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If an infinite slope of clay at a depth 5m has cohesion of 1 t/m2 and unit wt. of 2t/m3. Thenthe stability number will be
- a)0.1
- b)0.2
- c)0.3
- d)0.4
Correct answer is option 'A'. Can you explain this answer?
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Stability Number Calculation for Infinite Slope of Clay
Given data:
Depth of clay slope, h = 5m
Cohesion of clay, c = 1 t/m2
Unit weight of clay, γ = 2 t/m3
The stability number is defined as the ratio of the shear strength of the soil to the gravitational forces acting on the soil mass.
1. Calculation of Shear Strength of Clay
The shear strength of clay can be calculated using Mohr-Coulomb's theory. The shear strength equation is given by:
τ = c + σtanφ
Where,
τ = Shear strength
c = Cohesion of soil
σ = Effective stress
φ = Angle of internal friction
In this case, the angle of internal friction is not given. Therefore, it is assumed that the soil is in a fully saturated state and the angle of internal friction is equal to zero.
φ = 0
Thus, the equation for shear strength becomes:
τ = c
Substituting the values of c and γ, we get:
τ = 1 t/m2
2. Calculation of Gravitational Forces
The gravitational forces acting on the soil mass can be calculated using the following equation:
W = γAh
Where,
W = Weight of soil
A = Area of the slope
h = Height of the slope
γ = Unit weight of soil
Substituting the given values, we get:
W = 2 × 5 × A
3. Calculation of Stability Number
The stability number is given by the ratio of shear strength to the gravitational forces:
SN = τ / (W / A)
Substituting the values of τ and W, we get:
SN = 1 / (2 × 5)
Therefore, the stability number is:
SN = 0.1
Hence, the correct answer is option A.
Given data:
Depth of clay slope, h = 5m
Cohesion of clay, c = 1 t/m2
Unit weight of clay, γ = 2 t/m3
The stability number is defined as the ratio of the shear strength of the soil to the gravitational forces acting on the soil mass.
1. Calculation of Shear Strength of Clay
The shear strength of clay can be calculated using Mohr-Coulomb's theory. The shear strength equation is given by:
τ = c + σtanφ
Where,
τ = Shear strength
c = Cohesion of soil
σ = Effective stress
φ = Angle of internal friction
In this case, the angle of internal friction is not given. Therefore, it is assumed that the soil is in a fully saturated state and the angle of internal friction is equal to zero.
φ = 0
Thus, the equation for shear strength becomes:
τ = c
Substituting the values of c and γ, we get:
τ = 1 t/m2
2. Calculation of Gravitational Forces
The gravitational forces acting on the soil mass can be calculated using the following equation:
W = γAh
Where,
W = Weight of soil
A = Area of the slope
h = Height of the slope
γ = Unit weight of soil
Substituting the given values, we get:
W = 2 × 5 × A
3. Calculation of Stability Number
The stability number is given by the ratio of shear strength to the gravitational forces:
SN = τ / (W / A)
Substituting the values of τ and W, we get:
SN = 1 / (2 × 5)
Therefore, the stability number is:
SN = 0.1
Hence, the correct answer is option A.
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If an infinite slope of clay at a depth 5m has cohesion of 1 t/m2 and unit wt. of 2t/m3. Thenthe stability number will bea)0.1b)0.2c)0.3d)0.4Correct answer is option 'A'. Can you explain this answer?
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