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Maximum scour around cylinders induced by wave and current action Abusbeaa, Abubaker Mohamed 1986

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MAXIMUM SCOUR AROUND CYLINDERS INDUCED BY WAVE AND CURRENT ACTION  by ABUBAKER MOHAMED ABUSBEAA  A THESIS SUBMITTED I N P A R T I A L FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF A P P L I E D  SCIENCE  in FACULTY OF GRADUATE STUDIES Department  We a c c e p t  of C i v i l E n g i n e e r i n g  this  thesis  to the required  as  standard  THE U N I V E R S I T Y OF B R I T I S H JUNE,  conforming  COLUMBIA  1986  © ABUBAKER MOHAMED ABUSBEAA, 1 9 8 6  In p r e s e n t i n g  this thesis  r e q u i r e m e n t s f o r an of  British  it  freely available  agree that  in partial  advanced degree at  Columbia, I agree that for reference  permission  understood for  by  that  h i s or  be  her  shall  not  Civil  June,  and  study.  I  1986  the  of  further this  Columbia  thesis  head o f  this  my  It is thesis  a l l o w e d w i t h o u t my  Engineering  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3  Date  s h a l l make  representatives.  permission.  Department of  University  Library  g r a n t e d by  be  the  the  copying or p u b l i c a t i o n  f i n a n c i a l gain  the  f o r extensive copying of  f o r s c h o l a r l y p u r p o s e s may department or  f u l f i l m e n t of  written  ABSTRACT  T h e maximum p o s s i b l e  scour  action  of  c o m b i n e d wave a n d  review  of  the  methods  for  under  the  literature  predicting action  prediction  is  of  under  conditions. alone  and  waves  wave  for  alone  the  three  currents  for  were  there  are  scour  in this  no a d e q u a t e depths  the  of  three  a  using  dependence  was this  shown.  alone  study  and s t r u c t u r e  and  maximum  theories  or  structures a  scour  design of  sets  of  waves  size  scour  between  both  and  five  cylinder  provided that  dimensions are  on t h i s  scour the  flow  defined.  -  scour current waves were and  cylinder size  and g r a p h i c a l  under  scour  currents  and rela-  c o m b i n e d wave  a p p r o a c h i n g f l o w was  maximum  and  off-  experiments  alone,  studied  o f maximum s c o u r  i i  of  ranges  on  c a s e s was  made  v e l o c i t i e s under  and  T h e maximum s c o u r  -  A  such  c o m b i n e d wave  s c o u r and f l o w  sediment  The  the  c o m p a r i s o n was  conditions  flow  of  the  study.  around  Development  analyzed  three  under  w i t h experimental t e s t s of the  threshold c o n d i t i o n s i n the  criterion  properties  flow  established.  d e t a i l and the  estimated  were  using  size  flow  and  theories  sediment  in  started  Existing  dependence  at  structures  investigated  current.  waves  The  current  plus  alone,  sizes.  tionships  that  currents  for  plus  was  maximum p o s s i b l e  structures  currents  performed  showed  The s t u d y  cylindrical steady  current  cylindrical  o f c o n s i d e r a b l e economic importance f o r  shore structures. around  around  investigated  critical  depth  can  and  be  conditions,  threshold roughly sediment  TABLE OF  CONTENTS Page  ABSTRACT  i i  L I S T OF T A B L E S  v  L I S T OF FIGURES  vi  NOMENCLATURE  ix  ACKNOWLEDGEMENT  xii  1.  2.  3.  INTRODUCTION  1  1.1  GENERAL  1  1.2  LITERATURE REVIEW  2  1.2.1  SCOUR  2  1.2.2  UNIDIRECTIONAL  1.2.3  O S C I L L A T I N G FLOW - WAVES -  1.2.4  COMBINED WAVES AND CURRENTS FLOW SCOUR  1.2.5  SCOUR DEPTH P R E D I C T I O N FORMULAS  FLOWS -  STEADY CURRENTS SCOUR  SCOUR  2 8 8 14  THRESHOLD OF MOTION  17  2.1  HYDRODYNAMIC FORCES  18  2.1.1  DRAG  19  2.1.2  LIFT  20  2.1.3  GRAVITY  21  2.2  A N A L Y S I S OF THE SHIELDS C R I T E R I O N  24  2.3  THRESHOLD MEASUREMENTS  26  THEORETICAL BACKGROUND  31  3.1  31  WAVE AND CURRENT INTERACTION  -  i i i  -  TABLE OF CONTENTS (Continued)  3.2  4.  NEAR-BOTTOM  SHEAR STRESSES  34  3.2.1  UNIDIRECTIONAL FLOW SHEAR STRESSES  34  3.2.2  OSCILLATORY FLOW SHEAR STRESSES  35  3.2.3  COMBINED SHEAR STRESSES AT BED  36  3.2.4  SHEAR STRESSES COMPARISON  39  3.3  WAVE THEORIES  41  3.4  COEFFICIENT OF REFLECTION  42  3.5  SCALE EFFECTS  45  3.6  SOME IMPORTANT NUMBERS  45  3.6.1  FROUDE NUMBER  45  3.6.2  REYNOLDS NUMBER  46  3.6.3  KEULEGAN-CARPENTER NUMBER  47  EXPERIMENTAL SET UP AND PROCEDURE  48  4.1  EXPERIMENTAL APPARATUS AND EQUIPMENTS  48  4.2  EXPERIMENTAL PROCEDURE  48  5.  PRESENTATION AND DISCUSSION OF RESULTS  55  6.  CONCLUSIONS AND RECOMMENDATIONS  85  6.1  CONCLUSIONS  85  6.2  RECOMMENDATION FOR FURTHER STUDY  87  BIBLIOGRAPHY  89  - iv -  LIST OF TABLES Page Table 2.1  3.1  3.2  Shear v e l o c i t i e s and maximum near-bed a f t e r Quick e t a l . (1985)  velocities 29  Combined wave and c u r r e n t shear s t r e s s e s due t o d i f f e r e n t methods f o r t h r e e sediment s i z e s a t threshold conditions  39  ( M o d i f i e d a f t e r Sarpkaya and Isaacson, R e s u l t s o f Stokes second o r d e r t h e o r y  44  1981).  5.1  Experimental  5.2  Measured and e s t i m a t e d maximum scour depths i n (cm) at t h r e s h o l d c o n d i t i o n s i n the approaching flow f o r steady c u r r e n t s a l o n e ; sediment s i z e range = 0.85-1.16 mm  60  Measured and e s t i m a t e d maximum r e l a t i v e scour a t t h r e s h o l d c o n d i t i o n s i n the approaching flow f o r steady c u r r e n t s alone; sediment s i z e range = 0.85-1.16 mm  60  Measured and e s t i m a t e d maximum scour depths i n (cm) at t h r e s h o l d c o n d i t i o n s i n the approaching flow f o r steady c u r r e n t s a l o n e ; sediment s i z e range = 1.16-1.70 mm  61  Measured and e s t i m a t e d maximum r e l a t i v e scour a t t h r e s h o l d c o n d i t i o n s i n t h e a p p r o a c h i n g flow f o r steady c u r r e n t s a l o n e ; sediment s i z e range = 1.16-1.70 mm  61  5.6  Experimental  r e s u l t s o f o s c i l l a t o r y waves  62  5.7  Experimental  r e s u l t s of combined waves and c u r r e n t s  67  5.8  C o n t r i b u t i o n o f waves and c u r r e n t s i n t h r e s h o l d v e l o c i t y (%)  5.3  5.4  5.5  r e s u l t s under steady c u r r e n t s alone  - v -  56  72  LIST OF FIGURES Page Figure 1.1  1.2  1.3  1.4  1.5  1.6  1.7  1.8  2.1  T y p i c a l scour v e l o c i t y r e l a t i o n s h i p , Shen e t a l . (1969)  5  Graph o f scour v e r s u s P i e r Reynold's Shen e t a l . (1969)  6  number,  Graph o f scour v e r s u s P i e r Reynold's number f o r t h r e e d i f f e r e n t p i l e s i z e s , Shen e t a l . (1969)  7  Graph of scour v e r s u s P i e r Reynold's number f o r two d i f f e r e n t sand s i z e s , Shen e t a l . (1969)  7  R e l a t i v e scour v e r s u s r e l a t i v e depth, Wells and Sorensen (1970)  9  R e l a t i v e scour v e r s u s wave steepness, Wells and Sorensen (1970)  10  R e l a t i v e scour v e r s u s sediment Sorensen (1970)  11  number, Wells and  R e l a t i v e scour v e r s u s P i e r Reynold's and Sorensen (1970) Primary  number, W e l l s  f o r c e s a c t i n g on an i n d i v i d u a l  p a r t i c l e , W e l l s and Sorensen  12 sand  (1970)  22  2.2  The S h i e l d ' s entrainment  2.3  M o d i f i e d S h i e l d ' s diagram,  2.4  Measured t h r e s h o l d v e l o c i t y p r o f i l e s , Quick et a l . (1985)  30  D e f i n i t i o n s k e t c h f o r a p r o g r e s s i v e wave t r a i n on a steady c u r r e n t  31  Wave p r o f i l e s with and without c u r r e n t , ( a ) Rough boundary l a y e r ; (b) Smooth boundary l a y e r  32  Flow c h a r t diagram and Shuto (1984)  38  3.1  3.2  3.3  function Bagnold  25 (1966)  27  f o r c a l c u l a t i o n o f f ^ , Tanaka  3.4  D e f i n i t i o n s k e t c h f o r a p r o g r e s s i v e wave t r a i n  41  3.5  Measured and t h e o r e t i c a l wave v e l o c i t y Quick e t a l . (1983)  43  - vi -  profiles,  LIST OF FIGURES  4.1  (Continued)  E x p e r i m e n t a l equipment, schematic diagram,  Quick  (1983)  49  4.2  OTT c u r r e n t meter  50  4.3  Wave r e c o r d e r  51  4.4  Cylindrical piles  52  5.1  R e l a t i v e scour v e r s u s time under steady c u r r e n t s alone  57  5.2  R e l a t i v e scour v e r s u s time under steady c u r r e n t s alone  58  5.3  R e l a t i v e scour v e r s u s time under pure waves  63  5.4  R e l a t i v e scour v e r s u s time under pure waves  64  5.5  Maximum r e l a t i v e scour v e r s u s c y l i n d e r diameter f o r o s c i l l a t o r y f l o w a t t h r e s h o l d c o n d i t i o n s ; sediment s i z e range = 0.85-1.16 mm  65  R e l a t i v e scour v e r s u s time under combined waves and c u r r e n t s  70  R e l a t i v e scour v e r s u s time under combined waves and c u r r e n t s  71  Maximum scour v e r s u s combined waves and c u r r e n t s t h r e s h o l d v e l o c i t y ; sediment s i z e range = 0.3-0.85 mm  73  Maximum r e l a t i v e scour v e r s u s combined waves and c u r r e n t s t h r e s h o l d v e l o c i t y ; sediment s i z e range = 0.3-0.85 mm  74  5.6  5.7  5.8  5.9  5.10 Maximum scour v e r s u s c y l i n d e r diameter a t t h r e s h o l d c o n d i t i o n s o f combined waves and c u r r e n t s ; sediment s i z e range = 0.3-0.85 mm  76  5.11 Maximum r e l a t i v e scour v e r s u s c y l i n d e r diameter a t t h r e s h o l d c o n d i t i o n s o f combined waves and c u r r e n t s ; sediment s i z e range = 0.3-0.85 mm  77  5.12 Maximum scour depth v e r s u s c y l i n d e r diameter f o r t h r e e sediment s i z e s under t h r e s h o l d c o n d i t i o n s o f combined waves and c u r r e n t s ; 25% waves and 75% currents  78  - v i i-  LIST OF FIGURES ( C o n t i n u e d )  5.13 Maximum r e l a t i v e scour v e r s u s c y l i n d e r diameter f o r t h r e e sediment s i z e s a t t h r e s h o l d o f combined waves and c u r r e n t s ; 25% wave and 75% c u r r e n t s  79  5.14 T y p i c a l scour h o l e p a t t e r n f o r combined waves and currents  80  5.15 T y p i c a l scour hole p a t t e r n f o r combined waves and currents  81  5.16 T y p i c a l r i p p l e p a t t e r n f o r waves plus c u r r e n t s t e s t s  83  5.17 T y p i c a l r i p p l e p a t t e r n f o r waves plus c u r r e n t s t e s t s  83  - viii  -  NOMENCLATURE  maximum d i m e n s i o n o f amplitude  the  particle  of h o r i z o n t a l p a r t i c l e motion i n the  oscillatory  flow projected  area of object  intermediate cylinder  dimension of the  direction  particle  diameter  minimum d i m e n s i o n o f  the  wave c e l e r i t y r e l a t r i v e form  normal to flow  particle to the  fixed  coordinate  system  coefficient  form c o e f f i c i e n t particle  i n the  related  to the  effective  d i r e c t i o n o f the drag  surface  form c o e f f i c i e n t r e l a t e d to the e f f e c t i v e s u r f a c e p a r t i c l e i n the d i r e c t i o n of the l i f t force drag  coefficient  lift  coefficient  wave c e l e r i t y r e l a t i v e current water  depth  i n the  maximum s c o u r equilibrium  to the  the  area of  the  coordinate  from moving w i t h  channel  depth  scour  depth  diameter  o f a sphere having the  same v o l u m e a s  diameter  o f a s p h e r e h a v i n g t h e same s u r f a c e  particle mean p a r t i c l e  area of  force  s i z e o f bed roughness  characteristic  diameter  of the  particle  friction  factor  for unidirectional  friction  factor  for  oscillatory  elements  flow  flow  the  particle  a r e a as  the  f  wc  = friction » drag  F F  = lift  for  c o m b i n e d wave a n d  current  force  = gravity T  factor  force  force  la  F  = p i l e Froude  number  P F  r  = Froude  number  F,j,  = total  F* s  = entrainment  g  = gravitational  H  = wave  IL^  = height  H  max  k.  force function constant  height of reflected  wave  ,H . = maximum a n d m i n i m u m wave h e i g h t s min  i n the  flume  = wave number = 2TT/L  k  s  = height  o f bed roughness  element  K  c  = K e u l e g a n - C a r p e n t e r number U ^ T / b  K  r  = reflection coefficient  n P  measured  = Manning's roughness a  R  e  f o r f l u m e waves = H ^ / H  coefficient  = Pascal = Reynold's  number  R*  = p a r t i c l e R e y n o l d ' s number = U * D / v  Rp  = p i l e R e y n o l d ' s number = U b / v = hydraulic radius  S S  s o  S S  = s p e c i f i c g r a v i t y of = c h a n n e l bed  T  = shape = wave  T a  channel particles  slope  = maximum s c o u r F  of  depth  factor period  = p e r i o d o f wave o n c u r r e n t * frame  -  x  as  -  seen from moving  coordinate  U  = flow  TJ,  1 ro  velocity  = maximum o r b i t a l v e l o c i t y a t order  U  c  U U  cr w  = steady = flow  t h e bed a s p r e d i c t e d by  current average  critical  velocity  velocity  = maximum o s c i l l a t o r y w a t e r p a r t i c l e = friction  velocity =  U* cr  = friction  velocity  U* wc  = equivalent shear  v  = fall  a  =  Y  = s p e c i f i c weight of  fluid  •y  = specific  sediment  y  = dynamic  v  = k i n e m a t i c v i s c o s i t y = u/p  p  = fluid s  T x  o  x  c  (t/p)  at  threshold conditions  v e l o c i t y f o r c o m b i n e d wave a n d c u r r e n t  constant  weight of viscosity  density  = sediment  density  = shear  stress  = shear  stress at  bed  = steady  current  shear  stress  shear  T. w  = unsteady  flow shear  T  = c o m b i n e d wave a n d c u r r e n t  cr  wc  flow  velocity  = critical  T  velocity  1 / 2  U*  p  first  theory  stress stress  of the  shear  submerged  stress  cj>  = angle of repose  tj)  = a n g l e made by u n i d i r e c t i o n a l c u r r e n t w i t h t h e d i r e c t i o n o f wave p r o p a g a t i o n  -  x i  -  sediment  ACKNOWLEDGEMENTS  The by  his  author  i s very grateful  supervisor,  Dr.  f o r t h e guidance and encouragement  M . C . Quick  throughout  the  preparation  given  of  this  thesis. Financial University, The expertise The  support  in  the  form  Tripoli i s gratefully  author  wishes  to  author  f e l l o w graduate  is  thankful  a  scholarship  from  Al-Fatch  acknowledged.  thank  and I n v a l u a b l e s u p p o r t  of  Mr.  i n the  for  the  -  x i i -  students.  Kurt  Nielsen  for  his  technical  laboratory. encouragement  and  advice  by  his  1  INTRODUCTION  1.  GENERAL  1.1  In  the  growing  accelerated  need  to  considerations if  the  sea  material prevailing in  or  the  is  in  the  change.  a  vicinity  wave  of  In  important  the  the  other  areas.  s c o u r may c a u s e  main purpose  depth  and waves.  conducted produced  around  in by  will  this currents  be  of  this  Scour  thus  depth  to  on  rate  the  cause  of  a  Design  of  sand-bottom under is  the  placed  and  local  transported material  may  alone  determining  of for  supporting  will  in  some  structures  piles  for  the  for  is  fixed  "sit-on-bottom" members.  combined  cylindrical  made waves  between plus  in and  to develop p r e d i c t i o n s  was  scour  around  or  under  and  structure  erosion  depth  o f the  the  bottom topography  scour  bottom,  comparison  of  i n the  experiments  waves  the  vicinity  structures  and  disturbed  transported  investigation is  depth  alone,  restricted  and  changes  settlement  offshore  study  and  placed  A  stability  be  the  is  stability, particularly  when a n o b j e c t  minimum p e n e t r a t i o n  platforms  currents  objects  i n the  The  bed.  sediments.  may  in  sea  there  structures.  large  structure  the  dynamic  increased  increase  conditions  For  study  are  around the  structures.  The  non-cohesive of  resources  on  their  equilibrium  This  i n computing the  the  structures  condition  T h i s c h a n g e may c a u s e  deposition  scour  of  objects  scouring (erosion) and  offshore  and wave-induced c u r r e n t s ,  increased.  Current  the  composed  sea-bed,  around  or  of  i n c l u d e an a n a l y s i s of  is  currents  velocities  cause  must  objects  generally  on  material  place  bed  is  exploration  action piles the  currents.  depths around  of of  were scour The  cylindrical  2. structures the  placed i n non-cohesive  d i r e c t i o n of  with estimating  1.2  wave  g r a n u l a r bed m a t e r i a l and w i t h f l o w s  propagation.  The m a i n emphasis  t h e maximum p o s s i b l e  will  be  in  concerned  scour.  L I T E R A T U R E REVIEW  1.2.1  SCOUR  Many  types  level  degrades  scour  where  of  scour  because  the  into  live  sediment  bed  level  clear  equals  depths Jain  general, as  and  Fisher  with i n this  out  study.  has  of  been  Breusers et  al.  as  a  exceeds  drops,  scour.  around bridge the  et  usually  (1966). result  of  caused  These t y p e s a r e Live  removal w h i l e  bed clear  scour  many  hence  water  scour  depths are  greater  where occurs  investigators, only  clear  e.g.  water  than general  Melville  scour  cylindrical and  piles  ocean  many  has  jetties  J a i n and F i s h e r  Numerous  scour  waves  predicted  as  Neill  formulas scour  and dealt  alone,  section.  SCOUR of  such  (1979),  predictions but  been  be  importance  f o r more t h a n a c e n t u r y  investigations  (1977).  studies,  long  alone,  scour  (1975)  case w i l l  i n the f o l l o w i n g  these  local  sub-divided  occurs  p l u s waves i s d i s c u s s e d  of  bed local  by  scour  currents  piers  where  supply,  T h e s c o u r due t o s t e a d y  subject  al.  scour,  sediment  U N I D I R E C T I O N A L FLOWS - STEADY CURRENTS -  Scour design  general  supply.  by  (1980),  and combined c u r r e n t  1.2.2  locally  water  c l e a r water  pointed  removal  sediment  when t h e r e i s no s e d i m e n t In  example  flow around a s t r u c t u r e .  and  supply  for  sediment  bed  a c c e l e r a t i o n of the  exist,  Anderson (1964a)  have  been  depths  in  the  and  it  (1974), and  Shen  published  vary  widely,  3. especially range the of  of  when t h e  conditions  variations, general  there  which  have  regimes  This limited  experiments  at  high  flowing  the  flows  deposition of The eddy  long  vortex  Neill of  a to  developed.  However i n s p i t e  consensus.  Once t h e  of  conditions  i n a stream,  for  flows  the  onset  at  there  rate of  the  higher  of  investigations  beyond  will at  removal  onset  velocities,  general  sediment  is  because  performing  of  motion  (Threshold  supply or r e c i r c u l a t i o n o f sediment  produce  and  or  the  founded  local  and  on an e r o d i b l e  scouring.  deceleration these are  recognized Roper  of  system are  the  by  many  (1967),  an o b s t r u c t i o n i n the the  of  structure  features  systems  (1964b),  around  made  beyond  number  structure  dominant  been  the  material  of  the  the  sediment  This scouring water  regions  flow  of  local  bed  results  field  as  erosion  it and  sediment.  structure,  These  past  observed  the  outside  process.  acceleration  past  been  well  needs a c o n t i n u o u s  frequently  from  be  conditions  depth w i t h v e l o c i t y , because the r a t e  velocities  which i s a d i f f i c u l t  is  to  flow  process.  flow  Water  were  to  been e s t a b l i s h e d  i n scour  transport.  velocity)  they  motion have  investigations  for  applied  enters the r e g i o n of scour i s equal to the  scouring  i.e.,  are  does appear  increase  which sediment  Few  for  sediment  be no f u r t h e r  by t h e  formulas  base.  Due  to  flow,  the  pressure  the field  flow  near  a  pier  is  the  large-scale  of v o r t i c e s which develop around  the  basic  which  mechanism  investigators  Imberger  flow f i e l d ,  p i e r which increase  pier  the  the  et  locally tractive  non-uniform Induced  al.  by  of  local  scour,  including Melville (1982).  force  on the  the  pier:  (1)  placing produced  sediment  velocity distribution creates  in a  has  (1975),  Due t o t h e  high v e l o c i t i e s are  pier.  a  at  the  stream  downward  4. velocity  along  t h e lower  three-dimensional tion  of a  l e a d i n g f a c e o f the p i e r ;  and (2) produces a  s e p a r a t i o n o f t h e boundary l a y e r l e a d i n g t o t h e forma-  horseshoe  vortex.  According  to M e l v i l l e  p r o c e s s has begun, i t i s t h e downward f l o w impinging horseshoe scour. the  vortex  transporting dislodged p a r t i c l e s  In the case  strength  finally,  of  o f c l e a r water scour  t h e downward  flow  (1975),  on t h e bed,  i t c a n no l o n g e r d i s l o d g e p a r t i c l e s .  and t h e  away which causes t h e  as t h e scour  decreases  once the  near  depth  Increases,  t h e bottom  until  This c o n d i t i o n represents  t h e maximum scour t o be a t t a i n e d by t h e p r e v a i l i n g flow c o n d i t i o n s . Experimental slopes  o b s e r v a t i o n s by Roper e t a l . (1967) show t h a t t h e s i d e  of the scour  hole  i n the c l e a r  water  regime  a r e approximately  e q u a l t o t h e n a t u r a l a n g l e o f repose o f t h e bed m a t e r i a l . that  t h e scour  base,  mechanism  and t h e sediment  i s i n t h e immediate v i c i n i t y  slides  This indicates  o f the s t r u c t u r e  i n towards t h e base b e f o r e i t i s removed.  I n t h e c a s e i n which t h e r e i s a n e t sediment t r a n s p o r t i n t h e stream, t h e s t r e n g t h o f t h e f l o w near scour  depth,  but maximum  t h e bottom s i m i l a r l y scour  decreases with  increasing  i s a t t a i n e d when t h e r a t e o f sediment  removal i s e q u a l t o t h e r a t e o f sediment t r a n s p o r t e d i n t o t h e scour h o l e by  the stream.  general  scour  librium  exists  The v i s u a l  regime  a t high  i s stopped,  strong  t o support  than  t h e a n g l e o f repose  periodically encroaches  flow  o f the scour  velocities  between scour h o l e and stream  when t h e f l o w enough  observation  the flow  field  f l o w which i s n o t apparent t h e base o f the p i e r i s  t h e s i d e s o f the scour  o r as the f l u i d  become u n s t a b l e , see J a i n and F i s h e r  h o l e a t angles  greater  The s i d e s o f t h e scour  c o l l a p s e and dump sediment i n t o  upon t h e p i e r ,  i n the  show t h a t a dynamic e q u i -  near  o f t h e sediment.  process  the hole, e i t h e r  hole  as a dune  f o r c e s s u p p o r t i n g these s i d e s  (1980).  5. In  terms  increases the  of  1.1  reached,  Typical  Experimental Fisher  (1980),  increased,  Figure  then  show  slightly,  because  the  discharge  i n t o the  not  shown i n F i g u r e s 1 . 1  a  size.  supply  that  as  longer  unique  It for  results  through  et  the  Shen e t  al.  stream  increases flow  is  a l l the  are  conditions  al.  (1982)  the  the  also  1.4.  but,  in  Jain  is  fact,  producing  and  further decreases  a  sediment  studies. by  Shen  et  al.  These t e s t s employed a steady  scour hole.  i n scour F i g u r e 1.2  R e y n o l d ' s number.  are  available  (1967),  Imberger  et  al.  depth  in  (1982)  1.3  literature  such as  from  the  a n d 1.4  and sediment  the  and  resulted  indicates  Figures  depends on p i l e d i a m e t e r  formulas  in  (1969).  and  velocity  now  presented  p r e d i c t i o n i n case of u n i d i r e c t i o n a l flow al.  pier  s h o u l d be c l e a r t h a t t h e d e f i n i t i o n o f  T h e 10% r e d u c t i o n  to  of  depth Many  around a  (1969)  and  upstream  scour depth imply  that  et  as the  size. for  scour  depth  t h o s e g i v e n by R o p e r  Breusers  as  current.  shows t h e g e n e r a l t r e n d o f s c o u r f o r a g i v e n p i l e d i a m e t e r  function  scour  Imberger  approaching  experimental  F i g u r e 1.1  no  by  scour hole.  of motion Is Some  local  depth  1.1.  observations  depth  sediment  maximum s c o u r  scour-velocity relationship,  scour  onset  v e l o c i t y , the  w i t h i n c r e a s i n g v e l o c i t y u n t i l i n c i p i e n t sediment  stream are  Figure  stream  al.  (1977).  et An  K> 90 «0 4 '0.00073*t  TOT  !0 FOOT riUUC. 3 FOOT Pit*  ro  I  w o»  •7  oe m  1  o •  o*  *  V  • 01 OOB  • a  OO*  »  Pltr Silt.n to if* Ctobtrt 6 C*attfi*ftrl3) to its Chabtn a CnotlflnairtSI\03!3 030 SI**, r> alKSI 00833 Situ f al 0130 Shrn, tr al Oi Tiiax l&l oisr Tenpartliei OIST Toroport IPS)  h  nam am SaocimOSI Otto* (61 Cfitlt IS) CDiat IS)  °"~\\  OS OS 1 OS J*  0!S OS! 014 imi 04S fm) 04s rmi oso 030 0130 OIT Oft OIS OSS  004 10' Reynolds  F i g u r e 1.2 (1969).  »• Number,  It  Graph of scour v e r s u s P i e r Reynold's number, Shen e t a l .  10'  I0r  f1 •  *  • i  t  •  ;  1  / 1 J f 4  •  1 |  Al  :  '  1  Pilr  F i g u r e 1.3 Graph of scour v e r s u s P i e r Reynold' number f o r t h r e e d i f f e r e n t p i l e s i z e s , Shen e t a l . (1969).  Saint  • ShK. Hal  an  » oiobti a EnoHfinf  (3)  '  <£o«« t./l oftnm as JO  • • • • •  nt 10*  OUST m - tfi  RtynoM* Numbir, #7  F i g u r e 1.4 Graph o f s c o u r v e r s u s P i e r Reynold's number f o r two d i f f e r e n t sand s i z e s , Shen e t a l . (1969).  8. extensive et  al.  review of  little  oscillating scour  virtually state)  conditions,  in  open  are  the  flow,  some  experimental  wave  experiments  done  around b r i d g e p i e r s  O S C I L L A T I N G FLOW - WAVES -  Very  by  scour  channel same f o r  that  is,  work  has  whereas flow.  Ko  Since  in  (1967),  et  m o t i o n was  a  the  to  as  Breusers  Marphy  (1964),  and  al.  (1965).  conducted  A study  by W e l l s  for  to  knowledge  cause  scour  open c h a n n e l  (steady  knowledge gained  with  been  that  due  certain  reservations,  The m a j o r i t y concerned  from  of  the  work  primarily  with  transport. Van Wells  (1965)  and t h e i r  results  the  scour  Sorensen  (1980).  to  are  scour  summarized by  oscillatory  F i g u r e s 1.5  wave  through  d e f i n i t e r e l a t i o n s h i p between t h e r e l a t i v e s c o u r and the r e l a t i v e  depth  sediments.  Figures  1.5  investigation.  in  shows  various  from t h e i r  due  studied  F i g u r e 1.5  for  are graphs which r e s u l t e d  and  of  has  scour  a wealth of  the  o s c i l l a t o r y motion.  o s c i l l a t o r y motions  on  forces  hydrodynamic i n nature,  investigators  done  exists  o s c i l l a t i n g flow  of sea w a l l s of v a r i o u s angles,  Herbich  been  there  s c o u r o f beaches and l i t t o r a l s e d i m e n t  1.8  g i v e n by  SCOUR  i n o p e n c h a n n e l f l o w was a p p l i e d ,  on scour  front  is  (1977).  1.2.3  on  local  and  1.6  show  d e p t h w i t h a n i n c r e a s i n g wave p e r i o d .  F i g u r e s 1.7  tive  number,  scour  as  a  function  of  sediment  an  increasing  and 1.8  and  pier  show t h e  scour rela-  Reynold's  number  facilities is  becom-  respectively.  1.2.4  COMBINED WAVES AND CURRENTS FLOW SCOUR  S c o u r due t o w a v e s a n d c u r r e n t s ing  an  ever-increasing  problem  as  around o f f s h o r e the  marine  construction  industry  H/h  SYMBOL 0  • A O 0  •  A o  -cS>-  9  0128 0.198 0.146 O.203 0.212 0.330 0.240 O.I83  ± 0.000 ± 0.002 ± 0.002 ±0.004  ±003  A A  t  _0L  Q  °  A 10"  10  10"  F i g u r e 1.6.  R e l a t i v e s c o u r v e r s u s wave s t e e p n e s s , W e l l s  and S o r e n s e n  (1970)  N  S  INCIPIENT  o  SAND  NO. I  0.737  •  SAND  NO  0.906  A  SAND  NO. 3  2  0.935  5  / 1 1  1  ii 1  JQS?  2  ** ^ "™  ll  5  I0  2  5  5  10  Sediment Number NS = /(S -l)gD s  F i g u r e 1.7.  R e l a t i v e scour v e r s u s sediment  number, W e l l s and Sorensen  (1970).  . 6MCIPIENT  N„  p  O  SAND  NO. 1  3.26 X to'  •  SAND  NO. 2  3.33 X 10*  A  SAND  NO. 3  2.90 X 10*  /~\ /  oj o  / i  • •  /  /  o  / i 1 i 1 1 I 1 1 1 1 t  IC?  2  ru-  5  \0*  2  5  I  S  P i l e R e y n o l d ' s Number R = — P v F i g u r e 1.8.  R e l a t i v e scour versus  P i e r R e y n o l d ' s number,  W e l l s and S o r e n s e n  (1970).  *  13. c o n t i n u e s t o grow. seabed may at  the  s t r u c t u r e foundation.  There  the amount of scour  have  been many  field  depths  Lighthouse State  of  11  feet  t h a t can occur a t a s t r u c t u r e ' s base.  around  o f f t h e Coast  Port  waterfront  Authority warehouse.  the  foundation p i l i n g  o f North C a r o l i n a .  at  Morehead  Direct  City  River  Corey  Bridge  scour  depth  Crossing Abad  and of  the Beaver  10 f e e t  Shoal the  c o l l a p s e of  tidal  A  reported  of Diamond  the  exposure t o waves and  i n A l b e r t a , Canada  He  A l s o i n North C a r o l i n a ,  experienced  t h e cause of the f a i l u r e i n June 1962. Beaver  experienced observations  of these o b s e r v a t i o n s have been noted by Johnes (1970).  scour  non-cohesive  be h e a v i l y dependent upon the magnitude of scour  describing few  The s t a b i l i t y of a s t r u c t u r e p l a c e d i n a  currents  a was  F o r steady f l o w the f l o o d o f the  caused  excessive  Crossing Bridge.  a t t h e La Corey  scour  Neill  B r i d g e and  around  the  La  (1964b) r e p o r t e d a  17 f e e t a t the Beaver  Bridge. and  currents.  Machemehi  They  (1974) s t u d i e d scour  concluded  t h a t scour  due  t o combined  i n c r e a s e s w i t h an  waves  and  i n c r e a s e of wave  l e n g t h , but t h e i r t e s t s were l i m i t e d i n scope and t h i s i n c r e a s e would not be expected  t o c o n t i n u e when g e n e r a l sediment motion o c c u r r e d .  Armbrust produced  by  (1982)  wave and  in  his  experimental  c u r r e n t motion and  study  the  described  local  dependency o f scour  scour around  s t r u c t u r e s on flow c h a r a c t e r i s t i c s . Wang and H e r b i c h (1983) i n t r o d u e d a complex parameter and range o f t e s t s the scour depth formula.  The  parameter  is  i s related formed  for their  t o t h i s parameter by a c e r t a i n by  multiplying  together  d i m e n s i o n a l groups which a r e d e r i v e d from t h e i r d i m e n s i o n a l a n a l y s i s , no  j u s t i f i c a t i o n was  made f o r making such an assumption.  five but  T h i s parameter  i s a f u n c t i o n o f stream v e l o c i t y t o t h e power f o u r and wave h e i g h t t o the  14. same power.  I t can be  tion  limited,  i s not  velocity  and  conditions  have  been  scour  depth  that  the  w i t h scour due  will  i n c r e a s e which i s not  exceeded.  This  their  formula  majority of  should  scour  increase with  is  The  be  limited  current  to  the  used  with  In t h e l a s t two  great  i n the  care. past  limited  work,  as  cited  above,  has  been  In  dealt  decades some work has  been done on t h e scour r e s u l t i n g from o s c i l l a t o r y wave motion. only  test  f i n d i n g s of the p r e s e n t  s t u d i e s conducted  t o steady c u r r e n t s .  assump-  t r u e once the t h r e s h o l d  formula  r e l i a b l e i n t h a t range o n l y .  indicate  conclusion,  t h a t scour depth a c c o r d i n g t o t h e i r  i . e . the  wave h e i g h t  c o n d i t i o n s and study  seen  conducted  To  date,  involving  both  waves and c u r r e n t s .  1.2.5 In formula exist  SCOUR DEPTH PREDICTION FORMULAS  the  case  exists  of  for  pure waves and estimating  which r e l a t e  depth  o f scour  directional  f l o w - steady  experiments  on p i e r s can be  cover tion  a sufficiently of  critical  the  waves p l u s c u r r e n t s , no scour,  but  some  theoretical  empirical relations  t o v a r i o u s f l o w parameters.  For  c u r r e n t s -, numerous r e f e r e n c e s on l o c a l found  i n literature.  Few  In  velocity  initiation  for  most  cases of  velocities motion.  were  Some  scour  o f them, however,  g e n e r a l range o f c o n d i t i o n s w i t h independent  parameters.  uni-  of  below the  or  variaat  the  interesting  r e f e r e n c e s are summarized below.  1)  Larras  (1963,  Engeldinger  (1956).  He  velocity  of  threshold expressing and  scour  1960)  analyzed  the  data  given  by  Chabert  and  c o n c e n t r a t e d on the maximum scour depth near the  undisturbed  material  depth -as a f u n c t i o n o f p i e r  grain size neglected:  and  diameter,  gave  a  the  relation  w i t h water  depth  15.  d  = 1.05  b°*  7 5  (1.1)  sm where d  sm  b  = maximum p o s s i b l e scour = pier  2)  Hincu  4.7,  6,  scour (u  ).  depth  diameter  (1965) gave e x p e r i m e n t a l  13,  and  depth  20  was  r  cm)  results  i n coarse m a t e r i a l  constant  (d  s  = d  for circular  (Dgg  = 0.5,  piers  2 and  5 mm).  ) above a c e r t a i n c r i t i c a l  sm  At lower v e l o c i t i e s a l i n e a r r e l a t i o n w i t h v e l o c i t y  1  The  influence  o f water  were c o r r e l a t e d  depth  The  velocity J  (1 2)  -  cr  was  negligible  f o r d/b  >  1.  The  results  with the e x p r e s s i o n :  gb  with a r e l a t i o n given f o r u cr  U  i  c r  P  o / ^/ s~  = 1.2  f o r n a t u r a l sands,  p N  /oxO.2  / g D ( — — ) (—)  the r e l a t i o n may  b  3,  obtained  IT-IT— ) sm  (b =  3.3  .  = 1.54  _,0.3 . 0.2  D  d  be converted  0  <£) b  2  ( i ) b  0  *  1  Q  g  0.5  (1.4)  into:  3  (1.5)  16. where d  = water depth  Q  U  = steady flow v e l o c i t y  D  = sediment  3)  Shen,  size  Schneider,  Karaki  (1967), Shen (1971) concluded velocity  (1966a,  sm  = 0.00022 R e ° *  d  Roper,  Schneider,  t h a t t h e maximum l o c a l scour near  f o r i n i t i a t i o n o f sediment  d  1969),  Shen  critical  w i l l be:  6 1 9  (m - u n i t s )  (1.6)  d  . _ 0.43 , o.0.355 sm = 2 F r (r—) b  (1.7)  where Re  = Reynold's  Fr  = Froude number  4)  Laursen  U > U  c r  number  and T o c h  (1956) s u g g e s t e d  that  d  g  m  changes w i t h time f o r  and h i s f o r m u l a may be p r e s e n t e d a s :  d  sm — — b  d  o 0.3 = 1.35 ( r — ) * b  for circular piers  (1.8)  Most o f t h e above e q u a t i o n s g i v e maximum p o s s i b l e scour as a c l e a r water scour near Scour as  depth  given  slightly,  by  o r a t t h e t h r e s h o l d o f motion  i n the approaching  flow.  d o e s n o t i n c r e a s e w i t h steady flow v e l o c i t y U f o r U > ^ .) CJ  Chabert  and E n g e l d i n g e r  as r e p o r t e d by Chabert  (1965)  but, i n f a c t ,  and Shen (1956, 1965).  decreases  17. 2.  The  term  threshold  THRESHOLD OF MOTION  defines  a  limiting  condition  boundary between one s t a t e o f a f f a i r s and another. conditions absolute  the threshold  precision.  points".  In number very  o f flow  o f the p a r t i c l e  contact  this  threshold  a  threshold It  be  which  slightly  connecting  assumed  threshold  defined  with  the threshold of  t h e bed p a r t i c l e  to correspond  If threshold this  a r e soon more  forms t h e  reached when t h e r e s u l t a n t o f a l l a c t i v e  was  o f p a r t i c l e s moving.  Therefore  cannot  Some of these a c t i v e f o r c e s w i l l be d i s c u s s e d  study  particles,  motion  i n t e r s e c t the l i n e  few p a r t i c l e s moving,  light  sediment  L i k e many  E a g l e s o n and Dean (1961) d e s c r i b e d  movement a s , "a s t a t e forces  of  which  i s assumed  motion i s u s u a l l y removed,  active  t o a moderate  to correspond to  j u s t a few s m a l l o r  and the motion  particle  later.  movement  then  is a  ceases.  more  true  which w i l l be m a i n t a i n e d , and w i l l not cease.  i s generally  accepted  that  a fluid  flowing  over a sediment bed  e x e r t s a shear s t r e s s on t h e p a r t i c l e s which causes them t o move i f i t i s sufficiently move  large.  This  shear  s t r e s s a t which  the p a r t i c l e s b e g i n t o  i s known a s c r i t i c a l  shear  s t r e s s , and i s a s s o c i a t e d  with a  fluid  v e l o c i t y known as the c r i t i c a l v e l o c i t y . U s u a l l y , t h e S h i e l d s entrainment f u n c t i o n ( S h i e l d s , 1936) i s used t o define  the shear s t r e s s f o r i n i t i a l  results  p l o t t e d on t h e S h e i l d s  scatter  may  exerted  by t h e moving f l u i d ,  bed  diagram  show c o n s i d e r a b l e  scatter.  be a t t r i b u t a b l e t o such f a c t o r s as t h e random shear  particles,  (Williams  p a r t i c l e movement, but e x p e r i m e n t a l  and  and Kemp,  each  t h e random shear  observer's  1971).  Despite  s t r e s s necessary  definition  of  the s c a t t e r ,  critical  This stress  t o move movement  the Shields  curve  18. remains  about  the best  indicator  S h i e l d s c r i t e r i o n w i l l be g i v e n Bagnold ocillating placed and  flow.  motion;  details  plate to find  concluded  critical  data  that  of the  later.  (1946) has done a famous experiment u s i n g  his oscillatory  have  of c r i t i c a l  motion.  a sand bed on an  Komar and M i l l e r  on t h e u n i d i r e c t i o n a l flow  the Shields  curve  works  (1974) have  Shields  well  diagram  for oscillatory  T h i s f i n d i n g has been c o n f i r m e d by Madsen and Grant (1975) and i s  a n i m p o r t a n t advancement i n t h e study o f t h e o n s e t o f motion under waves. Observations the  shear  stress  o f sediment movement i s n o t t h e only  a n o t h e r mechanism mechanism tative It  i s t h e flow  i n the i n i t i a t i o n  turbulence  that  near  the turbulence  seems t o i n d i c a t e  that  f a c t o r i n t h e mechanism, but t h e r e i s o f p a r t i c l e movement.  the p a r t i c l e s ,  d e s c r i p t i o n o f t h e importance o f flow  i s apparent  old.  involved  threshold  plays  though  turbulence  a  The  quanti-  i s unavailable.  a r o l e i n the onset o f thresh-  Three primary a c t i v e f o r c e s i n v o l v e d and r e l a t i o n s h i p t o I n c i p i e n t  motion s h a l l be d i s c u s s e d .  2.1  HYDRODYNAMIC FORCES The  forces  influencing  bed p a r t i c l e  motion  c o n s i s t o f t h e f o r c e s o f steady f l o w d r a g , l i f t forces However  of  accelerating  since  (particle  the force  diameter  D  3  flow  as proposed  due t o i n e r t i a  i n this  n e v e r predominate and t h e r e f o r e dynamic  force  force.  The hydrodynamic f o r c e s  by  frictional  will  and t h e s o - c a l l e d i n e r t i a Morison  i t will  e t a l . (1950).  i s a function  case) which i s very  be t h e combination  forces.  by  a r e hydrodynamic and  small  be n e g l e c t e d . o f the l i f t  o f body  hence i t w i l l  The t o t a l force  volume  hydro-  and t h e drag  a r e opposed by t h e f o r c e o f g r a v i t y and  !9. 2.1.1 Due  DRAG  to v i s c o s i t y  and boundary  layer  effects  a s e p a r a t i o n o f flow  o c c u r s on t h e boundary o f t h e o b j e c t and a wake i s formed. separation Reynold's pressure  is a number.  function  o f the shape  The p o i n t o f  o f t h e o b j e c t and the l o c a l  The drag f o r c e i s t h e combination o f form drag due t o  differential  and t h e v i s c o u s drag  due t o s k i n  friction.  For  d i f f e r e n t b o d i e s , one type o f drag may dominate t h e o t h e r , as i n t h e case of  a p e r f e c t sphere when t h e t o t a l drag i s p r i m a r i l y p r e s s u r e d r a g .  The  p o i n t through which t h e drag f o r c e a c t s depends on t h e r e l a t i v e magnitude of  the l i f t  particles  and drag  geometry,  force  location,  components and l o c a l  which  are functions  Reynold's  number.  o f bed  The steady  f o r c e due t o d r a g as developed i n any elementary f l u i d mechanics t e x t c a n be shown t o be e q u a l  F  =  r-  D  p  A  ( 2  V  w h e r e A i s t h e p r o j e c t e d a r e a o f o b j e c t normal the drag velocity. primarily  coefficient,  1 }  to flow d i r e c t i o n , C i s Q  p i s t h e f l u i d d e n s i t y and U  c  i s the f r e e  stream  S i n c e drag i s a v i s c o u s phenomena, the c o e f f i c i e n t o f drag i s influenced  by t h e Reynold's  number.  s p h e r e s has been s t u d i e d by v a r i o u s a u t h o r s . v e l o c i t y data. the  *  The drag  coefficient for  Drag i s measured u s i n g  fall  Under steady s t a t e c o n d i t i o n s t h e f a l l v e l o c i t y i s c a l l e d  terminal velocity  submerged weight.  and t h e drag  on the p a r t i c l e  i s equal  t o the  T h e r e f o r e f o r a sphere,  C  D  =  ^  U  1  (  ^  )  (2-2)  20. where V i s t h e f a l l  velocity,  D i s the p a r t i c l e s i z e  diameter, g i s t h e  g r a v i t y and p i s t h e d e n s i t y o f sediment, s Alger irregular  and Simons shaped  (1968)  particles  a d j u s t e d t h e sphere  drag  coefficient for  through the use o f shape f a c t o r ,  d  A SF - p n  (2.3)  where SF i s Corey shape f a c t o r = c / a b , a i s t h e maximum dimension o f Q  the  particle,  minimum the  Q  i s t h e i n t e r m e d i a t e dimension o f t h e p a t i c l e ,  t h e same volume as t h e p a r t i c l e .  the shape f a c t o r  only  c i s the  d i m e n s i o n o f t h e p a r t i c l e , d^ i s t h e d i a m e t e r o f a sphere h a v i n g  same s u r f a c e a r e a as t h e p a r t i c l e and d  having as  b  The drag c o e f f i c i e n t  number, but a l s o  a l s o i n f l u e n c e d by a d j a c e n t p a r t i c l e s  The  i s t h e d i a m e t e r o f a sphere  i n c r e a s e s f o r t h e same Reynold's number.  a f u n c t i o n o f Reynold's  2.1.2  Q  particle  increases It i s not  geometry, and i s  as p o i n t e d out by White  (1940).  LIFT  relationship  f o r the f o r c e  due t o l i f t  i s similar  to that f o r  form drag and i s g i v e n by  F  where F  i s the l i f t  force  L  = ^ p A U  and C  Li  fluid the  particle,  taken  i s the l i f t  coefficient.  Since the  Li  i s p a s s i n g above a p a r t i c l e ,  hydrostatic. be  (2.4)  c  whereas  below  the p a r t i c l e  Although the l i f t  i n consideration 2  functions of U . c  t h e r e i s a d e c r e a s e i n p r e s s u r e above the p r e s s u r e  i s very d i f f i c u l t  among the drag  force  remains  fairly  t o measure, but i t c a n since  both of them a r e  2.1.3 The and  GRAVITY  hydrodynamic f o r c e s  friction.  angle - angle  a r e opposed by t h e weight o f t h e p a r t i c l e s  The f r i c t i o n  i s usually  expressed  i n terms  of f r i c t i o n  o f n a t u r a l repose -, and t h e g r a v i t y f o r c e may be  e x p r e s s e d a s t h e p a r t i c l e ' s submerged weight.  simply  The submerged weight o f a  p e r f e c t sphere i s g i v e n as  F  = g  where  i  0 3  (2.5)  < * - y> 8  i s g r a v i t a t i o n a l f o r c e , D i s t h e sphere diameter, y  g  i s the u n i t  weight of the sphere and y i s the u n i t weight o f the f l u i d . Figure particle. reached critical these the  shows t h e t h r e e  a value  that,  or threshold  critical  resisting  White  i f increased conditions  conditions  forces  on a h y p o t h e t i c a l  defined a c r i t i c a l  turbulent  flow,  slightly  the g r a i n w i l l  t o have been reached.  the hydrodynamic  p o i n t o f F^ and F^, e q u a l s (1940) s t u d i e d  even  are said  f o r c e of the p a r t i c l e ,  sand  forces  move, Under  a r e j u s t balanced by  i . e . , t h e sum o f t h e moments about zero.  the e q u i l i b r i u m  of a p a r t i c l e  i n laminar  flow  shear s t r e s s a s :  T  for  primary  When t h e s e hydrodynamic f o r c e s a c t i n g on a g r a i n o f sediment  the contact  and  2.1  cr  = 0.18  (y ~Y) D s  tan<t>  (2.6)  the drag f o r c e i s  (2.7)  22.  F i g u r e 2.1. Primary f o r c e s a c t i n g on an i n d i v i d u a l sand p a r t i c l e , W e l l s and Sornesen (1970).  where x  i s t h e bed shear s t r e s s , D  o  particle, stress  coefficient  that  Is  the  x , x denotes the c r i t i c a l o cr defining  area  perpendicular  to  conditions x  = x  For  diameter o f the  i s the e f f e c t i v e s u r f a c e a r e a o f the p a r t i c l e exposed t o  the shear  form  i s a characteristic  s  o fully  of  the e f f e c t i v e  the  of  of  the  the f l u i d  and C  isa  0  2  surface  projection  the d i r e c t i o n  shear s t r e s s  area  o f the p a r t i c l e ,  particle  flow.  on  a  F o r the  cr t u r b u l e n t flow c o n s i d e r i n g the drag and the l i f t  plane  critical  force  <Y -Y) S  (2.8)  cr — l  + — cot o> l  C  C  or cr ^ s ^ ^ s  C  w  h  e  r  e  k  i  C  = _ L_ 4 ,  C  ^  =  a form c o e f f i c i e n t ,  effective the l i f t sediment.  l  +  k  c  4  and  C  C  2  \ >  o  t  •  a r e form c o e f f i c i e n t s r e l a t e d  s u r f a c e a r e a o f the p a r t i c l e force respectively I f CL = 0 ,  2  2  C  is  (2.9) k  i n the d i r e c t i o n  t o the  o f the drag and  and $ i s t h e a n g l e o f repose o f the submerged  e q u a t i o n (2.9) reduces t o  24. T  The  parameter  cr r r — i s the r a t i o  s tional  force,  dimensionless  o f the drag f o r c e t o the g r a v i t a -  •Y)I  s  often  referred  number i s a  as  Sheilds  type o f Froude  g r a i n s i z e and the shear v e l o c i t y .  "  -  Y  >  D  number t h a t  Hence,  this  i s r e l a t e d t o the  A dimensional analysis y i e l d s  x <V  parameter.  p U* " V (  s  Y  (2.11) )  D  s  hence x  where U* cr  2.2  The  Shields  laboratory sediment  values  (2.12)  i s the shear v e l o c i t y a t the t h r e s h o l d '  ANALYSIS OF THE  profile  2  - p U* cr  cr  bed. had on  temporal  SHIELDS CRITERION  curve  flumes  with  (Figure fully  2.2)  the  assumed,  bed  mean s h e a r  for  has  developed  F o r the t u r b u l e n t been  been  based  boundary  i n defining  initial  particle  movement,  critical  shear  The  a graph of observed sediment  and  not  depend  on  a  experiments flows over  in flat  layer, a logarithmic v e l o c i t y  and  stress.  on  two-dimensional  extrapolating i t does  condition,  the  critical  shear  Sheilds  s t r e s s was  stress  used  the  o b t a i n e d by  d i s c h a r g e v e r s u s shear s t r e s s  qualitative  criterion  (Task  Committee,  1966). The the  data  Task Committee Report r e v e a l e d scatter  on  the  Shields  t h a t one o f the main reasons f o r  diagram  stems  from  the  difficulty  25. encountered ency by  In c o n s i s t e n t l y  is difficult  to achieve  the moving f l u i d ,  d e f i n i n g c r i t i c a l flow c o n d i t i o n s . because of  Consist-  the random shear s t r e s s e x e r t e d  and because of the random p a r t i c l e s u s c e p t i b i l i t y  movement under a l o c a l i n s t a n t a n e o u s shear  to  stress.  I  The e x e r t e d shear s t r e s s i s random because of the t u r b u l e n c e i n t h e fluid  flow,  and  any  instantanteous  temporal mean s h e a r s t r e s s ,  shear  stress  is a  f u n c t i o n of  the f l u i d d e n s i t y and v i s c o s i t y and  boundary c o n d i t i o n s i n c l u d i n g the p a r t i c l e  of  any  particle,  and  the  overall  the f l o w  geometry.  The p a r t i c l e s u s c e p t i b i l i t y depends on the shape, weight, ment  the  particle  and p l a c e -  susceptibility  can  be  d e s c r i b e d by a p r o b a b i l i t y d i s t r i b u t i o n (Grass, 1970). There i s t h e problem of d i f f e r e n t o b s e r v e r s having d i f f e r e n t t i o n s as t o the onset  of sediment motion.  Some may  percep-  p r e d i c t motion when  t h e very f i r s t g r a i n s a r e i n movement, and o t h e r s not u n t i l a s u b s t a n t i a l f r a c t i o n of the bed  p a r t i c l e s are i n motion.  26. A Grass  further  problem  i s caused  by  the  use  of d i f f e r e n t  e x p l a i n e d t h a t because d i f f e r e n t wave flumes  wave  flumes.  have d i f f e r e n t  ary  c o n d i t i o n s , the boundary r e g i o n t u r b u l e n c e a r e n e c e s s a r i l y  and  they no  bound-  different  l o n g e r show s i m i l a r i t y w i t h r e s p e c t t o the average  critical  shear s t r e s s v a l u e s d e r i v e d from the S h i e l d s c u r v e .  2.3  THRESHOLD MEASUREMENTS Much work has been done on the t h r e s h o l d under u n i d i r e c t i o n a l  current  conditions.  accepted  as  the  The  finding  fore-runner  of  Shields  i n sediment  (1936)  entrainment  is  steady  universally  studies.  Bagnold  (1966) has p r e s e n t e d a curve s i m i l a r t o t h a t o f S h i e l d s , but p r e s e n t e d i n a more c o n v e n i e n t form h a v i n g r e p l a c e d the p a r t i c l e Reynold's number w i t h the p a r t i c l e diameter  ( F i g u r e 2.3).  Much work has been done i n d e t e r m i n i n g the sediment movement t h r e s h old  under  from  oscillatory  the  data  of  flow  previous  conditions.  Komar and  researchers  that  the  Miller  (1974)  sediment  entrainment  c o n d i t i o n s a r e s i m i l a r f o r a l l types of o s c i l l a t i o n i n v e s t i g a t e d . conditions water  have  been  tunnels,  diameters, ordinary  and  tanks  and  the  oscillatory  orbital velocities because the  a r e a b l e t o generate recreate  a t t a i n e d by  use  waves  plates. cannot  p e r i o d i s so  these p r o t o t y p e  prototype  of  pressures  be  in  flumes,  These  oscillatory  Prototype  periods,  reproduced  i n wave t e s t s i n  restricted.  The  c o n d i t i o n s , but may and  found  convective  orbital  o t h e r methods not be a b l e t o  accelerations  as  e x p e r i e n c e d under waves. Komar and M i l l e r (1974) r e p o r t e d t h a t t h e s e methods o f g e n e r a t i n g an oscillating the  shear  f l o w over a sediment bed stress  lead  t o the s i m i l a r c o n c l u s i o n t h a t  r e q u i r e d t o move sediment under waves i s the  same  as  27.  Grain Size, i n M i l l i m e t e r s . F i g u r e 2.3. M o d i f i e d  S h i e l d ' s diagram a f t e r Bagnold (1966).  28. t h a t r e q u i r e d t o move sediment under a u n i d i r e c t i o n a l c u r r e n t . Miller  used  Bagnold  five  (1946)  Warren  sets  and  (1969)  Monohar  used  an  Watanabe (1967) nad wave  flume.  The  of published (1955)  data  i n analysis  of the  threshold.  used  oscillatory  plates,  Ranee  oscillating  water  E a g l e s o n , Dean and  last  two  sets  Komar and  of  tunnel,  Peralata  while  and  Horikawa  and  (1958) used waves i n a  d a t a were not used  much  except  to  s u p p o r t t h e c o n c l u s i o n s as determined u s i n g t h e f i r s t t h r e e d a t a s e t s . The their  sediment  particle  d e n s i t i e s from 1.52  diameters  t o 7.9  range 3  gm/cm .  from  0.009  to  4.8  cm,  and  The d a t a p o i n t s o b t a i n e d range  o v e r t h e e n t i r e spectrum o f Reynold's number used i n t h e S h i e l d s  diagram,  so  critical  a complete  comparison o f the u n i d i r e c t i o n a l  and  oscillatory  shear s t r e s s e s i s p o s s i b l e . Madsen and for  Grant  (1975,  1976)  demonstrated  that  criterion  t h e i n i t i a t i o n o f sediment movement as d e r i v e d from steady u n i d i r e c -  tional  f l o w c o n d i t i o n s s e r v e s as q u i t e an a c c u r a t e and g e n e r a l  f o r t h e i n i t i a t i o n o f sediment movement i n o s c i l l a t o r y the  Shields  boundary  criterion  flow provided  that  shear s t r e s s i s p r o p e r l y e v a l u a t e d .  Quick e t a l . (1985) have s t u d i e d the onset o f sediment motion under combined  waves and  sediment  motion  and very  they  represents  concluded that  close  to  the  tested,  currents,  assumed  that  one  steady c u r r e n t s .  roughness  bed, waves,  result  a critical  assumed  level  height  of t h a t  T a b l e 2.1 and F i g u r e  that  causes and  onset  combined  above  the bed  o f motion  a t the bed  condition,  f o r a l l the  waves p l u s  combine  the threshold of  o f shear s t r e s s  a s i m i l a r maximum v e l o c i t y  the near bed maximum wave and  r e a s o n a b l e agreement the  They  currents.  measured  conditions The  study  average c u r r e n t v e l o c i t y a t linearly  and  show t o be i n  w i t h S h i e l d s t h r e s h o l d c r i t e r i o n f o r steady c u r r e n t ; study f o r the maximum v e l o c i t y c r i t e r i o n i s shown i n 2.4.  29.  Ot/»K  Hs»»»T*4 *  i  IM.14.tll far t  (fcUMatll l*r 1  Maaolaf  r.«  i.n  1.12  1.11  It.7  }4.4  13.1  s.u  1.J1  3.12  14.1  2I.«  24.4  M.l  2.44  1.14"  2.S1  10.4  n.>  21.1  %4.»  S».»  I.M  1.41  1.14  11.1  4}. J  1T.J  W.J  M.l  l.«  4.04  l.*J  24.1  44.3  41.5  0.3 - 0.»S  H.T  M.I  f«.T  Jt.t  1.1* - 1.T0  12.4  11.>  i.n  - s.w  11.4  S.eo  -  M.«  S.»  'alKltlu fl«i.t)l  Fro •*sslat  Curat  l.«  Mauaaa  •)m 1 C i r m i  ».«.  t.»5 -  UlaAntt  tel.  M».  •UtMtO)  OJ.il  T a b l e 2.1. Shear v e l o c i t i e s and maximum near-bed v e l o c i t i e s a f t e r e t a l . (1985).  It results tions the  should  be  emphasized  obtained are usually  from which  that  some  sediment  motion  stresses  a t which  * As extended threshold  concluded that  i s a good t o o l particles  of the sediment shown  mentioned  they were d e r i v e d and a r e n o t o f t h e g e n e r a l n a t u r e o f  i s therefore  tive size  the p r e v i o u s l y  l i m i t e d by t h e range of e x p e r i m e n t a l c o n d i -  Shields c r i t e r i o n f o r unidirectional It  of  Quick  by  f o r any  Quick kind  the Shields  t o determine  f o r onset of  the l e v e l of c r i t i c a l  shear  range.  e t a l . (1985),  conditions w i l l  Criterion  s t a r t t o move, b e a r i n g i n mind a r e p r e s e n t a -  size  of  steady f l o w .  flow,  since  the Shields the c r i t i c a l  Criterion shear  c a n be  stresses at  be almost t h e same whether i t was a t t a i n e d by  steady c u r r e n t s a l o n e o r waves a l o n e o r combined  waves and c u r r e n t s .  30.  • l  e  V I.  »t  %.%  VO0CITT. C " ' S  I  ».t  g.e  «t  •(  *t  v a o c i i i . cn/i  (b)'Range 0.6S to 1.16mm  (a) R a n g * 0.30 Ie O.BBmm  o w• 5. ya  • •  IS.8  ID.O  T.f>  «C  V I  H I  11  W l C U I i . Cn-5  (c) Rang* 1.16 Ie 1.70mm  CtJ) Range 1.70 to 2.00mm  i ;  I.  / >r  n.  v u o t i u . cx i  (a) Range t.00 Ie t.96mm  F i g u r e 2.4  »c  *•«• mnr in.  M  •>•  tO Range 1.16 Ie I.TOmm - Ad»ef»e Current  Measured t h r e s h o l d v e l o c i t y p r o f i l e s  a f t e r Quick et a l . (1985).  31.  3.  3.1  THEORETICAL BACKGROUND  WAVE AND CURRENT INTERACTION A basic understanding  of wave current interation i s fundamental f o r  studying scour under combined waves and currents. interact  i n two ways.  The f i r s t  Waves and currents  i s the modification of a wave which  travels from a zero region to a region where currents exist.  The second  i s the behaviour of a wave which i s already superimposed on a current; for t h i s s i t u a t i o n the resultant i s a simple combination of the wave and the current flow f i e l d s . As  discussed by Quick  (1983), the major features of the wave and  current combination problem can be defined by transforming the s i t u a t i o n of a wave on a uniform current i n t o an exactly similar wave on water at rest.  This transformation i s achieved simply by subtracting the uniform  current  as shown  i n Figure  3.1.  The wave  u n a l t e r e d , but the wave period i s now T field  r >  height  and length are  on zero current.  The v e l o c i t y  of the equivalent wave can then be analyzed using standard wave  v. o  ^///////////////////7/f/////////////////////.  Figure 3.1. current.  D e f i n i t i o n sketch f o r a progressive wave t r a i n on a steady  32. theory.  This  argument  i s confirmed  concluded  that  comparison w i t h  by Kemp  theoretical  a d d i t i o n o f a c u r r e n t on a wave has l i t t l e between theory,  t h e measured provided  Figure profiles  of  3.2  waves and those  and Simons  profiles  t h e same  further  waves  with  F i g u r e 3.1, the f o l l o w i n g equations  L C  a  suggests  they  t h a t the  e f f e c t on t h e c l o s e agreement  of both  second-  t h a t the wave p e r i o d i s reasonably allows  (1982);  and t h i r d - o r d e r  adjusted.  comparison,  by  plotting  and without  currents.  equivalent  Referring to  hold:  C T = C T a a r r  (3.1)  C  (3.2)  r  + U  c  10  I  H  M.W.L.  10 s  F i g u r e 3.2. Wave p r o f i l e s w i t h and without c u r r e n t , (a) Rough boundary l a y e r ; (b) smooth boundary l a y e r . , wave w i t h c u r r e n t ; , wave a l o n e , Kemp and Simons (1982)  33. L T c a  where L i s t h e wave l e n g t h , T i s t h e wave p e r i o d , C i s t h e wave c e l e r i t y , and  "  i s t h e steady  c  to the a b s o l u t e  current v e l o c i t y .  The s u b s c r i p t s 'a' and ' r ' r e f e r  and r e l a t i v e c o o r d i n a t e with  Many i n v e s t i g a t o r s have attempted  to give a f u l l  t h e p r e s e n c e o f a wave c a n a f f e c t t h e steady is  important  when m o d e l l i n g  the c u r r e n t , r e s p e c t i v e l y .  problems.  e x p l a n a t i o n o f how  c u r r e n t boundary l a y e r which  Most  o f these  studies  rely  on  m a t h e m a t i c a l o r t h e o r e t i c a l models f o r t h e wave c u r r e n t i n t e r a c t i o n and attempt  to f i n d  consequently Grant the  and Madsen (1979) presented  using very  motion  o f waves  and t h e a s s o c i a t e d  velocities  r e l a t i o n s f o r near  bottom  velocities  and  f o r shear s t r e s s e s t i m a t i o n .  combined  bottom  theoretical  were d e f i n e d  an a n a l y t i c a l  and c u r r e n t s  boundary  shear  i n the v i c i n i t y  stress.  f o r wave and c u r r e n t  T h e maximum  bottom  to describe of a  rough  C h a r a c t e r i s t i c shear  boundary  a combined wave-current f r i c t i o n f a c t o r ' f complex form.  theory  l a y e r r e g i o n s by  ' which was g i v e n i n a  s h e a r s t r e s s | T,  | i s gven i  D y HI 3.X  as, |T. 1  b.max  |-7 2  f  1  cw  pa  1  |U. | b  2  (3.4)  1  where oc - 1 + (|U  where height  |/|U. | )  |u I i s t h e m a g n i t u d e a 1  1  a above t h e bottom;  2  + 2(|U |/|U,|) cos 4  o f t h e steady  (3.5)  current v e l o c i t y vector a t a  |U^| i s t h e maximum  near-bottom  orbital  v e l o c i t y from l i n e a r wave t h e o r y , and $ i s t h e a n g l e made by U w i t h t h e c a d i r e c t i o n of wave  propagation.  34. Brevik  and  behaviour.  Aas  Firstly  (1980) they  p e r i o d i c wave, i n i t i a l l y an  opposing  attenuation  current, on  studied  studied on s t i l l  f e d from  homogeneous  the  three wave  water,  amplitude  of  wave-current  variation  when  propagates i n t o a f o l l o w i n g  below.  currents  aspects  Secondly  or  on  they  still  investigated  water  and  the  a or  wave  results  were used t o determine the a p p r o p r i a t e bed f r i c t i o n f a c t o r .  T h i r d l y , the  horizontal  fluid  system  measured.  They  of  velocity  components  in  a  wave-current  gave the wave-current f r i c t i o n f a c t o r f wc  wave a t t e n u a t i o n  f a c t o r ~^(H)  as a f u n c t i o n  a l o n g the wave flume; i n the l i m i t i n g  c a s e f o r pure waves, t h i s f r i c t i o n f a c t o r i s c l o s e t o Jonsson's Kemp and boundary  layer  propagating roughness  factor.  Simons (1982,1983) concluded t h a t u n i d i r e c t i o n a l i s reduced  with  current  h e i g h t s of  i n thickness on  both  were  by  rough  the roughbed.  the  and  The  turbulent  superposition  smooth  bed  of  sand  waves  within  turbulence c h a r a c t e r i s t i c s  dominated by the p e r i o d i c f o r m a t i o n o f v o r t i c e s a t the bed.  2  are  According to  them the s h e a r s t r e s s measurements under waves a l o n e a r e i n a good a g r e e ment w i t h v a l u e s e s t i m a t e d c a l c u l a t e d f r o m I f "1/2 + 4 w  using log ° 10 i n  wave f r i c t i o n f a c t o r s fw (Jonsson) (^ f / ) = l . (a k " ) and f ^4 w "ID oi s w _ 1  2  1  o  ( K a j i u r a ) c a l c u l a t e d from fw = 0.37  g  n  (a /k )~2/3 h e r e a i s the maximum om s om wave d i s p l a e m e n t a t bottom e s t i m a t e d u s i n g p o t e n t i a l wave t h e o r y and k s is  the  roughness  size.  v e l o c i t y i n the combined  3.2  Fredsoe  w  (1984)  wave-current  calculated  the  mean  current  motion.  NEAR-BOTTOM SHEAR STRESSES  3.2.1 The  UNIDIRECTIONAL FLOW SHEAR STRESSES shear  stress  w e l l known formula  a t bed  under  unidirectional  flow i s g i v e n by  the  35. T = p U* o c  2  (3.6)  where T i s t h e shear s t r e s s a t bed, p i s t h e f l u i d d e n s i t y and U* i s t h e o c s h e a r v e l o c i t y o f t h e f r e e stream.  T h i s f o r m u l a has been i n use f o r l o n g  time and i t has been checked a g a i n s t The  mean  current  Manning-Strickler boundary  steady  re-written  velocity  near  l a b o r a t o r y and f i e l d  t h e bed can be  r e l a t i o n s h i p which flow  i n terms  open  channel  i s based  calculated using  on  measurements.  measurements.  a  This  wealth  of  equation  the rough  can be  o f s h e a r v e l o c i t y U* and t h e sediment o r roughness  s i z e D, by u s i n g the r e l a t i o n s h i p s (Henderson, 1966)  1  n = 0.038 D '  U*  Then the Manning e q u a t i o n  3  2  (d i n meters)  = g R  h  \ c  1/6  = 8.4 (-"-) D  U* c  i s t h e mean c u r r e n t v e l o c i t y ,  c  (3.8)  o  becomes,  U  where U  S  (3.7)  (3.9)  i s the hydraulic radius, D i s  t h e sediment s i z e , n i s t h e Manning's roughness c o e f f i c i e n t and S bed  slope.  size,  mean v e l o c i t y ,  flow  cross  the equation y i e l d s q u i t e robust estimates  3.2.2 The as:  For a given  q  i s the  s e c t i o n and sediment  o f U*.  OSCILLATORY FLOW SHEAR STRESSES  near-bottom  shear  s t r e s s due t o o s c i l l a t o r y  flow  i s expressed  36. \  (3.10)  fw  w  T  w  i s the shear s t r e s s  friction The  factor for x ,  and U"  w  friction  factor  smooth o r rough ness.  a t b o t t o m n due  f  is a  regimes,  o f t h e t y p e o f f l o w , l a m i n a r or  and  also  function  o f the bed  rough-  There a r e many formulas i n t h e l i t e r a t u r e f o r p r e d i c t i n g the f r i c -  tion factor, (1975).  see f o r i n s t a n c e K a j i u r a (1968), J o n s s o n (1966) and Kamphius  Under n a t u r a l c o n d i t i o n s , the bed boundary  l a y e r below sea waves  i s o f t e n rough t u r b u l e n t , see B r e v i k (1981) and Fredsoe  3.2.3 The  COMBINED SHEAR STRESSES AT shear  estimated fields, the  f w  r  i s wave p a r t i c l e v e l o c i t y a t the bottom.  lm  i s a function  turbulent  t o p u r e wave m o t i o n , »  stresses  i n different  under  (1984).  BED  combined  ways, assuming  a  waves  and  currents  s i m p l e combination  t h a t i s a l i n e a r a d d i t i o n o f the v e l o c i t y f i e l d s ,  mean  and  turbulent  components.  If  the  flow  can  of  the  be flow  i n c l u d i n g both  i s turbulent,  such  a  l i n e a r a d d i t i o n o f f l o w f i e l d s would r e s u l t i n a n o n l i n e a r combination o f shear  stresses x wc  where  x  i s the  wc  currents,  T  oscillatory results. be  called  c  i s the  flow  The  near  shear  n  bed  steady stress.  near-bottom  equivalent  = T  w  + T  shear  + y-2 T T w c  c  stress  current This  shear s t r e s s  shear  agrees  as:  t o c o m b i n e d waves stress,  with  Quick  and et  x  w  s h e a r v e l o c i t y U* . wc  and  i s the  a l . (1985)  can be e s t i m a t e d u s i n g what  or c h a r a c t e r i s t i c  s t r e s s i n t h i s case w i l l be d e f i n e d  due  (3.11)  The  will shear  37. T = p (U* )2 wc wc  Tanaka and Shuta  (1984) I n t h e i r  (3.12)  paper found  out t h a t shear  stress  f o r combined wave and c u r r e n t i s g i v e n a s :  T  wc  = T p f 2 wc K  2  U lm  (3.13)  where f i s a f r i c t i o n f a c t o r under combined wave and c u r r e n t and IL i s wc lm the  amplitude  of h o r i z o n t a l  velocity  o u t s i d e t h e boundary l a y e r .  o f the o s c i l l a t i n g  the  definition  calculated  v e l o c i t y component.  c a l c u l a t i o n i n c l u d e s t h e steady c u r r e n t component,  i n Equation ^  using  the flow  (3.13) i s n o t unreasonable.  The f  m  chart  diagram  as shown  i n Figure  roughness sity, J  '  wc  theory,  z^ i s t h e d e p t h  l e n g t h , a i s the a n g u l a r  T  The  component,  velocity,  of flow,  Z  q  i s the  v i s the kinematic  visco-  i s t h e maximum bottom shear s t r e s s , p i s t h e f l u i d d e n s i t y , R om  a  t h e R e y n o l d ' s number and e q u a l U a / v , R i s t h e Reynold's number and w m c J  equal U z,/v, c n f  3.3.  i s t h e h o r i z o n t a l e x c u r s i o n l e n g t h o f a water p a r t i c l e i n o s c i l l a t o r y  m o t o n g i v e n by p o t e n t i a l  is  can be wc  terms i n the f l o w c h a r t a r e : U i s t h e maximum v a l u e o f h o r i z o n t a l v e l o c i t y o f t h e unsteady w a  just  I t may a t f i r s t appear somewhat c u r i o u s t h a t  E q u a t i o n (3.13) e x p l i c i t l y c o n t a i n s o n l y t h e unsteady However b e c a u s e f  component  U  c  i s t h e h o r i z o n t a l v e l o c i t y o f t h e steady component, and  i s the f r i c t i o n  coefficient  f o r a wave-current  c o e x i s t i n g system,  noting that U i s g i v e n by the f o l l o w i n g f o r m u l a w  U  w  =  sinh (2, z /L) u  (  3  '  1  4  )  38.  j hyeriulic cr.aracceris cicf ind bea for= property  0  E" 0.738 f  ( -S- J " 2  4 0 8  Eq.CH)  - a • B «s. i u V  +  2  C -  -  U a In -Zrr + 0.568 )' }" 1  c  02  (0.25 + 0.101 ( In  Ea.(5)  1) - 0.5 ln £  cw  +2  V ) r J  1  /  2  F i g u r e 3.3 Flow c h a r t diagram f o r c a l c u l a t i o n and Shuto (1984).  T  OB  "z 0 • ^ f cw Uw 2  of f  w  c  after  Tanaka  39. where H i s t h e wave h e i g h t , L i s t h e wave l e n g t h , and T i s wave p e r i o d . The  compound  ing  flow.  cient  s i g n i s p o s i t i v e f o r opposing flow and n e g a t i v e For U /U c  obtained  f o r follow-  = 0.0, i . e . , f o r pure waves, t h e f r i c t i o n  w  by t h i s  method i s almost  identical  with  coeffi-  t h a t o f Jonsson  (1966).  3.2.4 The three  SHEAR STRESSES COMPARISON  s h e a r s t r e s s c a l c u l a t i o n s due t o d i f f e r e n t methods a r e g i v e n f o r  sediment  condition, limit  size  see T a b l e  ranges  3.1, n o t i n g  o f the sediment s i z e  Sediment S i z e Range (mm)  Me thod No.  f o r waves that  plus  currents  at  t h e roughness h e i g h t  threshold  i s the upper  range.  0.3 - 0.85  0.85 - 1.16  1.16 - 1.7  1  0.576  0.658  0.814  2  0.702  0.838  1.061  3  0.450  0.630  1.050  4  0.550  0.720  1.370  5  0.380  0.520  1.000  6  0.620  0.820  1.570  T a b l e 3.1 Combined wave and c u r r e n t shear s t r e s s e s i n (Pa) due t o d i f f e r e n t methods f o r three sediment s i z e s a t t h r e s h o l d c o n d i t i o n s .  The Method  d i f f e r e n t methods a r e summarized below: 1:  using Equation  the e q u i v a l e n t (3.12)  shear  velocity  concept  as  given  by  40. Method 2: u s i n g t h e f r i c t i o n f a c t o r f Method 3: u s i n g  g i v e n i n F i g u r e 3.3.  Shields c r i t e r i o n for threshold conditions.  Method 4: shear s t r e s s e s u s i n g Jonsson's shear f a c t o r f  10g 1  4/fw  f o r t h e unsteady  g i v e n as  ( J L _ ) = -0.08 + l o g . . (^2L) 4/rw  0  1 0  k  (3.15)  s  component.  Method 5: u s i n g Kamphius' shear f a c t o r f g i v e n as w  -1—+ 4/F" w  lOg 1  ( - i - ) - -0.35 4/f" w  0  Method 6: u s i n g K a j i u r a shear f a c t o r f  — + log 4/f w  1 Q  -  ( — ) 4/F" w  log..( ^ ) s  3  1 0  (3.16)  k  given as  = "0.254 + 1 0 g  1 Q  (^)  (3.17)  where a, lm  i s t h e amplitude o f h o r i z o n t a l p a r t i c l e motion j u s t o u t s i d e the  boundary  layer i n oscillating  oscillatory  flow,  and k  flow,  f  i s a f r i c t i o n factor for  i s the height of p a r t i c l e f o r equivalent s  sand roughness.  Referring  to  Table  3.1  i t can  be  seen  that  most  of  mentioned methods g i v e shear s t r e s s v a l u e s c l o s e t o each o t h e r f o r t h e s m a l l sediment s i z e ranges. the  equivalent  s h e a r v e l o c i t y U*  c  the  above  especially  I t i s a l s o seen t h a t Method 1 u s i n g g i v e s shear s t r e s s e s e s t i m a t i o n which  i s i n good agreement w i t h most o f t h e o t h e r methods.  41. 3.3  WAVE THEORIES Wave theory  tational  flow.  r e q u i r e s an incompressible,  inviscid  fluid  having  irro-  The wave t r a i n must be p r o g r e s s i v e and two-dimensional,  t r a v e l l i n g i n water o f c o n s t a n t depth a s shown i n F i g u r e ( 3 . 4 ) .  Wove speed, c  y  L d  Surfoce elevotion shown of t * 0  F i g u r e 3.4  D e f i n i t i o n s k e t c h f o r a p r o g r e s s i v e wave t r a i n .  A c h o i c e o f t h e most s u i t a b l e wave theory i s d i f f i c u l t first  problem i s t h a t f o r a s p e c i f i c wave t r a i n ,  will  adequately  reproduce  different  d i f f e r e n t wave t h e o r i e s  charateristics  of i n t e r e s t .  comparison between t h e o r i e s must be made f o r a p a r t i c u l a r and  no g e n e r a l i z a t i o n c a n be made  t h e o r i e s f o r other  regarding  t o make. The  A  characteristic,  t h e comparison  of these  characteristics.  Another p o i n t t o c o n s i d e r i s t h a t t h e most s u i t a b l e wave theory may n o t be t h e one t h a t i s simply in  a given  engineering  simple and convenient  t h e most a c c u r a t e .  application  The g o v e r n i n g  may be t o choose  criterion  a theory  t o u s e , a t the c o s t of some a c c u r a c y .  Based on t h e t h e o r e t i c a l comparison o f many i n v e s t i g a t o r s , and  Isaacson  that i s  (1981) c o n c l u d e d  that  t h e stokes  Sarpkaya  and c n o i d a l f i f t h  order  t h e o r i e s a r e s u f f i c i e n t l y a c c u r a t e f o r most e n g i n e e r i n g purposes,  and y e t  are  cnoidal  relatively  simple  t o use.  Fenton  (1979) recommended  that  42. theory  c a n be used  f o r L/d > 8  description  of d i f f e r e n t  detailed to  Sarpkaya  less  and I s a a c s o n  and Stokes  theory o t h e r w i s e .  wave t h e o r i e s ,  (1981), who  described  For a  the reader i s r e f e r r e d t h e w e l l known and the  w e l l known t h e o r i e s and some computation methods. Quick  e t a l . (1985) found  tests,  t h e near  theory  i s i n a r e a s o n a b l e agreement  F i g u r e 3.5.  bottom  out t h a t ,  The r e s u l t s  velocities  f o r t h e range o f e x p e r i m e n t a l  calculated with  o f Stokes second  by  Stokes  t h e measured  second  order  velocities,  see  order theory are presented i n  T a b l e 3.2.  3.4  COEFFICIENT OF REFLECTION In  of is  t h e wave  flume,  reflected  waves from  the energy  a b s o r b i n g end  t h e flume w i l l have an i n f l u e n c e on t h e water p a r t i c l e v e l o c i t i e s . important  t o determine  the amplitude  of t h e i r  contribution  It  t o the  p a r t i c l e v e l o c i t i e s near the bed. The  ratio  of  reflected  wave  height  d e s i g n a t e d by t h e r e f l e c t i o n c o e f f i c i e n t ,  K  where  H  r  o f the i n c i d e n t  wave  height i s  K , where  (3.18)  - H /H R  i s t h e height of the r e f l e c t e d  opposite d i r e c t i o n  to incident  wave, w h i c h  travel  i n the  waves.  As shown by Sarpkaya and I s a a c s o n (1981), t h e c o e f f i c i e n t  of r e f l e c -  t i o n c a n be determined simply by t r a v e r s i n g t h e flume i n t h e d i r e c t i o n o f wave p r o p a g a t i o n w i t h a wave probe t o measure t h e maximum and t h e minimum wave h e i g h t H and H max  , respectively.  K  r  =  Then  H - H min max H + H min max  (3.19)  43.  6 s  S 5"  I : a.i  •.t  *>• vCLOCltr, cn/S  »•  »«  e Ktior.itr. oi'S  too  tot  » t  (b) Range 0.86 l e 1.16mm  (a) Rang* 0.30 l e 0.66mm  f5 §  s  5*  m.e  •0  Ml  VtLOCIlf. £"'S  »o wo vUOCIIf. Cn-5  u r  ro.f>  (d) Range 1.70 to 2.00mm  (e) Rang* 1.16 to 1.70mm  o  P s.  J> yflU in. m i <e) Range «.00 1o t.36mm  F i g u r e 3.5  Measured and t h e o r e t i c a l wave v e l o c i t y p r o f i l e s a f t e r Quick  et a l . (1985).  44.  Velocity  Potential  .ffHcoshUs)  s i n ( e )  +  B"  Dispersion Relation Surface  Elevation  . , „»  sinh(kd) ffH,iTH,cosh{2ks)  ***T 3  Ff^sinh^kd)  /  5 1  2  "* **  °j£«j|tanh(kd)  7j=|cos(f3) +  (  l  2  +  ^ i l n T W H cosh(ks). ,  C  O  S  h  (  2  k  d  n  c  O  S  {  2  e  )  0  Horizontal Particle Displacement  .  H  H  1  -r f* l  f1-  3  VnC'sinh'UdiV  c  0  s  h  (  2  k  s  )  1 - i n f3 s?i nfl t2 e, )  2sinh'(kd)  .H,jTH,cosh(2ks) , l  Vertical Particle Displacement Horizontal Particle Velocity Vertical Particle Velocity  )  ^4 ^ ?TnTrTkQT , H sinh(ks) .»  ( c J t )  3H/TTH» sinh(2ks)  u  y =  1  cosh(ks)_^, sinh(kd)  /aN c 0 5 ( e )  —f +  f  .3  ffH,irH»cosM2ks)  4  "? T sinhMkd)  >  (  C O B ( 2 g )  TTH sinh(ks) . , „ v ^ f sTnTTTkcTT .3 ^ H , 7 T H v S j j } h ( 2 k s ) . _ , x e  Horizontal Particle Acceleration Vertical Particle Acceleration  3u  f  a  2ir H c o s h ( k s ) . , x 2  a  sinh(kd)  • S t - T T -  5 i n ( g )  . 3 j r ^ r H , c o s h ( 2 k s ) ._ f  2ir H sinh(ks) ^/^x •ot '-T^" s i n h ( k d ) 2  ot>  C 0 S m  =  2  37T H,7THxsinh(2ks) 7  (  )  — f " T iTHPlW ^1  Pressure  , .  c o s( 2 B ]  „cosh(ks) ^ „ , ., h  P°-pgy^pg cosh(kd) ^3 ,  V  g H (  f W  ^H  1  x  )  c o s ( e )  rCQsh(2ks)_1 T ^ ^ f f l ^ P  I  "L sinh(2kd) sinh^kd) I/sin  H  j  I H y  3  [cosh(2ks)-l]  s«y*d  Table 3.2  ( M o d i f i e d a f t e r Sarpkaya and Isaacson, 1981).  Stokes Second Order Theory.  Results  0  ] c O S ( 2 g )  45. and t h e i n c i d e n t wave h e i g h t H i s g i v e n by  H = 1/2 (H max  In  t h e wave flume used,  the r e f l e c t i o n  + H min )  (3.20)  coefficient  was found t o be l e s s  t h a n 0.07.  3.5  SCALE EFFECTS The  study  improper  of this  scaling  type.  of t h e sediment  size  i s usually  Proper sediment s i z e s c a l i n g would  accepted i n a  lead  t o a cohe-  s i v e model sediment, and a c o h e s i v e sediment p o s s e s s e s p r o p e r t i e s  vastly  d i f f e r e n t from a non-cohesive sediment. Wave damping due t o t h e s i d e w a l l s w i l l n o t pose a problem i n t h i s study s i n c e the wave p r o p e r t i e s w i l l be measured a t the t e s t According  to Bijker  (1967),  t h e boundary  layer  section.  resulting  from  a  c o m b i n a t i o n o f c u r r e n t and waves i s d i r e c t l y p r o p o r t i o n a l t o t h e boundary roughness, and thus t h e boundary boundary  layer  thickness  friction  factor.  f o r t h e model  and  This implies that the the prototype  will  be  a p p r o x i m a t e l y the same.  3.6  SOME IMPORTANT NUMBERS  3.6.1 In  FROUDE NUMBER  t h e case o f steady flows,  Froude  number F ^ i s d e f i n e d by t h e  following equation, U F  r  c  •gd  (3.21)  46. where d i s t h e f l o w  depth,  and  i s t h e steady  current v e l o c i t y .  The  P i e r o r P i l e Froude number F i s g i v e n a s : P  F P  U = — /lb  (3.22)  where b i s the p i e r diameter.  3.6.2  REYNOLD'S NUMBER  Under u n i d i r e c t i o n a l f l o w , Reynolds number Re i s g i v e n as  U Re = —  r —  (3.23)  where r i s a c h a r a c t e r i s t i c l e n g t h dimension; i n case o f open c h a n n e l s r I s e q u a l t o t h e h y d r a u l i c s r a d i u s R^, and v i s t h e k i n e m a t i c  viscosity.  F o r p i e r s o r p i l e s Reynold's number R^ i s g i v e n i n t h e form o f :  R  p  U =—  v  b —  v  (3.24) '  some r e f e r e n c e s g i v e i t as  U R  =— P  where  (p -p) g  b (p - p ) U  i s the sediment-fluid  dynamic v i s c o s i t y  densty  (3.25)  d i f f e r e n c e , a n d \i i s t h e  47.  v = 2-  i n case o f pure waves U  3.6.3  c  (3.26)  i n a l l t h e above e q u a t i o n s i s r e p l a c e d by U . ffl  KEULEGAN-CARPENTER NUMBER  F o r pure waves Keulegan-Carpenter number K  U K  where T i s the wave p e r i o d .  c  =  c  i s g i v e n by:  T b  (3.27)  48.  4.  4.1  EXPERIMENTAL SETUP AND  EXPERIMENTAL APPARATUS AND  PROCEDURE  EQUIPMENTS  The experiments were conducted i n a p l e x i g l a s s flume. approximately  23 m  long,  mounted i n a deeper  0.6  m wide, and  0.7  m deep.  The flume i s  A wave paddle i s  s e c t i o n 1 m deep a t one end o f the flume.  There i s  a l s o an e n t r y tank a p p r o x i m a t e l y 4 m l o n g , 2 m wide, and 1.3 m deep which is  used as a s t i l l i n g  b a s i n t o dampen waves.  u s i n g a pump and c i r c u l a t i n g  system.  The  C u r r e n t s can be generated  test  l o n g bed  o f sediment m a t e r i a l and  21 cm deep.  concrete  blocks  upstream  f o r most  of  m a t e r i a l as seen i n F i g u r e  the  section consists of a 4 m I t was  part  of  c o n v e n i e n t t o use the  This  generator  to  save  4.1.  V e l o c i t y measurements were t a k e n w i t h a p r o p e l l e r meter.  flume  c u r r e n t measuring  i s an o s c i l l a t i n g  type OTT  d e v i c e i s shown i n F i g u r e 4.2.  pendulum  type whose s t r o k e  current The wave  and c o n s e q u e n t l y  wave h e i g h t can be v a r i e d by a d j u s t i n g t h e e c c e n t r i c i t y o f the p a d d l e arm on the f l y w h e e l . The  The p e r i o d i s c o n t r o l l e d by a v a r i a b l e speed  wave h e i g h t was  measured by  a c a p a c i t a n c e wave gauge connected  t o a Hewlett Packard d u a l c h a n n e l r e c o r d e r 4.3  shows the wave r e c o r d e r .  4.2  EXPERIMENTAL PROCEUDRE A total  experiments and 11.43  (Model No.  17 501A).  o f s e v e n t y experiments were conducted f o r t h i s utilized  five  cylindrical  drive.  piles  cm i n diameter as shown i n F i g u r e  of 4.4.  1.27,  2.54,  Figure  study. 5.08,  The 8.26,  F i g u r e 4.1  Experimental equipment, schematic diagram a f t e r Quick  (1983).  53. Sand was t h e sediment m a t e r i a l f o r t h i s s t u d y .  These sediments were  s i e v e d i n t o a narrow s i z e range so t h a t f o r a p a r t i c u l a r experiment onset of  sediment  size,  motion  could  be a s s o c i a t e d  t h e s e sediment s i z e ranges a r e 0.3-0.85 mm,  1.70 mm.  For a particular  spread uniformly with  t h e same  classified  into  series,  water  depth  group  of t e s t s  runs under  the d i f f e r e n t  at different  was k e p t  meters.  velocity  o f 35  combined  pile  of c e r t a i n  sediment and 1.16size  was  A l l t e s t s were c a r r i e d out cm.  The experiments  waves and c u r r e n t s .  sizes  flow s t a t e s ,  can be  and sediment  F o r t h e case o f combined at a certain  ranges were threshold  F o r t h e c a s e o f waves a l o n e , t h e wave  c o n s t a n t a t 1.6 seconds  i s fixed  size  F o r each  i . e . below, a t , and above  c o n d i t i o n s o f each sediment s i z e . period  0.85-1.16 mm,  sediment  bed c o n d i t i o n .  specific  i n t o t h r e e groups, 15 runs under c u r r e n t s a l o n e , 12 runs w i t h  a l o n e , and 43  utilized  test  a flat  average  waves  2.69  with a f a i r l y  and hence  t h e wave l e n g t h  waves and c u r r e n t s ,  was  the current  v a l u e and t h e wave p e r i o d i s a d j u s t e d so  t h a t t h e r e l a t i v e wave p e r i o d i s k e p t t h e same (1.6 seconds) so t h a t t h e wave l e n g t h i s u n a l t e r e d . a d j u s t e d f o r each t e s t At  t h e onset  disturbing lated  The wave h e i g h t and t h e c u r r e n t v e l o c i t y were  to the r e q u i r e d  o f each  t h e sediment.  test,  After  t h e tank  setting.  was  a sufficient  i n t h e tank, the f l o w r a t e  appropriate  value.  The wave  through  slowly  filled  to avoid  amount o f water had accumu-  the tank was a d j u s t e d  g e n e r a t o r then  started  t o the  and the p e r i o d  s e t t i n g and s t r o k e l e n g t h were a d j u s t e d u n t i l t h e d e s i r e d wave l e n g t h and wave  height  were a t t a i n e d .  Once  this  was  t u r n e d o f f and t h e sand bed was r e l e v e l l e d , Scour  depth was r e c o r d e d a t v a r i o u s  under  way, t h e increments becoming  time longer  completed,  everything  b e f o r e t h e t e s t was  increments a f t e r as t h e t e s t  was  started.  the t e s t  continued.  was Each  54. test  was  conducted  s c o u r depth. hours, time  t h e r e appeared  F o r t h e wave-current  whereas  was  until  less.  f o r the wave only The maximum  d u r i n g the t e s t r u n .  tests,  t o be no f u r t h e r  t h e experiments r a n from 18-26  and c u r r e n t  scour  depth  increase i n  alone t e s t s ,  i s t h e maximum  the r u n n i n g  depth  reached  55. 5.  A  series  sediment  of  sizes,  PRESENTATION AND DISCUSSION OF RESULTS  tests  were  and under  performed  different  using  different  flow c o n d i t i o n s  cylinder  and  i n the approaching  f l o w , i . e . , below, a t , and above t h r e s h o l d o f motion.  These  experiments  c a n be grouped i n t o t h r e e s e t s o f t e s t s , c u r r e n t s a l o n e , waves a l o n e , and waves  plus  currents,  respectively. letter,  Each  and  are  given  r u n i n a s e t was  f o r example,  WC12  refers  the  letters  g i v e n a number  C,  W,  and  following  t o t h e r u n number  WC,  the set  12 i n the s e t o f  combined waves and c u r r e n t s . The r e a d e r s h o u l d n o t e t h a t b o t h water wave of  l e n g t h ) a r e k e p t c o n s t a n t throughout  depth and wave p e r i o d  a l l t h e experiments.  (hence The aim  t h e t e s t i n g was t o i n v e s t i g a t e t h e u l t i m a t e maximum scour which  could  o c c u r and t h i s was found t o be when t h e approach f l o w c o n d i t i o n s reached critical of  stress  o f sediment  particles,  irregardless  water depth or wave l e n g t h . The f i r s t  Cl  f o r onset o f motion  through  s e t o f t e s t s was under  C15, T a b l e  5.1  from  t h e a c t i o n o f c u r r e n t s a l o n e , runs  which  i t can be seen  that  t h e maximum  s c o u r o c c u r s a t t h r e s h o l d c o n d i t i o n s i n t h e a p p r o a c h i n g f l o w which  agrees  with the r e s u l t s o f Chabert and E n g e l d i n g e r (1956). The Figures cylinder scour  s c o u r development 5.1  and 5.2  diameter)  depth  w i t h time  i n the form  versus  as t h e flow  time.  f o r some o f these runs i s shown i n  of r e l a t i v e These  conditions  two  scour  figures  (scour  depth  over  show a d e c r e a s e i n  i n the approaching  flow exceed  the  t h r e s h o l d s t a t e which c o n f i r m s the f i n d i n g s o f Chabert and Shen (1966). In  order  comparison  to  check  the  test  was made w i t h some w e l l  results known  f o r steady  formulas which  current already  alone, exist.  Run Sediment No. S i z e D  Max. R e l a t i v e Roughness C y l i n d e r Water St eady D i a . b Depth C u r r e n t Scour Scour s S/b d Velocity S k  F r  State of Approaching Flow  u  (mm)  (mm)  (cm)  (cm)  u*  Bed Shear  R xl0 e  T  c (cm/sec) (cm)  o (cm/sec) (Pa)  Cl  1.16-1.70  1.70  11.43  35  27.48  4.50  0.39  0.148 Below T h r e s h o l d  0.0153  0.235  0.444  C2  1.16-1.70  1.70  11.43  35  30.28  6.50  0.57  0.163 Below T h r e s h o l d  0.0169  0.285  0.489  C3  1.16-1.70  1.70  11.43  35  36.44  14.00  1.22  0.197 Below T h r e s h o l d  0.0203  0.412  0.589  C4  1.16-1.70  1.70  11.43  35  44.60  17.00  1.49  0.241 Below T h r e s h o l d  0.0249  0.618  0.720  C5  1.16-1.70  1.70  11.43  35  47.73  19.50  1.71  0.258 At  0.0266  0.708  0.771  C6  1.16-1.70  1.70  11.43  35  53.80  19.00  1.66  0.290 Above T h r e s h o l d  0.0330  0.899  0.856  C7  1.16-1.70  1.70  11.43  35  59.20  18.50  1.62  0.320 Above T h r e s h o l d  0.0300  1.100  0.956  C8  1.16-1.70  1.70  2.54  35  41.38  4.25  1.67  0.223 Below T h r e s h o l d  0.0231  0.532  0.662  C9  1.16-1.70  1.70  2.54  35  47.73  8.10  3.18  0.258 At  0.0266  0.708  0.771  CIO 1.16-1.70  1.70  2.54  35  53.80  6.80  2.68  0.290 Above T h r e s h o l d  0.0300  0.899  0.869  0.85-1.16  1.16  11.43  35  41.00  22.20  1.94  0.221 At  Threshold  0.021  0.460  0.662  C12 0.85-1.16  1.16  8.26  35  41.00  18.10  2.19  0.221 At  Threshold  0.021  0.460  0.662  C13 0.85-1.16  1.16  5.08  35  41.00  13.10  2.57  0.221 At  Threshold  0.021  0.460  0.662  C14 0.85-1.16  1.16  2.54  35  41.00  9.30  3.66  0.221 At  Threshold  0.021  0.460  0.662  C15 0.85-1.16  1.16  1.27  35  41.00  4.80  3.78  0.221 At  Threshold  0.021  0.460  0.662  Cll  Table 5.1  Experimental  Threshold  Threshold  r e s u l t s of steady c u r r e n t s a l o n e .  5  Haxiwun r e l a t i v e scour 0.0  '  0.2  '. t  0.4  0.6  0.8  ',1,'  i J  1.0  | ,'  1.2  '  I  I  1.4  I  I  S/b  1.6  I  I  1.8  I  I  X  2.0  I  i  \  \  2.2  I  I  2.4 l_  i  ;  ) JO JO JO JO JO JO JO 3 3 3 3  \  \  I  /  o r> o o o o —i co cn -t* co  \  o  w  \  \ \  \  | 1  i  i  i  I  I  I  I  I  I  I  I  I  I  I  I  I—I  I  I  I  I  |  i  I  J  I  I I I  11II  J  I I I 1111  •  '  I  I 1111  I  I—I  I I 111  3  5 7 10  Run C1 Run C2 Run C 3 —  Run C4 Run C5  \ ~~ to -  - - - Run C6 Run C7  y  y  10'  I  3  i I • I • 'I  5 7 10*  I  3  ' I ' I  "I  5 7 10'  —i  1 i | i | 11|  3  S 7 10*  i ' i > i "i 3 s 7 io»  T  M l "  Time (min.) F i g u r e 5.2.  R e l a t i v e scour v e r s u s time under steady c u r r e n t s  alone.  4  59. The  comparison i s shown i n T a b l e s 5.2 through  sizes  t e s t e d under  sizes.  I t should  5.5 f o r t h e t h r e e sediment  threshold  c o n d i t i o n s and  for different  be  that  depths  noted  t h e scour  maximum p o s s i b l e depths a t t a i n e d d u r i n g t e s t i n g . in  good  agreement  verification  with  f o r these  most  o f the estimated  formulas.  cylindrical  reported  were t h e  The measured v a l u e s a r e values  which  Hence i t can be argued  i s another that  steady  c u r r e n t scour depths c o u l d form a base o r a r e f e r e n c e f o r comparison w i t h scour depths under waves or combined waves and c u r r e n t s . From T a b l e 5.1  i t i s seen  t h a t Froude number F  i s s m a l l and l e s s r  t h a n u n i t y , which makes t h e f l o w a s u b c r i t i c a l number  Re  The through  5  i s i n the order  turbulent  of 10 , a c c o r d i n g l y the flow  second W12.  s e t of t e s t s  The r s u i t s  the table,  was  o f these  t h e depth  the a c t i o n  o f steady  although  sediment p a r t i c l e s  vicinity  o f the c y l i n d e r ,  t h e m a t e r i a l away horizontal  because  velocity  this  versus  smaller depth.  that the r e l a t i v e scour  produced  the K , £  under  pure waves, runs  are presented  i n Table  Wl  5.6, a s  f l o w i s much l e s s than t h e scour The reason  turbulence  o f the wave.  diameter  runs  o f the r e v e r s a l  depth  relative  rough  f o r this  may  depth  be t h a t ,  a r e d i s l o d g e d due t o wave t u r b u l e n c e i n t h e  i n F i g u r e s 5.3 and 5.4. pile  performed  currents.  shown  seen  i s fully  o f scour f o r t h e same p i l e s i z e under t h e  same c o n d i t i o n s i n t h e a p p r o a c h i n g  be  The f l o w Reynolds  flow.  s e e n from  under  flow.  i s insufficient  f l o w and the o r b i t a l  The scour  development  F i g u r e 5.5 i s a p l o t  scour under b i g g e r diameters  by t h e s m a l l e r d i a m e t e r s .  with  type o f time i s  of r e l a t i v e  under t h e same c o n d i t i o n s , from  Keulegan-Carpenter  to transport  scour  which i t c a n  i s less  than t h e  I t follows that the  number, the b i g g e r i s t h e scour h o l e  Foraula No. (1.1)  (1.3)  (1.6)  (1.7)  1.27  3.97  3.40  4.39  5.90  4.64  4.80  2.54  6.68  5.39  6.75  9.23  7.53  9.30  5.08  11.24  8.56 10.36 14.44 12.24  13.10  8.26  16.17 11.29 14.06 19.65 17.20  18.10  11.43  20.64 14.69 17.14 22.61 21.59  22.20  Cyl. Size (cm)  T a b l e 5.2  (1.8) Measured Values  Measured and e s t i m a t e d maximum scour depth S (cm) a t t h r e s h o l d c o n d i t i o n s i n the approaching flow f o r sediment s i z e range 0.85-1.16mm under steady c u r r e n t s alone.  Formula No. (1.1)  (1-3)  (1.6)  (1.7)  1.27  3.13  2.67  3.46  4.65  3.65  3.78  2.54  2.36  2.12  2.66  3.63  2.97  3.66  5.08  2.21  1.69  2.04  2.84  2.41  2.57  8.26  1.96  1.43  1.70  2.38  2.08  2.19  11.43  1.81  1.29  1.50  1.99  1.89  1.94  Cyl. Size (cm)  T a b l e 5.3  (1.8) Measured Values  Measured and e s t i m a t e d maximum r e l a t i v e scour a t t h r e s h o l d c o n d i t i o n s i n t h e approaching flow f o r sediment s i z e range 0.85-1.16mm under steady c u r r e n t s a l o n e .  Formula No. Cyl. Size (cm) 2.54 11.43  T a b l e 5.4  (1.8) Measured Values  (1.1)  (1.3)  (1.6)  (1.7)  6.68  7.63  7.42  7.19  7.53  7.50  20.64 16.26  18.82  18.98  21.59  19.50  Measured and e s t i m a t e d maximum scour depth i n (cm) a t t h r e s h o l d c o n d i t i o n s i n the approaching flow f o r sediment s i z e range 1.16-1.70mm under steady c u r r e n t s alone.  Formula No. (1-1)  (1-3)  (1.6)  (1-7)  2.54  2.63  3.01  3.00  2.83  2.97  2.95  11.43  1.81  1.42  1.65  1.66  1.89  1.71  Cyl. Size (cm)  T a b l e 5.5  (1.8) Measured Values  Measured and e s t i m a t e d maximum r e l a t i v e scour a t t h r e s h o l d c o n d i t i o n s i n t h e approaching flow f o r sediment s i z e range 1.16-1.70mm under steady c u r r e n t s a l o n e .  Cylinder Dia. b  Run Sediment No. S i z e D (mm)  (mm)  State of Approaching Flow  (cm)  Max. R e l a t i v e Scour Maximum S Scour (cm) S/b  H  U  w  a  lm  R  e  K  c  x 105 (cm)  (cm/s)  (cm)  W3  1.16-1.70 1.70  11.43  At T h r e s h o l d  2.30  0.20  13.00  31.96  7.13  0.288  4.47  W4  1.16-1.70 1.70  11.43  Above T h r e s h o l d 1.68  0.51  14.60  36.47  8.01  0.292  5.11  W5  1.16-1.70 1.70  2.54  Below T h r e s h o l d 1.80  0.71  10.50  25.17  5.76  0.145 15.86  W6  1.16-1.70 1.70  2.54  At  3.10  1.22  13.00  31.96  7.13  0.288 20.13  W7  1.16-1.70 1.70  2.54  Above T h r e s h o l d 3.00  1.18  14.00  34.76  7.70  0.267 21.90  W8  0.85-1.16 1.16  11.43  At T h r e s h o l d  4.50  0.39  11.80  28.70  6.50  0.187  4.02  W9  0.85-1.16 1.16  8.26  At  Threshold  4.50  0.53  11.80  28.70  6.50  0.187  5.56  W10 0.85-1.16 1.16  5.08  At  Threshold  4.30  0.84  11.80  28.70  6.50  0.187  9.04  W l l 0.85-1.16 1.16  2.54  At T h r e s h o l d  3.70  1.46  11.80  28.70  6.50  0.187 18.08  W12 0.85-1.16 1.16  1.27  At T h r e s h o l d  3.50  2.80  11.80  28.70  6.50  0.187 36.16  T a b l e 5.6  Threshold  E x p e r i m e n t a l r e s u l t s of o s c i l l a t o r y  waves a l o n e .  I  I  I  I  i  i  I  I  I  t  t  l  l  l  l  l  l  I  I  I  I  I  I  I  I  I  I  I  I  Run U3 Run U4 CM  Run U5  eg"  ---  Run U6 Run U7  cn -  to. l_ —* a  •  8 3. OJ  > to —  -J  3  ;  1 as 1  5'  1  CO  I'  24'  CM  T—1—1—1—1—1—1—1—1—1—1—1—1—1—1—1—1—1—1—1—r-1—1—1—1—1—1—1—1—1—1—1—1—1—r 100  200  300  400  500  600  700  800  900  1000  1100  1200  1300  1400  1500  Time (min.) F i g u r e 5.3.  R e l a t i v e scour v e r s u s time under pure waves.  1600  1700 1800  Run  U3  Run  U4  Run  U5  Run  U6  Run  U7  t  T 10 •  1 I I I III| 3 5 7 10*  F i g u r e 5.4.  | 3  i | I | I 11 5 7 10'  1 i I i I "I 3 5 7 10* Time (min.) 1  T—|  3  I i I I I '| 5 7 10»  R e l a t i v e scour v e r s u s time under pure waves.  T  1—r • | i | 11 3 5 7 10  4  65.  o  o  O Csi'  D  •  0_|  0.0  ,  ,  2.0  4.0  r  6.0  8.0  10.0  12.0  Cylinder diameter (cm)  F i g u r e 5.5. Oscillatory  Maximum r e l a t i v e scour versus c y l i n d e r diameter f o r f l o w at t h r e s h o l d c o n d i t i o n s ; sediment s i z e 0.85-1.16  66. F u r t h e r s e r i e s o f t e s t s were c a r r i e d out t o i n v e s t i g a t e how produced under t h e a c t i o n o f combined waves and c u r r e n t s . the  scour i s  In p a r t i c u l a r ,  c o n d i t i o n s were i n v e s t i g a t e d which produce the maximum scour depth. This  third  labelled  set of  runs WC1  tests  under  the combined  through WC43, and  waves and  the r e s u l t s  currents  are tabulated  was  i n Table  5.7. R e l a t i v e maximum and  5.7,  both of  scour v e r s u s time  them show a development  u n i d i r e c t i o n a l flows (see F i g u r e s 5.1 Referring  plots  t o T a b l e 5.7,  under  similar  sediment  depths  are d i f f e r e n t ,  i t can  threshold  and  and be  a r e shown i n F i g u r e s  w i t h time  seen  that  conditions,  runs WC3  but  and WC11.  This  and  to  the  critical  steady c u r r e n t v e l o c i t y was  32.8  cm/sec. From  scour  the  depths  sediment of  velocity  first under  conditions  few  attempt  was  parameters, wave motion  made  tests  combined existed  to  current  i n each 10.5  threshold  a  due  t o combined  conclusion  waves and  cm  case  is  and  the  the wave h e i g h t  was  currents  wave and  reached,  current  that  o c c u r r e d when  size,  velocity.  the  influence  sediment  size,  on and  was  maximum threshold  t h e r e f o r e most  performed under t h i s t h r e s h o l d c o n d i t i o n .  investigate  the  30.28 cm/sec, f o r both o f the  i n the a p p r o a c h i n g f l o w , and  such as c y l i n d e r to  bed  23 cm/sec, whereas i n run WC6  a t bed  the r e s t o f t h i s s e t was  at  t h e wave h e i g h t was  and the steady c u r r e n t v e l o c i t y was velocity  although a  f o r a l l the r u n s , the c o n t r i b u t i o n o f  F o r example i n run WC3  the maximum  are  the same i s t r u e f o r runs WC9  waves  runs  WC6  scour  attained  9.4  and  resulting  c o n d i t i o n was  was  of  the  state  different.  to that  5.2).  d i f f e r e n c e i n s c o u r depth can be e x p l a i n e d because,  currents  similar  5.6  scour  of  An flow  the p r o p o r t i o n o f  Runs WC29 through WC43, C l l through  Run No.  Sediment Size D  s  Cylinder Dia. b  (mm)  (cm)  WC1  1.16-1.70 1.70  11.43  Below T h r e s h o l d  8.00  0.70  WC2  1.16-1.70 1.70  11.43  Below T h r e s h o l d 10.70  WC3  1.16-1.70 1.70  11.43  At T h r e s h o l d  WC4  1.16-1.70 1.70  WC5  (mm)  k  State of Approaching Flow  Max. Maximum c Scour R e l a t i v e S Sc our S/b (cm) (cm/sec) U  H  U  w  ^wc  Equiv. U* wc  T  wc  (cm)  (cm/s) (cm/s) (cm/sec)  23.00  6.00  13.72  24.00  2.08  0.434  0.94  23.00  8.50  19.96  30.24  2.61  0.683  15.00  1.31  23.00  10.50  25.17  32.80  2.85  0.814  11.43  Above T h r e s h o l d 14.00  1.42  23.00  12.00  29.21  40.00  3.48  1.210  1.16-1.70 1.70  11.43  Below T h r e s h o l d 16.20  1.51  30.28  7.20  16.68  31.04  2.70  0.729  WC6  1.16-1.70 1.70  11.43  At T h r e s h o l d  17.30  1.40  30.28  9.40  22.80  32.80  2.85  0.814  WC7  1.16-1.70 1.70  11.43  Above T h r e s h o l d 16.00  1.22  30.28  11.80  28.66  43.03  3.74  1.400  WC8  1.16-1.70 1.70  2.54  Below T h r e s h o l d  5.00  1.97  27.76  7.50  17.43  30.60  2.66  0.708  WC9  1.16-1.70 1.70  2.54  At T h r e s h o l d  5.00  1.97  27.76  9.40  22.30  32.80  2.85  1.040  WC10  1.16-1.70 1.70  2.54  Above T h r e s h o l d  5.00  1.97  27.76  10.00  23.85  37.00  3.22  0.814  WC11  1.16-1.70 1.70  2.54  At Threshold  3.50  1.38  13.70  10.50  25.17  32.80  2.85  0.814  WC12  1.16-1.70 1.70  2.54  At Threshold  5.00  1.97  22.30  9.10  21.50  32.80  2.85  0.814  WC13  1.16-1.70 1.70  2.54  Below T h r e s h o l d  7.10  2.80  31.12  6.50  14.95  32.80  2.85  0.814  WC14  1.16-1.70 1.70  11.43  At T h r e s h o l d  17.40  1.52  31.12  6.40  14.70  32.80  2.85  0.814  WC15  1.16-1.70 1.70  1.27  At T h r e s h o l d  4.00  3.14  31.12  7.70  17.93  32.80  2.85  0.814  T a b l e 5.7.  Experimental  r e s u l t s of combined waves and c u r r e n t s .  Pa  s  Cylinder Dia. b  (mm)  (cm)  WC16  1.16-1.70 1.70  2.54  At T h r e s h o l d  7.10  2.80  WC17  1.16-1.70 1.70  5.08  At T h r e s h o l d  10.50  WC18  1.16-1.70 1.70  8.26  At T h r e s h o l d  WC19  0.85-1.16 1.16  1.27  WC20  0.85-1.16 1.16  WC21  Run No.  Sediment Size D (mm)  k  State of Approaching Flow  Max. Maximum c Scour R e l a t i v e S Scour (cm) S/b (cm/sec) U  H  U  w  ^wc  Equiv. U* wc  T  wc (cm)  (cm/s) (cm/s) (cm/sec)  31.12  7.70  17.93  32.80  2.85  Pa 0.814  2.10  31.12  7.70  17.93  32.80  2.85  0.814  15.50  1.88  31.12  7.70  17.93  32.80  2.85  0.814  At T h r e s h o l d  4.50  3.54  31.12  6.80  15.68  29.50  2.57  0.658  2.54  At T h r e s h o l d  8.00  3.51  31.12  6.80  15.68  29.50  2.57  0.658  0.85-1.16 1.16  5.08  At Threshold  11.00  2.17  31.12  6.80  15.68  29.50  2.57  0.658  WC22  0.85-1.16 1.16  8.26  At T h r e s h o l d  16.20  1.96  31.12  6.80  15.68  29.50  2.57  0.658  WC23  0.85-1.16 1.16  11.43  At Threshold  18.30  1.60  31.12  6.80  15.68  29.50  2.57  0.658  WC24  0.30-0.85 0.85  11.43  At Threshold  5.00  3.94  28.60  6.75  15.56  27.60  2.40  0.576  WC25  0.30-0.08 0.85  2.54  At Threshold  8.50  3.35  28.60  6.75  15.56  27.60  2.40  0.576  WC26  0.30-0.08 0.85  5.08  At T h r e s h o l d  11.80  2.32  28.60  6.75  15.56  27.60  2.40  0.576  WC27  0.30-0.08 0.85  8.26  At Threshold  17.00  2.10  28.60  6.75  15.56  27.60  2.40  0.576  WC28  0.30-0.08 0.85  11.43  At Threshold  19.20  1.66  28.60  6.75  15.56  27.60  2.40  0.576  WC29  0.85-1.16 1.16  11.43  At Threshold  19.30  1.69  34.20  3.50  7.60  29.50  2.57  0.658  WC30  0.85-1.16 1.16  8.26  At Threshold  15.20  1.84  34.20  3.50  7.60  29.50  2.57  0.658  Table 5.7.  Continued  Run No.  Sediment Size D  Cylinder Dia. b  State of Approaching Flow  Max. Maximum c Scour R e l a t i v e S Scour (cm) S/b (cm/sec) U  H  U  w  ^wc  Equiv. U* wc  T WC  (mm)  (cm)  WC31  0.85-1.16 1.16  5.08  At T h r e s h o l d  11.10  2.20  34.20  3.50  7.60  29.50  2.57  0.658  WC32  0.85-1.16 1.16  2.54  At T h r e s h o l d  7.20  2.83  34.20  3.50  7.60  29.50  2.57  0.658  WC33  0.85-1.16 1.16  1.27  At Threshold  4.10  3.30  34.20  3.50  7.60  29.50  2.57  0.658  WC34  0.85-1.16 1.16  11.43  At Threshold  14.50  1.27  28.60  6.00  13.70  29.50  2.57  0.658  WC35  0.85-1.16 1.16  8.26  At T h r e s h o l d  10.30  1.25  28.60  6.00  13.70  29.50  2.57  0.658  WC36  0.85-1.16 1.16  5.08  At T h r e s h o l d  8.50  1.67  28.60  6.00  13.70  29.50  2.57  0.658  WC37  0.85-1.16 1.16  2.54  At T h r e s h o l d  5.90  2.30  28.60  6.00  13.70  29.50  2.57  0.658  WC38  0.85-1.16 1.16  1.27  At Threshold  4.00  3.15  28.60  6.00  13.70  29.50  2.57  0.658  WC39  0.85-1.16 1.16  11.43  At T h r e s h o l d  9.80  0.86  17.40  9.00  21.20  29.50  2.57  0.658  WC40  0.85-1.16 1.16  8.26  At Threshold  8.10  0.98  17.40  9.00  21.20  29.50  2.57  0.658  WC41  0.85-1.16 1.16  5.08  At T h r e s h o l d  5.80  1.14  17.40  9.00  21.20  29.50  2.57  0.658  WC42  0.85-1.16 1.16  2.54  At Threshold  4.70  1.85  17.40  9.00  21.20  29.50  2.57  0.658  WC43  0.85-1.16 1.16  1.27  At Threshold  3.70  2.90  17.40  9.00  21.20  29.50  2.57  0.658  (mm)  Table 5.7.  Continued  (cm)  (cm/s) (cm/s) (cm/sec)  Pa  1  1  1 1  I  I  I  l  J  I  '  '  '  '  '  '  «  '  I  I  ' ' I '  I  I  I  I  L  I  I  I  I  Run UC1 Run UC2 Run UC3  3" ---  3-  Run UC4 Run  UC5  - - - Run UC6  Run UC7  \  CO  -  to_ a  T—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—r 100  200  300  400  500  600  700  800  900  1000  1100  1200  1300  1400  1500  1600  1700  Time (min.)  F i g u r e 5.6.  R e l a t i v e scour v e r s u s time under combined waves and  currents.  1800  111  '  I I I I 11  •  •  •  I I 111  II  J  I I I 1111  Run UC1 Run UC2 Run UC3 Run UC4 Run UC5 - - - Run UC6 —  to-  Run UC7  T 3  F i g u r e 5.7.  > I i I 1 5 7 10' 11  T  3  I 5  'I'M 7 10'  —i  1 i | I | "I 3 5 7 10*  I 3  I I 5  11"I 7 10»  Time (min.)  R e l a t i v e scour versus time under combined waves and  currents.  I 3  'I'M 5 7 10'  72. C15,  and W8 through W12 were a t t h r e s h o l d c o n d i t i o n s f o r a sediment  range o f 0.85-1.16 mm u s i n g t h e f i v e divided tion  cylinder sizes.  size  These runs c a n be  i n t o f i v e groups as seen i n T a b l e 5.8 a c c o r d i n g t o t h e c o n t r i b u -  o f both  t h e wave and c u r r e n t f l o w  components t o t h e t o t a l  critical  v e l o c i t y a t the bed.  Percentage o f Wave i n T h r e s h o l d V e l o c i t y (%)  Run No. Cll  - C15  0  100  WC29 - WC33  25  75  WC34 - WC39  50  50  WC39 - WC43  75  25  100  0  W8  - W12  T a b l e 5.8  The 5.11,  C o n t r i b u t i o n of waves and c u r r e n t s i n t h r e s h o l d v e l o c i t y  results  each  plot  o f these contains  tests five  The p l o t o f t h e wave percentage wave  Percentage o f C u r r e n t i n T h r e s h o l d V e l o c i t y (%)  and c u r r e n t v e r s u s  threshold  curves,  a curve  i n Figures  5.8  through  f o r each c y l i n d e r  size.  i n t h e t h r e s h o l d v e l o c i t y o f t h e combined  t h e maximum  v e r s u s the maximum r e l a t i v e For  a r e presented  (%)  scour  i s shown  i n Figure  5.8 and  scour i s shown i n F i g u r e 5.9.  or c r i t i c a l  velocity  f o r onset  o f motion  a p p r o a c h f l o w , F i g u r e 5.8 shows t h a t t h e maximum scour  depth  i n the  Is varying  almost l i n e a r l y a c c o r d i n g t o t h e c o n t r i b u t i o n o f b o t h waves and c u r r e n t s . It  also  shows  that  t h e more i s t h e c u r r e n t percentage  combined f l o w v e l o c i t y , t h e more i s t h e scour depth. reaches sizes  t h e steady  tested.  sensitive sizes.  current value  I t should  and t h i s  be noted  t o changes i n t h e c r i t i c a l  i n the c r i t i c a l  At t h e l i m i t ,  scour  i s true f o r a l l the c y l i n d e r  that larger  cylinder  flow v e l o c i t y  sizes  a r e more  than f o r t h e s m a l l e r  73.  LEGEND • = Cyl. Diam. 1.27 cm o = Cyl. Diam. 2.54 cm A = Cyl. Diam. 5.08 cm o = Cyl. Diam. 8.26 cm v = Cyl. Diam. 11.43 cm  o..  O  0.0  i  25.0  a  •a  i  50.0  1  75.0  1  100.0  Wave contribution (%) to the threshold velocity F i g u r e 5.8. Maximum scour v e r s u s combined waves and c u r r e n t t h r e s h o l d v e l o c i t y , sediment s i z e 0.30 - 0.85.  74.  q • o A O  LEGEND Cyl. Diam. 1.27 cm Cyl. Diam. 2.54 cm Cyl. Diam. 5.08 cm Cyl. Diam. 8.26 cm Cyl. Diam. 11.43 cm  o  •-o Q CO O O cn  TO.  CD  "A..  > o q CD  ^  O..  3  "V..  A.  25.0  50.0  E X D  O 6_l  0.0  75.0  100.0  Wave contribution (%) to the threshold velocity  F i g u r e 5.9.  Maximum r e l a t i v e scour v e r s u s combined waves and c u r r e n t s  threshold v e l o c i t y ;  sediment s i z e 0.30 - 0.85  mm.  75. F i g u r e 5.10 the  cylinder  scour the  shows the change o f maximum scour depth w i t h r e s p e c t t o  size  for different  flow  combinations.  In t h i s  figure  the  depth under the a c t i o n o f pure c u r r e n t s i n c r e a s e s c o n s i d e r a b l y as  cylinder  size  increases, while  f o r pure waves the  change i n  scour  d e p t h as the c y l i n d e r s i z e v a r i e s i s n o t v e r y g r e a t . Figure  5.11  shows t h a t maximum r e l a t i v e  scour  f o r smaller  cylinder  s i z e s i s g r e a t e r than the r e l a t i v e s c o u r o f b i g g e r d i a m e t e r s , and t h i s i s valid  f o r the d i f f e r e n t Figure  threshold depth  5.12  and  5.13  c o n d i t i o n s are  i s plotted  ranges  flow cases t e s t e d .  tested.  s i z e ranges From  show  25%  scour  waves and  against cylinder  Although  results 75%  diameter  when  current. f o r the  The  maximum  scour  t h r e e sediment  size  the change i s n o t so h i g h , the s m a l l e r sediment  are scoured more than the b i g g e r sediment  the v i s u a l  c o n t r i b u t i o n s to  o b s e r v a t i o n s i t was  found  sizes.  t h a t the p a t t e r n of  the  s c o u r h o l e i s v e r y s i m i l a r f o r a l l t h e f l o w c a s e s t e s t e d ; f o r most o f the tests  the maximum  scour  depth  upstream s i d e of the f l o w . current  was  the  cylinder  under  the  the c u r r e n t t u r b u l e n c e and The  seems  of  the  pile  facing  and  5.15.  I t was of  noted  be  similar  i s restricted the  scour  to  the  waves and  scour  currents  takes  a r e d i s l o d g e d o r e n t r a i n e d by  the wave  then t r a n s p o r t e d by the flow c u r r e n t .  mechanism  t o a narrow w i d t h hole.  the  t h a t the  scour mechanism under the a c t i o n o f combined waves and  to  Erosion  front  combination  p l a c e because sediment p a r t i c l e s and  the  A t y p i c a l scour h o l e under combined wave and  i s shown i n F i g u r e s 5.14  around  at  The  rest  of  under  currents  or  currents  waves  a d j a c e n t to the p i l e and  bottom  of  scour  hole i s at  the  repose  and m a t e r i a l slumps i n t o the h o l e as the scour proceeds.  alone. at  the  angle  of  For  the  76.  • o A o v  LEGEND = 100% Wave = 75 % Wave = 50 % Wave = 25 % Wave = 0 % Wave  v'''  .o  • o-  0.0  1  1  1  1  1  2.0  4.0  6.0  8.0  10.0  Cylinder diameter (cm)  12.0  F i g u r e 5.10. Maximum scour v e r s u s c y l i n d e r diameter at t h r e s h o l d c o n d i t i o n s of combined waves and c u r r e n t s ; sediment s i z e 0.3 0.85 mm.  77.  LEGEND • = 0 % Wave o = 25 % Wave A = 50 % Wave o = 75 %. Wave v = 100 % Wave  •. Q  Q  D.  G-  A.  v  0.0  1 2.0  1 4.0  1 6.0  1 8.0  V  I 10.0  12.0  Cylinder diameter (cm)  F i g u r e 5.11. Maximum r e l a t i v e scour versus c y l i n d e r diameter at t h r e s h o l d c o n d i t i o n s o f combined waves and c u r r e n t s ; sediment s i z e 0.3 - 0.85 mm.  78.  LEGEND • = Sed. Size 1.16- 1.70 mm o = Sed. Size 0 . 8 5 - 1.16 mm = Sed. Size 0 . 3 0 - 0.85 mm  .A  .-A"  n '  A''  ••' a'.--' A .  g'  —1 2.0  0.0  1 4.0  n 6.0  1i 8.0  1 10.0  12.0  Cylinder diameter (cm) F i g u r e 5.12. Maximum scour depth v e r s u s c y l i n d e r diameter f o r t h r e e sediment s i z e s under t h r e s h o l d c o n d i t i o n s o f combined waves and c u r r e n t s ; 25% wave and 75% c u r r e n t . -  79.  Q Q  LEGEND • = Sed. Size iize 1.161.16- 1.70 mm o = Sed. Size 0 . 8 5 - 1.16 mm A = Sed. Size 0 . 3 0 - 0 . 8 5 mm  A.  \\  \  O. "  1  0.0  2.0  Q  .  "  A  .  1  1  1  4.0  6.0  8.0  1  10.0  1  12.0  Cylinder diameter (cm) F i g u r e 5.13. Maximum r e l a t i v e scour v e r s u s c y l i n d e r diameter f o r t h r e e sediment s i z e s a t t h r e s h o l d o f combined waves and c u r r e n t s ; 25% wave and 75% c u r r e n t .  82. case o f waves a l o n e o r waves p l u s c u r r e n t s , the sand shown i n F i g u r e s 5.16 A  comparison  results lack are  from  wave  from  the  and  height,  water  Also  current  test  partly  results  be  made because  with  because o f  the  studies that  the  problem  was  F o r example, p r e v i o u s s t u d i e s i n v e s t i -  sediment It  a  and  single  at  pile  flow size  velocities and  less  a single  than  sediment  the size  In t h e p r e s e n t study the emphasis  the maximum p o s s i b l e scour, namely when the sandbed t h i s c o n d i t i o n was  studied using several p i l e  was and  sizes. i s worthwhile  prediction  t o n o t e t h a t no d i s t i n c t formulas f o r maximum scour  were reached  studies i n this f i e l d . around  bed  etc.,  i n these o t h e r s t u d i e s .  onset o f motion, and  The  and  because even w i t h the few  cannot  viewpoint.  depth,  velocity.  t o determine  scour  wave  not been p o s s i b l e ,  partly  comparison  another  were u t i l i z e d  at  combined  the dependence o f scour on the f l o w parameters such as wavelength,  critical  was  the  a study,  available,  gated  of  5.17.  o t h e r s t u d i e s has  o f such  treated  and  bed might r i p p l e as  due  to  the  limited  number of t e s t s  and  limited  However a rough e s t i m a t e o f the amount o f maximum  cylindrical  piles  material c r i t i c a l  can  velocity  be  found  f o r onset  using  these  study  o f motion can  results.  be known i f  t h e m a t e r i a l p r o p e r t i e s a r e known, t h e n the f l o w v e l o c i t y a t bed  can  be  c a l c u l a t e d p r o v i d e d t h a t f l o w parameters a r e d e f i n e d , hence the c o n t r i b u tion  of  each flow  t h e maximum F i g u r e s 5.8  component  p o s s i b l e scour through  5.13.  i s determined. around  the  Knowing the s t r u c t u r e s i z e  s t r u c t u r e can  be  estimated  using  83.  F i g u r e 5.17. T y p i c a l r i p p l e p a t t e r n under waves and c u r r e n t s .  combined  84.  F i g u r e 5.16. T y p i c a l r i p p l e - p a t t e r n under combined waves and c u r r e n t s .  85. 6.  6.1  CONCLUSIONS AND RECOMMENDATIONS  CONCLUSIONS The  around  purpose  of this  study  i s t o compare t h e maximum  c y l i n d r i c a l p i l e s under  w i t h t h e scour produced  p o s s i b l e scour  t h e a c t i o n o f combined waves and c u r r e n t s  by pure waves and pure c u r r e n t s .  The f o l l o w i n g  c o n c l u s i o n s were reached:  1.  Scour  around  0.3-0.4  piles  starts  when t h e approach  of the c r i t i c a l  velocity.  This  velocity  i s as low as  i s because  the flow i s  a c c e l e r a t e d by the p i l e .  2.  The e q u i l b r i u m scour  conditions  l e s s time t h a n t h e e q u i l i b r i u m currents.  However maximum  f o r pure  currents  a r e reached i n  c o n d i t i o n s f o r t h e combined waves and  s c o u r under  pure wave a c t i o n i s reached  i n much l e s s time than f o r c u r r e n t s a l o n e o r waves and c u r r e n t s .  3.  F o r a l l t h e cases when  approach  critical  4.  flow  than  equilibrium  conditions  conditions the  time  slightly  possible  upstream  of  velocity  increases  f o r onset  as time i n c r e a s e s .  t o a maximum  the  particles.  of  velocity i s motion,  scour depths  The graphs o f scour development  scour  attained  reached  i . e . , the f l o w  scour depth i s l e s s t h a n t h e maximum  show t h a t  scour was  the p i l e  f o r sediment  a r e exceeded,  critical  threshold conditions. of  t h e maximum  s t r e s s f o r onset o f motion  If threshold greater  tested  the under  as a f u n c t i o n  and then d e c r e a s e s  T h i s decrease c o u l d p o s s i b l y  be caused  by s e l e c t i v e armouring o f the scour h o l e w i t h c o a r s e r m a t e r i a l .  86. 5.  The  development  similar  to  of  that  combined  of  The  p a t t e r n of  and  unidirectional  development as noted  6.  wave  current  flow,  scour  except  with  time  is  the  rate  of  for  i n (2).  scour  hole  i s quite similar  under  the  three  flow  cases t e s t e d .  7.  For  a l l the  cases,  l e a d i n g edge of the  8.  the  maximum  scour  depth  was  adjacent  to  the  pile.  F o r t h e c a s e o f combined waves and c u r r e n t s a t t h r e s h o l d c o n d i t i o n s , t h e maximum scour i s dependent on the r e l a t i v e c o n t r i b u t i o n of steady the  and unsteady  sediment  both  components of f l o w t o the t h r e s h o l d v e l o c i t y  material.  The  higher  the  steady  current  of  percentage,  t h e deeper i s the scour h o l e , so t h a t i n the l i m i t the pure c u r r e n t produces  the  deepest  contribution limit  of  the  scour. wave,  On  the  of pure waves, the scour  same s i z e o f c y l i n d e r i s used. scour know  depth the  under  amount  combined  of  each  the  less  i s the  depth  hand,  scour  the  depth  more and  the  in  the  i s minimum, p r o v i d e d t h a t the  T h e r e f o r e , when c o n s i d e r i n g maximum  waves and  flow  other  c u r r e n t s , i t i s necessary  component  i n the  combined  to  threshold  velocity.  9.  The flow  scour  depth  component  under waves p l u s c u r r e n t s i s more s e n s i t i v e t o c o n t r i b u t i o n s when the  cylinder  size  i s large  the than  when t h e c y l i n d e r I s s m a l l .  10.  I t was only  observed slightly  diameter  piles.  that  the  dependent  combined on  However,  wave and  sediment scour  size,  depths  c u r r e n t scour especially  for  small  depth  for  sediment  ranges a r e s l i g h t l y g r e a t e r t h a n f o r b i g g e r sediment s i z e  is  bigger size  ranges.  87. 11.  The measured estimated  values  using  available  scour  with  prediction  The measured v a l u e s a r e i n a good agreement w i t h most of  estimated  values  T h e r e f o r e steady the scour  12.  depths under c u r r e n t s a l o n e were compared  or calculated  formula. the  scour  flow  in  specific  estimates  formulas  (1.7) and  (1.8).  o f scour p r o v i d e an upper bound on  depth.  Knowing t h e f l o w parameters and t h e s t r u c t u r e s i z e and bed m a t e r i a l properties,  i t i s p o s s i b l e to get a t least  a rough e s t i m a t e o f the  maximum p o s s i b l e s c o u r .  6.2  RECOMMENDATIONS FOR FURTHER STUDY There a r e s e v e r a l a r e a s  improve the p r e s e n t  1.  I t would size  i n which  s t u d i e s c o u l d be made t o  study.  be d e s i r a b l e t o r e p e a t  sand  further  ranges  to evaluate  these  experiments  the e f f e c t  using  o f sediment  different size  more  precisely.  2.  Although  t h i s study was r e s t r i c t e d t o non-cohesive  experiments  3.  Using  material, similar  c a n be r u n a g a i n u s i n g c o h e s i v e m a t e r i a l .  larger  pile  sizes  and c o n d u c t i n g  the same experiments  in a  l a r g e r flume c o u l d i n d i c a t e t h e p i l e s i z e dependence, and t o f i n d a c e r t a i n c o r r e l a t i o n or formula  4.  Using  an a r r a y  spacing  of p i l e s  parameter  f o r maximum s c o u r .  and v a r y i n g  indicating  a t what  the spacing could distance  identify  the p i l e s  must  a be  s e p a r a t e d i n order f o r them t o scour i n d e p e n d e n t l y of one a n o t h e r .  88. 5.  Installation  o f a p r o t e c t i v e c o l l a r on p i l e s and r e p e a t i n g the same  experiments c o u l d i d e n t i f y t h e s p a c i n g and t h e s i z e o f t h e s e c o l l a r s to reduce s c o u r .  6.  Throughout  the  experiments  the  dimensional of the s i n u s o i d a l type. investigate  the  effect  of  random  wave  used  was  uniform,  two-  T h i s study c o u l d be extended t o waves  on  scour  depth  around  structures.  7.  Other shapes o f p i l e s - r a t h e r t h a n t h e c y l i n d r i c a l shape - c o u l d be tested.  89.  BIBLIOGRAPHY  Abad,  G.N. and Machemehl, J.L. 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