Soil that has never experienced a stress higher than the current effective stress ($\sigma'_o$). $S_c = \frac{C_c H}{1+e_o} \log_{10} \left( \frac{\sigma'_o + \Delta \sigma}{\sigma'_o} \right)$

• $C_c$: Compression Index ($\approx 0.009(LL-10)$).
• $H$: Thickness of clay layer.
• $e_o$: Initial void ratio.
• $\sigma'_o$: Initial effective overburden pressure.
• $\Delta \sigma$: Increase in vertical stress.

Soil that has experienced a higher stress in the past ($\sigma'_c > \sigma'_o$). Case 1: $\sigma'_o + \Delta \sigma \le \sigma'_c$ $S_c = \frac{C_r H}{1+e_o} \log_{10} \left( \frac{\sigma'_o + \Delta \sigma}{\sigma'_o} \right)$ Case 2: $\sigma'_o + \Delta \sigma > \sigma'_c$ $S_c = \frac{C_r H}{1+e_o} \log_{10} \left( \frac{\sigma'_c}{\sigma'_o} \right) + \frac{C_c H}{1+e_o} \log_{10} \left( \frac{\sigma'_o + \Delta \sigma}{\sigma'_c} \right)$

• $C_r$: Recompression/Swell Index (typically $C_c/5$ to $C_c/10$).

$T_v = \frac{C_v t}{H_{dr}^2}$

• $C_v$: Coefficient of consolidation.
• $t$: Time.
• $H_{dr}$: Length of drainage path.
  • $H_{dr} = H/2$ for double drainage (sand top and bottom).
  • $H_{dr} = H$ for single drainage.