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# Stresses due to Self Weight

The stresses due to self weight of the soil are known as ______________

a) geostatic stresses

b) boundary stresses

c) external stresses

d) boundary strain

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Answer: a

Explanation: The stresses due to self weight of the soil are sometimes known as geostatic stresses. The self weight of the soil is found by the multiplication of unit weight of soil γ and the depth of the of the point in soil z.

σ_{z}=γz.

If XY pane is considered to be ground surface and the z-axis as depth, then this condition is known as _______

a) semi-infinite

b) infinite

c) finite

d) semi- finite

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Answer: a

Explanation: 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.

When there is no eternal loading, the principal is _______

a) 5m below ground plane

b) ground plane

c) 10m below ground plane

d) at infinity

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Answer: b

Explanation: When there is no eternal loading, the ground plane becomes the principal plane. This is because the ground plane is devoid of any shear loading. The plane on which the shear stress is zero is called the principal plane and the normal stress on the principal plane is called the principal stress.

From the symmetry and orthogonality of principal planes ____________

a) both horizontal and vertical planes will be devoid of shear stress

b) both horizontal and vertical planes will have shear stress

c) only vertical plane has shear stress

d) only horizontal plane has shear stress

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Answer: a

Explanation: From the symmetry and orthogonality of principal planes, one can conclude that both horizontal and vertical planes will be devoid of shear stress.

∴ τ_{YX}= τ_{YZ} = τ_{XZ}=0.

The vertical stress at a point within soil mass at a depth z is ____________

a) σ_{z}=γ+z

b) σ_{z}=γ-z

c) σ_{z}=γ/z

d) σ_{z}=γz

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Answer: d

Explanation: From the symmetry and orthogonality of principal planes, one can conclude that both horizontal and vertical planes will be devoid of shear stress.

∴ τ_{YX}= τ_{YZ} = τ_{XZ}=0.

Substituting this in the equilibrium equation,

σ_{z}=γz.

On simplifying the compatibility equation in terms of stresses with respect to Poisson’s ratio is given by _________

a) σ_{z}=γz

b) σ_{x}=σ_{y}=μ1−μγz

c) σ_{x}=σ_{y}=1μγz

d) σ_{x}=σ_{y}=μγz

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Answer: b

Explanation: On simplifying the compatibility equation in terms of stresses with respect to Poisson’s ratio is given by

σ_{x}=σ_{y}=μ1−μγz

Where σ_{x},σ_{y} are the normal stresses in x and y direction respectively

μ= Poisson’s ratio

Ko=μ1−μ is the coefficient of lateral pressure at rest.

f z-axis is considered to be directed downward from ground surface, then the stress component in y-axis at a point at a depth z due to self weight of soil above it is ___________

a) σy=11−μγz

b) σ_{y}=μγz

c) σy=μ1−μ

d) σy=μ1−μγz

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Answer: d

Explanation: On simplifying the compatibility equation in terms of stresses with respect to Poisson’s ratio is given by

\(σ_{x}=σ_{y}=\frac{μ}{1-μ}γz \)

Where σ_{x},σ_{y} are the normal stresses in x and y direction respectively

μ= Poisson’s ratio

Ko=μ1−μ is the coefficient of lateral pressure at rest.

If z-axis is considered to be directed downward from ground surface, then the stress component in z-axis at a point at a depth z due to self weight of soil above it is ___________

a) σ_{z}=γz

b) σ_{z}=μγz

c) σ_{z}=μ1−μ

d) σ_{z}=μ1−μγz

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Answer: a

Explanation: When z-axis is considered to be directed downward from ground surface, then the stress component in z-axis at a point at a depth z due to self weight of soil above it is,

σ_{z}=γz, where σ_{z} is the normal the stress component in z-axis

γ=unit weight of soil

Z=depth at which the stress is calculated.

At a certain point within soil mass, the stresses are caused only because of surface loadings.

a) True

b) False

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Answer: b

Explanation: At a certain point within soil mass, the stresses are caused because of surface loadings as well as self-weight of the soil mass above that point. The surface loadings and the self-weight of the soil are calculated separately and then summed to get the total stress at a point.