06 - ch 02 - shallow foundations - elastic settlement

7/25/2019 06 - Ch 02 - Shallow Foundations - Elastic Settlement

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Settlement of Shallow Foundations

Practically,

2

Settlement can not be avoided

Prevent the foundation system fromreaching a serviceability limit state

Elastic Settlement

At least

Your task



ExampleServiceability Limit State

3

Tilting of structures (chimneys,retaining walls) & cracking in walls

Architectural damage(damage to appearance)

Cracked floors, misalignment ofmachinery, dislocation of pipe

joints, jammed doors & windowsLoss of serviceability

Sever differential settlement offootings causing buckling of

columns & overstressing beamsStructural damage

(collapse)



4

Types of Settlement



5

Total Foundation Settlement

Consolidation Settlement

Elastic Settlement

+

= Foundation Type(Rigid; Flexible)

Settlement Location(Center or Corner)

Primary

Secondary

cetotal S S S Therefore;

s petotal S S S S or

d i v i d e d i

n t o

d e p e n d s

o n



Elastic Settlement The elastic settlement of

shallow foundations can beestimated by using the theoryof elasticity.

Theoretically, if the foundationis perfectly flexible, then

For rigid foundation, the elasticsettlement can be estimated as

6

f s E oe I I BqS s

s21

),()( 93.0 center flexibleerigid e S S



Where

net applied pressure on the foundation

B/2 for center of foundation

B for corner of foundation

Poisson’s ratio of the soil

av. modulus of elasticity of the soil under the foundation,measured from z=0 ~ z=4B

factor that depends on the location on the foundation

where settlement is being calculated

depth factor (Fig. 5.15)shape factor

factors depend on & , (tables 3.4 & 3.5)

7

21 & F F

I I

E

B

q

s

f

s

s

o

21

211 F F I

s

s s

nm



To calculate the settlement, we use

Due to the non-homogeneous nature of soil deposits, the magnitudeof Es may vary with depth. For that reason, it is recommended touse the weighted average of Es in elastic settlement calculations.

soil modulus within a depth

whichever is smaller

8

2

4

B H

B L

n

m

at a corer of the foundationat the center of the foundation

B H

B L

n

m

1

z

z E E

i s

s

)( z )(i s E

Bor H z 5



12



Example 1

A rigid shallow foundation1mx2m. Calculate theelastic settlement at the

center of the foundation.

Solution

????

13



14

Solution

we are given that B=1m & L=2m.Note that

Therefore,

Bm z 55

2/400,10

5

2000,121000,82000,10

mkN

E s

z

z E E

i s

s

)(



15

For the center of the foundation

&

From tables 3.4 & 3.5

Therefore

Again, . From Fig. 5.15b

Since the foundation is rigid, then

4

10

21

5

2

21

2

B

H n

B

Lm

031.0&641.0 21 F F

3.0&2,1 s B L

B

D f 709.0 f I

716.0031.0641.0 3.013.02

21

21

1

F F I s

s

s

mm I I BqS f s E oe s

s 3.13709.0716.04150 400,103.01

211

22

mmS S center flexibleerigid e 4.123.1393.093.0 ),()(



Elastic Settlement of sandy Soil:Using the Strain Influence Factor Schmertmann et al. (1978) proposed a semi-empirical equation

using stain influence factor in order to evaluate the elasticsettlement of granular soils.

Wherestain influence factor

depth factor

creep (time) factorstress at the level of the foundation

16

2

021

z

s

z

e z

E

I qqC C S

f

z

Dq

qC

C

I

2

1



Empirical correlations for depth &creep factors are

Where t is the time in years

17

1.0log2.01

5.01

2

1

t C

qqqC

Note that,

for square or circular foundations,

Iz = 0.1 at z = 0

Iz = 0.5 at z = 0.5BIz = 0 at z = 2B

Similarly, for foundations with L/B ≥ 10

Iz = 0.2 at z = 0

Iz = 0.5 at z = B

Iz = 0 at z = 4BVariation of the strain

influence factor, Iz



18

Procedure for calculation of Se

using the strain influence factor



Step 1: Plot the foundation and the variation of Iz with depth to scale.

Step 2: Using the correlation from standard penetration resistance

(N 60 ) or cone penetration resistance (q c ), plot the actual variation of

E s with depth. Schmertmann et al. (1978) suggested the following

correlations for sand

for square & circular foundations E s ~2.5 q c

for strip foundation E s ~3.5 q c

Step 3: Approximate the actual variation of E s into a number of layers

soil having a constant E s , such as E s(1) , E s(2) , …, E s(i) , …, E s(n) .

Step 4: Divide the soil layer from z=0 to z= z2 into a number of layers

by drawing a horizontal lines. The number of layers will depend on

the break in continuity in the I z and E s diagrams. Step 5: Prepare a table (such as that shown in the next page) to

obtain the summation part of the equation.

Step 6: Calculate C 1 & C 2 .

Step 7: Calculate the elastic settlement.

19



Layer No. ∆z Es

Iz at the middle

of the layer(Iz / Es) ∆z

1 ∆z(1) Es(1) Iz(1) (Iz(1) / Es(1)) ∆z1

2 ∆z(2) Es(2) Iz(2) (Iz(2) / Es(2)) ∆z2

⁞ ⁞ ⁞ ⁞ ⁞

i ∆z(i) Es(i) Iz(i) (Iz(i) / Es(i)) ∆zi

⁞ ⁞ ⁞ ⁞ ⁞

n ∆z(n) Es(n) Iz(n) (Iz(n) / Es(n)) ∆zn

∑(Iz / Es) ∆z

20



21

Example 2A shallow continuous foundation

along with the variation of E s with depth obtained from conepenetration tests (the brokenline).

Given: B=8ft, Df=4ft, γ=110lb/ft3,and the stress at the level of

foundation = 25lb/in2.Estimate the elastic settlementusing the method of straininfluence factor.

Solution

????



22

SolutionGiven L/B>10. Based on this, the I z

diagram is plotted. The approximatevariation of E s is shown and the soilbelow the foundation has been dividedinto 5 layers.

Assume the time for creep is 10 years.

93.006.325

06.35.01

5.011

2/06.3

2/4404110

qq

qC

inlb

ft lb f Dq

4.1

1.0

10log2.01

1.0

log2.012

t C



Thus,

23

Layer No. ∆z

(in.)

Es

(lb/in.2

)

z at the middle

of the layer

(in.)

Iz at the middle

of the layer

(Iz / Es) ∆z

(in.3

/lb)

1 48 750 24 0.275 0.0176

2 48 1250 72 0.425 0.016

3 96 1250 144 0.417 0.032

4 48 1000 216 0.292 0.014

5 144 2000 312 0.125 0.009

∑ 0.0886

.53.20886.006.3254.193.0

0

21

2

in

z

z s E z I qqC C eS



The equation of elastic settlement depends mainly on Es and μs.

However, it must be realized that actual estimation of Es is difficult and

challenging. The reliability of the elastic settlement calculation primarilydepends on that.

Several approximate procedures are available in the literatures, such as:

1. E s in sandy soil can be approximated as

E s = α N 60 p a

Where pa = atmospheric pressure~100 kN/m2 (~2000 lb/ft2)5 for sands with fine

α = 10 for clean normally consolidated sand

15 for clean over-consolidated sand

2. E s in clayey soil can be approximated as

E s = β cu

Where c u is undrained shear strength, &

β is a factor from table 5.9

Table 5.8 shows some approximate values of Es and μs for various soils.

24



25



Consolidation Settlement (Sc)

(Time Dependent Settlement)

26

Consolidation settlement occurs in

cohesive soils due to the expulsion of

the water from the void

Because of the soil permeability the

rate of settlement may varied from

soil to another. Also the variation in the rate of

consolidation settlement depends on

the boundary conditions.

Primary Consolidation (S p): the

volume change is due to reduction in

pore water pressure. Secondary Consolidation (S s): the

volume change is due to the

rearrangement of the soil particles

(No pore water pressure change,

Δu=0, occurs after the primary

consolidation).

sS pS cS

06 - ch 02 - shallow foundations - elastic settlement

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