Practice Question: Water Content of a Clay Soil Sample
NCEES Civil PE Specification Materials: Soil properties
Problem
A clay sample being tested has a wet density ρ dry of 108 pcf.
Given a Degree of Saturation S = 45% and Void Ratio e = 0.3 , calculate the Water Content w .
Assume the density of water ρ w is 62.4 pcf.
CORRECT 😃
INCORRECT 😟
% Students Correctly Answered:
56.1%
Solution
Answer: B) 6%
Assume a value of 1.0 for the total volume:
$$ V_t=1.0\ ft^3 $$
$$ V_t=V_v+V_s $$
$$ 1.0=V_v+V_s $$
Determine volume of solids and volume of voids based on void ratio, e:
$$ e=0.3 $$
$$ e=\frac{V_v}{V_s} $$
$$ 1.0=V_v+V_s $$
$$ V_v=0.3V_s $$
$$ 1.0=1.3V_s $$
$$ V_s=0.77 $$
$$ V_v=0.23 $$
Determine the volume of water based on degree of saturation, S:
$$ S=0.45 $$
$$ S=\frac{V_w}{V_v} $$
$$ V_w=0.45V_v $$
$$ V_w=0.10 $$
Determine the water content, w:
$$ m_w=\rho_w\ \ast\ V_w=6.5\ lb $$
$$ m_s=p_{dry}\ \ast\ V_t=108\ lb $$
$$ w=\frac{m_w}{m_s} $$
$$ w=\frac{6.5\ lb}{108\ lb}\approx6 \% $$
