would not be possible (Fig. 2.2) (Campbell, 1975). This data i s , of course, specific to the Santa Monica Mountains where the range of 12\u00C2\u00B0 to 56\u00C2\u00B0 are l imiting angles. These l imiting angles depend on local geology and should be established on a site specific basis. Figure 2.3 shows an idealized debris source area as the conditions for land movement are being reached, in which shallow rooted vegetation with a thin mulch of dead leaves and grass growing in a regolith of co l luv ia l s o i l , the upper part of which contains abundant l iv ing and dead roots as well as animal burrows. When the rate of i n f i l t r a t i o n into and through the upper layers is equal to or less than the capacity of the bedrock to remove i t by deep percolation, the water moves towards the permanent water table below and the s tab i l i ty of the slope material is not affected. On the other hand i f this deep percola-tion is less than the i n f i l t r a t i o n a perched water table is formed and w i l l continue to rise unt i l surface runoff and downslope seepage takes place. The cr i ter ion for fai lure of a s o i l slab is that the ratio of the tangential and normal forces must exceed a c r i t i c a l value, which is dependent on the type of material. The effect of the addition of water in changing a slab of the source material from stable to unstable may be explained using the formula (Terzaghi, 1950, p.92) , 6 where T = c + (p - hw)tan T = shearing resistance/unit area = angle of internal f r i c t ion hw = porewater pressure p = pressure due to weight of solids and water c = cohesion/unit area The decrease in shearing resistance, when a water saturated zone forms above the s l ip surface is evident i f we consider the component of cohesion c (which is real ly apparent cohesion obtained from the air-water surface tension), this is reduced to zero as the water takes the place of a ir in the interstices and also the term (p-hw) is decreased due to increase in piezometric head. A formula developed by (Skempton and DeLory, 1957) for the condi-tion that ground water flow i s para l l e l to the slope at shallow depth gives the Terzaghi equation in more readily measured s o i l parameters, (r - m \u00E2\u0080\u00A2 Y )z cos 20 tand>' \u00E2\u0080\u00A2 . s ' w r c' + - r z sinG cosG ' s where F = factor of safety c' = cohesion intercept z = vert ica l depth of s l ip surface m = fraction of z such that mz is the vert ica l height of ground water table above s l ip surface (Fig. 2.4) 9 = slope angle 7 = unit weight so i l r, w = unit weight water = angle of shearing resistance For the special case of c' =0 the c r i t i c a l slope is given by tan9 = c m r, w tan' i . e . , F=l. It is now possible to show a family of curves for F=l, for various combinations of s o i l parameters y and tan' (Fig. 2.5) from which the c r i t i c a l angle 9 can be determined. This is however an idealized situation although such curves prepared for a given site should permit a preliminary evaluation of recurrence interval for failures due to rainstorms. The recurrence interval for values of m at F=l can be approximated from recurrence intervals for rainstorms of sufficient intensity and duration provided thickness and i n f i l t r a t i o n rates of regolith are known. If i n f i l t r a t i o n rates are low, duration of r a i n f a l l w i l l be dominant and i f they are high, intensity should be dominant. A study (Sidle and Swanston, 1982) on debris slides in coastal Alaska used much the same approach. They noted the great oversimplif i -cation in using a linear slope model which ignores many complex f i e ld situations. They found unreasonably high values of suggesting that cohesive properties existed in the so i l mantle. A multistage t r i a x i a l test was performed on an undisturbed sample on a site adjacent to the fa i lure , giving a much lower and more reasonable value of * C*(a-p)+p (A. l ) 37 in which \u00E2\u0080\u00A2= grain concentration by volume in the static debris bed. o,p = densities of grains and fluids respectively = internal f r i c t ion angle When case 2 occurs (Fig. A.lb) the following equation should be satisf ied C*(o-p) tan9 = tan (4.2) C^(o-p) + p ( l+h 0 a\u00C2\u00A3i ) in which a^ is the depth where x and x^ coincide. The whole bed i n case 1 and the part above the depth a^ in case 2 w i l l begin to flow as soon as the surface flow appears. This type of ins tab i l i ty in the bed is due not to the dynamic force of f lu id flow but to static disequilibrium, so that the flow should be called sediment gravity flow. The condition for occurrence of sediment gravity flow is therefore, i d in which d is the grain diameter. Substitute this condition into Equation (4.2) and we obtain C*(o-p) tan6 \u00C2\u00A3 tan (4.3) C^(o-p) + p( l+h 0 d - i ) but when a^ i s far less than h 0 grains cannot be uniformly dispersed throughout the whole depth due to rather small co l l id ing d i spers ib i l i ty . Therefore a sediment gravity flow that is appropriately called debris torrent should meet the condit ion a^ \u00C2\u00A3 K h 0 , in which K is a numerical coefficient, determined from experiment to be about 0.7. Substituting the condition a y \u00C2\u00A3 Kh 0 into Equation (4.3) gives 38 C*(o-p) tanS \u00C2\u00A3 tan (A.A) C * ( o - p ) + p( l+k- i ) Debris movement occur when Equations (A.3) and (A.A) are simultaneously sat isf ied. A.3 Suspension of Massive Material The debris torrent phenomenon occurs in surges spaced over several hours (Hungr et a l . , 198A). A typical surge through the lower reaches of a mountain creek begins by the rapid passage of a steep bouldery front, followed by the main body of the torrent. This consists of coarse particles ranging from gravel to boulders and logs, apparently floating in a s lurry of l iquefied sand and finer material. The inc lu -sion of debris larger than could be expected to be moved by normal hydraulic forces and the mechanism of such transport requires upward sediment-supporting forces that turbulence of the i n t e r s t i t i a l f lu id would be too weak to provide. Bagnold (195A) proved the existance of a dispersive pressure resulting from the exchange of momentum between the grains in neighbour-ing layers. When the voids are f i l l e d by dense clay s lurry, large stones can be dispersed under rather small dispersive pressure, helped by bouyancy in the f lu id phase. Bagnold also investigated the effect of dispersion of large sol id spheres on the shear resistance of a Newtonian f l u i d . He held that in a situation where a stream is transporting granular material, the only explanation was a dispersive grain pressure of such a magnitude that an 39 appreciable part of the moving grains is in equilibrium between i t and the force of gravity. 4.A Bagnold's Dilatant Fluid Model . A dispersion of neutrally bouyant particles were sheared in a Newtonian f lu id in the annular space between two concentric drums. The particles dilated to the extent of exerting pressure on the vert ica l walls perpendicular to the main flow. Bagnold reasoned that this dispersive pressure is the result of momentum exchange associated with grain encounters and he found that the dispersive pressure is propor-tional to the shear stress. When the applied shear strain du/dy is small the resulting shear stress is a mixed one due to the effect of f lu id viscosity as modified by the presence of grains, whereas when the applied shear strain is large the viscosity of the i n t e r s t i t i a l f lu id is insignificant and the resulting shear stress is essentially due to grain interaction. For the latter case Bagnold found - 2 P = a o [ ( tVC d ) -1] D 2 (du/dy) 2 cosa (A.5) T = P tan a P = dispersive pressure T = shear stress a = dynamic angle of internal f r i c t ion a = numerical constant = 0.0A2 D = grain diameter 40 It should be noted that the density p of the i n t e r s t i t i a l f lu id does not enter into Equation (4.5). If a single so l id body is moved through a f l u i d , the total rate of momentum transfer is measured by (o-p) because the f lu id tends to flow back around the body to take i t s place. In this case however, i t seems unlikely that \"its place\" can have a physical meaning, since the whole surrounding configuration changes during the grains' movement. It was assumed therefore that the movement of the displaced f lu id is of a random nature in relation to the movement of the grains. Bagnold's experiment shows that the fu l ly iner t ia l condition is sat isf ied at: G 2 = o D 2T [ ( t V C d ) 1 , 3 - l ] u - 2 > 3000 (4.6) where u is f lu id viscosity and G has the form of a Reynolds number or in terms of the conventional Reynolds number R > 55 This condition should easily be met in a debris torrent s ituation. Bagnold reasons that when grains of mixed sizes are sheared together the larger grains tend to dr i f t towards the free surface, because for a given shear strain the dispersive stress appears to increase as the square of the size (Eq. 4.5). Since the flow surface moves fastest, the larger material should dr i f t towards the front of the flow, thus explaining the bouldery front that is characteristic of the debris torrent. 41 4.5 Plastico-Viscous Rheological Models Another set of studies (Johnson, 1970; Middleton and Hampton, 1976; Rodine and Johnson, 1976) propose the use of a Bingham plast ic f lu id model since the flow of clay slurry is well modelled as a Bingham f l u i d . The stress-strain relationship in a Bingham f lu id is T = + ji du/dy where T = shear stress = y ie ld strength u = viscosity Middleton and Hampton (1976) distinguished debris flow from grain flow. They emphasize that the dispersive stress due to direct grain interaction plays an important role only in the case of grain flow, and that in the case of debris flow; the grains are supported by matrix strength, and the viscosity of the i n t e r s t i t i a l f lu id determines their hydraulic behaviour. They further claim that only a sl ight amount of clay in the i n t e r s t i t i a l f lu id w i l l drast ical ly influence grain flow and convert i t into debris flow. It should be noted that the above refers to debris flow and the phenomenon under consideration should be distinguished from a debris torrent proper. It is possible for a Bingham f lu id to flow in a channel of very low slope i f the depth of flow is large enough, this is not in accordance with a real debris torrent. 42 To avoid the contradiction of this low slope flow, Johnson (1970) proposed a Coulomb-viscous model in which the stress-strain relationship i s : T = C + o n tan + u du/dy C = cohesion o = normal stress n

) , and the equation of c r i t i c a l tractive force on a steep channel (Ashida et a l . , 1973) pu| 0.32(d/h 0) 7 r - r = 0.034 cosG [tan - . , tanG] x 10 (o-p)gd r (o-p) where = c r i t i c a l shear velocity [=(gh0sin9)^'^] g = acceleration due to gravity. The domain labelled 1 is that of no part ic le movement; 2 is the domain of individual part ic le movement due to the dynamic force of f lu id flow, i . e . bed transport; 3 is the domain of sediment gravity flow, in which the effect of dynamic force of f lu id flow coexists and in the flow there is a clear water layer over a dense mixture of grain and water. Numbers attached to the curves in this domain correspond to the thickness of the moving layer of grains. The effect of dynamic action should decrease for increasing thickness of the moving layer. Note that the domains of the transit ion and the upper regime in the bed form contain both domains of individual part ic le movement and sediment gravity flow; 4 is the domain of debris flow in which the grains are dispersed in the whole layer (debris torrent) ; 5 is the domain of the occurrence of both landslides and debris torrents; and 6 the sediment bed is unstable under no f lu id flow. (a) Case 1 (b) Case 2 Figure 4.1 Characteristic shear-stress d is tr ibut ion. Eq.2 tan8 / (o/o-l) Figure 4.2. Cr i t er ia for occurrence of various types of sediment transportation. The curves are obtained under the condition that c* = 0.7, a = 2.65 gem - 3 , p = 1.0 gem - 3 , < = 0.7, and tan = 0.8. 45 CHAPTER 5 FLOW REGIME OF A DEBRIS TORRENT Hungr et a l . (1984) plotted velocity depth profi les for laminar and turbulent flows in water and compared these with that of debris torrents, using eyewitness reports and superelevation data to establish velocit ies for the torrent flows (Fig. 5.1). The profi les suggested that the debris torrent flow was much closer to laminar than turbulent flow. However observation of video tapes of debris torrents in motion would suggest that the torrent flow is extremely turbulent. These video tapes were filmed by the C.B.C. at Charles Creek, Howe Sound and by a Japanese research group on a Japanese creek. Consequently the decision was made to examine the phenomenon mathematically, assuming the Bagnold (1954) dilatant f lu id theory which implies a tota l ly i n e r t i a l , i . e . turbulent regime. 5.1 Dilatant Flow Bagnold (1954) gives the relation for shear stress as where X = linear concentration of particles D = part ic le size x = shear stress 6 = density of mixture. X D du dy (5.1) 46 This equation is similar to the well known boundary layer theory of Prandtl except that the mixing length is assumed to depend on part ic le size D and not to vary with distance from the boundary Equation 5.1 can be integrated i f i t is assumed that the shear stress T is constant, i . e . x 1 / 2 1 However to be correct T varies l inearly with depth so that T = x - K \u00E2\u0080\u00A2 y o J when y = y x = 0 max _ ^max K so _y_ 1 = T c \" y max max Substituting in 5.1 and integrating we obtain T 1 ' 2 1 0 u (1 - - 2 \u00E2\u0080\u0094 ) 3 ' 2 \u00E2\u0080\u00A2 2/3 (-y ) + C \ n * w ^ y m a x X D 6 1 ' 2 -'max at the boundary u = 0, y = 0 0 = \u00E2\u0080\u0094 (1) \u00E2\u0080\u00A2 2/3 (-y ) + C X D 6 1 ' 2 m X 47 C = 2/3 \u00E2\u0080\u00A2 y X D fii'2 m a X then T 1 ' 2 T 1 ' 2 1 0 v 3 ' 2 L 0 u = 2/3 (1 - ) (-y ) + 2/3 \u00E2\u0080\u00A2 y a v n y \u00E2\u0080\u00A2'max . n 17max X D 6 1 / 2 ''max X D o 1 ' 2 1 1 ' 2 u = 2/3 \u00E2\u0080\u0094 v v {[-1 + -2\u00E2\u0080\u0094]\"* + 1} (5.2) let or . n , . , , \"max y X D 6 1 ' 2 \u00E2\u0080\u00A2'max T 1 ' 2 0 2/3 y = A a const. X D 6 1 ' 2 m a x u = A [ ( - l + ) + 1] ymax \u00E2\u0080\u00A2'max when u = u , y = y max y max so 5.2 yields T 1 ' 2 u = 2/3 \u00E2\u0080\u0094 y = A RAAX X D 6 i ' 2 m a X y . 3 ' 2 1 - (1 - -f\u00E2\u0080\u0094) (5.3) u y max Jmax A8 we may plot this relationship to determine a velocity depth prof i le for the assumed turbulent conditions of dilatant flow as shown in Fig . 5.2. A similar treatment was used assuming laminar condition of which yields the relationship _ y _ = + 1 _ ( 1 _ - Y \u00E2\u0080\u0094 ) a (5.4) u y max Jmax which is also plotted in F ig . 5.2 Experimental results given by Daily (1966, p. 235) for turbulent flow were also transposed to the same graph (Fig. 5.2). The results of this mathematical treatment give a similar prof i le as that derived by Hungr et a l . (198A), from eyewitness reports and superelevation data. We are confronted by a paradox here in that the dilatant flow condition were turbulent but y ie ld what appears to be an almost laminar prof i l e . To accept this as a laminar flow however must be erroneous and the implications of this velocity distribution w i l l now be analyzed. 5.2 Flow Around Bends Many estimates of the velocity of debris torrents have been made from superelevation data, collected from bends in the torrent channel using the equation, ^ = ^ (5.5) dR gR K ' } Henderson (1966, p. 255). 49 where h is the height of the free surface above the horizontal bend, R = radius of bend In which equation V is assumed constant with depth which is close to that of actual turbulent flow in water (see F ig . 5.2). For an open channel V is also assumed to vary as a free vortex, i . e . VR = C (5.6) If R is large enough to assume V constant with radius this gives Ah = AR ^ (5.7) where Ah is total superelevation AR is width of channel A more exact integration of Eq. 5.3 gives h 2 - h , - C T g ^ ~ ^ (5.8) Now the velocity distribution found from the dilatant flow is almost linear with depth, so we may assume that the actual relationship of velocity with depth is V = ky 50 i . e . , dh = k 2 y 2 dR gR Integration over the depth gives o o & at fixed radius assuming dh/dR to be constant with depth y dh = k i . 1 y dR gR 3 dh = k i # 1 = 1 k 2 h 2 dR gR * 3 3 gR for horizontal channel, for which Y=h. Integrating from R1 to R 2 and h x to h 2 gives I l k 2 * * 2 h l h 2 3 \u00C2\u00A7 R l To i l lus trate the numerical results of these equations we take some assumed values, i . e . , h = 1 m, V = 5 m/sec, AR = B = 5 m av av ' with RM = 42 .5 and substitute in Eq. 5 .8 we get 51 Ah = 0.3 m from Eq. 5.9 we have Ah k 2 \u00E2\u0080\u009E R i K K 3g R2 The maximum velocity, V\u00E2\u0080\u009E = k\u00C2\u00BBy . Therefore k 2 h j h 2 = V 2 , so that, Ah = ^ - Sn i . e . k 2 h.h. = V 2 gives V M = 8.65 m/sec M Which shows that the near linear velocity distribution for dilatant flow yields a much higher velocity from superelevation data than the usually assumed Eqn. 5.7. Hungr et a l . (1984) quote the equation A V v B V 2 Ah = K \u00E2\u0080\u00A2 \u00E2\u0080\u0094 \u00E2\u0080\u0094 Rg where B is surface with of flow, and K is given by Myzuyama et a l . (1981) to range from 2.5 to 5.0 and the 2.5 value is used to estimate velocit ies from the equation, Ah = \u00E2\u0080\u00A2 B V 2 Rg for the same Ah, this equation yields V = 3.16 m/s 52 which is much lower than the value 8.65 m/sec estimated above. No jus t i f i cat ion of the 2.5 factor is given. Also, Professor M. Sugawara (National Research Centre for Disaster Protection, Kyoto, Japan) recently read Myzugama's paper in the original Japanese and reported that there was no jus t i f i cat ion of the 2.5 factor in the paper. For design purposes these estimated velocit ies are used to calculate impact forces using the momentum equation (Hungr et a l . , 1984), F T = 6 A V 2 sinB, i . e . F T = 6 Q V sinB where F T = total thrust A = flow cross-section 6 = debris density 8 = angle of flow direction to face of barrier . This velocity difference would increase the thrust force by a multiple of 7.5. It should be noted from Ippen and Knapp (1938) that at highly supercrit ical flows Ah could be as much as twice that estimated by Eq. (5.4). However the Froude number range we are investigating is generally low enough to have a minimal effect on our calculated velocity, for example, at a Froude number of 1.6, (a high value for debris torrent flow) Ah would increase by 35% reducing the estimated velocity by 14%. 5.3 Further Applications of Turbulent Flow Again i f we accept Bagnolds iner t ia l range for debris torrent and agree that turbulent conditions prevail then we can apply Reynold's 53 (1884) turbulent stress analysis to the flow, this may have applications to the runout zone of the torrent, which can have important design applications, part icularly with respect to zoning. 5.4 Turbulent Stress At any given point in turbulent flow, the instantaneous velocity and indeed a l l the instantaneous continuum properties are found to fluctuate rapidly and randomly about a mean value with respect to time and spatial direction. In the theoretical analysis of turbulent flow, i t is convenient to consider an instantaneous quality such as u, as the sum of i t s time averaged part u and momentary fluctuation part u' as shown in Fig . 5.3, i . e . , u = u + u' In steady flow u does not change with time. By definit ion to u = \u00E2\u0080\u0094 f u dt 0 t 0 u 1 = 7 f u' dt = 0 t J o Although the time average of fluctuation quantity is zero, i . e . u 1 = 0 , the quantity u ' 2 , u 'v ' , u'w', etc. which are time averages of the products of any two fluctuation components, w i l l not necessarily equal zero. These values are used as a measure of the magnitude of turbulent fluctuations at any given point in a turbulent flow f i e l d , i . e . the intensity of turbulent I is defined by 54 = / u ' 2 + v ' 2 + w' 2 /3 7 u where u is the magnitude of the velocity at the same point. We may consider the turbulent component at right angles to the flow u as / v ' 2 which we w i l l c a l l v' the root mean square turbulent velocity in the lateral direction. This v' value w i l l be used to estimate lateral spreading when the torrent leaves the constraints of the channel. We can calculate this component from the turbulent shear stress equation T \u00C2\u00B0 = * H i S \u00C2\u00B0 = ^ V * = s ^ e a r velocity = V ) hydraulic radius slope or v- = (g R. S 0 ) 1 2 \"o From the random nature of this turbulence we may assume a normal distribution so that for any stream parameters a s ta t i s t i ca l analysis can be done to estimate the potential zone of deposition. This of course, is an ideal situation based on an equal size material but represents the extreme case of maximum spreading. Since when a range of material sizes are deposited we would expect the larger boulders to deposit f i r s t and inhibit movement of smaller material. There are some where So = 55 striking examples of streams carrying ranges of sizes of material, where the larger sized material builds a steep bank or levee on each side, containing the smaller material within these boundaries. The extreme case can be examined using a normal s ta t i s t i ca l d i s t r i b u t i o n , to represent the randomness of these turbulent fluctuations. We can predict the range of deposition by recognizing that the lateral velocity fluctuation v' is equivalent to the standard deviation s, so that approximately 68% of the material w i l l move la tera l ly at less than v 1 , while another 27% w i l l move at less than 2v' (see F ig . 5.4). e.g. In an ideal situation with a channel slope of 20\u00C2\u00B0 and an hydraulic radius of 1 and a mainstream velocity of 5 m/s S\u00E2\u0080\u009E - 36 u =5 m/s then v ' = (9.8.1 \u00E2\u0080\u00A2 36 ) 1 ' 2 = 1.9 m/s giving an angle of spread of tan\" 1 (1.9/5) = 21\u00C2\u00B0 Therefore we would expect 68% of the material to spread at within an angle of 2 1 \u00C2\u00B0 . A further 27% should spread within tan\" 1 (3.8/5) = 3 7 \u00C2\u00B0 . 56 We therefore see that the angle of spreading of a debris torrent when i t reaches the fan region is physically limited by the turbulent velocity fluctuations, and only a small portion of debris w i l l spread beyond 20\u00C2\u00B0 of the centreline of the torrent. 57 Figure 5.1 Velocity/depth relationships applicable to the peak of debris torrent surge (Hungr et al., 1984). 58 \u00E2\u0080\u00A21 -2 .3 .4 .5 .6 .7 '.8 .9 1.0 u u max Figure 5.2 Velocity/depth prof i l es , comparing dilatant flow with laminar and turbulent (theoretical) . 59 Figure 5.3 Fluctuations of instantaneous velocity component with respect to time at a fixed point in steady flow. 60 Figure 5.4 Normally distributed lateral velocities giving angles of spread for torrent material. 61 CHAPTER 6 CONCLUSIONS A debris torrent is a massive sediment motion in which a l l particles as well as the i n t e r s t i t i a l f lu id are moved by gravity, this only occurs in steep channels where there is a rapid movement of water charged s o i l , rock and organic material. Debris torrent events are usually triggered by debris slides or avalanches from adjacent h i l l slopes, in the debris source area, which enter a channel and move direct ly down stream. Rainfal l i s the most important factor in the i n i t i a t i o n of these debris movements that culminate in debris torrent act iv i ty . The type of events that are most c r i t i c a l are, sustained regional rainstorms i . e . 300 mm or more of precipitation in 48 hours or convective c e l l act iv i ty which is responsible for intense bursts of r a i n f a l l over short time intervals and may contribute as much as 50 mm of precipitation to the catchment area in one hour. The effect of the addition of water to the s o i l mantle and the associated conditions for ins tab i l i ty were investigated by Terzaghi (1950) and Skempton and Delong (1957) , from the work of the latter a family of curves for various combinations of s o i l parameters were derived (Fig. 25) , from which a c r i t i c a l slope angle p can be estimated. It was noted that this was for an ideal situation and that apparent cohesion due to true cohesion plus root strength of vegetation can alter the factor of safety quite dramatically. Removal of forest cover in the debris source area by logging was also found to be a major contributing factor, since this decreases root 62 strength, interrupts surface drainage and changes the distribution of mass on the slope surface by cut and f i l l construction. In addition shading of snow pack is reduced, increasing the incidence of snow avalanching which can in i t ia te debris movement. It was also concluded that not only the incidence of land movement is increased but rates of erosion can increase markedly due to denudation. An examination of the precipitation events associated with debris torrents was carried out with particular reference to the precipitation measurement networks and current practice of assuming stationary growth and decay of storms. Due to the sparse data network, in the area of Howe Sound, where most data stations are located along the major transportation routes, much of the actual precipitation in the higher catchments is not reflected in the gauging network. The main components of the precipitation not being picked up by the gauges are those of convective c e l l act iv i ty and the orographic effects of the mountains. In order to use data in a predictive fashion to account for this orographic effect a much more comprehensive data collection system is required along with a model to interpret the orographic component. The convective cel ls can be as small as 1.5 km and would require sophisticated radar tracking for accurate location, as discussed by Bonser (1982). The data network density in B.C. was compared to other areas of the world and to W.M.O. specifications and was found to f a l l far below these recommendations. The mechanism of movement of a torrent was considered, with special reference to the transportation of boulders by the flow. The apparent ease with which these large rocks are moved has been a subject for much 63 research to date. Two theories were examined, Bagnold's (1954) Dilatant Fluid Model, and Johnson's (1970) Plastico-Viscous Model. Bagnold's model showed that when particles were sheared together the larger particles tended to dr i f t toward the free surface and since the flow surface moves fastest, the larger material dr i f ts toward the front of the flow and is supported by exchanges in momentum with the smaller particles beneath. This model gave a good explanation of the phenomenon observed, where boulders appeared to \"float\" toward the front of the torrent. The Plastico-Viscous Model proposed that the particles are supported by matrix strength and that the viscosity of the i n t e r s t i t i a l f lu id determines the hydraulic behaviour. An evaluation of the models revealed that the grain r ich debris does not contain enough clay to be treated as a Bingham Fluid (Plastico-Viscous) and that apparent high viscosity was the result of the res i s t -ance caused by the col l i s ions of part ic les . It was concluded that the debris torrent could best be modelled as a dilatant f lu id in i t s fu l ly iner t ia l (turbulent) range. Other workers, Hungr et a l . (1984) have concluded that the debris torrent flow was laminar, due to i t s apparent calm surface and i t s velocity depth prof i l e . Hungr et a l . plotted velocity vs. depth based on eyewitness reports and superelevation data and found an almost linear relation very close to that of laminar flow. Since the dilatant flow model is a turbulent one i t was thought necessary to examine and plot velocity vs depth for this dilatant flow. This dilatant-turbulent velocity prof i le varies with depth to the power of 1.5, which when plotted is a close approximation to a linear velocity variat ion. This 64 contrasts with the logarithmic distribution of normal turbulent flow and the parabolic distribution of laminar flow. Superelevation of the debris flow in a bend has been used by some workers to estimate flow veloci t ies . Re-analysis of the flow in a bend using the near-linear velocity distribution predicted from the di latant-turbulent model indicates that the use of conventional superelevation theory may seriously underestimate debris veloci t ies . Design c r i t e r i a based on normal f lu id flow around bends gave velocit ies approximately 2.7 times less than these calculation using the linear relat ion. Further, when these velocit ies are used to calculate thrust forces which contain a V 2 term the thrust forces would be under-estimated by a factor of approximately 7.5. These numerical values are approximate and for i l lus tra t ive purposes, but they do show the possible range of errors. This dilatant-turbulent analysis has also been used to estimate lateral spreading of debris torrent material when i t s p i l l s out later-a l l y from a constrained channel on to the unconstrained debris fan region. An analysis is based on Reynolds turbulent stresses is used to give a s ta t i s t i ca l estimate of the spread of the debris when i t leaves the channel. This s ta t i s t i ca l analysis can be used to estimate lateral spreading of debris and hence to establish hazard zones on the debris fans. The most important item revealed in this research is the velocity v depth prof i le for the dilatant flow, which is very different from what one expects in turbulent flow in water. Further experimental research in this area is needed to continue this analysis and the predicted velocit ies and thrust forces based on this linear relationship. 65 REFERENCES 1. Ashida, K. , Daido, A . , Takahashi, T. and Mizuyama, T. Study on the Resistance Law and the Ini t iat ion of Motions of Bed Particles in a Steep Slope Channel: Annual Disaster Prevention Research Institute, Kyoto University 16B 481-94, 1973. 2. Aulitzky, H. Endangered Alpine Regions and Disaster Prevention Measures: Nature and Environment Series 6, Council of Europe, Strasbourg, 103 p, 1974. 3. Bagnold, R.A. Experiments on A Gravity Free Dispersion of Large Solid Spheres in a Newtonian Fluid Under Shear: Proceedings Royal Society of London, Vol . 225A, August 1954. 4. Bonser, J .D. 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Distribution of Precipitation in Mountainous Areas Symposium, 1973, Vol . 1. 18. Middleton, G.V. and Hampton, M.A. Subaqueous Sediment Transport and Deposition by Sediment Gravity Flow: in Marine Sediment Transport and Environmental Management, Ed. D . J . Stanley, D .J .P . Swift, 11: 197-218, N.Y. Wiley, 1976. 19. Miles, M.J . and Kellerhals , R. Some Engineering Aspects of Debris Torrents: CSCE 5th Canadian Hydrotechnical Conference, 1981. 20. Mizuyama, T. and Uehara, S. Debris Flow in Steep Channel Curves: Japanese C i v i l Engineering Journal 23, pp. 243-248, 1981. 21. Nasmith, H.W. and Mercer, A.G. Design of Dykes to Protect Against Debris Flows at Port Al i ce , B . C . : Canadian Geotechnical Journal, Vol . 16, No. 4, pp. 748-775, 1979. 22. Reynolds, 0. Experiments Showing Dilatancy: Proceedings Royal Institute of Great Bri ta in (1884-1886). 23. Russell , S.O. 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Swanston, D.N. and Swanson, F . J . Timber Harvesting, Mass Erosion and Steepland Forest Geomorphology in the Pacif ic North West: Geomorphology and Engineering, Editor Coates, D.R. , Dowden, Hutchinson and Ross, Inc. , Stroudsburg, Pennsylvania, pp. 199-221, 1976. 30. Takahashi, T. Debris Flow in Prismatic Open Channels: Journal of Hydraulic Divis ion, ASCE, March 1980. 31. Takahashi, T. Debris Flow: Annual Review of Fluid Mechanics, No. 13, pp. 57-77, 1981. 32. Terzaghi, K. Mechanism of Landslides: in Theory to Practice in Soi l Mechanics, Wiley & Sons, N .Y . , 1960. 33. Thurber Consultants. Debris Torrents and Flooding Hazards on Highway 99, Howe Sound, B . C . , Apr i l 1983. 34. Whitmore, J .S . The variation of Mean Annual Rainfal l with Altitude and Locality in South Afr ica , as Determined by Multiple Curvilinear Regression Analysis in World Meterological Office: Distribution of Precipitation in Mountainous Areas, Symposium, Vol . 1, 1973. 35. Woods, P . J . Province of Br i t i sh Columbia, Ministry of the Environment, Water Management Branch Memo: March 1, 1983. 36. World Meterological Office. Manual for Estimating of Probable Maximum Precipitation: WMO No. 332, Geneva, Switzerland, 1973. 37. Wright, J . B . Precipitation Patterns Over Vancouver City and Lower Fraser Valley: Meterological Branch, Department of Transport, CIR 4474 TEC 623, 1966. 38. Yoshimo, M.M. Climate in a Small Area: University of Tokyo Press, 1975. "@en . "Thesis/Dissertation"@en . "10.14288/1.0062526"@en . "eng"@en . "Civil Engineering"@en . "Vancouver : University of British Columbia Library"@en . "University of British Columbia"@en . "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en . "Graduate"@en . "Debris torrent mechanisms"@en . "Text"@en . "http://hdl.handle.net/2429/26739"@en .