Stress Distribution in the Soil

Stress Distribution in the Soil | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) PDF Download

Chapter 8
Stress Distribution in the Soil

VERTICAL STRESS:
Stress is induced in a soil mass due to weight  of overlying soil and due to applied load. This is called vertical stress. Stress in the soil may be caused by:
1. Self weight of soil

BOUSSINESQ’S THEORY
Assumption:
1. Soil mass is homogeneous, elastic and isotropic
2. Soil mass is semi-infinite (Surface in infinite but depth to finite)
3. Soil is weight less unstressed before application of load. (Self weight of soil is ignored)
4. No change in volume of soil takes place due to applical of the loads.
Boussinesq (1985) evolved equations that can be used to determine stresses at any point P at a depth z as a result of a surface point load.

At point P of above figure due to a point load Q,

where,
r = the horizontal distance between an arbitrary point P below the surface and the vertical axis through the point load Q.
z = the vertical depth of the point P from the surface.
IB=Boussinesq stress coefficient =

This intensity of vertical stress directly below the point load, on its axis of loading (r=0) is given by:

Boussinesq's Result:

WESTERGAARD’S THEORY:

Assumptions:
(1) The soil is elastic and semi-infinite.
(2) Soil is composed of numerous closely spaced horizontal layers of negligible thickness of an infinite rigid material.
(3) The rigid material permits only the downward deformation of mass in which horizontal deformation is zero.

NOTE: Boussinesq’s theory is applicable for Isotropic soil where as westergaards theory is applicable for non- Isotropic soil.

WESTERGAARDS RESULTS
(i) Vertical Stress due to Live Loads

where, σz = Vertical stress of any point having coordinate (x, z)
at X = 0

where,  σz = Vertical stress at point ‘p’

(iii)

(iv) Vertical stress below uniform load acting on a circular area.

NEWMARKS’S CHART METHOD:
This method is applicable to semi-infinite, homogeneous, isotropic and elastic soil mass. It is not applicable for layered structure. The greatest advantage of this method is that it can be applied for uniformly distributed area of irregular shape. Newmark’s chart is made of concentric circles and radial lines. Normally there are 10 concentric circles and 20 radial lines.
No.of concentric circle =10
Influence of area (1)=influence of area(2)=Influence of area(3)

σz = 0.005qNa

where, NA = Total number of sectorial area of Newmark’s chart.

APPROXIMATE METHOD:

(ii) Trapezoidal Method

(iii) Stress Isobar method : Area Bounded by 0.2q stress isobar is considered to be stressed by vertical stress on loading.

0.2q =20%Stress Isobar

The document Stress Distribution in the Soil | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course Civil Engineering SSC JE (Technical).
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FAQs on Stress Distribution in the Soil - Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

 1. What is stress distribution in soil?
Ans. Stress distribution in soil refers to the way that forces or loads are transmitted and distributed within the soil. It involves understanding how the soil carries and distributes the applied stress or load, which is important in various engineering and geotechnical applications.
 2. How is stress distributed in soil?
Ans. Stress distribution in soil is influenced by several factors, including the type of soil, its density, and the applied load. Generally, stress is distributed through the soil in a non-uniform manner, with higher stress concentrations near the load and lower stress levels further away from it. The stress distribution can be influenced by the soil's strength, stiffness, and its ability to withstand deformation.
 3. What are the factors that affect stress distribution in soil?
Ans. Several factors affect stress distribution in soil. These include the type of soil (e.g., clay, sand, silt), its compaction and density, the magnitude and distribution of the applied load, the shape and size of the load, the presence of water or pore pressure within the soil, and the soil's strength and deformation characteristics.
 4. Why is understanding stress distribution in soil important?
Ans. Understanding stress distribution in soil is crucial in various engineering and geotechnical applications. It helps in designing structures and foundations, determining the stability and safety of slopes and embankments, predicting soil settlement and deformation, analyzing the behavior of retaining walls, and assessing the overall performance and integrity of soil-based structures.
 5. How can stress distribution in soil be analyzed?
Ans. Stress distribution in soil can be analyzed through various methods, including theoretical calculations, numerical modeling, and laboratory testing. Techniques such as finite element analysis (FEA) and limit equilibrium analysis are commonly used to simulate and predict stress distribution in soil. Additionally, field tests like plate load tests and pressure cells can provide valuable data for understanding the stress distribution in situ.

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