Problem $4(25$ pts$.)$

Consider the upward flow of water through two layers of soil of different permeability $k_1=0\mathrm{.}01c\frac{m}{sec}$ and $k_2=0\mathrm{.}02c\frac{m}{sec},$ as shown in the figure below. The saturated unit weight of the two soil layers are ${}_{1,\text{s}\text{a}\text{t}}={}_{2,\text{s}\text{a}\text{t}}=25k\frac{N}{m^3}$ and the unit weight of water $10k\frac{N}{m^3}.$ Assume the cross sectional area of soils equal to $2m^2.$

a$)$ Determine the equivalent permeability $($in vertical direction$)$ of the layered soil. $(8pts.)$

b$)$ Determine the pore water pressures and effective stresses at points A and $B.(17$ pts$.)$