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Debris torrent mechanisms Smyth, Kenneth Jeffrey 1987-12-31

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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 o f 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  in THE FACULTY OF GRADUATE STUDIES Department o f C i v i l  Engineering  We a c c e p t t h i s t h e s i s as conforming to the required  standard  THE UNIVERSITY OF BRITISH COLUMBIA SEPTEMBER 1987  © K . J . SMYTH, 1987  In presenting t h i s thesis i n p a r t i a l f u l f i l l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library  s h a l l make i t  freely available  for reference  and study.  further agree that permission for extensive copying of t h i s thesis  I for  scholarly purposes may be granted by the Head of my Department or by his or her representatives.  It i s understood that copying or publication of  this thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission.  Department of C i v i l Engineering  The University of B r i t i s h Columbia 2075 Wesbrook Mall Vancouver, B . C . V6T 1W5  Date:  September,  1987  ABSTRACT  The phenomenon of the debris torrent i s  explored by examining the  mechanisms of i n i t i a t i o n , p a r t i c u l a r l y those of r a i n f a l l and deforestation.  The types of p r e c i p i t a t i o n l i k e l y to contribute to  are i d e n t i f i e d and data c o l l e c t i o n i s  instability  reviewed.  Debris torrents have characteristics unlike that of ordinary stream flow,  and are capable of transporting massive  material.  quantities  and sizes of  Models to explain this transport c a p a b i l i t y are compared and  contrasted.  A theoretical  analysis  of the  flow regime i s  carried out  which i s argued to be consistent with the observed turbulent nature of a debris torrent. elevation  in  This analysis i s extended to the c a l c u l a t i o n of superbends  and  shows  that  current  attempts  to  estimate  v e l o c i t i e s from super-elevation data may be very conservative. Further estimate the zone,  application of angle  and t h i s  of  the  spread of  turbulent the  stress analysis  debris torrent i n the  analysis may be useful  safeguard construction.  - ii -  is  used  to  deposition  i n zoning the downstream area to  TABLE OF CONTENTS Page ABSTRACT  i i  LIST OF TABLES  iv  LIST OF FIGURES  v  LIST OF SYMBOLS  vii  ACKNOWLEDGEMENT  viii  CHAPTER 1. INTRODUCTION  1  2. INITIATION IN SOURCE AREA  4  2.1 2.2 2.3  Instability Due to Rainfall Instability Due to Removal of Forest Cover Instability from Other Causes  3. PRECIPITATION  17  3.1 Classification 3.1.1 Synoptic or Macroscale 3.1.2 Mesoscale 3.1.3 Microscale 3.2 Data Collection 3.3 Precipitation Network 3.4 Predicting Orographic Effects 4. DEBRIS TORRENT MOVEMENT 4.1 4.2 4.3 4.4 4.5 4.6  17 17 17 17 18 23 24 36  Massive Sediment Motion Initiation of Movement in Torrent Stream Suspension of Massive Material Bagnold's Dilatant Fluid Model Plastico-Viscous Rheological Models Evaluation of Models  5. FLOW REGIME OF A DEBRIS TORRENT 5.1 5.2 5.3 5.4  4 8 10  Dilatant Flow Flow Around Bends . . • Further Applications of Turbulent Flow Turbulent Stress  6. CONCLUSIONS  36 36 38 39 41 42 45 45 48 52 53 61  REFERENCES  65  - iii -  LIST OF TABLES Page Table 3.1  Errors inherent i n sparse gauging network  28  3.2  Data from Beaufort Range, Vancouver Island  28  3.3  Network s p e c i f i c a t i o n recommended by WMO (1970)  29  3.A  P r e c i p i t a t i o n 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 i p s ,  13  2.3  Diagram showing buildup of perched water table i n c o l l u v i a l s o i l during heavy r a i n f a l l  14  Diagram showing z such that mz i s the v e r t i c a l height of ground water table above s l i p surface  15  Relation of f a i l u r e i n some t y p i c a l s o i l s to ground water content and slope angle  16  Comparison of hydrographcs from ten minute radar and equivalent hourly gauge data (after Bonser, 1982)  31  Relative d i s t r i b u t i o n s of land area, p r e c i p i t a t i o n stations and snow courses by elevation intervals i n B.C  32  Densities of p r e c i p i t a t i o n networks by elevation i n t e r v a l i n Switzerland, Norway and B.C  33  Simplified inflow and outflow wind p r o f i l e s over a mountain b a r r i e r  34  3.5  Data from WMO (1973), p. 64  35  4.1  Characteristic shear-stress d i s t r i b u t i o n s  44  4.2  C r i t e r i a for occurence of various types of transportation  2.4  2.5  3.1 3.2  3.3 3.4  5.1 5.2 5.3 5.4  Santa Monica mountains  sediment 44  Velocity/depth relationship applicable ot the peak of debris torrent surge (after Hungr et a l . , 1984)  57  Velocity/depth p r o f i l e s , comparing dilatant flow with laminar and turbulent flow (from mathematics)  58  Fluctuations of instantaneous v e l o c i t y component with respect to time at a fixed point i n steady flow  59  Normal d i s t r i b u t i o n applied to l a t e r a l fluctuation i n turbulent flow  60  - v -  velocity  LIST OF SYMBOLS A  constant  a  constant  B  surface width of flow  C  cohesion/unit area  c'  cohesion intercept  c^  grain concentration by volume i n s t a t i c debris bed  D  grain diameter  g  acceleration due to gravity  h  depth of flow  h  porewater pressure  w  k  constant  K  constant  m  f r a c t i o n of depth such that M i s the v e r t i c a l height of ground water table above s l i p surface (Fig. 2.4)  p  pressure due to weight of solids and water  P  dispersive pressure  APj,AP  2  inflow, outflow pressure difference i n mb hydraulic radius  R  radius of bend  R^  radius of centreline of stream bend  s  standard deviation of normal d i s t r i b u t i o n  S  slope  0  T  shear stress  t  time  u  v e l o c i t y of flow  u  time averaged part of v e l o c i t y u  u  momentary fluctuation of v e l o c i t y u  1  u^  c  c r i t i c a l shear v e l o c i t y  V  v e l o c i t y for c a l c u l a t i o n of thrust force  z  v e r t i c a l depth of s l i p surface  - vi -  LIST OF SYMBOLS (Continued) a  dynamic angle of internal  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  friction  T  shearing resistance/unit area  x  y i e l d strength  <J>'  angle of shearing resistance  A  l i n e a r concentration of p a r t i c l e s  - vii -  ACKNOWLEDGEMENT  I would l i k e and  to take this opportunity to express my appreciation  thanks to my advisor Professor M.C. Quick for his advice and guid-  ance during the research and the preparation of this t h e s i s .  - viii  -  1  CHAPTER 1 INTRODUCTION  A debris  torrent  stream which under  channel  suitable  is  often  conditions  a relatively can become the  quiet  mountain  transporter of  massive material that has great destructive power. The  physical processes which give  reviewed. and  rise  to  a debris  L o g i c a l l y , they are sub-divided into geologic,  particle  and hydrodynamic processes.  Some of  meters are shown to be reasonably well defined. necessary  for  the  formation of  considerable uncertainty,  a torrent  is  the  torrent  meteorologic, geologic  However, the shown to  are  be  para-  rainfall  subject  to  e s p e c i a l l y because of the lack of good data.  The main emphasis of this thesis i s on the p a r t i c l e and hydrodynamics of the debris movement. components  are  The physical interactions  re-analyzed  and i t  is  of the s o l i d and f l u i d  argued that  debris movement may have been underestimated.  peak v e l o c i t i e s  A consequence  of  underestimation would be a major r e v i s i o n of estimates of impact  of this  forces  and possible damage to structures. The disasters the  effects  of  debris  torrents  to property and l i f e ,  long term buildup of  are  manyfold,  ranging  from  the  by the movement of large boulders,  to  landforms by the formation of debris fans  in  the r i v e r v a l l e y s . Debris torrents contribute to the formation of a l l u v i a l fans.  The  widespread, perhaps dominant, influence of this mechanism i n the natural evolution of landforms has gone largely unrecognized owing to the long recurrent i n t e r v a l between events (Campbell, 1975).  2 A debris torrent can quickly f i l l rendering them ineffective  basins behind small check dams  i n c o n t r o l l i n g subsequent surface runoff.  The effects on small r e s i d e n t i a l dwellings range from quiet inundat i o n to complete destruction.  Flows of s u f f i c i e n t  volume and momentum  have smashed structures into pieces and move foundations, for example i n Alberta Creek, B r i t i s h Columbia: three  "Damages included t o t a l destruction of  houses and s t r u c t u r a l damage to  one other house  and c a r p o r t . . .  Five culverted road crossings were washed out and Highway 99 bridge was swept off i t s ings  foundations."  have had layers  accompanied by moving at  little  relatively  (Woods, 1983).  In other instances,  of muddy debris deposited s t r u c t u r a l damage. low v e l o c i t i e s ;  the  inside  them, commonly  Apparently the flows  build-  debris  entered the  was  dwellings  through open doors or windows and quietly flooded the i n t e r i o r s . It  is  also worth noting that  the destructive a b i l i t y ) volcanic rock w i l l  the size of the boulders  (and hence  depends on the character of the bedrock,  contribute large boulders, whereas a weak  w i l l only contribute clasts of pebble  sandstone  size.  A debris torrent may cause the channel to s h i f t , downstream depositional region.  i.e.  e s p e c i a l l y i n the  This channel s h i f t i n g can be triggered  by the 1)  sediment load, which varies greatly with debris torrent surges.  2)  local  deposition  may f i l l  during  lulls  i n the  storm, or between torrents,  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  boundaries and these levees may channel or divert subsequent  channel flows.  3 Channel bends are a p a r t i c u l a r hazard region,  for example,  Alberta Creek torrent of February 1983 the confines  i n the  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  life. The l i t e r a t u r e  is  f i l l e d with tragic  case h i s t o r i e s  like  that  Alberta Creek, but unfortunately these dangers are not always  of  obvious,  since the p e r i o d i c i t y of debris torrents i s i r r e g u l a r on any i n d i v i d u a l creek and long periods of dormancy often permit f u l l re-establishment forest cover over affected In debris  the  following  torrent  will  areas.  chapters, be  of  the  reviewed.  processes  which give  In p a r t i c u l a r ,  the  rise  to  a  precipitation  necessary to i n i t i a t e 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  rainfall  will  be  considered.  Consideration w i l l then be given to the dynamics of the sediment motion and Bagnold's dilatant  f l u i d model w i l l be compared with the  viscous rheological model. velocity  The Bagnold model i s  d i s t r i b u t i o n and special  bend.  This analysis  higher  than  indicates  previously  considerably higher.  then used to  analyze  application i s made to the flow i n a  that  estimated  plastico-  peak v e l o c i t i e s of debris may be  and  therefore  impact  loads  may be  4 CHAPTER 2 INITIATION IN SOURCE AREA  2.1  I n s t a b i l i t y Due to R a i n f a l l In order for a debris torrent to be i n i t i a t e d there must be s u f f i -  cient  material i n 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 i s t i e d to the c o r r e l a tion  between debris  Once s u f f i c i e n t debris  slides,  torrent  activity  water makes i t avalanches  or  and moderate  unstable debris  the  flows,  to heavy  rainfall.  source material moves i n making i t s  way into  the  creek. This s l i d i n g of material results tion  and downward percolation  at  from the i n t e r a c t i o n of  depth,  (Kesseli,  1943),  former takes place at a rate greater than the l a t t e r , of  infiltrawhere  the water  the  content  the top zone w i l l increase to a c r i t i c a l point at which s l i d i n g w i l l  originate.  When i n f i l t r a t i o n through the r e g o l i t h  1  exceeds the  trans-  missive capacity of the rocks below, a temporary perched water table formed  (Campbell,  continued  rainfall,  which a l l  the  bedrock i s  x  1975). until  rainfall  The head w i l l all  the  surface  to  s u r f i c i a l zone i s  i n excess of  d i s t r i b u t e d as  continue  increase, saturated,  is  with after  the transmissive  capacity of  the  runoff and downslope  seepage.  The  The loose incoherent mantle of rock fragments and s o i l which rests upon the bedrock.  5 association  of  debris  slides  with  rainstorms i s  clear  evidence  that  slope-mantle materials that are stable under "normal" conditions become unstable during r a i n f a l l of s u f f i c i e n t duration and i n t e n s i t y . For any s i t e i t soil  slips  continuous  i s possible to establish l i m i t i n g slopes at which  are u n l i k e l y and an upper slope above which retention of a mantle  (Campbell, 1975).  of  colluvium would  not  be  possible  (Fig.  2.2)  This data i s , of course, s p e c i f i c to the Santa Monica  Mountains where the  range of  12° to  56° are l i m i t i n g angles.  These  l i m i t i n g angles depend on l o c a l geology and should be established on a site specific basis.  Figure 2.3  shows an i d e a l i z e d debris source area  as the conditions for land movement are being reached, i n which shallow rooted vegetation with a t h i n mulch of dead leaves and grass growing i n a r e g o l i t h of c o l l u v i a l s o i l , the upper part of which contains abundant living  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 i s 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 t a b i l i t y of the slope material i s not affected. tion is will  On the other hand i f this deep percola-  less than the i n f i l t r a t i o n a perched water table i s formed and  continue to r i s e u n t i l  surface runoff and downslope seepage takes  place. The c r i t e r i o n for f a i l u r e of a s o i l slab i s that the r a t i o of the tangential  and normal  forces  must exceed  a critical  value,  which  is  dependent on the type of material. The effect source  material  of  the  from  addition of water  stable  to  formula (Terzaghi, 1950, p.92) ,  unstable  i n changing a slab may be  of  the  explained using  the  6 T = c + (p - hw)tan<J> where T  = shearing resistance/unit area  < > f  = angle of internal  hw  = porewater pressure  p  = pressure due to weight of solids and water  c  = cohesion/unit area  The decrease  friction  i n shearing resistance,  when a water saturated zone  forms above the s l i p surface i s evident i f we consider the component of cohesion  c  (which  is  really  apparent  cohesion  obtained  from  the  air-water surface tension),  this i s reduced to zero as the water takes  the  interstices  place  of  air  in  the  and also  the  term  (p-hw)  is  decreased due to increase i n piezometric head. A formula developed by (Skempton and DeLory, 1957)  for the condi-  t i o n that ground water flow i s p a r a l l e l to the slope at shallow depth gives the Terzaghi equation i n more r e a d i l y measured s o i l parameters,  (r - m • Y )z cos 0 tand>' • . s 'w c' + r z sinG cosG 's 2  r  where F  = factor of safety  c'  = cohesion intercept  z  = v e r t i c a l depth of s l i p surface  m  = f r a c t i o n of z such that mz i s the v e r t i c a l height of ground water table above s l i p surface (Fig. 2.4)  9  = slope angle  7 = unit weight s o i l = unit weight water  r,w  = angle of shearing  resistance  For the special case of c' = 0  the c r i t i c a l slope i s given by  m  tan9  c  =  r,w  tan<f>'  i . e . , F=l. It i s 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 prepared  is  however  for  a given  recurrence interval  interval  for values  intervals  an site  for of  idealized  situation  should permit  failures m at  due  to  although  are  rainstorms.  of  The recurrence  F=l can be approximated from recurrence  for rainstorms of s u f f i c i e n t  low,  curves  a preliminary evaluation  i n t e n s i t y and duration provided  thickness and i n f i l t r a t i o n rates of r e g o l i t h are known. rates  such  duration of r a i n f a l l  If i n f i l t r a t i o n  w i l l be dominant and i f  they are  high, i n t e n s i t y should be dominant. A study  (Sidle  and Swanston,  Alaska used much the same approach.  1982)  on debris  slides  in  coastal  They noted the great o v e r s i m p l i f i -  cation i n using a linear slope model which ignores many complex situations.  They found unreasonably high values of  cohesive properties existed i n the s o i l mantle.  field  suggesting that  A multistage  triaxial  test was performed on an undisturbed sample on a s i t e adjacent to f a i l u r e , giving a much lower and more reasonable value of <J)'.  the  When t h i s  8 value  was  substituted  obtained.  in  the  equation  a positive  This was a t t r i b u t e d , at least i n part,  value  of  c'  was  to root strength of  the vegetation. It  is  important to note  t e r r a i n where the  effective  that  for r e l a t i v e l y t h i n s o i l s  normal  forces  are  low,  small  i n steep  changes  apparent cohesion w i l l have a dramatic influence on the factor of (Sidle  and  Swanston,  1982).  For t h i s  site,  based  on  in  safety  a porewater  pressure at f a i l u r e of 2.17 kPa the factor of safety calculated for c' = 1.0 and 5.0 kPa were 0.75 and 1.73, This relationship between indicates  that  even  c'  small values  cohesion can be c r i t i c a l  respectively. and factor of safety for  rooting strength  i n determining the  for t h i n and true  s t a b i l i t y of  soils soil  these steep  slopes.  2.2  I n s t a b i l i t y Due to Removal of Forest Cover An important factor i n the creation of i n s t a b i l i t y i n the debris  source area i s the removal of forest cover by logging or f i r e . The effects of logging have been studied by many researchers and i s surrounded by much controversy. Eisbacher,  These effects are:  1982  • Intact forest absorbs some of the r a i n during storms and results i n less or at least delayed runoff. • A l i v i n g system of roots binds the colluvium to the substratum, adding some strength to the slope. A u l i t z k y , 1974 notes that: •  Rooting  strength  is  decreased  which possibly  generated stresses i n the s o i l root complex.  released  creep  9 • Transpiration i s decreased. • Shading of snowpack i s l o s t , •  increasing runoff.  Interruption of surface drainage associated with road surfaces, ditches and culverts.  •  A l t e r a t i o n of  subsurface water movements  e s p e c i a l l y where road  cuts intersect the water table. • Change i n d i s t r i b u t i o n of mass on a slope surface by cut and f i l l construction. It seems that the problem of large clearcutting i s generally compounded by unmanaged access roads which commonly are the f i r s t sources of debris into the adjacent creek. It  was  unstable  found  regions  (Aulitzky,  1974)  that  transported a two to  i n Alpine  eight  times  areas, greater  slides  in  volume of  material when clearcut than did those where forest cover was maintained. He also  found that  constituted  a  the  combined impact of roads and clearcut  five-fold  increase  in  erosion  relative  logging  to undisturbed  forested areas. In a study for protection works against Alice, slope  B . C . (Nasmith and Mercer,  1979)  it  debris movement at Port  was noted that much of  the  above the town was logged p r i o r 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  drainage and  debris  along  stream  courses  cause additional slope f a i l u r e s .  may impede  surface  10 Another cause of season vegetation  forest  cover  is  cover removal i s highly  flammable  burned and p r e c i p i a t i o n between the  fire  l i t t l e vegetative recovery i s possible a  storm h i t s  the  initial rainfall  fire.  Often i n the dry-  and i f  and the  (Scott,  the  watershed  first  1969).  storm i s  low,  Consequently when  would be absorbed by the  mantle and the watershed r a p i d l y saturated.  is  dry s o i l  When the next storm h i t s  conditions are i d e a l for slope f a i l u r e . In a study of 1936) ,  that  increased  when  by  flood erosion i n L . A . county i t was found (Eaton, the  fifty  watershed  to  one  cover  was  hundred times  destroyed  over  that  erosion  with  rates  undisturbed  vegetative cover and that the best protection from debris i s the normal vegetative  cover.  After  denudation,  secondary, far less e f f i c i e n t  2.3  any  protection  program  is  and much more costly.  I n s t a b i l i t y from Other Causes Terzaghi  (1950)  examines  land movement  in detail  and c i t e s  the  following causes of i n s t a b i l i t y : • Undercutting of the foot of the slope or deposition of earth or other material along the upper edge of the slope. an increase When  the  becomes  of  shearing  average equal  to  stresses  shearing the  stress  average  on the on  ground beneath  the  shearing  Both operations produce  potential  resistance  the  slide a  slope. surface  debris  slide  occurs. •  Earthquake shocks surface  of  unchanged.  the  increase sliding  the  shearing  whereas  the  stress along the  shearing  resistance  potential remains  11  All  the researches  ingredient  i n causing the  cited  agree t h a t  instability  disturbance  of  watershed  construction  can not o n l y  p r e c i p i a t i o n i s the e s s e n t i a l  i n the d e b r i s  by  accelerate  deforestation  source and  t h e phenomenon  amount o f d e b r i s a v a i l a b l e t o the t o r r e n t channel.  area  and  that  i t s attendant  but i n c r e a s e  the  Figure 2.1  C h a r a c t e r i s t i c of debris source area (Campbell, 1975)  13  F i g u r e 2.2  L i m i t i n g slopes f o r s o i l (Campbell, 1975).  slips,  Santa Monica  mountains  Figure 2.3.  Diagram showing buildup of perched water table in colluvial soil during heavy r a i n f a l l (Campbell, 1975).  15  Figure  2.4.  Diagram showing z such that mz i s 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 o f 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 c o n t e n t and s l o p e a n g l e . Computed c u r v e s f o r F = l ( f a i l u r e c r i t e r i o n ) a t s e l e c t e d v a l u e s o f y and The c u r v e s f o r most n a t u r a l n o n c l a y e y s o i l s l i e between c u r v e s 1 and 4. F i e l d s t o t h e l e f t and r i g h t o f each c u r v e a r e s t a b l e and u n s t a b l e , r e s p e c t i v e l y ( C a m p b e l l , 1975).  17 CHAPTER 3 PRECIPITATION  3.1  Classification Meterologists have adopted a q u a l i t a t i v e c l a s s i f i c a t i o n scheme and  view p r e c i p i t a t i o n phenomena on 3 scales.  3.1.1  Synoptic or Macroscale Storms  which  are  discernable  on weather  associated with low pressure and frontal systems. the order of hundreds of kilometers i n s i z e . are  usually  in  the  form  of  cyclonic  satellite  photographs,  They are generally i n  In the Vancouver area they  systems moving eastward  of  the  P a c i f i c Ocean.  3.1.2  Mesoscale Within  "pebbly  the  band of  structure"  precipitation.  as  p r e c i p i t a t i o n from the  seen by radar  (Bonser,  synoptic 1982),  of  system  is  patterns  a of  Generally they are t y p i c a l l y 10 to 50 km i n extent, up  to 60 km apart and move i n step as the band of p r e c i p i t a t i o n sweeps over the earth.  3.1.3  Thunderstorms are an example of a mesoscale system.  Microscale Convective c e l l s which are responsible for intense bursts of r a i n -  fall  over short time i n t e r v a l s .  last  up to an hour.  atmosphere, drafts .  They range from 2 to 10 km across and  They are generated by a l o c a l i n s t a b i l i t y i n the  grow r a p i d l y  and often  contain strong updrafts and down-  18 Types  of  precipitation  are  classified  in  3 p r i n c i p a l categories  (Bonser, 1982): Cyclonic  - R a i n f a l l arises when moist a i r masses i n a frontal system r i s e due to the horizontal convergence having different  Orographic  -  Rainfall graphic amount  is  of  temperatures.  caused by l i f t i n g  features  of envelopes of a i r  of  the  a i r mass by topo-  such as mountain b a r r i e r s .  precipitation  The maximum  comes on the middle part of  the  slope of a high mountain (Yoshino, 1975). Convective - D i f f e r e n t i a l heating of adjacent a i r masses generate l o c a l instability.  Individual convective  cells  form within the  broad r a i n f a l l areas and appear to remain i n p o s i t i o n r e l a t i v e to the broad r a i n f a l l areas. able for between 30 and 60 minutes.  C e l l s remain i d e n t i f i Peak i n t e n s i t i e s 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 i s  only by observing  these patterns that one begins to appreciate the complexity inherent i n the  precipitation,  a complexity not at a l l apparent  from conventional  hyetograph records."  3.2  Data C o l l e c t i o n When one  i.e.,  considers  the areas subject  to debris torrent  activity,  the steep upper reaches of small drainage basins, these variations  i n p r e c i p i t a t i o n patterns become very important. cates basins  subject  to torrent a c t i v i t y  The l i t e r a t u r e  indi-  ranging i n area from 0.03  to  19 0.17  km  (Scott,  2  A.7 km .  1969),  while  i n Howe Sound they  range  from O.A to  These small basins have the size and location to be influenced  2  s i g n i f i c a n t l y by the c e l l u l a r and orographic effects noted above. Current practice i s to analyse point r a i n f a l l data by ignoring the movement  of  storms,  assuming  a  stationary  rainfall  rate  consider  a constant  period.  An e x p l i c i t consideration of storm growth, v e l o c i t y and track  over  growth  an area  and decay,  for  or  a critical  to  time  i s a preferable approach but t h i s requires knowledge of the s p a t i a l and temporal v a r i a t i o n of p r e c i p i t a t i o n . In the elevation  Howe Sound area the  sites,  data coverage  is  biased towards  low  most stations are located along the major transporta-  t i o n 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  considerably according to differences  of  rainfall  in  a mountainous  differs  the method of observation and equally great  arise according to the density and position of observation  points because of the great l o c a l v a r i a b i l i t y of r a i n f a l l . Japan (Yoshino, 1975) Isohara.  area  shows the results  A study from  of studies i n the v i c i n i t y of  Table 3.1 shows the s t a t i s t i c s 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 i n a sparse gauging network. Miles  and Kellerhals (1981)  investigated  a debris torrent i n the  region of Hope, B . C . for the period of December 26-27, 1980, and estimated that the r a i n f a l l  of 75 mm i n 25 hours, measured at v a l l e y 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 t h i s rather large water d e f i c i t was made up from the "condensation  20 of melting snow". bottom  In the same paper they conclude that based on v a l l e y  precipitation  rainfall  of  the  return period  for  a debris  torrent  design  150 mm i n 2k hours would be upwards of 50 years but they  note that short term data collected  i n 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 i s due to c e l l u l a r and orographic phenomena which are not reflected i n the lower level gauges, as Bonser (1982) concludes, the microscale  p r e c i p i t a t i o n which i s most responsible  "it  is  for these peak  runoff responses i n small watersheds". Apart from the areal d i s t r i b u t i o n of the gauges i t i s important to consider  the  temporal nature  these high i n t e n s i t y  of  these high  intensity  hourly data and 10 minute radar data model showed that  estimated that  (Bonser,  the peak runoff  and although the timings of peaks agree, This i s  the hourly records (see F i g .  fell  A comparison of used i n an urban  from the hourly data underby a factor of 3,  a l l those for the hourly data  due to the averaging of peak i n t e n s i t i e s i n 3.1).  The Vancouver area exhibits 1973).  1982)  from the 10 minute radar measurements  show lower flows.  Since  c e l l s can l a s t for less than one hour, the hourly  r a i n gauge can miss the peaks within the hour period.  runoff  events.  strong orographic controls  (Shaeffer,  In a storm analysis of July 1972 i t was shown that while 50 mm  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 p r e c i p i t a t i o n i s produced  by vigorous f r o n t a l storms similar to the one i n question and Shaeffer (1973) contends  that  the r a i n f a l l  d i s t r i b u t i o n of such a storm should  resemble the d i s t r i b u t i o n of mean annual p r e c i p i t a t i o n since orographic  21 controls are fixed.  A comparison of published maps of mean annual  p r e c i p i t a t i o n over the lower Fraser v a l l e y (Wright, 1966) contention. influences  Thus over most of the area inferences  supported t h i s  concerning orographic  could bear relationships to these represented by mean annual  distribution.  R a i n f a l l rates for the same storm were calculated by  dividing t o t a l p r e c i p i t a t i o n at each point by the duration, which also increased with elevation and i t was found that i n t e n s i t i e s doubled between sea l e v e l and the mountains north of the c i t y .  These are  general trends and should be considered where return periods are being estimated from v a l l e y bottom data, but due to the sparcity of the data points, they should not be expected to apply to every storm since parameters 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 s i t e s across the Beaufort Range on Vancouver Island.  The available  results  showed a general increase i n p r e c i p i t a t i o n with elevation, horizontal variations being s i g n i f i c a n t at a l l levels and indicating that l o c a l variations i n exposure, slope and aspect are important (Table 3.2). The Department of Highways have i n s t a l l e d r a i n gauges at upper elevations i n the Howe Sound area, but they have been malfunctioning and, the data c o l l e c t so far i s not useful.  When these gauges are  operating they may give the information required to estimate the r a i n f a l l events that trigger torrent events.  As i t i s we can say, that i n  these high elevation catchments prone to torrents, the orographic i n f l u ences are s i g n i f i c a n t and produce greater amounts of p r e c i p i t a t i o n than our available gauging networks show.  This coupled with high i n t e n s i t y  c e l l u l a r a c t i v i t y are the major contributing factors i n debris torrent  22 initiation. conditions  Sustained  greater  durations  and i n t e n s i t i e s  leave  field  (ground water levels) requiring perhaps only a short intense  burst of r a i n f a l l to cause i n s t a b i l i t y .  Such intense c e l l u l a r a c t i v i t y  may not pass over the gauges. Thurber indicates km  or  (1983) questions  on the basis that t h e i r information  that these c e l l s appear to have dimensions i n the order of 10  greater.  However,  1982;  Penny, C . A . E . S .  (Bonser,  this  there  may be  pers.  greater  comm.).  c e l l s may indeed be as small as 1.5 km.  variation  in  size,  They suggest that  these  Thurber concludes,  "If  there  had been exceptionally high r a i n f a l l i n t e n s i t i e s associated with most of the events i n the study area, s i m i l a r l y high i n t e n s i t i e s would have been recorded  nearby at  conclusive  evidence  least that  on some occasions"  and that,  "there  is  no  climatic conditions alone have controlled the  occurrence of debris torrents". However, i n Japan, studies have shown that debris s l i d e s and landslips  are strongly correlated with heavy r a i n .  In one study (Yoshino,  1975)  i t was found that the areal d i s t r i b u t i o n 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 l a s s i f i c a t i o n by rocks, but it  closely  correlated to  amount of r a i n f a l l of  30°-50°  is  that  rainfall  to  landslide  In another study,  the areas with most  frequent  areas where the maximum r a i n f a l l mm/hour.  d i s t r i b u t i o n and that  when the  surpassed a certain l i m i t any slope with a gradient  subject  geological features.  the  regardless  of  the  (Yoshino, 1975)  landslides  difference  in  i t was confirmed  nearly coincide with the  exceeds 10-15  mm/10 minutes  or 30-50  23 Although there may be other contributing factors that may a i d the process and increase the extent of land movement there i s a vast amount of evidence to support the b e l i e f  that r a i n f a l l  i s the decisive  factor  i n the occurrence of debris slides and debris torrents (Eisbacher, 1982; Eaton,  1936;  and Campbell,  these r a i n f a l l facilities. it  1975).  In addition i t appears that many of  events are outside the scope of our present measurement  Attempts to take the available v a l l e y bottom data and from  predict  rainfall  rates  and durations  at  higher  elevations  is  a  complicated procedure requiring some caution. 3.3  P r e c i p i t a t i o n Network As suggested e a r l i e r the gauging networks i n B r i t i s h Columbia are  quite sparse and i n higher elevation zones, put this  into a world context,  generally non-existent.  To  Ferguson (1973) has provided guidelines  for the density of p r e c i p i t a t i o n , snow course, hydrometric and evaporat i o n networks tions  (see  polar  regions,  for various classes of physiographic and climatic condi-  Table 3.3). average  This table  indicates  that except for a r i d or  p r e c i p i t a t i o n network densities  i n mountainous  regions should be approximately 3 to 6 times as large as those i n f l a t terrain.  Table 3.A provides information on current p r e c i p i t a t i o n net-  works i n a number of countries and only Switzerland meets or exceeds the WMO s p e c i f i c a t i o n . reference  to F i g s .  The important area to note i s 3.2  and 3.3,  we see  that of B . C . and by  that the p r e c i p i t a t i o n network  i n B . C . f a l l s very far below the WMO recommendations, with most stations i n low lying areas, below 600 m. A major problem i n a l l areas i s the r e l a t i v e sparseness of data at high elevation. seen i n F i g . 3.3.  Stations tend to be concentrated at v a l l e y locations as  24 3.4  Predicting Orographic Effects There are a number of models that can predict to some degree what  the orographic effects model i s If  it  of a mountain barrier may be.  A simple linear  used by the World Meterological Organization (W.M.O.,  is  assumed  that  the  air  is  saturated  and  that  1973) .  temperature  decreases along r i s i n g streamlines at the moist adiabatic r a t e , and the flow  is  nodal  treated  surface,  as  a single  layer of  a i r between the  between 400 and 100 mb where the  ground and the  a i r flow  is  assumed  h o r i z o n t a l , the rate of p r e c i p i t a t i o n i s  Mi ( W l  R = V,  ~* w? w  where R V  = r a i n f a l l rate i n cm/sec = mean inflow wind speed i n cm/sec  x  W ,W a  = inflow  2  and outflow  water equivalent)  p r e c i p i t a t i o n water  in  cm ( l i q u i d  found from tables of p r e c i p i t a b l e water  i n a saturated pseudo-adiabatic atmosphere (W.M.O., Y  = horizontal distance i n cm  AP ,AP 1  2  = inflow and outflow pressure differences  The model considers  the  see  the  temperature.  v a r i a t i o n of  i n mb  flow of a i r i n a v e r t i c a l plane at right  angles to a mountain chain or ridge can  1973)  (Fig. 3.4),  orographic effects  From the equation one  with wind d i r e c t i o n and  25 This model i s condensate  does  highly s i m p l i f i e d as i t  not  fall  out  on  the  i s well known that a l l the  mountain  barrier.  Thus  the  "efficiency" with which the condensate i s removed i s less than one.  The  measure for the condensate i s the p r e c i p i t a b l e water which expresses the t o t a l mass of water vapour i n a v e r t i c a l column of the atmosphere, say that the a i r contains 3 cm of p r e c i p i t a b l e water s i g n i f i e s  to  that each  v e r t i c a l column of 1 cm cross-section contains 3 gm of water i n vapour 2  form.  If  the water vapour were a l l  condensed  into  l i q u i d water and  deposited at the base of the column the accumulated l i q u i d would be 3 cm deep.  No natural process w i l l p r e c i p i t a t e a l l the water vapour i n the  atmosphere. There appears to be an elevation range where t h i s  "efficiency"  maximum and related to a s p e c i f i c cloud type ( E l l i o t , 1977).  is  When data  from the Blue Canyon, C a l i f o r n i a was plotted against that calculated by the W.M.O. model a marked increase i n e f f i c i e n c y was found at approximately 1250 m (Fig.  3.5).  Whitmore (1972), i n examining the effects of a l t i t u d e on p r e c i p i t a tion fairly  in  South A f r i c a  concluded  that  mean annual r a i n f a l l  s t e a d i l y up to about 1300 m, above which a l t i t u d e the  increases  only s l i g h t l y .  Lessman et  vapour decreases with height,  al.  (1972)  tropical rainfall  found that, increases  increases rainfall as water  with height  only up to a certain level and decreases with additional height, features  vary with extent,  location r e l a t i v e  slope  and orientation of  to humidity sources,  these  the b a r r i e r ,  its  p r e v a i l i n g wind directions and  v e l o c i t y as well as the v e r t i c a l extent and degree of s t a b i l i t y of the humid  layers  meteorological  in  the  atmosphere  and  (Shaw,  1972)  found that  all  the  c h a r a c t e r i s t i c s are greatly influenced by a l t i t u d e , and  26 aspect has an added effect decrease  with height  on p r e c i p i t a t i o n .  and above the  Temperature and humidity  layer of maximum cloud development  (1000-2000 m) humidity drops off s i g n i f i c a n t l y .  On reaching plateaus i n  high mountains r a i n f a l l and cloud amounts become less and the of r a i n diminishes. this  intensity  A more sophisticated model which attempts to take  "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 c h a r a c t e r i s t i c s of the orographic cloud, e s p e c i a l l y with respect  to  its  cloud top temperature since  this  is  a measure of  the  abundance of the available ice-forming n u c l e i that get the p r e c i p i t a t i o n process  started.  The  "efficiencies"  associated  with  various  cloud  formations must be found by reference to actual storm data that include, besides p r e c i p i t a t i o n rates, upwind v a l l e y . terrain, cloud  The model depends i n a complex way upon character of the  the e f f i c i e n c y  condensate  depth of  frequent sounding data from the immediate  as  with which the microphysical mechanisms remove  precipitation,  cloud and the  the  wind d i r e c t i o n and speed  a i r mass s t a b i l i t y .  It  the  gives a transferable  method of computing mean areal p r e c i p i t a t i o n over basins where the real time p r e c i p i t a t i o n s data i s limited such as B . C . The output of the program i s  a grid point map of the  efficiency,  which represents a prediction of the orographic component of p r e c i p i t a t i o n over the b a r r i e r times grid  for a given case.  a number that i s  In order to use  constant over the  this map i t  is  entire  necessary  to  adjust the magnitude at g r i d points by the use of an observed p r e c i p i t a t i o n value.  The input e  (efficiency)  measures  the f r a c t i o n of cloud  water that i s removed as p r e c i p i t a t i o n and i s assumed constant over the entire  barrier  for  any given  cloud type.  The model i d e n t i f i e s  four  27 basic cloud types, cold  (unstable  stable warm, stable c o l d , unstable warm, and 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 b a r r i e r i s warmer than -30"C). The  results  show a  fair  correlation i n some s i t e s  but poor  others where"barrier wind effects are too complex for the model".  in One  should note however that while other researchers note a marked change i n efficiency  with altitude  this  model assumes i t  constant  for  a  given  cloud type. This model uses 37 parameters i n a l l and i f the data required were available and i t great  aid  in  could be "tuned" to the Howe Sound area i t would be a  dealing  with  the  unmeasureable  orographic component  of  p r e c i p i t a t i o n that i s so important i n the debris torrent s i t u a t i o n . The Howe Sound s i t u a t i o n effects, linear  but  the  extrapolation  precipitation, account  models  the  but  of for  many other  requires  examined valley  all  estimation have  of these orographic  shortcomings,  bottom data may be useful  an i n d i v i d u a l storm this parameters.  At present  certainly a for annual  does not  take  the  collection  data  into  network does not enable us to correlate the actual basin p r e c i p i t a t i o n with torrent  events and u n t i l such time as the network i s  return period prediction based on synoptic patterns i s  expanded a  impossible.  Number of Stations Area Per Station km  3  6  9  12  15  18  21  24  280  140  90  70  60  50  40  35  25  18  13  10  8  6  5  3  2  Error %  Table 3.1  Errors inherent i n sparse gauging network (after Yoshino, 1975)  STA  El(m)  A B C D E F G H I J  425 842 1395 740 425 425 750 1380 760 425  Table 3.2  Relative Precip. to A % 100 106 147 110 75 88 102 165 116 73  Data from Beaufort Range, Vancouver Island.  Table 3.3 Network specifications recommended by WMO (1970). Figures show maximum s p e c i f i c areas (inverse of network density) i n km per s t a t i o n . Provisional networks may be tolerated under d i f f i c u l t conditions. 2  PRECIPITATION TYPE OF REGION  Provisional  900-3000  1000-2500  3000-10,000  250-1000  300-1000  Provisional  1. Flat regions of temperate mediterranean and t r o p i c a l zones.  600-900  2. Mountainous regions of temperate mediterranean and t r o p i c a l zones.  100-250  4. Homogeneous plains areas. 5. Less homogeneous regions - Arid regions - Humid temperate - Cold regions  EVAPORATION Range of Norms  Range of Norms  3. Arid and polar zones.  HYDROMETRIC SNOW COURSES  1000-5000  5000-20,000  1500-10,000  5000 2000-3000 30,000 50,000 100,000  30 Table 3.4 P r e c i p i t a t i o n network data for selected regions (Ferguson, 1973) 10*km TOTAL AREA 2  REGION Switzerland  DAILY PRECIPITATION STATIONS  DENSITY STATIONS/ 10*km 2  1971.  SPECIFIC AREA km /STATION 2  4.1  463  112  Sweden  44.6  918  20.6  486  Norway  32.4  730  22.5  445  B r i t i s h Columbia, Canada  94.1  380  4.1  2480  Utah, U.S.A.  21.2  166  7.8  1280  89  31  FRASERVIEW CATCHMENT OUTLEI HYDROGRAPH T—i  CO  1  1  1  1  1  1  1  1  1  1  1  1  1  i  1  1  r  IP MINLTfC DATA HOURLY DAIA  20.0  40.0  tC.O  60.0  CO.O  1 2 0 . 0 U O . O 16D.C  tsC.C  TCC.C  TIMC (MINUTtS) ( X 1 0 ) 1  Figure 3.1.  Comparison of SWMM hydrographs from ten minute radar and equivalent hourly gauge data (Bonser, 1982).  32  L a n d Mass  I  Precipitation Stations. / ,  12 Snow courses  •1 0-6  6-12 ELEVATION INTERVAL  Figure 3.2.  12-18  18-24  24-30  (hundreds of metres)  Relative d i s t r i b u t i o n s of land area, p r e c i p i t a t i o n stations and snow courses by elevation i n t e r v a l i n B r i t i s h Columbia. In early 1971 there were 370 p r e c i p i t a t i o n stations and 215 snow courses i n operation (Ferguson, 1973).  33  3 127) (28)  100 9  100 (16)  8 7  Ringe Rscommtrxtad bv WMO (1970)  6 5  260  160)  (16) 500  1)9)  (321  10 9 8 7 6  1.000  z  o  (41)  1.0 9  10.000  132)  0 1 0 6  6-12  12- 18  18-24  ELEVATION RANGE (HUNDREDS OF METRES)  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 i s i n the range 600 to 1200 metres (Ferguson, 1973).  F i g u r e 3.4.  Simplified barrier.  i n f l o w and o u t f l o w wind p r o f i l e s over a  mountain  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 i s  the  falling,  sediment,  sliding  a form of massive sediment motion which means  or flowing  of  i n which a l l p a r t i c l e s  conglomerate  or the  dispersion  as well as the i n t e r s t i t i a l  of  f l u i d are  moved by g r a v i t y , so that the r e l a t i v e v e l o c i t y between the s o l i d phase and  fluid  role.  i n the d i r e c t i o n of displacement  By contrast,  i n f l u i d flow,  lift  of mass plays only a minor  and drag forces due to  relative  v e l o c i t y are essential for i n d i v i d u a l p a r t i c l e transport.  A.2  I n i t i a t i o n of Movement i n Torrent Stream Once s u f f i c i e n t  material from the debris source area i s  deposited  in the stream bed, the channel i s then a potential debris torrent given the right conditions of slope and p r e c i p i t a t i o n . Imagine  a  thick  uniform  grains, whose slope angle i s  layer  8.  parallel  0  seepage flow occurs.  shear stress i n the bed i s  loosely  packed  non-cohesive  It i s assumed that at the moment when  surface flow of water of depth h and  of  appears the pore spaces are saturated The c h a r a c t e r i s t i c  d i s t r i b u t i o n of  l i k e that shown i n F i g . A . l , i n which x i s  the applied tangential stress and  the internal r e s i s t i v e stress.  Case 1 (Fig. A.la) occurs under the condition (Takahashi, 1981),  C^ (o-p) tan<J> *  C*(a-p)+p  (A.l)  37 i n which •= grain concentration by volume i n the s t a t i c debris bed.  When  o,p  = densities of grains and fluids  <f>  = i n t e r n a l f r i c t i o n angle  case  2  occurs  (Fig.  A.lb)  the  respectively  following  equation  should  be  satisfied C*(o-p) tan9 =  tan<f>  (4.2)  C^(o-p) + p ( l + h a £ i ) 0  i n which a^ i s the depth where x and x^ coincide. The whole bed i n case 1 and the part above the depth a^ i n case 2 will  begin to flow as soon as the surface  flow appears.  This type of  i n s t a b i l i t y i n the bed i s due not to the dynamic force of f l u i d flow but to  static  disequilibrium, so  that  the  flow  should be c a l l e d  sediment  gravity flow. The condition for occurrence of sediment gravity flow i s i  d i n which d i s the grain diameter.  Equation (4.2)  therefore,  Substitute this condition into  and we obtain C*(o-p) tan6 £  tan<J>  (4.3)  C^(o-p) + p ( l + h d - i ) 0  but when a^ i s  f a r l e s s than h  0  grains  cannot be uniformly dispersed  throughout the whole depth due to rather small c o l l i d i n g d i s p e r s i b i l i t y . Therefore torrent  a sediment  gravity flow that  should meet the  coefficient,  y  debris  0  to be about 0.7.  £ Kh into Equation (4.3) 0  appropriately c a l l e d  c o n d i t i o n a^ £ K h , i n which K i s a numerical  determined from experiment  the condition a  is  gives  Substituting  38 C*(o-p) tanS £  tan<f> C*(o-p)  (A.A)  + p(l+k-i)  Debris movement occur when Equations (A.3) and (A.A) are simultaneously satisfied.  A.3  Suspension of Massive Material The debris torrent phenomenon occurs i n surges spaced over several  hours of  (Hungr et a l . ,  198A).  A t y p i c a l surge through the lower  a mountain creek begins  front,  followed  coarse  particles  by the  by the  rapid passage of  main body of  the  torrent.  a steep bouldery This  consists  ranging from gravel to boulders and logs,  floating i n a s l u r r y of l i q u e f i e d sand and finer m a t e r i a l . sion  of  hydraulic  debris forces  larger  than could be  and the  sediment-supporting  mechanism of  forces  that  expected  to  reaches  of  apparently The i n c l u -  be moved by normal  such transport requires upward  turbulence  of  the  existance  of  a  interstitial  fluid  would be too weak to provide. Bagnold  (195A)  proved  the  dispersive  pressure  resulting from the exchange of momentum between the grains i n neighbouring  layers.  When the  voids  are  filled  by dense  clay  slurry,  stones can be dispersed under rather small dispersive pressure,  large helped  by bouyancy i n the f l u i d phase. Bagnold also investigated  the effect  of dispersion of large  spheres on the shear resistance of a Newtonian f l u i d . situation  where  a stream i s  solid  He held that i n a  transporting granular material,  the  only  explanation was a dispersive grain pressure of such a magnitude that an  39  appreciable part of the moving grains i s  i n equilibrium between i t and  the force of gravity.  4.A  Bagnold's Dilatant F l u i d Model . A dispersion  of  neutrally  bouyant  particles  were  sheared  in a  Newtonian f l u i d i n the annular space between two concentric drums. particles walls  dilated  to  the  perpendicular  dispersive  pressure  to is  extent of the  main  flow.  the result  to  the  shear  small the resulting fluid viscosity  stress. shear  pressure  Bagnold  on the  reasoned  vertical that  this  of momentum exchange associated with  grain encounters and he found that tional  exerting  The  the dispersive  When the  stress i s  pressure  applied shear  i s propor-  s t r a i n du/dy  is  a mixed one due to the effect  of  as modified by the presence of grains, whereas when the  applied shear s t r a i n i s large the v i s c o s i t y of the i n t e r s t i t i a l f l u i d i s insignificant  and the resulting shear stress i s e s s e n t i a l l y due to grain  interaction.  For the l a t t e r case Bagnold found  P = a o[(tVC ) d  -1]  - 2  D (du/dy) 2  2  cosa (A.5)  T = P tan a  P  = dispersive  pressure  T  = shear stress  a  = dynamic angle of internal f r i c t i o n  a  = numerical constant = 0.0A2  D  = grain diameter  40 It  should be noted that  does not enter  the  total  rate  p of the i n t e r s t i t i a l  If a single  fluid  s o l i d body i s moved  of momentum transfer  is  measured by  because the f l u i d tends to flow back around the body to take  place. have  density  into Equation (4.5).  through a f l u i d , (o-p)  the  In this a  case however,  physical  meaning,  it  since  seems u n l i k e l y that the  whole  changes during the grains' movement.  "its  surrounding  its  place" can  configuration  It was assumed therefore that the  movement of the displaced f l u i d i s of a random nature i n r e l a t i o n to the movement of the grains. Bagnold's satisfied  experiment  shows that  the  fully  inertial  condition  is  at:  G  2  = o D T [(tVC ) 2  1 , 3  d  -l]u-  2  > 3000  (4.6)  where u i s f l u i d v i s c o s i t y and G has the form of a Reynolds number or i n terms of the conventional Reynolds number  R > 55  This condition should e a s i l y be met i n a debris torrent s i t u a t i o n . Bagnold together because increase  the for  reasons  that  larger  grains  a  given  shear  when tend  grains to  strain  as the square of the size  of  drift the  mixed towards  dispersive  (Eq. 4.5).  sizes the  are free  stress  sheared surface,  appears  Since the flow  to  surface  moves fastest, the larger material should d r i f t towards the front of the flow,  thus explaining the bouldery front that i s  debris torrent.  c h a r a c t e r i s t i c of  the  41 4.5  Plastico-Viscous Rheological Models Another set of studies (Johnson, 1970; Middleton and Hampton, 1976;  Rodine and Johnson, model  since  the  1976)  flow  of  propose clay  the use  slurry is  of a Bingham p l a s t i c well  modelled  as  fluid  a Bingham  fluid. The s t r e s s - s t r a i n relationship i n a Bingham f l u i d  T  is  + ji du/dy  =  where = shear stress  T  = y i e l d strength u  = viscosity  Middleton and Hampton (1976) distinguished debris flow from grain flow.  They emphasize  that  the  dispersive  stress due to direct grain  i n t e r a c t i o n plays an important role only i n the case of grain flow, and that  in  strength,  the  case of  debris  and the v i s c o s i t y  hydraulic behaviour.  flow;  the  grains  are supported by matrix  of the i n t e r s t i t i a l  f l u i d determines  They further claim that only a s l i g h t  their  amount of  clay i n the i n t e r s t i t i a l f l u i d w i l l d r a s t i c a l l y influence grain flow and convert i t into debris flow. It  should be noted that the above refers  phenomenon under consideration torrent proper.  to debris flow and the  should be distinguished  from a  debris  It i s possible for a Bingham f l u i d to flow i n a channel  of very low slope i f the depth of flow i s large enough, this i s not i n accordance with a r e a l debris torrent.  42 To avoid the contradiction of this low slope flow,  Johnson (1970)  proposed a Coulomb-viscous model i n which the s t r e s s - s t r a i n  relationship  is: T = C+ o  n  C  = cohesion  o n  = normal stress  <p  = angle of i n t e r n a l f r i c t i o n  This  model,  as  did  the  tan<J> + u du/dy  Bingham  fluid,  still  attributes  the  transport of large boulders to t h e i r bouyancy due to the strength of the interstitial  clay  relationships  bewteen the  competence  to  slurry.  float  Hampton clay  grains.  (1975)  contents These  obtained  i n clay-water  results  show  experimental  s l u r r y and the  that  sand  sized  p a r t i c l e s can be floated but larger ones cannot.  4.6  Evaluation of Models Takahashi  (1980)  re-evaluates  the  role  of  clay  content  in  the  ordinary g r a i n - r i c h debris and emphasizes that the effects of clay are minor and consequently the flow i s d i l a t a n t .  He concludes:  • Ordinary g r a i n - r i c h debris contains much less clay component for i t be treated as a Bingham f l u i d .  to  The apparent high v i s c o s i t y should be  the result of the resistance caused by c o l l i s i o n s of p a r t i c l e s . • Debris flows of the ordinary scales may be modelled by Bagnold*s grain flows i n the f u l l y i n e r t i a l range. The debris range.  torrent  is  of  course  a debris  flow  i n the  fully  inertial  However i t i s important to draw the d i s t i n c t i o n between the clay  43 charged mudflow  that  is  modelled  as  a Bingham f l u i d  and the  torrent phenomenon that appears best modelled as a dilatant As shown i n F i g . 4.2,  condition  for  fall  fluid.  the domain of occurrence of various types of  sediment transportation are defined by Equations 4.1, the  debris  (0=<j>) ,  and the  force on a steep channel (Ashida et a l . ,  equation  4.2,  of  4.3,  and 4.4,  critical  tractive  1973)  pu| 0.32(d/h ) 7 r - r = 0.034 cosG [tan<f> - . , tanG] x 10 (o-p)gd (o-p) 0  r  where = c r i t i c a l shear v e l o c i t y g  [=(gh sin9)^'^] 0  = acceleration due to gravity.  The domain l a b e l l e d  1 is  that  of no p a r t i c l e movement;  2 is  domain of i n d i v i d u a l p a r t i c l e movement due to the dynamic force of flow,  i.e.  bed transport; 3 i s  the fluid  the domain of sediment gravity flow,  which the effect of dynamic force of f l u i d flow coexists and i n the there  is  Numbers thickness  in flow  a clear water layer over a dense mixture of grain and water. attached  to  the  curves  in  this  of the moving layer of grains.  domain  correspond  to  the  The effect of dynamic action  should decrease for increasing thickness of the moving layer.  Note that  the  the  bed form  and  sediment  domains  contain  both  gravity flow; dispersed  of  the  transition  domains 4 is  of  and the  individual  upper regime  particle  in  movement  the domain of debris flow i n which the grains are  i n the whole layer  (debris  torrent) ; 5 i s  occurrence of both landslides  and debris  bed i s unstable under no f l u i d  flow.  torrents;  the domain of and 6 the  the  sediment  (a) Case 1  Figure 4.1  (b) Case 2  Characteristic shear-stress d i s t r i b u t i o n .  Eq.2  tan8/(o/o-l)  Figure 4.2.  C r i t e r i a for occurrence of various types of sediment transportation. The curves are obtained under the condition that c* = 0.7, a = 2.65 g e m , p = 1.0 g e m , < = 0.7, and tan<J> = 0.8. -3  -3  45 CHAPTER 5 FLOW REGIME OF A DEBRIS TORRENT  Hungr et a l . turbulent  flows  (1984) plotted v e l o c i t y depth p r o f i l e s for laminar and in  water  and  compared  these  with  that  of  debris  torrents, using eyewitness reports and superelevation data to  establish  velocities  suggested  for the  torrent  flows  (Fig. 5.1).  The p r o f i l e s  that the debris torrent flow was much closer to laminar than turbulent flow.  However observation of video tapes of debris torrents i n motion  would suggest that the torrent flow i s extremely turbulent. tapes were filmed by the C . B . C .  These video  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  fluid  theory  which  implies  a totally  inertial,  i.e.  turbulent regime.  5.1  Dilatant Flow Bagnold (1954) gives the r e l a t i o n for shear stress as  XD  du dy  where X  =  linear concentration of p a r t i c l e s  D  =  p a r t i c l e size  x  =  shear stress  6  =  density of mixture.  (5.1)  46 This  equation  is  similar  to  the  well  known boundary layer theory of  Prandtl except that the mixing length i s assumed to depend on p a r t i c l e size D and not to vary with distance from the boundary Equation 5.1 can be  integrated  if  it  is  assumed that  the  shear  stress  T is  i.e. x  1  /  1  2  However to be correct T varies l i n e a r l y with depth so that  T  = x - K • y o J  when y = y max  x = 0  _  ^max  K  so 1  =  T  _y_ y max  c "  max Substituting i n 5.1 and integrating we obtain  T  u  1  0  1' 2  (1 - - 2 — ) ' y -'max 3  \  n  1 2^ * w  X D 6 '  2  • 2/3  (-y  m  a  x  at the boundary u = 0, y = 0  0 = —  (1)  X D6 ' 1  2  • 2/3  (-y  ) +C m  X  ) +C  constant,  47  C = 2/3  • y X D  fii'  2  m  a  X  then T  u = 2/3  1  1 ' 2 0  Xn D  (1 6  1  (-y ) + 2/3 •'max .  ) ''max  y  1 / 2  T L  3 ' 2  v  0 n  1' 2  X Do  • y max ' 17  1  a  v  2  1 ' 2  u = 2/3 — . ,.,, XD6 ' n  1  2  6 '  2  v {[-1 "max v  + -2—]"* y •'max  + 1}  (5.2)  let T  2/3 X  0  1' 2  D  y 1  = A a const. m  a  x  or u = A[(-l +  ) y  + 1]  max  •'max  when u = u , y = y max max y  so 5.2  yields  T  u RAAX  = 2/3  1' 2  X D 6i' y  u max  y  —  1 - (1 - -f—) y max J  2  =A m a X  . 3 ' 2  (5.3)  A8 we may plot t h i s relationship to determine a v e l o c i t y depth p r o f i l e for the assumed turbulent conditions of d i l a t a n t flow as shown i n F i g . 5.2. A s i m i l a r treatment was used assuming laminar condition of  which yields the relationship  _y_ = u max  +  1  _  (  1  (5.4)  _ -Y—)a y max J  which i s also plotted i n F i g . 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 as  that  of this mathematical treatment give a s i m i l a r p r o f i l e  derived by Hungr et  superelevation data.  al.  (198A),  from eyewitness reports and  We are confronted by a paradox here i n that the  d i l a t a n t flow condition were turbulent but y i e l d what appears to be an almost laminar p r o f i l e .  To accept this as a laminar flow however must  be erroneous and the implications of this v e l o c i t y d i s t r i b u t i o n w i l l now be analyzed.  5.2  Flow Around Bends Many estimates of the v e l o c i t y of debris torrents have been made  from superelevation data,  collected  from bends i n the torrent channel  using the equation,  ^ = ^ dR gR  Henderson (1966, p.  255).  K  (5.5) ' }  49 where h i s  the  height  of the  free  surface  above the horizontal bend,  R = radius of bend  In which equation V i s  assumed constant  with depth which i s  that of actual turbulent flow i n water (see F i g . For an open channel V i s  close  to  5.2).  also assumed to vary as a free  vortex,  i.e. VR = C  (5.6)  If R i s large enough to assume V constant with radius t h i s gives  Ah = AR ^  (5.7)  where Ah  is total  superelevation  AR  i s width of channel  A more exact integration of Eq. 5.3 gives  h -h, 2  Now the v e l o c i t y linear  with  -  C  T  g  ^  ~  ^  d i s t r i b u t i o n found from the  depth,  so we may assume that  v e l o c i t y with depth i s V = ky  the  (5.8)  dilatant  flow  is  almost  actual relationship  of  50  i.e.,  dh dR  k y gR 2  =  2  Integration over the depth gives  o  o  &  at fixed radius assuming dh/dR to be constant with depth  y dh  dh dR  =  dR  y  ki . 1 gR 3  ki 1 gR * 3  =  1 k h 3 gR 2  #  =  2  for horizontal channel, for which Y=h. Integrating from R  1  to R and h 2  I h  To i l l u s t r a t e assumed values,  the  l  l  k h  2  to h  x  *  2  3  numerical results  *  §  gives  2  2  R  of  l  these  equations  i.e.,  h  av  = 1 m,  V = 5 m/sec, av '  with RM = 4 2 . 5  and substitute i n Eq. 5 . 8 we get  AR = B = 5 m  we take some  51 Ah = 0.3 m from Eq. 5.9 we have Ah  k  KK The maximum v e l o c i t y , V„ = k » y .  2  „  3g  R  i  R  2  Therefore k h j h 2  Ah = ^ - Sn  i.e. k  2  = V , so that, 2  2  h.h. = V  2  gives V = 8.65 m/sec M M  Which shows that the near l i n e a r v e l o c i t y d i s t r i b u t i o n for d i l a t a n t flow y i e l d s a much higher v e l o c i t y from superelevation data than the usually assumed Eqn. 5.7. Hungr et a l . (1984) quote the equation  AV BV Ah = v K • — — Rg 2  where  B is  surface with of  flow,  and K i s  given by Myzuyama et  al.  (1981) to range from 2.5 to 5.0 and the 2.5 value i s used to estimate v e l o c i t i e s from the equation,  Ah =  Rg  • BV  for the same Ah, t h i s equation y i e l d s  V = 3.16 m/s  2  52 which i s  much lower  justification (National recently  than the  of the 2.5  Research  value  factor i s  Centre  for  read Myzugama's paper  8.65  m/sec estimated  given.  No  Also, Professor M. Sugawara  Disaster i n the  above.  Protection,  Kyoto,  o r i g i n a l Japanese  Japan)  and reported  that there was no j u s t i f i c a t i o n of the 2.5 factor i n the paper. For  design  calculate  purposes  impact  forces  these using  estimated  the  velocities  momentum equation  are  used  (Hungr et  to al.,  1984), F  = 6 AV  T  sinB,  2  i.e.  F  T  = 6 Q V sinB  where F  =  total  A  =  flow  6  =  debris  8  =  angle of flow d i r e c t i o n to face of b a r r i e r .  T  thrust cross-section density  This v e l o c i t y difference of 7.5.  the thrust force by a multiple  It should be noted from Ippen and Knapp (1938) that at highly  supercritical (5.4).  flows Ah could be as much as twice that estimated by Eq.  However  the  Froude  generally  low  enough  velocity,  for  example,  debris  would increase  torrent  flow)  to at  number  have  a  range  minimal  we  effect  a Froude number of  Ah would increase  are  1.6,  investigating on  our  calculated  (a high value  by 35% reducing the  is  for  estimated  v e l o c i t y by 14%.  5.3  Further Applications of Turbulent Flow Again i f we accept  agree  that  turbulent  Bagnolds i n e r t i a l range for debris torrent and  conditions  prevail  then we can apply  Reynold's  53 (1884) turbulent stress analysis to the flow, t h i s may have applications to  the  runout zone  of  the  torrent,  which can have  important design  applications, p a r t i c u l a r l y with respect to zoning.  5.4  Turbulent Stress At any given point i n turbulent flow,  and  indeed  all  the  instantaneous  the instantaneous  continuum properties  are  velocity found  to  fluctuate r a p i d l y and randomly about a mean value with respect to time and s p a t i a l d i r e c t i o n .  In the t h e o r e t i c a l analysis of turbulent flow,  i t i s convenient to consider an instantaneous quality such as u , as the sum of i t s  time averaged p a r t u and momentary fluctuation part u' as  shown i n F i g . 5.3,  i.e., u = u + u'  In steady flow u does not change with time. By d e f i n i t i o n u  = — f  to  u dt  0  t u  Although the u  1  time  1  = 7 f t  0  u' dt = 0  J  average  o  of  fluctuation quantity i s  zero,  i.e.  = 0 , the quantity u ' , u ' v ' , u'w', etc. which are time averages of  the  2  products of  equal  zero.  turbulent i.e.  any two fluctuation components,  These values  fluctuations  at  are used as  will  not  necessarily  a measure of the magnitude of  any given point  i n a turbulent flow  the i n t e n s i t y of turbulent I i s defined by  field,  54  /u'  + v'  2  7 =  + w'  2  u  /3  2  where u i s the magnitude of the v e l o c i t y at the same point. We may consider the turbulent component at r i g h t angles to the flow u as / v '  2  in  lateral  the  which we w i l l c a l l v' the root mean square turbulent v e l o c i t y  lateral  direction.  spreading  channel.  when  This  the  v'  value  torrent  We can calculate  this  will  leaves  component  be  the  used  to  constraints  from the  estimate of  turbulent  the shear  stress equation  T  °  *Hi  =  S  °  ^  =  V  *  =  s  ^  e a r  velocity = V )  where hydraulic radius S  slope  o =  or v- = (g R. S ) "o  1 2  0  From the random nature of t h i s distribution  so that  can be done  to  course,  is  an  turbulence we may assume a normal  for any stream parameters a s t a t i s t i c a l  estimate ideal  the  potential  situation  based  zone  of  on an equal  represents the extreme case of maximum spreading. material  sizes  are  deposition.  deposited we would expect  size  analysis This  of  material but  Since when a range of  the  larger boulders  deposit f i r s t and i n h i b i t movement of smaller material.  to  There are some  55 s t r i k i n g 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  distribution,  case  to  fluctuations.  can  We can predict  s,  so  examined  represent  that the l a t e r a l v e l o c i t y deviation  be  that  the the  using  a  randomness range  fluctuation v'  approximately  of is  normal  of  these  deposition equivalent  68% of  the  statistical  by  turbulent recognizing  to the standard  material  will  move  l a t e r a l l y at less than v , while another 27% w i l l move at less than 2v' 1  (see F i g .  e.g.  In  5.4).  an  ideal  situation  with  a  channel  slope  of  20°  and  an  hydraulic radius of 1 and a mainstream v e l o c i t y of 5 m/s  then  S„  - 36  u  =5  v'  = (9.8.1 • 3 6 ) '  m/s  1  2  = 1.9 m/s giving an angle of spread of tan"  (1.9/5) = 21°  1  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 i s p h y s i c a l l y limited by the turbulent fluctuations,  velocity  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 a l . , 1984).  58  •1  -2  .3  .4  .5  .6  .7  '.8  .9  1.0  u u  max  Figure 5.2  Velocity/depth p r o f i l e s , comparing d i l a t a n t flow with laminar and turbulent ( t h e o r e t i c a l ) .  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  p a r t i c l e s as well as the i n t e r s t i t i a l  sediment  motion  in  which  all  f l u i d are moved by g r a v i t y ,  only occurs i n steep channels where there i s  this  a rapid movement of water  charged s o i l , rock and organic material. Debris avalanches  torrent  events  are usually triggered by debris  from adjacent h i l l  slopes,  slides  or  i n the debris source area, which  enter a channel and move d i r e c t l y down stream. Rainfall  is  the most important factor  i n the  i n i t i a t i o n of  debris movements that culminate i n debris torrent a c t i v i t y . events that  are most c r i t i c a l are,  sustained  these  The type of  regional rainstorms  i.e.  300 mm or more of p r e c i p i t a t i o n i n 48 hours or convective c e l l a c t i v i t y which i s  responsible  for  intense bursts  of  rainfall  over  short  intervals  and may contribute as much as 50 mm of p r e c i p i t a t i o n to  time the  catchment area i n one hour. The  effect  associated  of  the  conditions  addition of water for  instability  to  were  the  soil  mantle and the  investigated  by Terzaghi  (1950)  and Skempton and Delong  (1957) , from the work of the  family  of  combinations  curves  for  various  of  soil  latter  parameters  a  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 i d e a l  situation  and that  apparent  cohesion due to true cohesion plus root strength of vegetation can a l t e r the factor of safety quite dramatically. Removal of  forest  cover i n the debris source area by logging was  also found to be a major contributing factor,  since this decreases root  62 strength,  interrupts  mass on the shading  slope  of  surface  drainage and changes the d i s t r i b u t i o n of  surface by cut and f i l l  snow pack  is  reduced,  avalanching which can i n i t i a t e  construction.  increasing  the  debris movement.  In addition  incidence  of  snow  It was also concluded  that not only the incidence of land movement i s increased but rates of erosion can increase markedly due to denudation. An examination of the p r e c i p i t a t i o n events associated with debris torrents was carried out with p a r t i c u l a r reference to the p r e c i p i t a t i o n measurement networks and current practice of assuming stationary growth and decay of storms. Howe  Sound,  where  Due to the  most  transportation routes,  data  sparse  stations  data network, are  located  the  p r e c i p i t a t i o n not  convective In  order  cell to  activity  use  orographic effect  data  along  the  major  much of the actual p r e c i p i t a t i o n i n the higher  catchments i s not reflected i n the gauging network. of  i n the area of  being picked up by the  The main components gauges are those of  and the orographic effects in  a predictive  fashion  a much more comprehensive  of the mountains.  to  account  data c o l l e c t i o n  for  system  required along with a model to interpret the orographic component. convective  cells  sophisticated  can  radar  be  as  tracking  small for  as  accurate  1.5  km  and  location,  as  this  would  is The  require  discussed  by  Bonser (1982). The data network density i n 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. Fluid  Model,  model  showed  particles  Two theories were examined, Bagnold's (1954) Dilatant  and Johnson's that  when  tended to  the  flow  and i s  toward the  the  sheared  free  Bagnold's  together  the  surface and since  larger material d r i f t s  larger  the  toward the  flow  front of smaller  This model gave a good explanation of the phenomenon  where boulders  torrent.  were  Model.  supported by exchanges i n momentum with the  p a r t i c l e s beneath. observed,  Plastico-Viscous  particles  drift  surface moves fastest,  (1970)  appeared to  The Plastico-Viscous  "float"  toward the  Model proposed that  front of  the  the p a r t i c l e s  are  supported by matrix strength and that the v i s c o s i t y of the  interstitial  f l u i d determines the hydraulic behaviour. An evaluation of  the models  revealed  that  the  grain r i c h  does not contain enough clay to be treated as a Bingham F l u i d  debris  (Plastico-  Viscous) and that apparent high v i s c o s i t y was the result of the ance caused by the c o l l i s i o n s  of p a r t i c l e s .  resist-  It was concluded that  debris torrent could best be modelled as a d i l a t a n t f l u i d i n i t s inertial  (turbulent)  flow  was  fully  range.  Other workers, Hungr et a l . torrent  the  laminar,  v e l o c i t y depth p r o f i l e .  due  (1984) have concluded that the debris to  its  apparent  calm surface  and  its  Hungr et a l . plotted v e l o c i t y vs. depth based  on eyewitness reports and superelevation data and found an almost linear r e l a t i o n very close to that of model i s  a turbulent one i t  velocity  vs  velocity  profile  plotted i s  depth  for  varies  this with  laminar flow.  Since the d i l a t a n t  was thought necessary dilatant  flow.  depth  the  to  This power  flow  to examine and plot dilatant-turbulent of  1.5,  which when  a close approximation to a linear v e l o c i t y v a r i a t i o n .  This  64 contrasts with the logarithmic d i s t r i b u t i o n of normal turbulent flow and the parabolic d i s t r i b u t i o n of laminar flow. Superelevation of the debris flow i n a bend has been used by some workers to estimate flow v e l o c i t i e s .  Re-analysis of the flow i n a bend  using the near-linear v e l o c i t y d i s t r i b u t i o n predicted from the d i l a t a n t turbulent model indicates  that  the use  of conventional  theory may seriously underestimate debris Design  criteria  based  on  normal  superelevation  velocities. fluid  flow  around bends  gave  v e l o c i t i e s approximately 2.7 times less than these c a l c u l a t i o n using the linear r e l a t i o n .  Further, when these v e l o c i t i e s are used to  thrust forces which contain a V  2  calculate  term the thrust forces would be under-  estimated by a factor of approximately 7.5.  These numerical values are  approximate and for i l l u s t r a t i v e purposes, but they do show the possible range of e r r o r s . This  dilatant-turbulent  analysis  has  also been used  l a t e r a l spreading of debris torrent material when i t ally  from  region.  a constrained  An analysis  give a s t a t i s t i c a l the channel.  channel  on to  the  to  spills  unconstrained  estimate  out  later-  debris  fan  i s based on Reynolds turbulent stresses i s used to  estimate of the spread of the debris when i t  This s t a t i s t i c a l  analysis  leaves  can be used to estimate l a t e r a l  spreading of debris and hence to establish  hazard zones on the debris  fans. The most important item revealed i n t h i s research i s the v e l o c i t y v depth p r o f i l e for the d i l a t a n t flow,  which i s very different  one expects i n turbulent flow i n water. in  this  area  is  needed  to  continue  this  from what  Further experimental research analysis  and the  v e l o c i t i e s and thrust forces based on this linear r e l a t i o n s h i p .  predicted  65 REFERENCES  1.  Ashida, K. , Daido, A . , Takahashi, T. and Mizuyama, T. Study on the Resistance Law and the I n i t i a t i o n of Motions of Bed Particles i n a Steep Slope Channel: Annual Disaster Prevention Research I n s t i t u t e , Kyoto University 16B 481-94, 1973.  2.  A u l i t z k y , 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 S o l i d Spheres i n a Newtonian F l u i d Under Shear: Proceedings Royal Society of London, V o l . 225A, August 1954.  4.  Bonser, J . D . P r e c i p i t a t i o n Radar as a Source of Hydrometerological Data: M.A.Sc. Thesis, University of B r i t i s h Columbia, 1982.  5.  Campbell, R.H. S o i l S l i p s , Debris Flows and Rainstorms i n the Santa Monica Mountains and V i c i n i t y , Southern C a l i f o r n i a : U.S. Geological Survey Professional Paper 851, 51 p, 1975.  6.  D a i l y , J.W. and Harleman, D . R . F . , 1966.  7.  Eaton, C. Flood and Erosion Control Problems and Their Solutions: A . S . C . E . Proceeding, V o l . 62, No. 8, Part 2, Transaction No. 101, 1930.  8.  Eisbacher, G.H. Slope S t a b i l i t y and Land Use i n Mountain V a l l e y s : Geoscience Canada, V o l . 9, No. 1, 1982.  9.  E l l i o t , R.D. F i n a l Report on Methods for Estimating Areal P r e c i p i t a t i o n i n Mountain Areas: Report 77-13, Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service Office of Hydrology, 1977.  10.  Ferguson, H . L . P r e c i p i t a t i o n Network Design Areas: World Meterological O f f i c e , 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 C o . , I n c . ,  13.  Hungr, 0., Morgan, G . C . and K e l l e r h a l s , 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 i n Curved Channels: U.S. Engineers O f f i c e , L . A . 1938.  F l u i d Dynamics: Addison Wesely,  for  Large Mountain  1966.  66 15.  Johnson, 1970.  A.M.  Physical  Processes  in  Geology:  Freeman Cooper,  16.  K e s s e l i , J . E . Disintegrasting S o i l Slips of the Coast Ranges of Central C a l i f o r n i a : Journal of Geology, V. 51, No. 5, p. 343-352, 1943.  17.  Lessman, H. and Stamesu, S. Some R a i n f a l l Features i n Mountainous Areas of Colombia and t h e i r Impact on Network Design: W.M.O. D i s t r i b u t i o n of P r e c i p i t a t i o n i n Mountainous Areas Symposium, 1973, V o l . 1.  18.  Middleton, G.V. and Hampton, M.A. Subaqueous Sediment Transport and Deposition by Sediment Gravity Flow: i n Marine Sediment Transport and Environmental Management, Ed. D . J . Stanley, D . J . P . Swift, 11: 197-218, N.Y. Wiley, 1976.  19.  M i l e s , M . J . and K e l l e r h a l s , R. Some Engineering Aspects of Debris Torrents: CSCE 5th Canadian Hydrotechnical Conference, 1981.  20.  Mizuyama, T. and Uehara, S. Debris Flow i n 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 A l i c e , B . C . : Canadian Geotechnical Journal, V o l . 16, No. 4, pp. 748-775, 1979.  22.  Reynolds, 0. Experiments Showing Dilatancy: Institute of Great B r i t a i n (1884-1886).  23.  R u s s e l l , S.O. Behaviour of Steep Creeks i n Large Flood: B r i t i s h Columbia Geographic Series No. 14, Tantalus Research L t d . , 1972.  24.  Schaeffer, D.G. A Record Breaking Summer Rainstorm Over the Lower F r a s e r V a l l e y : Atmospheric Environment S e r v i c e , Dept. of Environment Canada, Tech. Paper 787, June 1973.  25.  Scott, K.M. Origin and Sedimentology of 1969 Debris Flow Near Glendora C a l i f o r n i a : Geological Survey Research Paper No. 750C, p. C242-C247, 1971.  26.  Shaw, E.M. A Hydrological Assessment of P r e c i p i t a t i o n i n Western Highlands of New Guinea: W.M.O. Distribution P r e c i p i t a t i o n i n Mountainous Areas, Symposium, V o l . I I , 1973.  27.  S i d l e , R . C . and Swanston, D.N. Analysis of Small Debris Slides i n Coastal Alaska: Canadian Geotechnical Journal, V. 19, 1982.  28.  Skempton, A.W. and Delory, F . A . S t a b i l i t y of Natural Slopes i n London Clay: International Conference on S o i l Mechanics and Foundation Engineering, 4th London Proceedings, v. 2, p. 378-381, 1957.  Proceedings  Royal  the of  67 29.  Swanston, D.N. and Steepland Geomorphology Hutchinson and 1976.  and Swanson, F . J . Timber Harvesting, Mass Erosion Forest Geomorphology i n the P a c i f i c North West: and Engineering, Editor Coates, D . R . , Dowden, Ross, I n c . , Stroudsburg, Pennsylvania, pp. 199-221,  30.  Takahashi, T. Debris Flow i n Prismatic Open Channels: Journal of Hydraulic D i v i s i o n , ASCE, March 1980.  31.  Takahashi, T. Debris Flow: Annual Review of F l u i d Mechanics, No. 13, pp. 57-77, 1981.  32.  Terzaghi, K. Mechanism of Landslides: i n Theory to Practice S o i l Mechanics, Wiley & Sons, N . Y . , 1960.  33.  Thurber Consultants. Debris Torrents and Flooding Highway 99, Howe Sound, B . C . , A p r i l 1983.  34.  Whitmore, J . S . The v a r i a t i o n of Mean Annual R a i n f a l l with Altitude and L o c a l i t y i n South A f r i c a , as Determined by Multiple Curvilinear Regression Analysis i n World Meterological Office: D i s t r i b u t i o n of P r e c i p i t a t i o n i n Mountainous Areas, Symposium, V o l . 1, 1973.  35.  Woods, P . J . Province of B r i t i s h Columbia, Ministry Environment, Water Management Branch Memo: March 1, 1983.  36.  World Meterological O f f i c e . Manual for Estimating of Probable Maximum P r e c i p i t a t i o n : WMO No. 332, Geneva, Switzerland, 1973.  37.  Wright, J . B . P r e c i p i t a t i o n Patterns Over Vancouver City and Lower Fraser Valley: Meterological Branch, Department of Transport, CIR 4474 TEC 623, 1966.  38.  Yoshimo, M.M. 1975.  in  Hazards on  of  the  Climate i n a Small Area: University of Tokyo Press,  

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