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Debris torrent mechanisms Smyth, Kenneth Jeffrey 1987

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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 © 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 . . • 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 <J>' 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° to 56° 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<J> T = shearing resistance/unit area <f> = 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 • Y )z cos 20 tand>' • . 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<f>' 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<J>' (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 <J)'. When this 8 value was substituted in the equation a positive value of c' was obtained. This was attributed, at least in part, to root strength of the vegetation. It is important to note that for re lat ive ly thin soi ls in steep terrain where the effective normal forces are low, small changes in apparent cohesion w i l l have a dramatic influence on the factor of safety (Sidle and Swanston, 1982). For this s i te , based on a porewater pressure at fai lure of 2.17 kPa the factor of safety calculated for c' = 1.0 and 5.0 kPa were 0.75 and 1.73, respectively. This relationship between c' and factor of safety for thin soi ls indicates that even small values for rooting strength and true s o i l cohesion can be c r i t i c a l in determining the s tab i l i ty of these steep slopes. 2.2 Instabi l i ty Due to Removal of Forest Cover An important factor in the creation of ins tab i l i ty in the debris source area is the removal of forest cover by logging or f i r e . The effects of logging have been studied by many researchers and is surrounded by much controversy. These effects are: Eisbacher, 1982 • Intact forest absorbs some of the rain during storms and results in less or at least delayed runoff. • A l iv ing system of roots binds the colluvium to the substratum, adding some strength to the slope. Aulitzky, 1974 notes that: • Rooting strength is decreased which possibly released creep generated stresses in the so i l root complex. 9 • Transpiration is decreased. • Shading of snowpack is lost , increasing runoff. • Interruption of surface drainage associated with road surfaces, ditches and culverts. • Alteration of subsurface water movements especially where road cuts intersect the water table. • Change in distribution of mass on a slope surface by cut and f i l l construction. It seems that the problem of large clearcutting is generally compounded by unmanaged access roads which commonly are the f i r s t sources of debris into the adjacent creek. It was found (Aulitzky, 1974) that in Alpine areas, slides in unstable regions transported a two to eight times greater volume of material when clearcut than did those where forest cover was maintained. He also found that the combined impact of roads and clearcut logging constituted a f ive-fold increase in erosion relative to undisturbed forested areas. In a study for protection works against debris movement at Port Al i ce , B.C. (Nasmith and Mercer, 1979) i t was noted that much of the slope above the town was logged prior to construction of the town and that the debris movement had started at an upper logging road. It was concluded (Eisbacher and Clague, 1981) that deforestation due to urbanization and clearcut logging may increase the incidence of debris avalanches and slides on moderate to steep slopes. In addition, logging debris along stream courses may impede surface drainage and cause additional slope fai lures . 10 Another cause of forest cover removal is f i r e . Often in the dry-season vegetation cover is highly flammable and i f the watershed is burned and precipiation between the f ire and the f i r s t storm is low, l i t t l e vegetative recovery is possible (Scott, 1969). Consequently when a storm hits the i n i t i a l r a i n f a l l would be absorbed by the dry s o i l mantle and the watershed rapidly saturated. When the next storm hits conditions are ideal for slope fa i lure . In a study of flood erosion in L . A . county i t was found (Eaton, 1936) , that when the watershed cover was destroyed erosion rates increased by f i f t y to one hundred times over that with undisturbed vegetative cover and that the best protection from debris is the normal vegetative cover. After denudation, any protection program is secondary, far less eff icient and much more costly. 2.3 Instabi l i ty from Other Causes Terzaghi (1950) examines land movement in detai l and cites the following causes of ins tabi l i ty : • Undercutting of the foot of the slope or deposition of earth or other material along the upper edge of the slope. Both operations produce an increase of shearing stresses on the ground beneath the slope. When the average shearing stress on the potential sl ide surface becomes equal to the average shearing resistance a debris slide occurs. • Earthquake shocks increase the shearing stress along the potential surface of the s l iding whereas the shearing resistance remains unchanged. 11 A l l the researches c i t e d agree that p r e c i p i a t i o n i s the e s s e n t i a l ingredient i n causing i n s t a b i l i t y i n the debris source area and that disturbance of the watershed by deforestation and i t s attendant construction can not only accelerate the phenomenon but increase the amount of debris a v a i l a b l e to the torrent channel. Figure 2.1 Characteristic of debris source area (Campbell, 1975) 13 Figure 2.2 L i m i t i n g slopes for s o i l s l i p s , Santa Monica mountains (Campbell, 1975). Figure 2.3. Diagram showing buildup of perched water table in colluvial soil during heavy rainfall (Campbell, 1975). 15 Figure 2.4. Diagram showing z such that mz is the v e r t i c a l height of ground water table above s l i p surface (Campbell, 1975). 16 SLOPE ANGLE. IN DEGREES Figure 2.5. R e l a t i o n of f a i l u r e i n some t y p i c a l s o i l s t o ground water content and slope angle. Computed curves f o r F=l ( f a i l u r e c r i t e r i o n ) at s e l e c t e d values of y and The curves f o r most n a t u r a l nonclayey s o i l s l i e between curves 1 and 4. F i e l d s to the l e f t and r i g h t of each curve are s t a b l e and un s t a b l e , r e s p e c t i v e l y (Campbell, 1975). 17 CHAPTER 3  PRECIPITATION 3.1 Class i f icat ion Meterologists have adopted a qualitative c lass i f icat ion scheme and view precipitation phenomena on 3 scales. 3.1.1 Synoptic or Macroscale Storms which are discernable on weather sa te l l i t e photographs, associated with low pressure and frontal systems. They are generally in the order of hundreds of kilometers in size. In the Vancouver area they are usually in the form of cyclonic systems moving eastward of the Pacific Ocean. 3.1.2 Mesoscale Within the band of precipitation from the synoptic system is a "pebbly structure" as seen by radar (Bonser, 1982), of patterns of precipitat ion. Generally they are typical ly 10 to 50 km in extent, up to 60 km apart and move in step as the band of precipitation sweeps over the earth. Thunderstorms are an example of a mesoscale system. 3.1.3 Microscale Convective cel ls which are responsible for intense bursts of ra in -f a l l over short time intervals . They range from 2 to 10 km across and last up to an hour. They are generated by a local ins tab i l i ty in the atmosphere, grow rapidly and often contain strong updrafts and down-drafts . 18 Types of precipitation are c lass i f ied in 3 principal categories (Bonser, 1982): Cyclonic - Rainfal l arises when moist a ir masses in a frontal system rise due to the horizontal convergence of envelopes of a ir having different temperatures. Orographic - Rainfal l i s caused by l i f t i n g of the a ir mass by topo-graphic features such as mountain barriers . The maximum amount of precipitation comes on the middle part of the slope of a high mountain (Yoshino, 1975). Convective - Differential heating of adjacent air masses generate local ins tab i l i ty . Individual convective cel ls form within the broad r a i n f a l l areas and appear to remain in position re la -tive to the broad r a i n f a l l areas. Cells remain i d e n t i f i -able for between 30 and 60 minutes. Peak intensities are usually observed to be of 10 minutes or shorter. Progression of these systems across the B.C. coast have been followed by radar and i t was concluded by Bonser (1982): "It is only by observing these patterns that one begins to appreciate the complexity inherent in the precipitat ion, a complexity not at a l l apparent from conventional hyetograph records." 3.2 Data Collection When one considers the areas subject to debris torrent act iv i ty , i . e . , the steep upper reaches of small drainage basins, these variations in precipitation patterns become very important. The l i terature i n d i -cates basins subject to torrent act iv i ty ranging in area from 0.03 to 19 0.17 km2 (Scott, 1969), while in Howe Sound they range from O.A to A.7 km 2. These small basins have the size and location to be influenced s ignif icantly by the ce l lular and orographic effects noted above. Current practice is to analyse point r a i n f a l l data by ignoring the movement of storms, assuming a stationary growth and decay, or to consider a constant r a i n f a l l rate over an area for a c r i t i c a l time period. An expl ic i t consideration of storm growth, velocity and track is a preferable approach but this requires knowledge of the spatial and temporal variation of precipitat ion. In the Howe Sound area the data coverage is biased towards low elevation s i tes , most stations are located along the major transporta-tion routes and the large block of mountains between the Fraser Canyon and Highway 99 has data coverage only along i t s southern margin. The measured amount of r a i n f a l l in a mountainous area differs considerably according to the method of observation and equally great differences arise according to the density and position of observation points because of the great local v a r i a b i l i t y of r a i n f a l l . A study from Japan (Yoshino, 1975) shows the results of studies in the v i c in i ty of Isohara. Table 3.1 shows the s tat i s t ics of every r a i n f a l l of over 30 mm per one cyclone from September 1950 to September 1951. This table shows the large errors inherent in a sparse gauging network. Miles and Kellerhals (1981) investigated a debris torrent in the region of Hope, B.C. for the period of December 26-27, 1980, and estima-ted that the r a i n f a l l of 75 mm in 25 hours, measured at valley bottom, to have a return period of 2 to 5 years whereas the flood discharges from the same storm indicated a 50 year return period. It was concluded that this rather large water def ic i t was made up from the "condensation 20 of melting snow". In the same paper they conclude that based on valley bottom precipitation the return period for a debris torrent design r a i n f a l l of 150 mm in 2k hours would be upwards of 50 years but they note that short term data collected in the mountain passes by the B.C. Ministry of Highways indicate that this r a i n f a l l has a recurrence period of 15 years. It would seem possible that the main causes of these high runoff events is due to cel lular and orographic phenomena which are not reflected in the lower level gauges, as Bonser (1982) concludes, "it is the microscale precipitation which is most responsible for these peak runoff responses in small watersheds". Apart from the areal distribution of the gauges i t i s important to consider the temporal nature of these high intensity events. Since these high intensity cel ls can last for less than one hour, the hourly rain gauge can miss the peaks within the hour period. A comparison of hourly data and 10 minute radar data (Bonser, 1982) used in an urban runoff model showed that the peak runoff from the hourly data under-estimated that from the 10 minute radar measurements by a factor of 3, and although the timings of peaks agree, a l l those for the hourly data show lower flows. This is due to the averaging of peak intensities in the hourly records (see F ig . 3.1). The Vancouver area exhibits strong orographic controls (Shaeffer, 1973). In a storm analysis of July 1972 i t was shown that while 50 mm f e l l at Delta Tsawwassen Beach over 250 mm f e l l at Hollyburn Ridge, e l . 930 m. In the lower Fraser Valley much annual precipitation is produced by vigorous frontal storms similar to the one in question and Shaeffer (1973) contends that the r a i n f a l l distribution of such a storm should resemble the distribution of mean annual precipitation since orographic 21 controls are fixed. A comparison of published maps of mean annual precipitation over the lower Fraser valley (Wright, 1966) supported this contention. Thus over most of the area inferences concerning orographic influences could bear relationships to these represented by mean annual distr ibution. Rainfal l rates for the same storm were calculated by dividing total precipitation at each point by the duration, which also increased with elevation and i t was found that intensities doubled between sea level and the mountains north of the c i ty . These are general trends and should be considered where return periods are being estimated from valley bottom data, but due to the sparcity of the data points, they should not be expected to apply to every storm since para-meters such as wind speed, wind duration, cloud type and cloud height can affect the orographic component. The B.C. Water Resources and C . A . E . S . operated 10 instrument sites across the Beaufort Range on Vancouver Island. The available results showed a general increase in precipitation with elevation, horizontal variations being significant at a l l levels and indicating that local variations in exposure, slope and aspect are important (Table 3.2). The Department of Highways have instal led rain gauges at upper elevations in the Howe Sound area, but they have been malfunctioning and, the data collect so far is not useful. When these gauges are operating they may give the information required to estimate the ra in -f a l l events that trigger torrent events. As i t is we can say, that in these high elevation catchments prone to torrents, the orographic i n f l u -ences are significant and produce greater amounts of precipitation than our available gauging networks show. This coupled with high intensity ce l lular act iv i ty are the major contributing factors in debris torrent 22 i n i t i a t i o n . Sustained greater durations and intensities leave f i e ld conditions (ground water levels) requiring perhaps only a short intense burst of r a i n f a l l to cause ins tab i l i ty . Such intense ce l lular act iv i ty may not pass over the gauges. Thurber (1983) questions this on the basis that their information indicates that these cel ls appear to have dimensions in the order of 10 km or greater. However, there may be greater variation in size, (Bonser, 1982; Penny, C . A . E . S . pers. comm.). They suggest that these cel ls may indeed be as small as 1.5 km. Thurber concludes, "If there had been exceptionally high r a i n f a l l intensities associated with most of the events in the study area, s imilarly high intensities would have been recorded nearby at least on some occasions" and that, "there is no conclusive evidence that climatic conditions alone have controlled the occurrence of debris torrents". However, in Japan, studies have shown that debris slides and land-sl ips are strongly correlated with heavy ra in . In one study (Yoshino, 1975) i t was found that the areal distribution of density of landslides in the central part of the landslides does not correspond to the d i s t r i -bution pattern of the degradation density c lass i f icat ion by rocks, but i t closely correlated to the r a i n f a l l distribution and that when the amount of r a i n f a l l surpassed a certain l imit any slope with a gradient of 3 0 ° - 5 0 ° is subject to landslide regardless of the difference in geological features. In another study, (Yoshino, 1975) i t was confirmed that the areas with most frequent landslides nearly coincide with the areas where the maximum r a i n f a l l exceeds 10-15 mm/10 minutes or 30-50 mm/hour. 23 Although there may be other contributing factors that may aid the process and increase the extent of land movement there is a vast amount of evidence to support the bel ief that r a i n f a l l i s the decisive factor in the occurrence of debris slides and debris torrents (Eisbacher, 1982; Eaton, 1936; and Campbell, 1975). In addition i t appears that many of these r a i n f a l l events are outside the scope of our present measurement f a c i l i t i e s . Attempts to take the available valley bottom data and from i t predict r a i n f a l l rates and durations at higher elevations is a complicated procedure requiring some caution. 3.3 Precipitation Network As suggested earl ier the gauging networks in Br i t i sh Columbia are quite sparse and in higher elevation zones, generally non-existent. To put this into a world context, Ferguson (1973) has provided guidelines for the density of precipitat ion, snow course, hydrometric and evapora-tion networks for various classes of physiographic and climatic condi-tions (see Table 3.3). This table indicates that except for arid or polar regions, average precipitation network densities in mountainous regions should be approximately 3 to 6 times as large as those in f lat terrain. Table 3.A provides information on current precipitation net-works in a number of countries and only Switzerland meets or exceeds the WMO specification. The important area to note is that of B.C. and by reference to Figs. 3.2 and 3.3, we see that the precipitation network in B.C. fa l l s very far below the WMO recommendations, with most stations in low lying areas, below 600 m. A major problem in a l l areas is the relative sparseness of data at high elevation. Stations tend to be concentrated at valley locations as seen in F ig . 3.3. 24 3.4 Predicting Orographic Effects There are a number of models that can predict to some degree what the orographic effects of a mountain barrier may be. A simple linear model is used by the World Meterological Organization (W.M.O., 1973) . If i t i s assumed that the air is saturated and that temperature decreases along r is ing streamlines at the moist adiabatic rate, and the flow is treated as a single layer of a ir between the ground and the nodal surface, between 400 and 100 mb where the a ir flow is assumed horizontal, the rate of precipitation is R = V, M i ( W l ~ w* w? where R = r a i n f a l l rate in cm/sec V x = mean inflow wind speed in cm/sec Wa ,W2 = inflow and outflow precipitation water in cm ( l iquid water equivalent) found from tables of precipitable water in a saturated pseudo-adiabatic atmosphere (W.M.O., 1973) Y = horizontal distance in cm AP 1 ,AP 2 = inflow and outflow pressure differences in mb The model considers the flow of a ir in a vert ica l plane at right angles to a mountain chain or ridge (Fig. 3.4), From the equation one can see the variation of orographic effects with wind direction and temperature. 25 This model is highly simplified as i t is well known that a l l the condensate does not f a l l out on the mountain barrier . Thus the "efficiency" with which the condensate is removed is less than one. The measure for the condensate is the precipitable water which expresses the total mass of water vapour in a vert ica l column of the atmosphere, to say that the a ir contains 3 cm of precipitable water signif ies that each vert ica l column of 1 cm2 cross-section contains 3 gm of water in vapour form. If the water vapour were a l l condensed into l iquid water and deposited at the base of the column the accumulated l iquid would be 3 cm deep. No natural process w i l l precipitate a l l the water vapour in the atmosphere. There appears to be an elevation range where this "efficiency" is maximum and related to a specific cloud type ( E l l i o t , 1977). When data from the Blue Canyon, Cal i fornia was plotted against that calculated by the W.M.O. model a marked increase in efficiency was found at approxi-mately 1250 m (Fig. 3.5). Whitmore (1972), in examining the effects of altitude on precipi ta-tion in South Africa concluded that mean annual r a i n f a l l increases f a i r l y steadily up to about 1300 m, above which altitude the r a i n f a l l increases only s l ight ly . Lessman et a l . (1972) found that, as water vapour decreases with height, tropical r a i n f a l l increases with height only up to a certain level and decreases with additional height, these features vary with extent, slope and orientation of the barrier , i t s location relative to humidity sources, prevailing wind directions and velocity as well as the vert ica l extent and degree of s tab i l i ty of the humid layers in the atmosphere and (Shaw, 1972) found that a l l the meteorological characteristics are greatly influenced by alt itude, and 26 aspect has an added effect on precipitat ion. Temperature and humidity decrease with height and above the layer of maximum cloud development (1000-2000 m) humidity drops off s ignif icantly . On reaching plateaus in high mountains r a i n f a l l and cloud amounts become less and the intensity of rain diminishes. A more sophisticated model which attempts to take this "efficiency" into account was developed by U.S. Dept. of Commerce, Office of Hydrology ( E l l i o t , 1977). He states that the "efficiency" varies with the characteristics of the orographic cloud, especially with respect to i t s cloud top temperature since this is a measure of the abundance of the available ice-forming nuclei that get the precipitation process started. The "efficiencies" associated with various cloud formations must be found by reference to actual storm data that include, besides precipitation rates, frequent sounding data from the immediate upwind valley. The model depends in a complex way upon character of the terrain, the efficiency with which the microphysical mechanisms remove cloud condensate as precipitat ion, the wind direction and speed the depth of cloud and the a ir mass s tab i l i ty . It gives a transferable method of computing mean areal precipitation over basins where the real time precipitations data is limited such as B.C. The output of the program is a grid point map of the efficiency, which represents a prediction of the orographic component of precipi ta-tion over the barrier times a number that is constant over the entire grid for a given case. In order to use this map i t is necessary to adjust the magnitude at grid points by the use of an observed precipi ta-tion value. The input e (efficiency) measures the fraction of cloud water that is removed as precipitation and is assumed constant over the entire barrier for any given cloud type. The model identifies four 27 basic cloud types, stable warm, stable cold, unstable warm, and unstable cold (unstable i f the positive area on the thermodynamic chart extends through a layer deeper than 75 mb and warm i f cloud top temperature over the barrier is warmer than -30"C). The results show a fa ir correlation in some sites but poor in others where"barrier wind effects are too complex for the model". One should note however that while other researchers note a marked change in efficiency with altitude this model assumes i t constant for a given cloud type. This model uses 37 parameters in a l l and i f the data required were available and i t could be "tuned" to the Howe Sound area i t would be a great aid in dealing with the unmeasureable orographic component of precipitation that is so important in the debris torrent situation. The Howe Sound situation requires estimation of these orographic effects, but the models examined a l l have shortcomings, certainly a linear extrapolation of valley bottom data may be useful for annual precipitat ion, but for an individual storm this does not take into account the many other parameters. At present the data col lection network does not enable us to correlate the actual basin precipitation with torrent events and unt i l such time as the network is expanded a return period prediction based on synoptic patterns is impossible. Number of Stations 3 6 9 12 15 18 21 24 Area Per Station km2 280 140 90 70 60 50 40 35 Error % 25 18 13 10 8 6 5 3 Table 3.1 Errors inherent in sparse gauging network (after Yoshino, 1975) STA El(m) Relative Precip. to A % A 425 100 B 842 106 C 1395 147 D 740 110 E 425 75 F 425 88 G 750 102 H 1380 165 I 760 116 J 425 73 Table 3.2 Data from Beaufort Range, Vancouver Island. Table 3.3 Network specifications recommended by WMO (1970). Figures show maximum specific areas (inverse of network density) in km2 per station. Provisional networks may be tolerated under d i f f i c u l t conditions. TYPE OF REGION PRECIPITATION Range of Norms Provisional SNOW COURSES HYDROMETRIC Range of Norms Provisional EVAPORATION 1. Flat regions of temperate mediter-ranean and tropical zones. 2. Mountainous regions of temperate mediterranean and tropical zones. 3. Arid and polar zones. 4. Homogeneous plains areas. 5. Less homogeneous regions - Arid regions - Humid temperate - Cold regions 600-900 100-250 1500-10,000 900-3000 1000-2500 3000-10,000 250-1000 300-1000 1000-5000 5000-20,000 5000 2000-3000 30,000 50,000 100,000 30 Table 3.4 Precipitation network data for selected regions - 1971. (Ferguson, 1973) REGION 10*km2 TOTAL AREA DAILY PRECIPITATION STATIONS DENSITY STATIONS/ 10*km2 SPECIFIC AREA km2/STATION Switzerland 4.1 463 112 89 Sweden 44.6 918 20.6 486 Norway 32.4 730 22.5 445 Br i t i sh Columbia, Canada 94.1 380 4.1 2480 Utah, U.S.A. 21.2 166 7.8 1280 31 FRASERVIEW CATCHMENT OUTLEI HYDROGRAPH T — i 1 1 1 1 1 1 1 1 1 1 1 1 1 i 1 1 r IP MINLTfC DATA HOURLY DAIA C O 2 0 . 0 4 0 . 0 tC.O 6 0 . 0 C O . O 120.0 U O . O 16D.C tsC.C TCC.C TIMC (MINUTtS) (X10 1 ) Figure 3.1. Comparison of SWMM hydrographs from ten minute radar and equivalent hourly gauge data (Bonser, 1982). 32 0-6 • 1 Land Mass I Precipitation Stations. / , 12 Snow courses 6-12 12-18 18-24 E L E V A T I O N INTERVAL (hundreds of metres) 24-30 Figure 3.2. Relative distributions of land area, precipi tat ion stations and snow courses by elevation interval in B r i t i s h Columbia. In early 1971 there were 370 precipitat ion stations and 215 snow courses in operation (Ferguson, 1973). 33 3 -100 9 8 7 6 5 10 9 8 7 6 1.0 9 0 1 127) 160) (28) 1)9) (16) (321 (41) Ringe Rscommtrxtad bv WMO (1970) (16) 132) 100 260 500 1.000 z o 10.000 0 6 6-12 12- 18 ELEVATION RANGE (HUNDREDS OF METRES) 18-24 Figure 3.3. Densities of precipitation networks (daily reporting stations, 1971) by elevation interval in Switzerland, Norway and British Columbia. Figures in brackets represent percentages of the total area of each region falling in the elevation range. For example 41 per cent of British Columbia is in the range 600 to 1200 metres (Ferguson, 1973). Figure 3.4. S i m p l i f i e d i n f l o w and outflow wind p r o f i l e s over a mountain b a r r i e r . Figure 3.5. Data from W.M.O. (1973), p. 64. 36 CHAPTER A  DEBRIS TORRENT MOVEMENT A . l Massive Sediment Motion A debris torrent is a form of massive sediment motion which means the f a l l i n g , s l iding or flowing of conglomerate or the dispersion of sediment, 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, so that the relative velocity between the so l id phase and f lu id in the direction of displacement of mass plays only a minor role . By contrast, in f lu id flow, l i f t and drag forces due to relative velocity are essential for individual part ic le transport. A.2 Ini t iat ion of Movement in Torrent Stream Once sufficient material from the debris source area is deposited in the stream bed, the channel is then a potential debris torrent given the right conditions of slope and precipitat ion. Imagine a thick uniform layer of loosely packed non-cohesive grains, whose slope angle is 8. It is assumed that at the moment when surface flow of water of depth h 0 appears the pore spaces are saturated and para l le l seepage flow occurs. The characteristic distribution of shear stress in the bed is l ike that shown in F ig . A . l , in which x is the applied tangential stress and the internal resist ive stress. Case 1 (Fig. A.la) occurs under the condition (Takahashi, 1981), C^ (o-p) tan<J> * C*(a-p)+p (A. l ) 37 in which •= grain concentration by volume in the static debris bed. o,p = densities of grains and fluids respectively <f> = 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<f> (4.2) C^(o-p) + p ( l+h 0 a£i ) 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 £ tan<J> (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^ £ K h 0 , in which K is a numerical coefficient, determined from experiment to be about 0.7. Substituting the condition a y £ Kh 0 into Equation (4.3) gives 38 C*(o-p) tanS £ tan<f> (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<J> + u du/dy C = cohesion o = normal stress n <p = angle of internal f r i c t ion This model, as did the Bingham f l u i d , s t i l l attributes the transport of large boulders to their bouyancy due to the strength of the i n t e r s t i t i a l clay s lurry. Hampton (1975) obtained experimental relationships bewteen the clay contents in clay-water s lurry and the competence to float grains. These results show that sand sized particles can be floated but larger ones cannot. 4.6 Evaluation of Models Takahashi (1980) re-evaluates the role of clay content in the ordinary grain-rich debris and emphasizes that the effects of clay are minor and consequently the flow is di latant. He concludes: • Ordinary grain-rich debris contains much less clay component for i t to be treated as a Bingham f l u i d . The apparent high viscosity should be the result of the resistance caused by col l is ions of part ic les . • Debris flows of the ordinary scales may be modelled by Bagnold*s grain flows in the fu l ly iner t ia l range. The debris torrent is of course a debris flow in the fu l ly iner t ia l range. However i t is important to draw the dist inction between the clay 43 charged mudflow that is modelled as a Bingham f lu id and the debris torrent phenomenon that appears best modelled as a dilatant f lu id . As shown in F ig . 4.2, the domain of occurrence of various types of sediment transportation are defined by Equations 4.1, 4.2, 4.3, and 4.4, the condition for f a l l (0=<j>) , 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<f> - . , 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<J> = 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 • 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 — ) 3 ' 2 • 2/3 (-y ) + C \ n * w ^ y m a x X D 6 1 ' 2 -'max at the boundary u = 0, y = 0 0 = — (1) • 2/3 (-y ) + C X D 6 1 ' 2 m X 47 C = 2/3 • 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 • y a v n y •'max . n 17max X D 6 1 / 2 ''max X D o 1 ' 2 1 1 ' 2 u = 2/3 — v v {[-1 + -2—]"* + 1} (5.2) let or . n , . , , "max y X D 6 1 ' 2 •'max T 1 ' 2 0 2/3 y = A a const. X D 6 1 ' 2 m a x u = A [ ( - l + ) + 1] ymax •'max when u = u , y = y max y max so 5.2 yields T 1 ' 2 u = 2/3 — y = A RAAX X D 6 i ' 2 m a X y . 3 ' 2 1 - (1 - -f—) (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 — ) 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 § 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 „ R i K K 3g R2 The maximum velocity, V„ = k»y . 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 • — — 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 = • 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 = — 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 ° = * H i S ° = ^ 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° and an hydraulic radius of 1 and a mainstream velocity of 5 m/s S„ - 36 u =5 m/s then v ' = (9.8.1 • 36 ) 1 ' 2 = 1.9 m/s giving an angle of spread of tan" 1 (1.9/5) = 21° Therefore we would expect 68% of the material to spread at within an angle of 2 1 ° . A further 27% should spread within tan" 1 (3.8/5) = 3 7 ° . 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° 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 •1 -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. Precipitation Radar as a Source of Hydrometerological Data: M.A.Sc. Thesis, University of Br i t i sh Columbia, 1982. 5. Campbell, R.H. Soi l S l ips , Debris Flows and Rainstorms in the Santa Monica Mountains and V i c i n i t y , Southern Cal i fornia: U.S. Geological Survey Professional Paper 851, 51 p, 1975. 6. Daily, J.W. and Harleman, D . R . F . , Fluid Dynamics: Addison Wesely, 1966. 7. Eaton, C. Flood and Erosion Control Problems and Their Solutions: A . S . C . E . Proceeding, Vol . 62, No. 8, Part 2, Transaction No. 101, 1930. 8. Eisbacher, G.H. Slope Stabi l i ty and Land Use in Mountain Valleys: Geoscience Canada, Vol . 9, No. 1, 1982. 9. E l l i o t , R.D. Final Report on Methods for Estimating Areal Precipitation in Mountain Areas: Report 77-13, Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service Office of Hydrology, 1977. 10. Ferguson, H.L. Precipitation Network Design for Large Mountain Areas: World Meterological Office, 1973. 11. Hampton, M.A. Competence of Fine-Grained Debris Flows: Journal of Sedimentary Petrology 45, No. 4, December 1975. 12. Henderson, F.M. Open Channel Flow: MacMillan Co. , Inc. , 1966. 13. Hungr, 0. , Morgan, G.C. and Kellerhals , R. Quantitative Analysis of Debris Torrent Hazards for Design of Remedial Measures: Canadian Geotechnical Journal, 1984. 14. Ippen, A . T . and Knapp, R.T. Experimental Investigation of Flow in Curved Channels: U.S. Engineers Office, L .A. 1938. 66 15. Johnson, A.M. Physical Processes in Geology: Freeman Cooper, 1970. 16. Kessel i , J . E . Disintegrasting Soi l Slips of the Coast Ranges of Central Cal i fornia: Journal of Geology, V. 51, No. 5, p. 343-352, 1943. 17. Lessman, H. and Stamesu, S. Some Rainfal l Features in Mountainous Areas of Colombia and their Impact on Network Design: W.M.O. 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. Behaviour of Steep Creeks in Large Flood: Br i t i sh Columbia Geographic Series No. 14, Tantalus Research L t d . , 1972. 24. Schaeffer, D.G. A Record Breaking Summer Rainstorm Over the Lower Fraser V a l l e y : Atmospheric Environment Serv ice , Dept. of Environment Canada, Tech. Paper 787, June 1973. 25. Scott, K.M. Origin and Sedimentology of 1969 Debris Flow Near Glendora Cal i fornia: Geological Survey Research Paper No. 750C, p. C242-C247, 1971. 26. Shaw, E.M. A Hydrological Assessment of Precipitation in the Western Highlands of New Guinea: W.M.O. D i s t r i b u t i o n of Precipitation in Mountainous Areas, Symposium, Vol . II , 1973. 27. Sidle, R.C. and Swanston, D.N. Analysis of Small Debris Slides in Coastal Alaska: Canadian Geotechnical Journal, V. 19, 1982. 28. Skempton, A.W. and Delory, F .A. Stabi l i ty of Natural Slopes in London Clay: International Conference on Soi l Mechanics and Foundation Engineering, 4th London Proceedings, v. 2, p. 378-381, 1957. 67 29. 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. 


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