Stress Distribution 1

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Stress Distribution in

Soil Mass – Part 1

KAEA 3233 - SOIL MECHANICS II

Dr. Tan Chee GhuanDepartment of Civil Engineering

Faculty of Engineering

University of Malaya1


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What is Stress Distribution ?

• When a structure is erected on a soil, it transmits

its weight as a load to the foundation.

• The foundation, in turn, imposes loads on the

soil.

• These loads induce stresses inside the soil. Thedistribution of these stresses is referred to as

stress distribution.

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Why is it important?• The stability of the foundation and the safety of

the structure depend on the stress distribution.

• It is important for all structures, especially incase of the large structure in today’s context.

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Where is it important?


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What factors affect their distribution?

The stresses developed depend on:• the nature of loads

• the geometry of the foundation

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the nature of soil• the theory/method used to compute them

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What are the methods available for

its determination?

• It would be ideal to determine the stresses inthe field. But, it is costly and time consuming.

• It is important to have methods to computethem in advance for a suitable foundationdesign.

• Theory of Elasticity (Boussinesq method,Newmark Influence chart)

• Approximation method

• Numerical Modelling

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Stresses in Soil

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In this chapter, we

will only concern on

normal stress in

vertical direction, σz x

y

z


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Stresses in soil

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• Stresses in soil are caused due to:

1. Self weight of soil, geostatic stresses

2. Structural loads, applied at or below the surface

• The estimation of vertical stresses at any point

in a soil mass due to external loading is essential

to the prediction of settlements of buildings,

bridges and pressure.


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Stress – Strain characteristics of Soil

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• Extremely complex and it depend upon a largenumber of factors.

• For example: drainage conditions, water content,void ratio, rate of loading, the load level, and thestress path.

• Simplifying assumptions are generally made in the

analysis of soil behaviour to obtain stresses.


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Boussinesq’s Theory

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• Boussinesq (1885) has given the solution for the stresses

caused by the application of the point load at the surface

of a elastic medium with the aid of the mathematical

theory of elasticity.

Assumptions:

1. The soil medium is an elastic continuum having a constantvalue of modulus of elasticity (E). i.e. Hooke’s law

2. The soil is homogeneous, i.e. it has identical elastic

properties at all points in identical directions.3. The soil is isotropic, i.e. it has identical elastic properties inall direction at a point.

4. The soil is weightless, compared to the applied loads

5. The load is a point load acting on the surface


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Vertical Stress Caused by a Point Load

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where:


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Table 1: Variation of I 1 for Various Values of r/z



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Vertical pressure distribution on horizontal plane

P

0.4775 P/z2

P

σz


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Example 1

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Consider a point load P = 1000 lb, plot the variation of vertical

stress, σz :

a) in z-direction for x = 3 ft and y = 4 ft

b) in x-direction for z = 6 ft and y = 4 ft

Stress Distribution 1

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