Math Problem Statement

A drained triaxial test was conducted on a normally consolidated clay specimen with a chamber confining pressure of 145 kN/m2 . At failure, the deviator stress was 198 kN/m2 . Determine the soil friction angle

Solution

The soil friction angle ϕ\phi can be determined using the results of the drained triaxial test. For a normally consolidated clay, the friction angle is derived using the relationship between the confining pressure, deviator stress, and effective stress at failure.

In a drained triaxial test, the deviator stress σd\sigma_d is the difference between the axial stress σ1\sigma_1 (major principal stress) and the confining pressure σ3\sigma_3 (minor principal stress):

σd=σ1σ3\sigma_d = \sigma_1 - \sigma_3

Given:

  • Confining pressure (σ3\sigma_3) = 145 kN/m²
  • Deviator stress (σd\sigma_d) = 198 kN/m²

To find the major principal stress σ1\sigma_1:

σ1=σ3+σd=145+198=343kN/m²\sigma_1 = \sigma_3 + \sigma_d = 145 + 198 = 343 \, \text{kN/m²}

Now, the relationship between the major and minor principal stresses and the friction angle ϕ\phi is given by:

σ1σ3=1+sinϕ1sinϕ\frac{\sigma_1}{\sigma_3} = \frac{1 + \sin\phi}{1 - \sin\phi}

Substituting the values of σ1\sigma_1 and σ3\sigma_3:

343145=1+sinϕ1sinϕ\frac{343}{145} = \frac{1 + \sin\phi}{1 - \sin\phi}

First, simplify the ratio:

343145=2.3655\frac{343}{145} = 2.3655

Now, solve for sinϕ\sin\phi:

2.3655=1+sinϕ1sinϕ2.3655 = \frac{1 + \sin\phi}{1 - \sin\phi}

Multiplying both sides by 1sinϕ1 - \sin\phi:

2.3655(1sinϕ)=1+sinϕ2.3655(1 - \sin\phi) = 1 + \sin\phi

Expanding the equation:

2.36552.3655sinϕ=1+sinϕ2.3655 - 2.3655\sin\phi = 1 + \sin\phi

Combine like terms:

2.36551=sinϕ+2.3655sinϕ2.3655 - 1 = \sin\phi + 2.3655\sin\phi

1.3655=(1+2.3655)sinϕ1.3655 = (1 + 2.3655)\sin\phi

1.3655=3.3655sinϕ1.3655 = 3.3655\sin\phi

Solving for sinϕ\sin\phi:

sinϕ=1.36553.3655=0.4058\sin\phi = \frac{1.3655}{3.3655} = 0.4058

Now, to find ϕ\phi:

ϕ=arcsin(0.4058)23.94\phi = \arcsin(0.4058) \approx 23.94^\circ

Therefore, the soil friction angle ϕ\phi is approximately 23.9423.94^\circ.


Would you like further details or have any questions?

Here are 5 related questions:

  1. What is the significance of the soil friction angle in geotechnical design?
  2. How would the results change for an undrained triaxial test on the same specimen?
  3. What assumptions are made when using the Mohr-Coulomb failure criterion in triaxial tests?
  4. How does the effective stress principle apply in a drained triaxial test?
  5. Can the presence of cohesion affect the calculation of the friction angle?

Tip: In normally consolidated clays, the friction angle tends to be constant, while the cohesion is often assumed to be zero.

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Math Problem Analysis

Mathematical Concepts

Soil Mechanics
Effective Stress
Friction Angle

Formulas

σ_d = σ_1 - σ_3 (Deviator stress formula)
Major and minor principal stress relationship: (σ_1 / σ_3) = (1 + sinφ) / (1 - sinφ)

Theorems

Mohr-Coulomb Failure Criterion

Suitable Grade Level

University Level (Civil Engineering or Geotechnical Engineering)