CE222 SM 11 in-situ Stresses

SoilMechanicsICE222

Waterinsoil:Insitustresses

CE 222

1

Insitu/geostaticstress 2

Geostaticstressesarecausedbygravityactingonthesoilorrock,sothedirectionresultisavertical,normalstressz.

This stress has a significant impact on theThisstresshasasignificantimpactontheengineeringbehaviorofsoil,andisoneisneededtobecomputed.

Thisverticalstressindirectlyproduceshorizontalnormal stress and shear stresses, which arenormalstressandshearstresses,whichareimportanttogeotechnicalengineer.


V ti l t

Area = AGround surface

Verticalstresses

Consideracolumnofsoilthatextendsfrom ground surface down to a point

H1 1st stratum

fromgroundsurfacedowntoapointwherewewishtocomputez.Itsweightis

H2

= 1

2nd stratumdxdyHdxdyHdxdyHW 332211 ++=

HdxdyW H3

= 2

3rd stratum

= HdxdyW Thegeostaticstress,z atbottomofl i 3

rd stratum = 3columnis

=== HHdxdyW dy dx

=== HdxdyAz


Area = AGround surface

Thetotalverticalstressatanypointinthesoilmassisdue

H1 1st stratum p

solelytotheweightofsoilandwateraboveit. H2

= 1

2nd stratum

H3

= 2

3rd stratum3rd stratum = 3

dy dx

Totalandeffectivestress 5

Insaturatedconditions,thenormalstress iscarriedpartiallybythesolidparticlesandpartiallybytheporewaterpresentinvoids.

Itiscalledthetotalstressbecauseitissumofthestressescarriedbytwophasesinthesoil:

The effective stress , which is the portion carried by theTheeffectivestress ,whichistheportioncarriedbythesolidparticles,and

The pore water pressure, u, which is the portion carried byTheporewaterpressure,u,whichistheportioncarriedbytheporewater.

Karl Terzaghi was first to recognize the importance ofKarlTerzaghiwasfirsttorecognizetheimportanceofeffectivestress.

Submergedsphereanalogy 6

Tounderstandthephysicsofsoilparticlesundergroundwatertableanddifferencebetweentotalandeffectivestresses,considerthesphererestingonascaleasshownbelow.BuoyancyforceFB onthep g y y Bsphereinwatertankis

wB VF == (0.1 m3)(9.8 kN/m3)= 0.98 kNThecontactforcebetween

sphereandscaleisreducedto

Volume0 1 3

F=2.60kN 0.98kN=1.62kN

Scale2.60kN

0.1m3

Scale1.62kN

Theweightofspherehasnotchanged,butisnowg ,supportedpartiallybyscaleandpartiallybywater.

Theprincipleofeffectivestress 7

Theprincipleofeffectivestressismostimportantprincipleinsoilmechanics.

Deformations of soils are a function of effective stresses notDeformations of soils are a function of effective stresses notDeformationsofsoilsareafunctionofeffectivestressesnotDeformationsofsoilsareafunctionofeffectivestressesnottotalstresses.totalstresses.

Theprincipleofeffectivestressesappliesonlytonormalstresses

u+= Principal of effective stress (first recoganized by Terzaghi in mid-1920s.andnottoshearstresses.Why?

Pore-water pressure

Effective stress

Total stress

Example 8

Computetotalverticalstress,porewaterpressure,effectiveverticalstressatmidheightofclaylayer.

Solution:Solution:

Totalstress = .H= (18.363.66/2) + (19.627.92) + (9.813.05) = 218.9 kN/m2=(18.363.66/2)+(19.627.92)+(9.813.05)=218.9kN/m

Porewaterpressureisduetototalwatercolumnabovethemidpoint

u= w.Hw=(9.813.66/2)+(9.817.92)+

(9.813.05)=125.6kN/m2

sat =19.62kN/m3Effectivestress= u=218.9 125.693 3 kN/ 2

sat =18.36kN/m3

=93.3kN/m2

Example 9

Calculatethetotalstress,porepressure,andeffectivestressesatA,B,C,andD.

Solution:AtpointA AA =0,uA=0,A=0AtpointB = 3x16 5 = 49 5 kN/m2

3m

3m

B

C

Drysanddry =16.5kN/m3

B =3x16.5=49.5kN/muB=0,B=49.5 0=49.5kN/m2

i 13 mClay

AtpointCC =6x16.5=99kN/m2uC=0C=99 0=99kN/m2

13m

D

ysat =19.25kN/m3

C /

AtpointDD =(6x16.5)+(13x19.25)=349.25kN/m2

13 9 81 127 53 kN/m2

Impermeablelayer

uD=13x9.81=127.53kN/m2D=349.25 127.53=221.72kN/m2

Example 10

ATotalstress Porepressure Effectivestress

B

C

Drysanddry =16.5kN/m3

99.0 0.0 99.0

Clayk / 3

D

sat =19.25kN/m3

349.25 127.53 221.72

Impermeablelayer

Z(m) Z(m) Z(m)( ) ( ) ( )

Example 11

Thesoilprofileisshownbelow.WhatarethetotalstresseseffectivestressesatpointA

Example 12

Thesoilprofileisshownbelow.Ploteffectivestress,totalstressandporepressurewithdepthfortheentireprofile.

Stressesinsat.soilwithoutseepage 13

Seepagevelocity 14

Themovementofwaterthroughasoilmassisgenerallytermedseepage.

Onamicroscopicscale,thewaterh fl i f ll t twhenflowingfollowsatortuous

routethroughthevoidsinthesoil.

Fromapracticalpointofview,however,itisassumedtofollowastraightlinepath.

InDarcysequation,thevelocityvDischargevelocityisthevelocityofflowrelativetoa soil cross section area Aisinterpretedastheapparent,or

superficial,ordischargevelocity.

asoilcrosssectionareaA

Seepagevelocity 15

Theactualvelocitythroughporeswillbegreater,andthisistermedtheseepagevelocity(vs).

vvs = n

Dischargeandseepagevelocity 16

svvAAvq == sv AAA +=( ) AAA + l( ) svsv vAvAAq =+=( ) ( ) ( ) V

VvVVvLAAvAA s

v

svsvsv

++++ 1

vs:seepagevel.

( ) ( ) ( ) vVVV

vVVLA

vA

vv

s

v

s

v

sv

v

sv

v

svs

====ve + 11 Vs nvv

nv

eevs =

=

+= 11

nvvs =

Seepageforce 17

hS

O O

V l

Area=AReservoir

S

hA A

Valve

B B

L

F

l

o

w

Soil

C C

Soil

Seepageforce 18

Theworkdonebywaterduringseepageresultsinaseepageforce, J,being

hS

O O

ValveArea=A Reservoir

exertedontheparticles.h

B B

A A

AhJ sw=Since,flowvelocityisconstant,therefore,the

f ti th

L

F

l

o

w

seepageforceactingonthesoilwillalsobeconstantbetweenCCandBB.

C CSoil

Therefore,seepageforceperunitvolume,j,is

wsw i

LAAhj == gradient hydraulic== iL

hswhere

Seepagepressure 19

hS

O O

ValveArea=A Reservoir

h

B B

A Awij =

L

o

w

Theseepageforceperunitvolume,j,is usually referred

C CF

l

o

Soil

isusuallyreferredtoastheseepagepressure.

C C

Quickcondition 20

Theeffectofupwardflowingwaterinasoilmassincreatingaseepagepressureontheparticlesistoreducetheintergranularoreffectivestress.

If a sufficiently high enough flow rate is achieved the seepageIfasufficientlyhighenoughflowrateisachieved,theseepagepressurecancancelouttheeffectivestresscompletelycausingaquickcondition.

Thisisessentiallyaconditioninwhichthesoilhasnoshearstrength, since the intergranular stress has been reduced tostrength,sincetheintergranularstresshasbeenreducedtozero.

Quickcondition&criticalhydraulicgradient 21

Atthequickcondition,theflowwillcauseaseepageforceatCCwhichwillbeequalandoppositetotheeffectivestress.(Note:effective stress is due to the weight of soil)

hS

O O

V lArea=A Reservoir

effectivestressisduetotheweightofsoil).

E i f C C S

hB B

A A

ValveEquatingforcesatCC:

( ) ( )AhLAhhL wsatsw +=++L

F

l

o

w

( )Lh wsatsw =

C CF

Soil( )wsatsw Lh =

( )wsatcwi =


( )wsatcwi = whereic istermedthecriticalhydraulicgradient,i.e.,thehydraulicgradientatwhichthequickconditionoccurs

hS

O O

V lArea=A Reservoir

occurs

w

wsatci

=S

hB B

A A

ValveAsweknowthat

( )eG ws += L

F

l

o

w

esat +1( )

+= ws eGi 1

C CF

Soil += wwc e

i 1G 1

eGi sc +

=1

1


Incohesionlesssoils,particularlyinmediumtofinesands,thequickconditionislikelytooccurathydraulicgradientsofabout1.0.

Contrarytopopularbelief,however,thisisnotasinkingsanddi icondition.

Quicksand lackingshearresistance,isreallyaliquid,butitsd it i hl t i th t f t h b d lddensityisroughlytwicethatofwater:ahumanbodywould,therefore,floathalfsubmerged.

I il i i ifi t t f h i h Insoilspossessingasignificantamountofcohesion,suchassiltsandclay,thecriticalhydraulicgradientcriteriondoesnotapply,sincetheyhavesomeshearstrengthatzeronormalstress

Seepageforce&safetyofsheetpile 24

Theseepageforceperunitvolumeofsoilis

l t i d iequaltoiw,andinisotropicsoils,theforceactsinthesamedi ti th di tidirectionasthedirectionofflow.

The concept of seepageTheconceptofseepageforcecanbeeffectivelyusedtoobtainthefactorof safety against heaveofsafetyagainstheaveonthedownstreamsideofahydraulicstructure.


Terzaghi (1922)Terzaghi(1922)

concludedthatheaving

generallyoccurswithina

distanceofD/2fromthe

sheetpiles(whenD

equals the depth ofequalsthedepthof

embedmentofsheet

pilesintothepermeable

layer)


where

FS = factorofsafety

W= submergedweightofsoilintheheavezoneperunitlengthofsheetpileg p

= (Vol)=D(0.5D)(1)(sat )=0.5D2U = upliftingforcecausedbyseepageonthesame

volumeofsoil

= (iavew )(Vol)=0.5D2whwhere

iave = averagehydraulicgradientatthebottomoftheblockofsoil.


2W= 0.5D2U = 0.5D2w

Forthecaseofflowaroundasheet pile in a homogeneoussheetpileinahomogeneoussoil,itcanbedemonstratedthat


whereCoisafunctionofD/T.

Hence FS can be written asHenceFScanbewrittenas

30Soilmigrationandfiltration

Geotechnical engineers intentionallyGeotechnicalengineersintentionallyplacehighlypervioussoilsinkeylocationstocaptureanddraingroundwater Uniformly (or poorly)groundwater.Uniformly(orpoorly)gradedgravelsareespeciallyusefulinthisregardbecausetheyhavehigh hydraulic conductivityhighhydraulicconductivity.

TheSoilmigrationoffinesoilmayt k l th h ltakeplacethroughcoarsegraveldrainagelayer.

Soilmigrationandfiltration 31

Thesoilmigrationhastwodetrimentalresults.

1) Thedrainagelayerbecomescloggedandnolongerfunctionsproperlyproperly.

2) Migrationofsoilsleavesvoidsinupstreamstrata.Insomecases,thesevoidscanpropagateforlongdistances,creatingundergroundchannelsleadingtopipingfailure.

Migrationproblemscanbeavoidedbyprovidingfilterswhichareintended to pass water but retain potentially migration soils There areintendedtopasswaterbutretainpotentiallymigrationsoils.Therearetwoprincipaltypesoffilters:gradedsoilsfiltersandgeosynthetic filters.

Selectionoffiltermaterial 32

TerzaghiandPeck(1948)filtermaterialselectioncriterion

33

(Dia)a =6.5(Dia)b

Filterselectioncriteria 34

D15(F) > D15(B)D15(F) >D15(B)

D15(F) < D85(B)Increasingsize

D15(F)

Capillaryriseinsoils 35

Forpurewaterandcleanglass, = 0 thus above equation =0,thusaboveequationbecomes

ForT=72mN/m,andweget

The smaller the capillary tubeThesmallerthecapillarytubediameter,thelargerthecapillaryrise.


The smaller the capillary tube diameter, the larger the capillary rise.Thesmallerthecapillarytubediameter,thelargerthecapillaryrise.

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CE222 SM 11 in-situ Stresses