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In Situ Stresses

ChihChih--Ping LinPing LinNational National ChiaoChiao TungTung [email protected]@mail.nctu.edu.tw

Soil Mechanics −

Outline

Stresses in Saturated SoilStresses in Saturated SoilWithout seepageWithout seepage

Upward seepageUpward seepage

Downward seepageDownward seepage

Seepage ForceSeepage Force

Capillary ForceCapillary Force

Stresses in Saturated Soil

satAw )HH(H γ−+γ=σ

The total stress at the elevation of point A

σ = σ’ + u=(HA-H) γ’

Effective Stress

Stresses in Saturated SoilStresses in Saturated Soil

Stress Components in SoilsLoading

Reference particle

( ) ''1 ' RAau Sig +−−+= σσ

For soil with low plasticity: uig −≈= σσσ '


Layer 1

Layer 2

Layer 3

d1

d2

d3

γ γbulk = 1

γ γbulk = 2

γ γbulk = 3

Surcharge q

σ v

z

Calculation of Effective StressStresses in Saturated SoilStresses in Saturated Soil

d1

d2

q

z

A

Plan

ElevationCalculation of Total Vertical Stress

z

Force on base = Force on top + Weight of soil

A σv = A q + A γ1 d1 + A γ2 d2 +

A γ3 ( z - d1 - d2 )

σv = q + γ1 d1 + γ2 d2 +γ3 ( z - d1 - d2 ) σ v


Water table

H

P u P Hw w( ) = γ

• The water table is the level of the water surface in a borehole.

• It is the level at which the pore water pressure uw = 0

Calculation of pore water pressureStresses in Saturated SoilStresses in Saturated Soil

Dry

Saturated

2 m

3m

γ γbulk dry=

γ γbulk sat=

Step 1: Draw ground profile showing soil stratigraphyand water table

Example: determining the effective stress


Distribution by Volume

Solid

VoidsVv=e Vs

= 0.7m3

Distribution by weight for the dry soil

Distribution by weightfor the saturated soil

Vs= 1m3

W V kN

kN

kN

w v w= ×= ×=

γ0 7 9 8

686

. .

.

W V G

kN

kN

s s s w= × ×= × ×=

γ1 27 98

2646

. .

.

W V G

kN

kN

s s s w= × ×= × ×=

γ1 2 7 9 8

26 46

. .

.

Ww=0

γγ

γγ

drys w

satw s

kN

mkN m

G

e

kN

mkN m

G e

e

= = =+

=+

= =+

+

26 46

1701556

1

26 46 6 86

17019 60

1

33

33

.

.. /

( . . )

.. /

( )

Step 2: Calculation of relevant bulk unit weights


2 m

3m

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

Step 3 Calculate total stress

u kPaw = × =3 9 8 29 40. .

Step 4 Calculate pore water pressure

Step 5 Calculate effective stress

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


0 50 100 150

0m

2m

4m

6m

8m

kPa

pore waterpressure Effective

stress

TotalStress (5m)

Depth

Vertical stress and pore pressure variationStresses in Saturated SoilStresses in Saturated Soil

No seepageNo seepage

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Upward seepageUpward seepage

Boiling/quick condition


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Downward seepageDownward seepage


Seepage Force

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Upward seepage

Downwardseepage


Heaving due to seepage

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Example


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Use of filters to increase FS against heave


Surface Tension• Two forms of soil moisture

• Absorbed• Free moisture

• Polar nature of water• Molecular attraction

• Water to water – contract to least possible area• Waxed surface

• Water to glass• Air – water interface

• Balancing forces

• Surface tensionF

To

• To = -0.075 gm/cm

Demo: http://www.wtamu.edu/~crobinson/SoilWater/capact.html


Capillary TensionCapillary Tension

d

F

To

α α

F T o π⋅ d⋅ cos α( )⋅

u cF

A

π d⋅ T o⋅ cos α( )⋅

π d2⋅

4

⎛⎜⎝

⎞

⎠

u c4 T o⋅ cos α( )⋅

d

u c0.3−d

gm/cm

Negative sign denoted Tension in the pore water


Capillary Tension (cont.)Capillary Tension (cont.)

F

W

y

F v∑ F W−

F W

To π⋅ d⋅π4

d2⋅ hc⋅ γ w⋅

At equilibrium hc isat a maximum, thereforeSolving for hcmax yields

h cmax4 T o⋅

d γ w⋅

0.3−

d γ w⋅

hc


Capillary Tension (cont.)Capillary Tension (cont.)

hc1

hc2hc3

hc4

Height of capillary riseis a function of diameterof capillary tube

For soils dD 10

5


Height of the capillary rise and radius effects


Capillary effect in sandy soil

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Capillary Rise in SoilCapillary Rise in Soil

1801800.0060.006SiltSilt

MetersMeters< 2 mm< 2 mmClayClay

1201200.020.02Medium SandMedium Sand

68680.060.06Silty GravelSilty Gravel

20200.30.3Fine GravelFine Gravel

660.820.82Course GravelCourse Gravel

Capillary Capillary Head Head (cm)(cm)

DD1010 SizeSizeSoil TypeSoil Type


Implication of capillarity

( ) wcwc zz' γ+σ=γ−−σ=σ

The pore water pressure due to capillarity is negative (suction), so it will increase the effective stress.


Capillary Rise in Soil (Stress Profile)Capillary Rise in Soil (Stress Profile)

It is reasonable to assume that pore spaces between soilparticles of various diameters, behaves in much the samemanner as that of a capillary tubes

hc

uc hcγw

-hcγw


Capillary Rise in SoilCapillary Rise in Soil

Surface Tension air/water surface Interface

u Sr

Discontinuous Water

Capillary Fringe

Capillary Saturationhc

-hcγw


Effective Stresses Due to CapillarityEffective Stresses Due to Capillarity

G.S. σT u σ’

-hcγwγdry

γsat

γw

γdry

γwsat - γw


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