COMPRESSIBILITY  OF    SOILS  Part  3  

OUTLINE  3  1.  TIME  RATE  OF  CONSOLIDATION  2.  COEFFICIENT  OF  CONSOLIDATION  3.  CALCULATION  OF  CONSOLIDATION  SETTLEMENT  

UNDER  A  FOUNDATION  4.  METHODS  FOR  ACCELERATING  CONSOLIDATION  

SETTLEMENT  5.  PRECOMPRESSION  

TIME  RATE  OF  CONSOLIDATION  

Gives   informaCon   regarding   the   rate   of   primary  consolidaCon.    Terzaghi  (1925)  proposed  the  first  theory  to  consider  the   rate   of   one-­‐dimensional   consolidaCon   for  saturated  clay  soils.    

ASSUMPTIONS:    1.  The  clay  –  water  system  is  homogeneous.  2.  SaturaCon  is  complete.  3.  Compressibility  of  water  is  negligible.  4.  Compressibility  of  soil  grains  is  negligible  (but  soil  

grains  rearrange).  5.  The  flow  of  water  is  one  direcCon  only  (that  is,  in  

the  direcCon  of  compression).  6.  Darcy’s  law  is  valid.    

USING  DARCY’S  LAW:  Q  =  KIA    

During   consolidaCon,   the   rate   of   change   in   the  volume   of   the   soil   element   is   equal   to   the   rate   of  change  in  the  volume  of  voids.    

By  assumpCon  No.  4,    

The  change  in  the  void  raCo  is  caused  by  the  increase  of   effecCve   stress,   and   a   decrease   of   excess   pore  water  pressure.  Assuming  they  are  related  linearly:    

This  is  the  basic  differenCal  equaCon  of   Terzaghi’s   consolidaCon   theory  and  can  be  solved  with  the  following  boundary  condiCons:    

Sivaram  &  Swamee:    

EXAMPLE:  

The  Cme  required  for  50%  consolidaCon  of  a  25mm-­‐thick  clay  layer  (drained  at  both  top  and  bohom)  in  the   laboratory   is   2min   20   sec.   How   long   (in   days)  will   it   take   for  a  3m-­‐thick   layer  of   the  same  clay   in  the   field   under   the   same   pressure   increment   to  reach  50%  consolidaCon?  In  the  field,  there  is  a  rock  layer  at  the  bohom  of  the  clay.    How   long   in   days   will   it   take   in   the   field   for   30%  primary  consolidaCon  to  occur?    

EXAMPLE:  

A  3m-­‐thick  layer  (double  drainage)  of  saturated  clay  under  a   surcharge   loading  underwent  90%  primary  consolidaCon   in   75   days.   Find   the   coefficient   of  consolidaCon  of  clay  for  the  pressure  range.    

COEFFICIENT  OF  CONSOLIDATION  

GRAPHICAL  Methods  used   for  determining  cv   from  laboratory  one-­‐dimensional  consolidaCon  tests:    1.  logarithm-­‐of-­‐Cme   method   (Casagrande   &  

Fadum)  2.  Square-­‐root-­‐of-­‐Cme  method  (Taylor)  3.  Hyperbola  Method  (Sridharan  &  Prakash)  4.  Early  stage  log-­‐t  method  (Robinson  &  Allam)    

LOGARITHM-­‐OF-­‐TIME  METHOD:  

STEPS:  

CALCULATION  OF  CONSOLIDATION  SETTLEMENT  UNDER  A  FOUNDATION  

The  increase  in  the  verCcal  stress  in  soil  caused  by  a  load   over   a   limited   area   decreases   with   depth   z,  measured  from  the  ground  surface  downward.    The   increase  of   effecCve   stress,  Δσ’,   should  be   the  average   increase   in   the   pressure   below   the   center  of  the  foundaCon.    

METHODS  FOR  ACCELERATING  CONSOLIDATION  SETTLEMENT  

In   many   instances,   sand   drains   and   prefabricated  verCcal   drains   are   used   in   the   field   to   accelerate  consolidaCon   sehlement   in   son   normally  consol idated   clay   layers   and   to   achieve  precompression   before   the   construcCon   of   a  desired  foundaCon.    

Sand   drains   are   constructed   by   drilling   holes   through  the  clay  layers  in  the  field  at  regular  intervals.      The  holes  then  are  backfilled  with  sand.    Aner  backfilling  the  drill  holes  with  sand,  a  surcharge  is  applied   at   the   ground   surface.   This   surcharge   will  increase  the  pore  water  pressure  in  the  clay.    The   excess   pore   water   pressure   in   the   clay   will   be  dissipated  by  drainage  –  both  verCcally  and  radially  to  the  sand  drains  –  which  accelerates  sehlement  of   the  clay  layer.    

Prefabricated   verCcal   drains   (PVD),   which   also   are  referred   to   as   wick   or   strip   drains,   originally   were  developed   as   a   subsCtute   for   commonly   used   sand  drains.    The  drains  are  manufactured  from  syntheCc  polymers  such  as  polypropylene  and  high  density  polyethylene.        

ASSIGNMENT:  

Write   a   wrihen   report   on   other   methods   used   in  determining  the  coefficient  of  consolidaCon,  and  make  necessary   computaCons   as   to   how   these   methods  differ  from  each  other.    Re-­‐do   your   problem   in   prelim,   using   the   weighted  average  value  of  effecCve  stress   in  the  clay   layer.  Use  the  formula  proposed  by  Simpson.    To   be   passed   next   meeCng,   in   a   short   bond   paper,  black  ink.