chapter 6: vertical stress increase in...

Civil Engineering Department: Foundation Engineering (ECIV 4052)

Engr. Yasser M. Almadhoun

Chapter 6: Vertical Stress Increase in Soil

Introduction

Recall that shallow foundations must have two main satisfactorily

characteristics:

(1) They have to be safe against overall shear failure in the soil that

supports them.

(2) They cannot undergo excessive displacement, or settlement.

(The term excessive is relative, because the degree of settlement

allowed for a structure depends on several considerations.)

Therefore, the allowable settlement of a shallow foundation may control

the allowable bearing capacity. Thus, the allowable bearing capacity will

be the smaller of the following two conditions:

To calculate foundation settlement, it is required to estimate the vertical

stress increase in the soil mass due to the net load applied on the

foundation. Hence, at first, we will discuss the general principles for

estimating the vertical stress increase at various depths in soil due to the

application of (on the ground surface).

A point load

Circularly loaded area

Vertical line load

Strip load

Rectangularly loaded area

Embankment type of loading

Stress Due to a Concentrated Load

Boussinesq developed the mathematical relationships for determining the

normal and shear stresses at any point inside homogeneous, elastic, and

isotropic mediums due to a concentrated point load located at the surface.



Stress Due to a Circularly Loaded Area

The Boussinesq equation can also be used to determine the vertical stress

below the centre of a flexible circularly loaded area.



Stress Due to a Line Load

The vertical stress increase inside the soil mass can be determined by using

the principles of the theory of elasticity, or by using Table 6.2.



Stress below a Vertical Strip Load (Finite Width

and Infinite Length)

The fundamental equation for the vertical stress increase at a point in a soil

mass as the result of a line load (Stress Due to a Line Load) can be used to

determine the vertical stress at a point caused by a flexible strip load of

width B.



Stress below a Rectangular Area

(a) Below the corner

The total stress increase caused by the entire loaded area at point A may

now be obtained by integrating the preceding equation with the supplement

of Table 6.3.



(b) Below the centre

a. Method 1

In most cases, the vertical stress below the centre of a rectangular area is

of importance. This can be given by the relationship with the supplement

of Table 6.5.



b. Method 2

Foundation engineers often use an approximate method to determine the

increase in stress with depth caused by the construction of a foundation.

The method is referred to as the 2:1 method. According to this method, the

increase in stress at depth z is:



Average Vertical Stress Increase Due to a Rectangularly

Loaded Area (Stress in a layer)

(a) Method 1

a. Below the corner

In many cases, one must find the average stress increase below the corner

of a uniformly loaded rectangular area with limits of z = 0 to z = H.

b. Below the centre

In most practical cases, however, we will need to determine the average

stress increase between z = H1 and z = H2 below the centre of a loaded area.



Note: Ia can be found from the following figure:



(b) Method 2

Another approximate procedure to determine the average stress is to use

the relationship:

Average Vertical Stress Increase below the Centre of a

Circularly Loaded Area

The average vertical stress increase below the centre of a flexible circularly

loaded area of diameter B between z = H1 and z = H2 can be estimated

using:



Or Table 6.1.



Stress Increase under an Embankment

The vertical stress increase for this two-dimensional loading condition of

an embankment of height H may be expressed as given as under:

(a) Method 1

(b) Method 2

where I` is a function of B1 / z and B2 / z.



Problems

See examples demonstrated in the textbook.

Solve problems 6.3/4/8/11 in the textbook.

chapter 6: vertical stress increase in...

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