Upload
bryan-ewe
View
222
Download
1
Embed Size (px)
Citation preview
8/17/2019 Stress Distribution 1
1/15
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
8/17/2019 Stress Distribution 1
2/15
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.
2
8/17/2019 Stress Distribution 1
3/15
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.
3
Where is it important?
8/17/2019 Stress Distribution 1
4/15
What factors affect their distribution?
The stresses developed depend on:• the nature of loads
• the geometry of the foundation
•
the nature of soil• the theory/method used to compute them
4
8/17/2019 Stress Distribution 1
5/15
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
5
8/17/2019 Stress Distribution 1
6/15
Stresses in Soil
6
In this chapter, we
will only concern on
normal stress in
vertical direction, σz x
y
z
8/17/2019 Stress Distribution 1
7/15
Stresses in soil
7
• 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.
8/17/2019 Stress Distribution 1
8/15
Stress – Strain characteristics of Soil
8
• 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.
8/17/2019 Stress Distribution 1
9/15
Boussinesq’s Theory
9
• 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
8/17/2019 Stress Distribution 1
10/15
Vertical Stress Caused by a Point Load
10
where:
8/17/2019 Stress Distribution 1
11/15
11
Table 1: Variation of I 1 for Various Values of r/z
Vertical Stress Caused by a Point Load
8/17/2019 Stress Distribution 1
12/15
12
Vertical Stress Caused by a Point Load
8/17/2019 Stress Distribution 1
13/15
13
Vertical Stress Caused by a Point Load
8/17/2019 Stress Distribution 1
14/15
14
Vertical Stress Caused by a Point Load
Vertical pressure distribution on horizontal plane
P
0.4775 P/z2
P
σz
8/17/2019 Stress Distribution 1
15/15
Example 1
15
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