5- Effective Stress Concept

University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi

Asst. Prof. Khalid R. Mahmood (PhD.)

215

Effective Stress Concept

Topics Effective Stress Concept Effective Stress in Saturated Soil with

no Seepage Effective Stress in Saturated Soil with

Seepage Seepage Force Filter Requirements and Selection of Filter Material Capillary Rise in Soil Effective Stress in Capillary Zone

Water

Water Table (W.T.)

Ground Surface (G.S.) Air

Voids

Solid



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Effective Stress Concept Soil is a multi phase system To perform any kind of analysis - we must understand stress distribution The concept of effective stress:

The soil is loaded (footing for example) The resulting stress is transmitted to the soil mass The soil mass supports those stresses at the point to point contacts of the individual soil grains



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The total stress at A is calculated from: The weight of the soil above A The weight of the water above A = Hw + (HA - H) sat = Total Stress at A w = Unit Weight of Water sat = Saturated Unit Weight HA = Height of A to Top of water H = Height of water



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is the stress applied to the soil by its own weight As you go deeper in the soil mass, the stress increases The soil carries the stress in 2 ways:

A portion is carried by the water (acts equally in all directions)

A portion is carried by the soil solids at their point of contact.



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/= (P1v+P2v+P3v .....+Pnv) / A If as = a1 + a2 + a3 +...an Then the space occupied by water = A - as Assume u = HAw HA = Height of water = / + u(A - as) / A



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Since as is very small, assume = 0 = / + u

Recall the following equation: = Hw + (HA - H) sat Now, / = - u Substituting: / = [Hw + (HA - H) sat] - HAw Rearranging: / = (HA - H)(sat - w) = Hsoil/ Effective Stress is independent of height of water In the equation: = / + u / is the soil skeleton stress u is the stress in the water, or pore water pressure



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Effective Stress in Saturated Soil with no Seepage



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Effective Stress in Saturated Soil with Seepage Upward flow



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Note that the h/H2 is the hydraulic gradient that caused flow therefore,

wc izz JJV c c And limiting conditions may occur when 0 c c wc izz JJV which lead to icr = critical hydraulic gradient

wcri J

J c

for most soils 0.9-1.1 ith average value of 1



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Downward flow



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Seepage Force

Azp J c c1

AizforceseepageforceseepagepAizzp

w

w

JJJ

c c c 12 )(

AizforceseepageforceseepagepAizzp

w

w

JJJ

c c c 33 )(



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The volume of the soil contributing to the effective stress force equals zA, so the seepage force per unit volume of the soil is

ww i

zAAiz JJ

in the direction of seepage (see the fig.) Therefore, in isotropic soil and in any direction, the force acts in the same direction as the direction of flow. Thus, the flow nets can be used to find the hydraulic gradient at any point to find seepage force at that point. This concept is useful to estimate F.S against heave



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Factor of Safety against heave at the downstream of hydraulic structures Terzaghi (1922)

H1 H2

Sheet pile

Impermeable layer

Permeable layer

D

D/2

D

D/2

W c

U

Heave zone



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wavwav

wav

wsat

iiD

D

ixvolumesoilDD

UW

seepagebycausedforceUpliftweightSubmergedSF J

JJ

JJ

JJ c c

c 2

2

21

21

)())(2/(.



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Estimation of iav

a b c

e d

nd = 10

Dri

ving

hea

d

a b c



230

point driving head

a H104

b H

107.6

c H

105.2

Dhi

hhhh

avav

bcaav

2

2/)(



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Filter Requirements and Selection of Filter Material In practice, for the safe of the hydraulic structure, a minimum value of 4 to 5 for F.S against heaving is used, because of the uncertainty in the analysis. One way to increase the F.S is using filter. Filter:- is a granular material with opening small enough to

prevent the movement of the soil particles upon which is placed and, at the same time, is previous enough to offer little resistance to seepage through it.



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a b c

e d

nd = 10

D

D/2

W cW

U

D1



233

wav

F

wav

FF

iDD

iD

DDD

UWWSF J

JJ

J

JJ c

c

cc

cc 1

2

12

21

21

21

.



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Selection of Filter Material Capillary R



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Capillarity rise in Soil



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For pure water and clean glass = 0

wc d

Th J4 ?

For water T = 72 m.N/m

dhc

1v

the smaller the capillarity tube, the larger capillary rise



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For soils, the capillary tubes formed because of the continuity of voids have variable cross sections. The results of the nonuniformity on capillary can be demonstrated as shown in the fig.

Variation of S in the soil



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Hazen (1930) give a formula to estimate the height of capillary

10

)(eD

Cmmh c



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Effective Stress in Capillary Zone The general relationship of effective stress is u c VV For soil fully saturated by capillary wchu J

For soil partially saturated by capillary wchSu J

100



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Examples EXAMPLE1. Plot the variation of total and effective vertical stresses, and pore water pressure with depth for the soil profile shown below in Fig.



241



242



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The values of v, u and /v computed above are summarized in Table 1.

Table 6.1 Values of v, u and /v in Ex. 1



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EXAMPLE2. Plot the variation of total and effective vertical stresses, and pore water pressure with depth for the soil profile shown below in Fig.

Dry Sand

Gs = 2.66

Moist Sand Zone of capillary rise

Gs = 2.66

Saturated Clay

= 42%

A

H1 = 2 m

B

H2 = 1.8 m

C

H3 = 3.2 m

G.W.

Rock



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Dry sand 84.1681.955.0166.2

e1G

ws

d J J kN/m3

Moist sand 58.1881.955.0155.0*5.066.2

e1SeG

ws

t J

J kN/m3

Saturated Clay 138.1

142.0*71.2

SGe s Z

66.1781.9138.11

138.166.2e1eG

ws

sat J

J kN/m3



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Point v kN/m2 u kN/m2 /v kN/m2

A 0 0 0

0 33.68 B 2*16.84=33.68 - S w H2 = - 0.5*9.81*1.8 =

- 8.83 33.68-(-8.83) =

42.51

C 2*16.84+1.8*18.58 = 67.117 0 67.117

D 2*16.84+1.8*18.58+3.2*17.66 =123.68 3.2*9.81=31.39 123.68-31.39 = 92.24



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The plot is shown below in Fig.

Variation of v, u and /v with depth

0

1

2

3

4

5

6

7

8

-20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

Stress, kN/m2

dept

h, (m

)

Total stress

Pore water pressure

Effective stress

5- Effective Stress Concept

Documents

effective stress concept

seepage effective stress

concept of effective

saturated soil

total stress

soil skeleton stress

hsoil effective stress

stress distribution