$(1)$ Constant head permeability test was conducted on two soils filled in a column as shown in Figure $3.$ The hydraulic conductivity values of Soil $1$ and Soil $2$ are $4\mathrm{.}0{10}^{-4}\frac{m}{s}$ and $1\mathrm{.}0{10}^{-4}\frac{m}{s},$ respectively. Determine the elevation heads, pressure heads and total heads at Point A and C$.$ Assume that the bottom level of the system is the datum as indicated in the fi$$uro

I

$(2)$ Let $i1$ and $i2$ be the hydraulic gradients "between A and $B"$ and "between B and C$",$ respectively. Describe the relationship between $i1$ and $i2.$

$(3)$ Determine the flow velocity in the soils.

$(4)$ Draw the variations of elevation head, pressure head and total head from the datum to the elevation of $100cm($the top of the column$).$ Then, determine the effective stress at Point B$,$ assuming that the unit weight of water is $9\mathrm{.}8k\frac{N}{m^3}.$