Civil Engineering Department: Foundation Engineering (ECIV 4052)
Engr. Yasser M. Almadhoun Page 1
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.
Civil Engineering Department: Foundation Engineering (ECIV 4052)
Engr. Yasser M. Almadhoun Page 2
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.
Civil Engineering Department: Foundation Engineering (ECIV 4052)
Engr. Yasser M. Almadhoun Page 3
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.
Civil Engineering Department: Foundation Engineering (ECIV 4052)
Engr. Yasser M. Almadhoun Page 4
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.
Civil Engineering Department: Foundation Engineering (ECIV 4052)
Engr. Yasser M. Almadhoun Page 5
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.
Civil Engineering Department: Foundation Engineering (ECIV 4052)
Engr. Yasser M. Almadhoun Page 6
(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.
Civil Engineering Department: Foundation Engineering (ECIV 4052)
Engr. Yasser M. Almadhoun Page 7
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:
Civil Engineering Department: Foundation Engineering (ECIV 4052)
Engr. Yasser M. Almadhoun Page 8
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.
Civil Engineering Department: Foundation Engineering (ECIV 4052)
Engr. Yasser M. Almadhoun Page 9
Note: Ia can be found from the following figure:
Civil Engineering Department: Foundation Engineering (ECIV 4052)
Engr. Yasser M. Almadhoun Page 10
(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:
Civil Engineering Department: Foundation Engineering (ECIV 4052)
Engr. Yasser M. Almadhoun Page 11
Or Table 6.1.
Civil Engineering Department: Foundation Engineering (ECIV 4052)
Engr. Yasser M. Almadhoun Page 12
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.
Civil Engineering Department: Foundation Engineering (ECIV 4052)
Engr. Yasser M. Almadhoun Page 13
Problems
See examples demonstrated in the textbook.
Solve problems 6.3/4/8/11 in the textbook.
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