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 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 is the difference between the axial stress (major principal stress) and the confining pressure (minor principal stress):
Given:
- Confining pressure () = 145 kN/m²
- Deviator stress () = 198 kN/m²
To find the major principal stress :
Now, the relationship between the major and minor principal stresses and the friction angle is given by:
Substituting the values of and :
First, simplify the ratio:
Now, solve for :
Multiplying both sides by :
Expanding the equation:
Combine like terms:
Solving for :
Now, to find :
Therefore, the soil friction angle is approximately .
Would you like further details or have any questions?
Here are 5 related questions:
- What is the significance of the soil friction angle in geotechnical design?
- How would the results change for an undrained triaxial test on the same specimen?
- What assumptions are made when using the Mohr-Coulomb failure criterion in triaxial tests?
- How does the effective stress principle apply in a drained triaxial test?
- 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)
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