1.21 For a sand given: D_(85)=0.21mm D_(50)=0.13mm D_(15)=0.09mm Uniformity coefficient. C_(n)=2.1 Void ratio. e=0.68 Relative density =53% Estimate the soil friction angle using Eq.(1.83) b Eq.(1.84) 1.22 A consolidated -drained triaxial test on a normally consolidated clay yields the fol- lowing results. All around confining pressure. sigma _(3)'=138kN/m^2 Added axial stress at failure. Delta sigma =276kN/m^2 Determine the shear-strength parameters.

### 1.21 Estimating the Soil Friction AngleGiven:- - - - Uniformity coefficient, - Void ratio, - Relative density = 53%We need to estimate the soil friction angle using the given equations.#### Using Eq. (1.83):The formula for the soil friction angle ( ) using the uniformity coefficient is: Substitute the given values: Calculate each term: Now, sum up the terms: Finally, find the friction angle: #### Using Eq. (1.84):The formula for the soil friction angle ( ) using the relative density ( ) is: Substitute the given values: Calculate each term: Now, sum up the terms: Finally, find the friction angle: ### 1.22 Determining the Shear-Strength ParametersGiven:- Confining pressure, - Added axial stress at failure, The total stress at failure ( ) is: The major principal stress ( ) is: The minor principal stress ( ) is: The intermediate principal stress ( ) is: The shear stress ( ) is: The Mohr-Coulomb failure criterion is given by: Where:- is the cohesion intercept.- is the normal stress.- is the friction angle.Assuming a typical clay behavior, let's