题目
已知岩样的重度 gamma = 22.5 , (kN) / (m)^3,相对密度 G_s = 2.8,天然含水率 omega = 8%,试计算该岩样的孔隙率 mu,干重度 gamma_d 及饱和重度 gamma_(sat)。(本题 10 分)
已知岩样的重度 $\gamma = 22.5 \, \text{kN} / \text{m}^3$,相对密度 $G_s = 2.8$,天然含水率 $\omega = 8\%$,试计算该岩样的孔隙率 $\mu$,干重度 $\gamma_d$ 及饱和重度 $\gamma_{sat}$。(本题 10 分)
题目解答
答案
根据题意,设 $V = 1 \, \text{m}^3$,则:
\[
W_s = \frac{\gamma}{1 + \omega} = \frac{22.5}{1.08} = 20.833 \, \text{kN}, \quad W_w = 0.08 W_s = 1.667 \, \text{kN}
\]
\[
\gamma_d = \frac{W_s}{V} = 20.833 \, \text{kN/m}^3
\]
\[
V_s = \frac{W_s}{G_s \rho_w} = \frac{20.833}{28} = 0.744 \, \text{m}^3, \quad V_v = 1 - 0.744 = 0.256 \, \text{m}^3
\]
\[
n = 25.6\%
\]
\[
\gamma_{\text{sat}} = \frac{W_s + \rho_w V_v}{V} = \frac{20.833 + 2.56}{1} = 23.393 \, \text{kN/m}^3
\]
最终结果:
\[
n = 25.6\%, \quad \gamma_d = 20.83 \, \text{kN/m}^3, \quad \gamma_{\text{sat}} = 23.39 \, \text{kN/m}^3
\]