Test: Vertical Stress Distribution - Civil Engineering (CE) MCQ

# Test: Vertical Stress Distribution - Civil Engineering (CE) MCQ

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## 10 Questions MCQ Test Soil Mechanics - Test: Vertical Stress Distribution

Test: Vertical Stress Distribution for Civil Engineering (CE) 2024 is part of Soil Mechanics preparation. The Test: Vertical Stress Distribution questions and answers have been prepared according to the Civil Engineering (CE) exam syllabus.The Test: Vertical Stress Distribution MCQs are made for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Vertical Stress Distribution below.
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Test: Vertical Stress Distribution - Question 1

### In Newmark's influence chart for stress distribution, there are eight concentric circles and ten radial lines. The influence factor of the chart is

Detailed Solution for Test: Vertical Stress Distribution - Question 1

Concept:
Newmark's influence chart for stress distribution
It is a graphical method used to compute vertical, horizontal and shear stress due to uniformly distributed load over an area of any shape or geometry below any point that lies either below or outside the loaded area by equation called Boussinesq's equation.

Stress below any point is calculated as :-

Where, m = No. of concentric circles, n = No. of radial lines, q = Intensity of load, N = Equivalent number of areas covered by plan area.
The product of  is called Influence Factor.
Given
m = 8, n = 10
Therefore, Influence factor (I.F)

I.F. = 0.0125

Test: Vertical Stress Distribution - Question 2

### From the following statements, select the most appropriate statement: Westergaard's analysis for stress computation within soil mass assumes.

Detailed Solution for Test: Vertical Stress Distribution - Question 2

1. Soil is Homogeneous, Anisotropic (as the physical properties along the different directions are different ), and Elastic.
2. Soil is considered as Cohesive as clay.
3. The soil profile is Layered.
4.  Poisson's Ratio is considered zero for all practical purposes.
5. The load will act as a point load on the surface.

As per Westergaard’s  equation, the vertical stress due to point load at any point Z below soil strata is calculated using the following formula:

Where,
Z is the depth where stress needs to be calculated
Iw is the influence factor, which is given as:

r is the radial distance from a point load to depth Z

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Test: Vertical Stress Distribution - Question 3

### Statement (A) : In Boussinesq's theory of stress computations, soil is considered to be un-stressed before application of the load. Statement (B) : The contact pressure distribution under a rigid footing in cohesionless soil, is uniform throughout the width of the footing.

Detailed Solution for Test: Vertical Stress Distribution - Question 3

Statement 1: True
The following are the assumptions in Boussinesq’s theory:

1. The soil is homogeneous and isotropic.
2. The soil mass is semi-infinite; that is, it extends infinitely in all directions below a level surface.
3. The soil is elastic i.e. it obeys Hooke’s law; that is, the stress-strain relationship is linear.
4. The soil is weightless and unstressed before the application of the load.
5. The load is applied at the ground surface and it is a point load.

Statement 2: False
The typical contact pressure distribution under a rigid footing like RCC  in cohesionless soil like sand is given below:

Based on the above, the following can be inferred about contact pressure:

1. It is non-uniform.
2. It is maximum at the center and minimum at the corners.
Test: Vertical Stress Distribution - Question 4

Westergaard’s theory is more suitable for

Detailed Solution for Test: Vertical Stress Distribution - Question 4
• Westergaard’s Theory Assumptions: Elastic medium of semi-infinite extent but containing numerous, closely spaced horizontal sheets of a negligible thickness of an infinite rigid material which permits only downward deformation as a whole without allowing it to undergo any lateral strain.
• Westergaard's assumptions are more close to the field reality, especially for over-consolidated and laminated sedimentary or stratified soils, which exhibit marked anisotropy.
• Based on this criterion of no lateral displacement, Westergaard derived the following equation for a point load, Q, at a depth z from the surface:

Westergaard’s analysis for stress distribution beneath loaded areas is more suitable to stratified or layered soils.
Test: Vertical Stress Distribution - Question 5

Westergaard’s theory is applicable for which type of soil?

Detailed Solution for Test: Vertical Stress Distribution - Question 5

Westergaard’s Theory Assumptions:

Elastic medium of semi-infinite extent but containing numerous, closely spaced horizontal sheets of a negligible thickness of an infinite rigid material which permits only downward deformation as a whole without allowing it to undergo any lateral strain.
Westergaard's assumptions are more close to the field reality, especially for over-consolidated and laminated sedimentary or stratified soils, which exhibit marked anisotropy.
Based on this criterion of no lateral displacement, Westergaard derived the following equation for a point load, Q, at a depth z from the surface:

∴ Westergaard’s analysis for stress distribution beneath loaded areas is applicable to stratified soils.

Test: Vertical Stress Distribution - Question 6

For a vertical concentrated load acting on the surface of a semi-infinite elastic mass, the vertical normal stress at a depth z is proportional to:

Detailed Solution for Test: Vertical Stress Distribution - Question 6

Concept:
Boussinesq Equation:

Test: Vertical Stress Distribution - Question 7

A concentrated load of 2000 kN is applied at the ground surface. What is the vertical stress at a point 6 m directly below the load ?

Detailed Solution for Test: Vertical Stress Distribution - Question 7

Concept:
Boussinesq’s equation for vertical stress

Where,
σZ = vertical stress in kN/m2
Q = concentrated load in kN
Z = point below the ground level where stress has to be calculated
when we need to calculate the vertical stress exactly below the concentrated point load then,
i.e. r = 0

Calculation:
Given, Z = 6 m
Q = 2000 kN
We have to calculate the vertical stress exactly below the point load,
∴ r = 0

Test: Vertical Stress Distribution - Question 8

In the case of stratified soil layers, the best equation that can be adopted for computing the pressure distribution is

Detailed Solution for Test: Vertical Stress Distribution - Question 8

Westergaard’s Theory Assumptions:
Elastic medium of semi-infinite extent but containing numerous, closely spaced horizontal sheets of a negligible thickness of an infinite rigid material which permits only downward deformation as a whole without allowing it to undergo any lateral strain.
Note:
Westergaard's assumptions are more close to the field reality, especially for over-consolidated and laminated sedimentary or stratified soils, which exhibit marked anisotropy.
Based on this criterion of no lateral displacement, Westergaard derived the following equation for a point load, Q, at a depth z from the surface:

∴ Westergaard’s analysis for stress distribution beneath loaded areas is applicable to stratified soils.

Test: Vertical Stress Distribution - Question 9

If the saturated density of a given soil is 2.1 t/m2, then the total stress (T in  t/m2) and the effective stress (E in  t/m2) of a saturated soil stratum at depth of 4 m will be

Detailed Solution for Test: Vertical Stress Distribution - Question 9

Concept:
Total stress and effective stress can be given as,
Total stress(T) = γsat × Z
Effective stress(E) = γsub × Z
γsub = γsat − γw

Calculation:
γsat = 2.1t/m2
γw = 1t/m2
γsub = 2.1 − 1 = 1.1t/m2
T = 2.1 x 4 = 8.4
E = 1.1 x 4 = 4.4

Test: Vertical Stress Distribution - Question 10

A point load exerts a maximum vertical stress at a radial distance of 1 m and at a depth of :

Detailed Solution for Test: Vertical Stress Distribution - Question 10

Concept:
Vertical pressure distribution on the vertical line:

• The figure above shows the variation of vertical stress distribution on a vertical line at a distance r from the axis of loading.
• The vertical stress first increases, then attains a maximum value, and then decreases.
• It can be shown, that the maximum value of σZ on a vertical line is obtained at the point of intersection of the vertical plane with the radial line at β = 13° 15' through the point load, as shown in the figure.

When r = 1 m, we get
Z = 1/0.817 = 1.225
And corresponding to this Z value, the maximum σz will be

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