Shallow Foundations: Settlement Calculation and Analysis - Prof. Brown, Cheat Sheet of Mechanics

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Shallow Foundations

Geotechnical Serviceability

Limit States

Settlement calculation

Introduction

Apart from the bearing resistant, the other major design consideration for

shallow footings is settlement

Excessive settlement (primarily differential settlement) can cause a

number of problems especially for large footing size

a

for both total and differential settlements

Components of Settlement

• Initial or elastic settlement, 

e

• Primary consolidation settlement, 

c

• Secondary compression or creep, 

s

occurs at constant effective stress (i.e. no drainage of pore

water occurs) and is irreversible.

• Total settlement, S = 

e

c

s

In general, primary consolidation settlement is

more significant than the others in inorganic clays

Elastic Settlement

e

= H s/ E = H .e

z

E

s

H

e

z

Q

Generalized stress

and strain field

E

e

= e

z

.dz

0



Influence Factors I

0

and I

1

General Method for Elastic Settlement

Settlement Analysis Based on In-Situ Tests

• Settlement can be estimated based on in-situ tests (SPT, CPT, DMT,

and PMT)

• The calculation is usually performed for sandy soils
• Apart from other empirical methods, Schmertmann’s method was

developed from field and laboratory tests with an assumed physical

model

Settlement in Sandy Soil

use of strain influence factor

The method was developed as a means to computing the

settlement of spread footings on sandy soils

It has a physical base and calibrates with empirical data

CPT results are often used with this method

Schmertmann (1970) conducted extensive research on

the distribution of vertical strain below the spread footings

He found that the greatest strains do not occur

immediately below the footing but at a depth of ½ B to B

depends on the footing shape

The distribution of vertical strain is idealized as two

straight lines

Maximum Strain Influence Factor I

ep

q

1. 5 0. 1 (8.11)

Zp

ZD

p

q

I

s

s

e







 

s’

zp

I

ep

s’

zD

Settlement in Sandy Soil

1. 03 0. 03 0. 73 (8.20)

(8.19)

1. 1

1 0. 2 log

1 0. 5 (8.18)

( ) (8.17)

3

2

1

1 2 3

  













 

















 



 



  

B

L

C

t

C

q

C

E

I H

CC C q

ZD

ZD

s

ZD

s

s

 s

e

Typically we use t = 50 years, C

2

Schmertmann’s method

Example of Schmertmann’s method

A footing 2.5 m square carries a net foundation pressure of 150

kN/m

2

at a depth of 1 m in a deep deposit of fine sand. The

water table is at a depth of 4 m. Above the water table the

unit weight of the sand is 17 kN/m

3

and below the water

table the saturated unit weight is 20 kN/m

3

. The variation of

cone penetration resistance with depth is given in following

table.

Estimate the immediate settlement of the footing using the

Schmertmann’s method.

Depth (m) 1 - 1.9 1.9-2.4 2.4- 8

q

c

(MN/m

2

) 2.3 3.6 5

Layer

D

z q

c

E I

e

I

e

D

z/E

C

1

= 1 – 0.5(117)/150 = 0.

 = 0.943 * 150 * 0.181 = 25.57 ~ 26 mm

Stress Due to a Concentrated Load

• Boussinesq solution

Homogeneous elastic weightless materials

r

R

z

P

s

z

s

y

s

x

y

5/ 2

2

2

2 2

3

2 1

P

r

z

z

where

r x y

s

D 

 

 



 

 

 

 

 

 