Question

cylindrical sample of soil is isotropically compressed under drained condition with a vertical stress of 100 kPa and a radial stress of 100 kPa. Subsequently, the axial stress was held constant and the radial stress was increased to 300 kPa under an un-drained condition.

(a) Calculate the initial mean effective stress and deviatoric stress. Create a graph with the x-axis as p, p’ and the y-axis as q (p, q space). Plot these values in (p,q) space

(b) Calculate the increase in mean total stress and deviatoric stress.

(c) Plot the total and effective stress paths (assume the soil is a linear, isotropic, elastic material).

(d) Determine the slopes of the total and effective stress paths and the maximum excess pore water pressure for each space.

Answer 1

a)Initial Condition

$s'=s \frac{\sigma_a+\sigma_r}{2}=\frac{100+100}2=100kPa$

$t=\frac{\sigma_a- \sigma_r}2=\frac{100-100}2=0$

b) Loaded Condition

$\triangle s= \frac{\triangle \sigma_a+ \triangle \sigma_r}2= \frac{0+200}2=100kPa$

$\triangle s'=0=$ Slope of effective stress path (ESP) for elastic soil

$\triangle t= \frac{\triangle \sigma_a- \triangle \sigma_r}2=\frac{0-200}2 kPa=-100kPa$

c)

d) Slope =1.5