A $15$ m high concrete gravity dam will be constructed with the dimensions shown in the figure below. The dam is composed of three blocks of equal heights. It is intended to implement an internal drainage facility, which would reduce uplift pressure by about $20\%.$ Consider minimum freeboard requirement. Carry out a stability analysis for the upper block considering unusual loading $($hydrostatic force, uplift force, dead loads, and silt load$)$ only.

Given:

There is no tailwater,

Compressive strength of concrete, ${}_c=35000k\frac{N}{m^2}$

Shear strength of concrete, ${}_5=5000k\frac{N}{m^2}$

Coefficient of friction between concrete blocks and concrete$-$foundation, $f=0\mathrm{.}75$

Specific weight of water, ${}_w=10k\frac{N}{m^3},$

Specific weight of concrete ${}_c=24k\frac{N}{m^3},$

Depth of sediment accumulation, $h_s=3m,$

Angle of repose $=32,$

Specific weight of sediment ${}_s=11k\frac{N}{m^3}.$