Elastic Half-space-Soil Mechanics and Foundations-Lecture 23 Slides-Civil and Environmental Engineering, Slides of Soil Mechanics and Foundations

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CE 240

Soil Mechanics & Foundations

Lecture 8.

Stresses in a soil mass II

(Das, Ch. 9)

Class Outline

• Green’s functions: Kevin’s problem, Boussinesq’s

problem, Cerruti’s problem, and Love’s Problem

• Vertical stress caused by a vertical line load
• Vertical stress caused by a horizontal line load
• Vertical stress caused by a vertical strip load
• Vertical stress caused by a horizontal strip load
• Vertical stress caused by a rectangular areal load

Elastic Half-Space Green’s

Functions

Boussinesq' Problem

Cerruti' Problem

Mindlin' Problem

Figure 9.

F

v

I1 versus r/z

0

1. 1
2. 2
3. 3
4. 4
5. 5
6. 6

1

r/z

0 10

It is noteworthy to point out that the vertical normal stress

is free of any material property parameters (such as the

Poisson's ratio). We only discuss the vertical normal stress.

For the Boussinesq's

3 3

5 2 2 5 / 2

2 2

5 2 2 5 / 2

Problem:

For the Cerruti's Problem ( in x-direction):

This is part of the reason we only discuss the vertical stress,

no complications re

v

z

h

h h

z

F z P z

L r z

F

F F

xz xz

L r z

sulting from material properties.

Vertical stress caused by a vertical line load

Vertical stress caused by a vertical line load

Vertical stress caused by a horizontal line load

h

For a line of horizontal load in x-direction with a load

density of q along the y-direction extending

from - to + , we need to use the solution of the

Cerruti's Problem as the kernal and integrate to

2

2 2 2 5 / 2

2 2

2 2 2 5 / 2 2 2 5 / 2

2

2 2 2

get

h

z

h h

h

q xz dy

x y z

q xz dy q xz dy

x z y a y

q xz

x z

Vertical stress caused by a vertical strip load

Vertical stress caused by a vertical strip load