A penetration test device is shown in Figure $3-23.$ The permeability coefficient $k$ of sand

sample $I=410-c\frac{m}{s},$ the permeability coefficient h $2$ of sand sample III$=110-2c\frac{m}{s},$ and the

cross$-$sectional area of sand sample $A=100cm2.$ The pore ratio of sand sample $I=0\mathrm{.}70,$ the

specific gravity of soil particles G$.=2\mathrm{.}67,$ yw takes $10\mathrm{.}0k\frac{N}{m}3,$ and

$(1)$ If a piezometer pipe is installed at the interface between sand I and

sand II$,$ how high will the water surface in the piezometer pipe rise above the

water surface at the right end?

$(2)$ What is the amount of water seepage through the sand sample per

unit time?

$(3)$ Will the sand sample I be damaged by quicksand?$)$ A penetration test device is shown in Figure $3-23.$ The permeability coefficient $k$ of sand

sample $I=410-c\frac{m}{s},$ the permeability coefficient h $2$ of sand sample III$=110-2c\frac{m}{s},$ and the

cross$-$sectional area of sand sample $A=100cm2.$ The pore ratio of sand sample $I=0\mathrm{.}70,$ the

specific gravity of soil particles G$.=2\mathrm{.}67,$ yw takes $10\mathrm{.}0k\frac{N}{m}3,$ and

$(1)$ If a piezometer pipe is installed at the interface between sand I and

sand II$,$ how high will the water surface in the piezometer pipe rise above the

water surface at the right end?

$(2)$ What is the amount of water seepage through the sand sample per

unit time?

$(3)$ Will the sand sample I be damaged by quicksand?