Question

A clay sample was consolidated in a triaxial test under an all-around conning pressure of 15 lb/in.2. The sample was then loaded to failure in undrained condition by applying an additional axial stress of 22 lb/in.2. A pore water pressure sensor recorded an excess pore pressure of (Dud)f 5 29 lb/in.2 at failure. Determine the undrained and drained friction angles for the soil

Answer 1

Answer:

- the undrained friction angles for the soil is 25.02°

- the drained friction angles for the soil is 18.3°

Explanation:

Given the data in the question;

First we determine the major principle stress using the express;

σ₁ = σ₃ + (Δσ$_d$ )$_f$

where σ₃ is the total minor principle stress at failure ( 15 lb/in² )

(Δσ$_d$ )$_f$ is the deviator stress ( -9 lb/in² )

so

σ₁ = 15 lb/in² + 22 lb/in²

σ₁ = 37 lb/in²

Now, we calculate the consolidated-undrained friction angle as follows;

∅ = sin⁻¹[ (σ₁ - σ₃ ) / ( σ₁ + σ₃ ) ]

∅ = sin⁻¹[ (37 - 15 ) / ( 37 + 15 ) ]

∅ = sin⁻¹[ 22 / 52  ]

∅ = sin⁻¹[ 0.423 ]

∅ = 25.02°

Therefore, the undrained friction angles for the soil is 25.02°

-  The drained friction angles for the soil;

∅ = sin⁻¹[ (σ₁ - σ₃ ) / ( σ₁ + σ₃ - 2(Δσ$_d$ )$_f$ ) ]

so we substitute

∅ = sin⁻¹[ (37 - 15 ) / ( 37 + 15 - 2( -9 ) ]

∅ = sin⁻¹[ 22 / ( 37 + 15 + 18 ) ]  

∅ = sin⁻¹[ 22 / 70 ]

∅ = sin⁻¹[ 0.314 ]

∅ = 18.3°

Therefore, drained friction angles for the soil is 18.3°