A clay layer of thickenss H has a preconsolidation pressure pc and an initial void ratio e0. The initial effective overburden stress at the mid-height of the layer is p0. At the same location, the increment in effective stress due to applied extrenal load is Δp. The comprssion and swelling indices of the clay are Cc and Cs, respectively. If P0 < Pc <(P0 + Δp), then the the correct expression to estimate the consolidation settlement (Sc) of the clay layers is

• A. \({s_c} = \frac{H}{{1 + {e_0}}}\left[ {{C_c}\log \frac{{{p_c}}}{{{p_0}}} + {C_s}\log \frac{{{P_0} + {{\rm{\Delta }}_p}}}{{{p_c}}}} \right]\)
• B. \({s_c} = \frac{H}{{1 + {e_0}}}\left[ {{C_c}\log \frac{{{p_0}}}{{{p_c}}} + {C_s}\log \frac{{{P_0} + {{\rm{\Delta }}_p}}}{{{p_c}}}} \right]$\)
• C. \({s_c} = \frac{H}{{1 + {e_0}}}\left[ {{C_s}\log \frac{{{p_0}}}{{{p_c}}} + {C_c}\log \frac{{{P_0} + {{\rm{\Delta }}_p}}}{{{p_c}}}} \right]$\)
• D. \({s_c} = \frac{H}{{1 + {e_0}}}\left[ {{C_s}\log \frac{{{p_c}}}{{{p_0}}} + {C_c}\log \frac{{{P_0} + {{\rm{\Delta }}_p}}}{{{p_c}}}} \right]\)