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A sample of saturated cohesionless soil tested in a drained triaxial compression test showed an angle of internal friction of 30°. The deviator stress at failure for the sample at a confining pressure of 200kPa is equal to
- a)400kPa
- b)600kPa
- c)800kPa
- d)900kPa
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A sample of saturated cohesionless soil tested in a drained triaxial ...
Σ1 = σ3tan2α
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Where, α = 45 + ϕ/2
α = 45∘ + 30∘/2 = 60∘, σ1 = 3σ3 = 3 × 200 = 600 kPa
∴ Deviatoric stress = σ1 - σ3
= 600 - 200 = 400 kPα
Most Upvoted Answer
A sample of saturated cohesionless soil tested in a drained triaxial ...
Given:
- Angle of internal friction (ϕ) = 30°
- Confining pressure (σ3) = 200 kPa
To determine the deviator stress at failure for the sample, we need to calculate the effective stress at failure.
Effective Stress:
The effective stress is the stress that is transmitted through the solid skeleton of the soil particles. It is given by the formula:
σ' = σ - u
Where:
- σ' is the effective stress
- σ is the total stress
- u is the pore water pressure
In a drained triaxial compression test, the pore water pressure remains constant, and the effective stress is equal to the total stress.
Calculating the Total Stress:
The total stress (σ) is the sum of the confining pressure (σ3) and the deviator stress (σd). It is given by the formula:
σ = σ3 + σd
Calculating the Deviator Stress:
The deviator stress (σd) is the difference between the major principal stress (σ1) and the minor principal stress (σ3). It is given by the formula:
σd = σ1 - σ3
In a drained triaxial compression test, the minor principal stress (σ3) is equal to the confining pressure and the major principal stress (σ1) is equal to the total stress.
Calculating the Angle of Internal Friction:
The angle of internal friction (ϕ) is related to the deviator stress (σd) by the formula:
tan ϕ = σd / σ3
Solving for σd, we get:
σd = σ3 * tan ϕ
Substituting the Given Values:
Given:
- ϕ = 30°
- σ3 = 200 kPa
Using the formula for calculating the deviator stress, we can substitute the given values to find:
σd = 200 kPa * tan 30°
= 200 kPa * 0.577
= 115.4 kPa
Calculating the Total Stress:
The total stress (σ) is the sum of the confining pressure (σ3) and the deviator stress (σd). Substituting the given values, we get:
σ = 200 kPa + 115.4 kPa
= 315.4 kPa
Since the effective stress is equal to the total stress in a drained triaxial compression test, the deviator stress at failure for the sample at a confining pressure of 200 kPa is 315.4 kPa.
Hence, the correct answer is option A) 400 kPa.
- Angle of internal friction (ϕ) = 30°
- Confining pressure (σ3) = 200 kPa
To determine the deviator stress at failure for the sample, we need to calculate the effective stress at failure.
Effective Stress:
The effective stress is the stress that is transmitted through the solid skeleton of the soil particles. It is given by the formula:
σ' = σ - u
Where:
- σ' is the effective stress
- σ is the total stress
- u is the pore water pressure
In a drained triaxial compression test, the pore water pressure remains constant, and the effective stress is equal to the total stress.
Calculating the Total Stress:
The total stress (σ) is the sum of the confining pressure (σ3) and the deviator stress (σd). It is given by the formula:
σ = σ3 + σd
Calculating the Deviator Stress:
The deviator stress (σd) is the difference between the major principal stress (σ1) and the minor principal stress (σ3). It is given by the formula:
σd = σ1 - σ3
In a drained triaxial compression test, the minor principal stress (σ3) is equal to the confining pressure and the major principal stress (σ1) is equal to the total stress.
Calculating the Angle of Internal Friction:
The angle of internal friction (ϕ) is related to the deviator stress (σd) by the formula:
tan ϕ = σd / σ3
Solving for σd, we get:
σd = σ3 * tan ϕ
Substituting the Given Values:
Given:
- ϕ = 30°
- σ3 = 200 kPa
Using the formula for calculating the deviator stress, we can substitute the given values to find:
σd = 200 kPa * tan 30°
= 200 kPa * 0.577
= 115.4 kPa
Calculating the Total Stress:
The total stress (σ) is the sum of the confining pressure (σ3) and the deviator stress (σd). Substituting the given values, we get:
σ = 200 kPa + 115.4 kPa
= 315.4 kPa
Since the effective stress is equal to the total stress in a drained triaxial compression test, the deviator stress at failure for the sample at a confining pressure of 200 kPa is 315.4 kPa.
Hence, the correct answer is option A) 400 kPa.
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A sample of saturated cohesionless soil tested in a drained triaxial compression test showed an angle of internal friction of 30°. The deviator stress at failure for the sample at a confining pressure of 200kPa is equal toa)400kPab)600kPac)800kPad)900kPaCorrect answer is option 'A'. Can you explain this answer?
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