Question

A CU triaxial compression test was performed on saturated sand at a cell pressure of 100 kPa. The ultimate deviator stress was 350 kPa and the pore pressure at the peak stress was 40 kPa (suction). Estimate the total and effective stress shear strength parameters.

• A. 33.75

Answer 1

The correct option is A 33.75
Given,

Total Stresses

${\sigma }_3=100kN/m^2$

${\sigma }_1-{\sigma }_3=350kN/m^2$

${\sigma }_1-100=350$

${\sigma }_1=450kN/m^2$

$u=-40kN/m^2$

(Because of suction)

Effective stresses, ${\overline{\sigma }}_3={\sigma }_3-u$

= 100 -(-40)

$=140kN/m^2$

${\overline{\sigma }}_1={\sigma }^{}-u$

=450 -(-40)

$=490kN/m^2$

Calculation of total stress shear strength parameters

${\sigma }_1={\sigma }_{3}ta{n}^2(45+\frac{\varphi }{2})+2ctan(45+\frac{\varphi }{2})$

For sand, C = 0

${\sigma }_1={\sigma }_{3}ta{n}^2(45+\frac{\varphi }{2})$

$450=100ta{n}^2(45+\frac{\varphi }{2})$

$\varphi ={39.52}^{\circ }$

c = 0

Calculation of effective stress shear strength parameters

${\overline{\sigma }}_1={\overline{\sigma }}_{3}ta{n}^2(45+\frac{{\varphi }^{\prime }}{2})+2c^{\prime }tan(45+\frac{{\varphi }^{\prime }}{2})$

For sand, C' = 0

${\overline{\sigma }}_1={\overline{\sigma }}_{3}ta{n}^2(45+\frac{{\varphi }^{\prime }}{2})$

$490=140ta{n}^2(45+\frac{{\varphi }^{\prime }}{2})$

${\varphi }^{\prime }={33.75}^{\circ }$

c' = 0