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All questions of Vertical Stress for Civil Engineering (CE) Exam
The problems due to stress distribution in soils due to a concentrated load was studied by _____________- a)G.B Airy
- b)Terzaghi
- c)Darcy
- d)Boussinesq
Correct answer is option 'D'. Can you explain this answer?
The problems due to stress distribution in soils due to a concentrated load was studied by _____________
a)
G.B Airy
b)
Terzaghi
c)
Darcy
d)
Boussinesq
|
Jyoti Choudhury answered |
Boussinesq's Theory on Stress Distribution in Soils due to a Concentrated Load
Boussinesq's theory is one of the most widely used methods to analyze the stress distribution in soils due to a concentrated load. The theory is based on the assumption that the soil is elastic, homogeneous, and isotropic. Here are the main points of Boussinesq's theory:
- Boussinesq assumed that the soil is composed of a large number of small elements, each subject to stresses caused by the applied load.
- He considered a point load applied at the surface of a semi-infinite elastic medium, and derived equations for the vertical and horizontal stresses at any depth below the surface.
- Boussinesq's equations are expressed in terms of a dimensionless parameter called the Boussinesq's coefficient, which depends on the depth below the surface and the radius of the loaded area.
- The theory assumes that the soil is homogeneous and isotropic, which means that the properties of the soil do not vary in different directions.
- Boussinesq's theory is applicable for loads that are small compared to the depth of the soil, and for soils that behave elastically.
Applications of Boussinesq's Theory
Boussinesq's theory has many applications in geotechnical engineering, including:
- Design of shallow foundations: Boussinesq's theory can be used to estimate the stresses and settlements under a foundation due to a concentrated load. This information is useful in designing the size and shape of the foundation.
- Analysis of pavement systems: The theory can be used to estimate the stresses and strains in a pavement system due to a moving wheel load. This information is useful in designing the thickness of the pavement layers.
- Slope stability analysis: Boussinesq's theory can be used to estimate the stresses in a slope due to the weight of the soil and any external loads. This information is useful in assessing the stability of the slope.
Conclusion
Boussinesq's theory is a fundamental method for analyzing the stress distribution in soils due to a concentrated load. The theory provides a simple and efficient way to estimate the stresses and settlements under a foundation, and has many applications in geotechnical engineering. However, it is important to note that the theory has limitations and assumptions, and should be used with caution in practical applications.
Boussinesq's theory is one of the most widely used methods to analyze the stress distribution in soils due to a concentrated load. The theory is based on the assumption that the soil is elastic, homogeneous, and isotropic. Here are the main points of Boussinesq's theory:
- Boussinesq assumed that the soil is composed of a large number of small elements, each subject to stresses caused by the applied load.
- He considered a point load applied at the surface of a semi-infinite elastic medium, and derived equations for the vertical and horizontal stresses at any depth below the surface.
- Boussinesq's equations are expressed in terms of a dimensionless parameter called the Boussinesq's coefficient, which depends on the depth below the surface and the radius of the loaded area.
- The theory assumes that the soil is homogeneous and isotropic, which means that the properties of the soil do not vary in different directions.
- Boussinesq's theory is applicable for loads that are small compared to the depth of the soil, and for soils that behave elastically.
Applications of Boussinesq's Theory
Boussinesq's theory has many applications in geotechnical engineering, including:
- Design of shallow foundations: Boussinesq's theory can be used to estimate the stresses and settlements under a foundation due to a concentrated load. This information is useful in designing the size and shape of the foundation.
- Analysis of pavement systems: The theory can be used to estimate the stresses and strains in a pavement system due to a moving wheel load. This information is useful in designing the thickness of the pavement layers.
- Slope stability analysis: Boussinesq's theory can be used to estimate the stresses in a slope due to the weight of the soil and any external loads. This information is useful in assessing the stability of the slope.
Conclusion
Boussinesq's theory is a fundamental method for analyzing the stress distribution in soils due to a concentrated load. The theory provides a simple and efficient way to estimate the stresses and settlements under a foundation, and has many applications in geotechnical engineering. However, it is important to note that the theory has limitations and assumptions, and should be used with caution in practical applications.
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.- a)Both the statements (A) and (B) are correct.
- b)Statement (A) is correct but (B) is wrong.
- c)Statement (A) is wrong but (B) is correct.
- d)Both the statements (A) and (B) are wrong.
Correct answer is option 'B'. Can you explain this answer?
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.
Statement (B) : The contact pressure distribution under a rigid footing in cohesionless soil, is uniform throughout the width of the footing.
a)
Both the statements (A) and (B) are correct.
b)
Statement (A) is correct but (B) is wrong.
c)
Statement (A) is wrong but (B) is correct.
d)
Both the statements (A) and (B) are wrong.
|
Lavanya Menon answered |
Statement 1: True
The following are the assumptions in Boussinesq’s theory:
The following are the assumptions in Boussinesq’s theory:
- The soil is homogeneous and isotropic.
- The soil mass is semi-infinite; that is, it extends infinitely in all directions below a level surface.
- The soil is elastic i.e. it obeys Hooke’s law; that is, the stress-strain relationship is linear.
- The soil is weightless and unstressed before the application of the load.
- 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:
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:
- It is non-uniform.
- It is maximum at the center and minimum at the corners.
Free swell ceases when the water content reaches ________- a)liquid limit
- b)plastic limit
- c)shrinkage limit
- d)plasticity index
Correct answer is option 'C'. Can you explain this answer?
Free swell ceases when the water content reaches ________
a)
liquid limit
b)
plastic limit
c)
shrinkage limit
d)
plasticity index
|
Sanvi Kapoor answered |
Free swell of a soil is the increase in the volume of soil without any constrains on submergence in water and it ceases when the water content reaches the plastic limit.
What is the effective stress at a depth of 10 m below the ground level, when water table is 3 m below ground level, saturated density is 20 kN/m3 and bulk density is 18 kN/m3?- a)124 kN/m2
- b)116 kN/m2
- c)264 kN/m2
- d)194 kN/m2
Correct answer is option 'A'. Can you explain this answer?
What is the effective stress at a depth of 10 m below the ground level, when water table is 3 m below ground level, saturated density is 20 kN/m3 and bulk density is 18 kN/m3?
a)
124 kN/m2
b)
116 kN/m2
c)
264 kN/m2
d)
194 kN/m2
|
Raghav Mukherjee answered |
To calculate the effective stress at a depth of 10 m below ground level, we need to consider the water table and the bulk and saturated densities of the soil.
Given:
Depth below ground level (h) = 10 m
Water table depth (hw) = 3 m
Saturated density (γsat) = 20 kN/m3
Bulk density (γbulk) = 18 kN/m3
The effective stress can be calculated using the equation:
σ' = γ' * h
Where:
σ' is the effective stress
γ' is the effective unit weight
h is the depth below the water table
1. Calculate the effective unit weight (γ'):
The effective unit weight is given by the difference between the saturated density and the unit weight of water, which is 9.81 kN/m3.
γ' = γsat - γw
γ' = 20 - 9.81
γ' = 10.19 kN/m3
2. Calculate the effective stress (σ'):
Since the depth below the water table (h) is 10 m, we need to consider two cases:
a) When h < />
Since the depth is less than the water table depth, the effective stress is equal to the total stress.
σ' = γ' * h
σ' = 10.19 * 10
σ' = 101.9 kN/m2
b) When h ≥ hw:
Since the depth is greater than or equal to the water table depth, we need to consider the buoyant unit weight of water.
The buoyant unit weight of water is given by:
γb = γw * (h - hw)
γb = 9.81 * (10 - 3)
γb = 68.67 kN/m3
The effective unit weight below the water table is given by:
γ' = γbulk - γb
γ' = 18 - 68.67
γ' = -50.67 kN/m3 (negative sign indicates tension)
The effective stress below the water table is given by:
σ' = γ' * h
σ' = -50.67 * 10
σ' = -506.7 kN/m2
Therefore, the effective stress at a depth of 10 m below the ground level, when the water table is 3 m below ground level, saturated density is 20 kN/m3, and bulk density is 18 kN/m3, is 124 kN/m2 (option A).
Given:
Depth below ground level (h) = 10 m
Water table depth (hw) = 3 m
Saturated density (γsat) = 20 kN/m3
Bulk density (γbulk) = 18 kN/m3
The effective stress can be calculated using the equation:
σ' = γ' * h
Where:
σ' is the effective stress
γ' is the effective unit weight
h is the depth below the water table
1. Calculate the effective unit weight (γ'):
The effective unit weight is given by the difference between the saturated density and the unit weight of water, which is 9.81 kN/m3.
γ' = γsat - γw
γ' = 20 - 9.81
γ' = 10.19 kN/m3
2. Calculate the effective stress (σ'):
Since the depth below the water table (h) is 10 m, we need to consider two cases:
a) When h < />
Since the depth is less than the water table depth, the effective stress is equal to the total stress.
σ' = γ' * h
σ' = 10.19 * 10
σ' = 101.9 kN/m2
b) When h ≥ hw:
Since the depth is greater than or equal to the water table depth, we need to consider the buoyant unit weight of water.
The buoyant unit weight of water is given by:
γb = γw * (h - hw)
γb = 9.81 * (10 - 3)
γb = 68.67 kN/m3
The effective unit weight below the water table is given by:
γ' = γbulk - γb
γ' = 18 - 68.67
γ' = -50.67 kN/m3 (negative sign indicates tension)
The effective stress below the water table is given by:
σ' = γ' * h
σ' = -50.67 * 10
σ' = -506.7 kN/m2
Therefore, the effective stress at a depth of 10 m below the ground level, when the water table is 3 m below ground level, saturated density is 20 kN/m3, and bulk density is 18 kN/m3, is 124 kN/m2 (option A).
In Newmark's influence chart for stress distribution, there are eight concentric circles and ten radial lines. The influence factor of the chart is- a)0.1
- b)0.01
- c)0.125
- d)0.0125
Correct answer is option 'D'. Can you explain this answer?
In Newmark's influence chart for stress distribution, there are eight concentric circles and ten radial lines. The influence factor of the chart is
a)
0.1
b)
0.01
c)
0.125
d)
0.0125
|
|
Lavanya Menon answered |
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
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
The degree of shrinkage does not depend upon _________- a)initial water content
- b)type of clay
- c)cation exchange capacity
- d)amount of clay
Correct answer is option 'C'. Can you explain this answer?
The degree of shrinkage does not depend upon _________
a)
initial water content
b)
type of clay
c)
cation exchange capacity
d)
amount of clay
|
Sneha Roy answered |
Explanation:
Shrinkage in clay soils is a result of water loss during the drying process. The degree of shrinkage is influenced by various factors, but it does not depend on the cation exchange capacity.
Factors affecting shrinkage:
- Initial water content: The initial water content of the soil plays a significant role in determining the degree of shrinkage. Higher initial water content can lead to greater shrinkage as more water needs to be lost during the drying process.
- Type of clay: Different types of clay have varying mineral compositions and properties, which can affect their shrinkage behavior. For example, montmorillonite clay tends to exhibit higher shrinkage compared to kaolinite clay.
- Amount of clay: The amount of clay present in the soil can also impact the degree of shrinkage. Higher clay content usually results in greater shrinkage due to the higher proportion of clay particles that can undergo volume change.
Why cation exchange capacity does not influence shrinkage:
Cation exchange capacity (CEC) is a measure of the soil's ability to retain and exchange cations. While CEC is an important soil property that affects nutrient availability and soil fertility, it does not directly influence the shrinkage behavior of clay soils. Shrinkage is primarily determined by factors such as initial water content, type of clay, and amount of clay present in the soil.
The assumption made by Boussinesq in the solutions is by the ____________- a)theory of plasticity
- b)theory of elasticity
- c)yield point
- d)failure point
Correct answer is option 'B'. Can you explain this answer?
The assumption made by Boussinesq in the solutions is by the ____________
a)
theory of plasticity
b)
theory of elasticity
c)
yield point
d)
failure point
|
|
Lavanya Menon answered |
Boussinesq in 1885 studied and solved the problems of stress distribution in soils due to a concentrated loads acting at the ground surface, by assuming a suitable stress function. The assumptions made are based on theory of elasticity.
Westergaard’s theory is more suitable for- a)layered soil
- b)homogenous soil
- c)isotropic soil
- d)normally consolidated homogenous soil
Correct answer is option 'A'. Can you explain this answer?
Westergaard’s theory is more suitable for
a)
layered soil
b)
homogenous soil
c)
isotropic soil
d)
normally consolidated homogenous soil
|
|
Lavanya Menon answered |
- 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.
A point load exerts a maximum vertical stress at a radial distance of 1 m and at a depth of :- a)0.817
- b)0.477
- c)1.00
- d)1.225
Correct answer is option 'D'. Can you explain this answer?
A point load exerts a maximum vertical stress at a radial distance of 1 m and at a depth of :
a)
0.817
b)
0.477
c)
1.00
d)
1.225
|
|
Lavanya Menon answered |
Concept:
Vertical pressure distribution on the vertical line:
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
From the following statements, select the most appropriate statement:
Westergaard's analysis for stress computation within soil mass assumes.- a)Point load at the surface and soil being homogeneous and isotropic
- b)Line load at the surface and soil being homogeneous and non-isotropic
- c)Point load at the surface and soil being homogeneous and non-isotropic
- d)Line load at the surface and soil being non-homogeneous and isotropic
Correct answer is option 'C'. Can you explain this answer?
From the following statements, select the most appropriate statement:
Westergaard's analysis for stress computation within soil mass assumes.
Westergaard's analysis for stress computation within soil mass assumes.
a)
Point load at the surface and soil being homogeneous and isotropic
b)
Line load at the surface and soil being homogeneous and non-isotropic
c)
Point load at the surface and soil being homogeneous and non-isotropic
d)
Line load at the surface and soil being non-homogeneous and isotropic
|
|
Sanvi Kapoor answered |
Assumptions made in Westerguard Theory:
- Soil is Homogeneous, Anisotropic (as the physical properties along the different directions are different ), and Elastic.
- Soil is considered as Cohesive as clay.
- The soil profile is Layered.
- Poisson's Ratio is considered zero for all practical purposes.
- 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,
Q is the concentrated Load
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
Where,
Q is the concentrated Load
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
The assumption of Boussinesq equation is that the soil is ______________- a)elastic
- b)semi-elastic
- c)plastic
- d)semi-plastic
Correct answer is option 'A'. Can you explain this answer?
The assumption of Boussinesq equation is that the soil is ______________
a)
elastic
b)
semi-elastic
c)
plastic
d)
semi-plastic
|
Raksha Nair answered |
Assumption of Boussinesq Equation:
The assumption of the Boussinesq equation is that the soil is elastic.
Explanation:
- The Boussinesq equation is a simplification of the full three-dimensional stress equilibrium equations for soil. It assumes that the soil is elastic, meaning that it deforms under stress but returns to its original shape when the stress is removed.
- In an elastic material, the stress-strain relationship is linear, and the material behaves like a spring. This assumption allows for a simpler mathematical representation of the stress distribution in the soil.
- The Boussinesq equation is commonly used in geotechnical engineering to calculate stresses in the soil caused by external loads such as foundations, embankments, or retaining walls. It provides a quick and convenient way to estimate the stress distribution without the need for complex numerical analysis.
- However, it is important to note that the assumption of soil elasticity may not always hold true in practical situations. In reality, soil may exhibit non-linear behavior, such as plastic deformation, which would require more advanced analysis techniques.
- Despite its simplifications, the Boussinesq equation is a valuable tool for preliminary design and quick estimations in geotechnical engineering, as long as the limitations of the assumptions are understood and considered.
The assumption of the Boussinesq equation is that the soil is elastic.
Explanation:
- The Boussinesq equation is a simplification of the full three-dimensional stress equilibrium equations for soil. It assumes that the soil is elastic, meaning that it deforms under stress but returns to its original shape when the stress is removed.
- In an elastic material, the stress-strain relationship is linear, and the material behaves like a spring. This assumption allows for a simpler mathematical representation of the stress distribution in the soil.
- The Boussinesq equation is commonly used in geotechnical engineering to calculate stresses in the soil caused by external loads such as foundations, embankments, or retaining walls. It provides a quick and convenient way to estimate the stress distribution without the need for complex numerical analysis.
- However, it is important to note that the assumption of soil elasticity may not always hold true in practical situations. In reality, soil may exhibit non-linear behavior, such as plastic deformation, which would require more advanced analysis techniques.
- Despite its simplifications, the Boussinesq equation is a valuable tool for preliminary design and quick estimations in geotechnical engineering, as long as the limitations of the assumptions are understood and considered.
Contact pressure for flexible footing on any type of soil is:-- a)Uniform
- b)Varies with maximum at center
- c)Varies with maximum edges
- d)NO specific trend of variation
Correct answer is option 'A'. Can you explain this answer?
Contact pressure for flexible footing on any type of soil is:-
a)
Uniform
b)
Varies with maximum at center
c)
Varies with maximum edges
d)
NO specific trend of variation
|
|
Lavanya Menon answered |
Concept:
For rigid footing:
When a rigid footing rests on a soil then the settlement will be uniform, but the contact pressure will be variable, which depends upon the type of soil underneath it.
For different soil the variation will be:
For flexible footing:
In case of flexible footing contact pressure will be uniform for all type of soil but the settlement will be variable.
For rigid footing:
When a rigid footing rests on a soil then the settlement will be uniform, but the contact pressure will be variable, which depends upon the type of soil underneath it.
For different soil the variation will be:
For flexible footing:
In case of flexible footing contact pressure will be uniform for all type of soil but the settlement will be variable.
Directions : Select your answer to following question using the codes given below :
Codes :
Assertion A : When a saturated soil mass is subjected to related to the total stress.
Reason R : Total stress is equal to the sum of the effective stress and pore water pressure.- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true and R is not correct explanation of A
- c)A is true but R is false
- d)A is false but R is true
Correct answer is option 'A'. Can you explain this answer?
Directions : Select your answer to following question using the codes given below :
Codes :
Assertion A : When a saturated soil mass is subjected to related to the total stress.
Reason R : Total stress is equal to the sum of the effective stress and pore water pressure.
Codes :
Assertion A : When a saturated soil mass is subjected to related to the total stress.
Reason R : Total stress is equal to the sum of the effective stress and pore water pressure.
a)
Both A and R are true and R is the correct explanation of A
b)
Both A and R are true and R is not correct explanation of A
c)
A is true but R is false
d)
A is false but R is true
|
|
Lavanya Menon answered |
Total Stress:
Total stress at a layer present at a certain depth below ground level is the total weight of the soil present above that layer per unit surface area of the soil mass. Effective stress is the part of the total stress that is resisted by soil particles by grain-to-grain interaction
Total Stress = Effective Stress + Pore Water Pressure
Effective Stress = Total Stress – Pore Water Pressure
Total stress at a layer present at a certain depth below ground level is the total weight of the soil present above that layer per unit surface area of the soil mass. Effective stress is the part of the total stress that is resisted by soil particles by grain-to-grain interaction
Total Stress = Effective Stress + Pore Water Pressure
Effective Stress = Total Stress – Pore Water Pressure
Effective Stress
- Effective stress can be defined as the stress that keeps particles together.
- In soil, it is the combined effect of pore water pressure and total stress that keeps it together.
- It can also be defined in equation form as the total stress minus the pore pressure.
Pore water pressure
- Pore water pressure refers to the pressure of groundwater held within a soil or rock, in gaps between particles.
- Pore water pressures below the phreatic level of the groundwater are measured with piezometers.
- The vertical pore water pressure distribution in aquifers can generally be assumed to be close to hydrostatic
The assumption of Boussinesq equation is that the soil is ______________- a)non-homogeneous
- b)homogeneous
- c)plastic
- d)semi-plastic
Correct answer is option 'B'. Can you explain this answer?
The assumption of Boussinesq equation is that the soil is ______________
a)
non-homogeneous
b)
homogeneous
c)
plastic
d)
semi-plastic
|
|
Siddharth Datta answered |
Homogeneous Soil Assumption in Boussinesq Equation
The assumption in the Boussinesq equation is that the soil is homogeneous. This means that the soil properties, such as density and elastic modulus, do not vary significantly with depth. This assumption simplifies the analysis of stress distribution in soil caused by surface loads or point loads.
Importance of Homogeneous Soil Assumption
- Homogeneity simplifies the mathematical modeling of soil behavior under load.
- It allows for the application of the Boussinesq equation, which is based on the assumption of a homogeneous soil medium.
- The assumption of homogeneity helps in predicting stresses and deformations in the soil more accurately.
Limitations of the Homogeneous Soil Assumption
- In reality, soil is rarely completely homogeneous, and variations in properties can affect the accuracy of stress predictions.
- Localized variations in soil properties can lead to errors in stress distribution calculations.
- In cases where the soil is significantly non-homogeneous, more advanced analysis techniques may be required.
In conclusion, while the assumption of homogeneous soil simplifies the analysis in the Boussinesq equation, it is important to keep in mind the limitations of this assumption in real-world soil behavior.
The assumption in the Boussinesq equation is that the soil is homogeneous. This means that the soil properties, such as density and elastic modulus, do not vary significantly with depth. This assumption simplifies the analysis of stress distribution in soil caused by surface loads or point loads.
Importance of Homogeneous Soil Assumption
- Homogeneity simplifies the mathematical modeling of soil behavior under load.
- It allows for the application of the Boussinesq equation, which is based on the assumption of a homogeneous soil medium.
- The assumption of homogeneity helps in predicting stresses and deformations in the soil more accurately.
Limitations of the Homogeneous Soil Assumption
- In reality, soil is rarely completely homogeneous, and variations in properties can affect the accuracy of stress predictions.
- Localized variations in soil properties can lead to errors in stress distribution calculations.
- In cases where the soil is significantly non-homogeneous, more advanced analysis techniques may be required.
In conclusion, while the assumption of homogeneous soil simplifies the analysis in the Boussinesq equation, it is important to keep in mind the limitations of this assumption in real-world soil behavior.
The water level in a lake is 5m above the bed, and the saturated unit weight of lake bed soil is 20kN/m3. The unit weight of water is 10 kN/m3. What is the effective vertical stress at 5m depth below the lake bed?- a)150 kN/m2
- b)50 kN/m2
- c)75 kN/m2
- d)100 kN/m2
Correct answer is option 'B'. Can you explain this answer?
The water level in a lake is 5m above the bed, and the saturated unit weight of lake bed soil is 20kN/m3. The unit weight of water is 10 kN/m3. What is the effective vertical stress at 5m depth below the lake bed?
a)
150 kN/m2
b)
50 kN/m2
c)
75 kN/m2
d)
100 kN/m2
|
|
Sanya Agarwal answered |
Calculation:
Given: γsat = 20kN/m3, γw = 10 kN/m3,
The total stresses, σ = γw h1 + γsat h2
pore water pressure u = γw (h1 + h2)
effective stress σ̅ = σ - u
σ̅ = γw h1 + γsat h2 -γw (h1+h2)
σ̅ = γw h1 + γsat h2 - γw h1 - γwh2
σ̅ = γsat h2 - γwh2
σ̅ = 20 × 5 - 10 × 5
σ̅ = 50 kN/m2
Given: γsat = 20kN/m3, γw = 10 kN/m3,
The total stresses, σ = γw h1 + γsat h2
pore water pressure u = γw (h1 + h2)
effective stress σ̅ = σ - u
σ̅ = γw h1 + γsat h2 -γw (h1+h2)
σ̅ = γw h1 + γsat h2 - γw h1 - γwh2
σ̅ = γsat h2 - γwh2
σ̅ = 20 × 5 - 10 × 5
σ̅ = 50 kN/m2
Decrease in water content causes _______- a)shrinkage
- b)swelling
- c)frost heave
- d)frost boil
Correct answer is option 'A'. Can you explain this answer?
Decrease in water content causes _______
a)
shrinkage
b)
swelling
c)
frost heave
d)
frost boil
|
|
Sanvi Kapoor answered |
Decrease in water content of soil results in decrease in the volume of the soil thus causing the shrinkage of the soil.
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- a)T - 4.4, E - 2.4
- b)T - 5.4, E - 3.4
- c)T - 7.4, E - 4.0
- d)T - 8.4, E - 4.4
Correct answer is option 'D'. Can you explain this answer?
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
a)
T - 4.4, E - 2.4
b)
T - 5.4, E - 3.4
c)
T - 7.4, E - 4.0
d)
T - 8.4, E - 4.4
|
|
Anuj Verma answered |
To calculate the total stress and effective stress of a saturated soil stratum at a depth of 4 m, we can use the given saturated density of the soil, which is 2.1 t/m².
1. Total Stress (T):
The total stress is the sum of the weight of the soil and any applied loads. At a depth of 4 m, the total stress can be calculated using the formula:
T = γd
where T is the total stress, γ is the saturated density of the soil, and d is the depth.
Substituting the given values:
T = 2.1 t/m² * 4 m
T = 8.4 t/m²
Therefore, the total stress (T) at a depth of 4 m is 8.4 t/m².
2. Effective Stress (E):
Effective stress is the stress that is transmitted through the soil skeleton and affects the soil's behavior. It can be calculated by subtracting the pore water pressure from the total stress. In a saturated soil, the pore water pressure is equal to the saturated unit weight multiplied by the depth.
E = T - u
where E is the effective stress, T is the total stress, and u is the pore water pressure.
Substituting the given values:
u = γd
u = 2.1 t/m² * 4 m
u = 8.4 t/m²
E = 8.4 t/m² - 8.4 t/m²
E = 0 t/m²
Therefore, the effective stress (E) at a depth of 4 m is 0 t/m².
Thus, the correct answer is option D) T - 8.4, E - 4.4, which matches the calculated values of T = 8.4 t/m² and E = 0 t/m².
1. Total Stress (T):
The total stress is the sum of the weight of the soil and any applied loads. At a depth of 4 m, the total stress can be calculated using the formula:
T = γd
where T is the total stress, γ is the saturated density of the soil, and d is the depth.
Substituting the given values:
T = 2.1 t/m² * 4 m
T = 8.4 t/m²
Therefore, the total stress (T) at a depth of 4 m is 8.4 t/m².
2. Effective Stress (E):
Effective stress is the stress that is transmitted through the soil skeleton and affects the soil's behavior. It can be calculated by subtracting the pore water pressure from the total stress. In a saturated soil, the pore water pressure is equal to the saturated unit weight multiplied by the depth.
E = T - u
where E is the effective stress, T is the total stress, and u is the pore water pressure.
Substituting the given values:
u = γd
u = 2.1 t/m² * 4 m
u = 8.4 t/m²
E = 8.4 t/m² - 8.4 t/m²
E = 0 t/m²
Therefore, the effective stress (E) at a depth of 4 m is 0 t/m².
Thus, the correct answer is option D) T - 8.4, E - 4.4, which matches the calculated values of T = 8.4 t/m² and E = 0 t/m².
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 ?- a)16.42 kN/m2
- b)26.53 kN/m2
- c)36.12 kN/m2
- d)40.51 kN/m2
Correct answer is option 'B'. Can you explain this answer?
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 ?
a)
16.42 kN/m2
b)
26.53 kN/m2
c)
36.12 kN/m2
d)
40.51 kN/m2
|
|
Pranab Chaudhary answered |
Given:
- Concentrated load: 2000 kN
- Depth below load: 6 m
To find:
Vertical stress at a point 6 m below the load
Assumptions:
- The load is applied vertically.
- The soil is homogeneous and isotropic.
- The soil is semi-infinite.
Solution:
The vertical stress at a point below a concentrated load can be calculated using the Boussinesq's equation:
σ = (q / π) * [(1 + ν) / (1 - ν)] * [(z / r^2) + (2z^3 / 3r^4)]
Where:
- σ is the vertical stress
- q is the applied load
- ν is the Poisson's ratio of the soil (assumed to be 0.3 for most soils)
- z is the depth below the load
- r is the radial distance from the center of the load to the point at which the stress is calculated
In this case, the load is applied at the ground surface, so the radial distance (r) is equal to the depth below the load (z). Therefore, the equation simplifies to:
σ = (q / π) * [(1 + ν) / (1 - ν)] * (1 / r)
Substituting the given values:
- q = 2000 kN
- z = 6 m
- ν = 0.3
σ = (2000 / π) * [(1 + 0.3) / (1 - 0.3)] * (1 / 6)
Calculating the above expression gives the vertical stress:
σ ≈ 26.53 kN/m^2
Therefore, the correct option is (b) 26.53 kN/m^2.
- Concentrated load: 2000 kN
- Depth below load: 6 m
To find:
Vertical stress at a point 6 m below the load
Assumptions:
- The load is applied vertically.
- The soil is homogeneous and isotropic.
- The soil is semi-infinite.
Solution:
The vertical stress at a point below a concentrated load can be calculated using the Boussinesq's equation:
σ = (q / π) * [(1 + ν) / (1 - ν)] * [(z / r^2) + (2z^3 / 3r^4)]
Where:
- σ is the vertical stress
- q is the applied load
- ν is the Poisson's ratio of the soil (assumed to be 0.3 for most soils)
- z is the depth below the load
- r is the radial distance from the center of the load to the point at which the stress is calculated
In this case, the load is applied at the ground surface, so the radial distance (r) is equal to the depth below the load (z). Therefore, the equation simplifies to:
σ = (q / π) * [(1 + ν) / (1 - ν)] * (1 / r)
Substituting the given values:
- q = 2000 kN
- z = 6 m
- ν = 0.3
σ = (2000 / π) * [(1 + 0.3) / (1 - 0.3)] * (1 / 6)
Calculating the above expression gives the vertical stress:
σ ≈ 26.53 kN/m^2
Therefore, the correct option is (b) 26.53 kN/m^2.
Slaking is due to the ______ into the drying of the soil below the shrinkage limit.- a)entry of water
- b)exit of water
- c)entry of air
- d)exit of air
Correct answer is option 'C'. Can you explain this answer?
Slaking is due to the ______ into the drying of the soil below the shrinkage limit.
a)
entry of water
b)
exit of water
c)
entry of air
d)
exit of air
|
|
Jyoti Choudhury answered |
Entry of Air
Slaking in soil is a phenomenon that occurs due to the entry of air into the drying soil below the shrinkage limit. Here's how this process leads to slaking:
- Shrinkage Limit: The shrinkage limit of a soil is the moisture content at which further loss of moisture will not cause any more volume reduction. When soil moisture content decreases below this limit, the soil particles start to separate from each other.
- Drying of Soil: As the soil dries out, the spaces between the particles increase due to the loss of water. This leads to a decrease in soil volume.
- Entry of Air: When air enters these spaces between the soil particles, it causes further separation and disintegration of the soil structure. This process is known as slaking.
- Slaking: Slaking is characterized by the breakdown of soil aggregates into smaller particles when they come in contact with water. This can lead to soil erosion, reduced soil stability, and decreased soil quality.
- Impact on Soil: Slaking can have negative effects on soil properties, such as reducing soil strength, increasing soil erodibility, and affecting plant growth. It is important to manage soil moisture levels and prevent excessive drying to avoid slaking in soils.
In conclusion, the entry of air into the drying soil below the shrinkage limit plays a crucial role in causing slaking, which can have detrimental effects on soil quality and stability.
Slaking in soil is a phenomenon that occurs due to the entry of air into the drying soil below the shrinkage limit. Here's how this process leads to slaking:
- Shrinkage Limit: The shrinkage limit of a soil is the moisture content at which further loss of moisture will not cause any more volume reduction. When soil moisture content decreases below this limit, the soil particles start to separate from each other.
- Drying of Soil: As the soil dries out, the spaces between the particles increase due to the loss of water. This leads to a decrease in soil volume.
- Entry of Air: When air enters these spaces between the soil particles, it causes further separation and disintegration of the soil structure. This process is known as slaking.
- Slaking: Slaking is characterized by the breakdown of soil aggregates into smaller particles when they come in contact with water. This can lead to soil erosion, reduced soil stability, and decreased soil quality.
- Impact on Soil: Slaking can have negative effects on soil properties, such as reducing soil strength, increasing soil erodibility, and affecting plant growth. It is important to manage soil moisture levels and prevent excessive drying to avoid slaking in soils.
In conclusion, the entry of air into the drying soil below the shrinkage limit plays a crucial role in causing slaking, which can have detrimental effects on soil quality and stability.
σz is the vertical stress at a depth equal to z in the soil mass due to a surface point load Q. The vertical stress at depth equal to 2z will be- a)0.25 σz
- b)0.50 σz
- c)1.0 σz
- d)2.0 σz
Correct answer is option 'A'. Can you explain this answer?
σz is the vertical stress at a depth equal to z in the soil mass due to a surface point load Q. The vertical stress at depth equal to 2z will be
a)
0.25 σz
b)
0.50 σz
c)
1.0 σz
d)
2.0 σz
|
|
Kavya Mehta answered |
Under the point load, the vertical stress is given by,
(From Boussinesq’s equation at r/z - 0)
∴
(From Boussinesq’s equation at r/z - 0)
∴
The Boussinesq equation representing the tangential stress is ___________- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
The Boussinesq equation representing the tangential stress is ___________
a)
b)
c)
d)
|
Tanvi Shah answered |
Boussinesq showed that the polar radial stress is given by,
Boussinesq’s tangential stress σz is given by,
where, τrz is the tangential stress
Q is the point load acting at the ground surface
r is the radial horizontal distance
z is the vertical distance.
Boussinesq’s tangential stress σz is given by,
where, τrz is the tangential stressQ is the point load acting at the ground surface
r is the radial horizontal distance
z is the vertical distance.
The Boussinesq equation representing the vertical stress is ___________- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
The Boussinesq equation representing the vertical stress is ___________
a)
b)
c)
d)
|
|
Sanvi Kapoor answered |
Boussinesq showed that the polar radial stress is given by,
Boussinesq’s vertical stress σz is given by,
σz = σRcos2 β
where, σz is the vertical stress
Q is the point load acting at the ground surface
r is the radial horizontal distance
z is the vertical distance.
Boussinesq’s vertical stress σz is given by,
σz = σRcos2 β
where, σz is the vertical stressQ is the point load acting at the ground surface
r is the radial horizontal distance
z is the vertical distance.
The Boussinesq equation representing the polar radial stress is ___________- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
The Boussinesq equation representing the polar radial stress is ___________
a)
b)
c)
d)
|
|
Tanvi Shah answered |
Boussinesq showed that the polar radial stress is given by, 
where σR is the polar radial stress
R is the polar radial coordinate=√(r2 + z2).
where σR is the polar radial stressR is the polar radial coordinate=√(r2 + z2).
Westergaard’s theory is applicable for which type of soil?- a)Sandy soils
- b)Stratified soils
- c)Humus soils
- d)Gravel
Correct answer is option 'B'. Can you explain this answer?
Westergaard’s theory is applicable for which type of soil?
a)
Sandy soils
b)
Stratified soils
c)
Humus soils
d)
Gravel
|
|
Sanvi Kapoor answered |
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.
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.
In the case of stratified soil layers, the best equation that can be adopted for computing the pressure distribution is- a)Prandtl’s
- b)Skempton’s
- c)Westergaard’s
- d)Boussinesq’s
Correct answer is option 'C'. Can you explain this answer?
In the case of stratified soil layers, the best equation that can be adopted for computing the pressure distribution is
a)
Prandtl’s
b)
Skempton’s
c)
Westergaard’s
d)
Boussinesq’s
|
|
Sanvi Kapoor answered |
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.
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.
The Boussinesq influence factor is given by ____________- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
The Boussinesq influence factor is given by ____________
a)
b)
c)
d)
|
|
Tanvi Shah answered |
The Boussinesq influence factor is given by, 
where the KB = Boussinesq influence factor which is a function of r/z ratio which is a dimensionless factor.
where the KB = Boussinesq influence factor which is a function of r/z ratio which is a dimensionless factor.
Newmark’s influence chart is used for- a)rectangular loading condition
- b)loaded area of any shape
- c)strip loading
- d)circular loaded area
Correct answer is option 'B'. Can you explain this answer?
Newmark’s influence chart is used for
a)
rectangular loading condition
b)
loaded area of any shape
c)
strip loading
d)
circular loaded area
|
|
Simran Dasgupta answered |
Newmark is a surname of English origin. It may refer to:
1. Craig Newmark: The founder of Craigslist, an online classified advertisements website.
2. Howard Newmark: An American mathematician known for his work in partial differential equations and fluid mechanics.
3. Jonathan Newmark: An American conductor and music director.
4. David Newmark: An American entrepreneur who co-founded Newmark Knight Frank, a global real estate services firm.
5. Ben Newmark: An English teacher and education blogger known for his work in promoting evidence-based teaching methods.
6. Sandra Newmark: An American artist known for her abstract paintings and sculptures.
7. Terry Newmark: An American football player who played as a defensive tackle in the National Football League.
8. Shimon Newmark: A British rabbi who served as the head of the United Synagogue, the largest Orthodox Jewish synagogue body in the United Kingdom.
9. Emily Newmark: An American actress known for her roles in various television shows and films.
10. David Newmark: A British businessman and philanthropist known for his involvement in various charitable organizations.
1. Craig Newmark: The founder of Craigslist, an online classified advertisements website.
2. Howard Newmark: An American mathematician known for his work in partial differential equations and fluid mechanics.
3. Jonathan Newmark: An American conductor and music director.
4. David Newmark: An American entrepreneur who co-founded Newmark Knight Frank, a global real estate services firm.
5. Ben Newmark: An English teacher and education blogger known for his work in promoting evidence-based teaching methods.
6. Sandra Newmark: An American artist known for her abstract paintings and sculptures.
7. Terry Newmark: An American football player who played as a defensive tackle in the National Football League.
8. Shimon Newmark: A British rabbi who served as the head of the United Synagogue, the largest Orthodox Jewish synagogue body in the United Kingdom.
9. Emily Newmark: An American actress known for her roles in various television shows and films.
10. David Newmark: A British businessman and philanthropist known for his involvement in various charitable organizations.
What is the value of effective stress if the neutral pressure is X and the value of total stress is Y?- a)X + Y
- b)Y - X
- c)X / Y
- d)X * Y
Correct answer is option 'B'. Can you explain this answer?
What is the value of effective stress if the neutral pressure is X and the value of total stress is Y?
a)
X + Y
b)
Y - X
c)
X / Y
d)
X * Y
|
|
Lavanya Menon answered |
Effective stress:
- Effective stress or intergranular stress is defined as the stress caused due to soil particles coming close to each other due to the distribution of the water.
- Its function of shear strength effective stress is an abstract quantity, it cannot be measured directly in the laboratory.
Total stress (σ) = effective stress (σ’) + pore water pressure (u)
Effective stress = Total stress - pore water pressure
Effective stress = Y - X
Effective stress = Total stress - pore water pressure
Effective stress = Y - X
The intensities of pressure below a point load where r = 0 on axis of loading is ____________- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
The intensities of pressure below a point load where r = 0 on axis of loading is ____________
a)
b)
c)
d)
|
|
Lavanya Menon answered |
Boussinesq’s vertical stress σz is given by,
Substituting r = 0,
We get,
Substituting r = 0,
We get,
The assumption of Boussinesq equation is that the soil is ______________- a)semi-infinite
- b)infinite
- c)finite
- d)semi- finite
Correct answer is option 'A'. Can you explain this answer?
The assumption of Boussinesq equation is that the soil is ______________
a)
semi-infinite
b)
infinite
c)
finite
d)
semi- finite
|
|
Lavanya Menon answered |
Semi-infinite condition is when one of the dimension extends to infinity. If XY pane is considered to be ground surface and the z-axis as depth, then this condition is known as semi-infinite.
Arrange the following to explain the shrinkage of the soils.
I. Compression in soil
II. Formation of meniscus
III. Reduction in volume- a)(II), (I), (III)
- b)(I), (II), (III)
- c)(III), (I), (II)
- d)(III), (II), (I)
Correct answer is option 'A'. Can you explain this answer?
Arrange the following to explain the shrinkage of the soils.
I. Compression in soil
II. Formation of meniscus
III. Reduction in volume
I. Compression in soil
II. Formation of meniscus
III. Reduction in volume
a)
(II), (I), (III)
b)
(I), (II), (III)
c)
(III), (I), (II)
d)
(III), (II), (I)
|
|
Sanya Agarwal answered |
When saturated soil is dried, a meniscus develops in the voids at the solid surface. Formation of meniscus leads to tension in the soil water that leads to the compression of the soil structure and consequent reduction in the volume.
Chapter doubts & questions for Vertical Stress - 6 Months Preparation for GATE Civil Engg 2025 is part of Civil Engineering (CE) exam preparation. The chapters have been prepared according to the Civil Engineering (CE) exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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