1

Shallow Foundations

– Settlement (Suite)

Reference:

Foundation Design, Principles and Practices,

Donald P. Coduto, Part B, Chapter 7

2

Settlement Analysis Based on

Laboratory Tests

Approach used when good quality

“undisturbed” samples can be obtained from

soil

Perform consolidation test

Obtain Cc, Cr , e0, and ´p

Perform settlement analysis

3

Two Methods of Analysis

Classical Method

Based on Terzaghi’s Theory

One dimensional compression

Skempton and Bjerrum Method

Considers distortion settlement

Uses an adjustment factor for 3D compression

4

Foundation Rigidity Effects• For cylindrical steel water tank, the water inside the tank

weighs much more than the tank itself, and this weight is supported directly on the plate-steel floor. In addition, the floor is relatively thin, and could be considered to be perfectly flexible.

• A square spread footings is much more rigid than plate steel tank floors. Although the center of the footing "wants" to settle more than the edge, the rigidity of the footing forces the settlement to be the same everywhere.

• A mat foundation is more rigid than the tank, but less rigid than the footing. Thus, there will be some differential settlement between the center and the edge, but not as much as with a comparably-loaded steel tank.

• When performing settlement analyses on spread footings, we account for this rigidity effect by computing the settlement values beneath the center of the footing, then multiplying the result by a rigidity factor, r.

• Use of r = 1 is conservative.

5

Classical Method; Foundation

Rigidity Factor

6

Settlement Predictions

N.C. Clays

00

log1 z

zfcc H

e

Cr

7

Settlement Predictions

O.C. Clays…… Case I

00

log1 z

zfrc H

e

Cr

8

Settlement Predictions

O.C. Clays…… Case II

c

zfc

z

crc H

e

CH

e

Cr

log

1log

1 000

9

Settlement Computation

We compute the consolidation settlement by dividing the soil beneath the foundation into layers, computing the settlement of each layer, and summing.

The top of first layer should be at the bottom of the foundation, and the bottom of the last layer should be at a depth such that:

'

010.0 zz

Unless the soil is exceptionally soft, the strain below this depth is negligible, and thus may be ignored.

10

Classical

Method

The classical method

divides the soil beneath

the footing into layers.

The best precision is

obtained when the

uppermost layer is thin

and they become

progressively thicker with

depth.

11

Thickness of Soil Sub-layers

12

Example 7.3

13

Example 7.3

14

Example 7.4

15

Example 7.4

16

Distortion Settlement

The classical method is based on the

assumption that settlement is a one-dimensional

process in which all of the strains are vertical.

This assumption is accurate when evaluating

settlement beneath the center of wide fills, but it

is less accurate when applied to shallow

foundations, especially spread footings, because

their loaded area is much smaller.

17

Distortion Settlement

Skempton and Bjerrum (1957) presented another method of

computing the total settlement of shallow foundations.

This method accounts for three-dimensional effects by

dividing the settlement into two components:

Distortion settlement, (also called immediate settlement,

initial settlement, or undrained settlement) is that caused by

the lateral distortion of the soil beneath the foundation.

Consolidation settlement, (also known as primary

consolidation settlement), is that caused by the change in

volume of the soil that results from changes in the effective

stress.

In addition, they accounted for differences in the way excess

pore water pressures are generated when the soil experiences

lateral strain. This is reflected in the parameter ψ.

18

Distortion Settlement

19

Skempton & Bjerrum Method

Settlement,

Distortion Settlement (d)

Consolidation Settlement (c)

21

)(II

E

Bq

u

zDd

cd

20

Influence Factors, I1 and I2

I1

D

21

22

I2

23

3D Adjustment Factor,

zh

24

3D Adjustment Factor,

25

Settlement Analysis based on In-Situ

Tests

Techniques for estimating settlements in sands are nearly always based on in-situ test results

In sands, settlement analysis is not performed based on consolidation analysis

Instead, we use Equivalent Modulus of Elasticity, Es

26

Es from SPT Data (Table 7.4)

6010 NOCREs

27

Es from CPT Data (Table 7.3)

28

29

Schmertmann’s Method

s

zDE

HIqCCC )(321

C1 = depth factor =

C2 = Secondary creep factor =

C3 = Shape factor =

zD

zD

q

5.01

1.0log2.01

t

73.0/03.003.1 BL

30

31

Strain Influence Factor

The greatest strains do not occur

immediately below the footing, as one

might expect, but at a depth of 0.5 B to B

below the bottom of the footing, where B

is the footing width.

This distribution is described by the strain

influence factor, I which is a type of

weighting factor.

32

33

Strain Influence Factor

zp

zDp

qI

1.05.0

3434

Shmertmann method – Analysis procedure

1. Perform appropriate in-situ tests to define the subsurface

conditions.

2. Consider the soil from the base of the foundation to the depth

of influence below the base. This depth ranges from 2B for

square footings or mats to 4B for continuous footings. Divide

this zone into layers and assign a representative E, value to

each layer. The required number of layers and the thickness of

each layer depend on the variations in the E vs. depth profile.

Typically 5 to 10 layers are appropriate.

3. Compute the peak strain influence factor, Iεp using Equation …

4. Compute the strain influence factor, lε at the midpoint of each

layer. This factor varies with depth using Equations …

5. Compute the correction factors C1, C2 and C3 using equations

…

6. Compute the settlement using Equation …

35

Example 7.6

36

37

38

39

40

41

Example 8.1

42

Example 8.1

43

44

45

46

47

Simplified Schmertmann Method

When Es is uniform with depth over the

depth of influence

For square/circular footings:

s

pzD

E

BIqCCC )025.0)((321

For continuous footings:

s

pzD

E

BIqCCC )1.02)((321

48

Settlements in Stratified Soils

When the soil profile primarily consists of

clays and silts – use procedures described in

Section 7.4 to estimate settlement

For clays/silts use laboratory consolidation tests

to determine Cc/(1+e0) and Cr/(1+e0)

For sands use Cc/(1+e0) or Cr/(1+e0) from Table

3.7

49

Settlements in Stratified Soils When the soil profile primarily consists of

sands and silts – estimate settlement based

on Schmertmann Method

Use in-situ test data to determine Es for sand

Use following equation to determine Es for

clays

)1/(

30.2

0eCE

c

zs

)1/(

30.2

0eCE

r

zs

or

50

Settlements in Stratified Soils

Alternative Approach

Conduct separate analysis for clays/silts and

sands

Add the computed settlements