Question

In a drained triaxial compression test conducted on sand, failure occurred when the deviatric stress was 200 kN/m${}^2$ at confining pressure of 75 kN/m${}^2$. By conducting the undrained test on same soil specimen, the pore water pressure at failure was measured as 50 kN/m${}^2$, the undrained angle of internal friction is

• A. 34.85${}^o$
• B. 26.38${}^o$
• C. 29.32${}^o$
• D. 19.37${}^o$

Answer 1

The correct option is B 26.38${}^o$

Given: Drained test (effective stresses)

$Sand:{\sigma }_d=200$kN/m${}^2$

${\sigma }_c=75$kN/m${}^2$

$\therefore {\sigma }_3^{\prime }=75kPa$

${\sigma }_1^{\prime }={\sigma }_c+{\sigma }_d=275kPa$

$Undrainedtest:Sand(C_u=0)$

$\therefore u_f=50kN/m^2$

$(C_u=0)$

${\varphi }_u=si{n}^{-1}\left(\frac{{\sigma }_1-{\sigma }_3}{{\sigma }_1+{\sigma }_3}\right)$

$=si{n}^{-1}\left(\frac{({\sigma }_1^{\prime }+u)-({\sigma }_3^{\prime }+u)}{({\sigma }_1^{\prime }+u)+({\sigma }_3^{\prime }+u)}\right)$

${\varphi }_u=si{n}^{-1}\left(\frac{{\sigma }_1^{\prime }-{\sigma }_3^{\prime }}{{\sigma }_1^{\prime }+{\sigma }_3^{\prime }+2u}\right)$

$\therefore {\varphi }_u=si{n}^{-1}\left(\frac{275-75}{275+75+2\times 50}\right)$

${\varphi }_u={26.38}^o$