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Effective Stress

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Introduction

External load will be distributedwithin soil mass

External load changes stress statewithin the soilThe stress distribution is importantto study soil stability anddeformation

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Total stress

Total vertical stress acting at thepoint below the ground

σ v Vertical Stress Vertical ForceCross Sectional Area= =

∑= zv γ σ

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Total stress below the river or lake

Free water at a river or lake will addadditional force to the ground

wwsat v z z γ γ σ +=

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Total stress for multilayer soil

The sum of the weights of soil ineach layer thickness above

( )2132211 d d zd d v −−++=

γ γ γ σ

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Total stress for unsaturated soil

Above the GWT soil will remainsaturated, but after certain distanceit become unsaturated

( )wwwuv z z z −+= γ γ σ

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Total stress with asurface surcharge load

A surface surcharge load willincrease total stressIf the surcharge loading is

extensively wide, the increasein vertical total stress isconstant

For narrow surcharge, theincrease will be decrease withdepth

q zv += γ σ

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Pore pressure ( u )

Porewater: water fills the voids orpore among soil grains

Pore pressure: the pressure withingthe pore waterDepend on:

The depth below the water tableCondition of seepage flow

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Pore pressure ( u )

Under hydrostatic condition: porepressure at a point is hydrostaticpressure

ww hu γ =

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Pore pressure ( u )

Below the water table, porepressure is positive

Above the water table, porepressure is negative (suction)

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Pore pressure ( u )

The height of saturatedsoil above water table is

called capillary rise anddepends on the grain sizeand type of soil

in coarse soils capillary riseis very smallin silts it may be up to 2min clays it can be over 20m

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Effective stress concept

At saturated soil, voids are fullyfilled by water

External load will be carried by bothgrains and waterSoil behavior under loading willdepend both of external force andthe water pressure in the pores

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Effective stress concept

Effective stress: normal stressacting on the soil grains => inter-granular stress

uu vv −=→−= σ σ σ σ ''

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The importance of effective stress

W

W

Soil loaded by anapplied weight W

Soil loaded by waterweighing W

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The importance of effective stress

W

W

Soil loaded by anapplied weight W

Soil loaded by waterweighing W

Compression No deformation

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σ v

Vertical Stress Vertical Force

Cross Sectional Area= =

σ σ v v wu' = −

(1)

(2)

Definition of Total and Effective Stress

Effective vertical stress

∆σ v ∆ u w ∆σ v ´

Case (a) W A

0 W A

Case (b) W A

W

A0

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Dry

Saturated

2 m

3m

Fig 5 Soil Stratigraphy

γ γ bulk dry=

γ γ bulk sat=

Step 1: Draw ground profile showing soil stratigraphyand water table

Example: determining the effective stress

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Distribution byVolume

Solid

VoidsVv=e V s

= 0.7m 3

Distribution by weightfor the dry soil

Distribution by weightfor the saturated soil

Vs = 1m 3

W V kN

kN

kN

w v w= ×= ×=

γ0 7 9 8

6 86

. .

.

W V G

kNkN

s s s w= × ×

= × ×=

γ

1 2 7 9 82646

. ..

W V G

kNkN

s s s w= × ×

= × ×=

γ

1 2 7 9 826 46

. ..

W w =0

γ γ

γγ

drys w

satw s

kNm

kN m Ge

kN

m

kN m G e

e

= = =+

=+

= =+

+

2646170

15561

2646 686

170

19 60

1

33

33

..

. /

( . . )

.

. / ( )

Step 2: Calculation of relevant bulk unit weights

Example

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2 m

3m

σ v kPa kN m= × + × =1556 2 19 60 3 89 92 2. . . ( / )

Step 3 Calculate total stress

Example

u kPaw = × =3 9 8 29 40. .

Step 4 Calculate pore water pressure

Step 5 Calculate effective stress

′ = − = − = v v wu kPa89 92 29 40 60 52. . .

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0 50 100 150

0m

2m

4m

6m

8m

kPa

pore waterpressure Effectivestress

TotalStress (5m)

Depth

Vertical stress and pore pressure variation

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ExamplePlot the variation of total and effectivevertical stresses, and pore water pressurewith depth for the soil profile shown below

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