A fully saturated soil sample is contained in an inclined tube between points a and b as shown in Figure $2.$ The tube has a uniform cross$-$sectional area $($A $=10$ cm$2)$ from point a to b$.$ Measurements of the apparatus determined that L$1=3$L$2($with L$1=15$ cm$)$ and that the permeability between points a and c$,$ kac, was related to the permeability between points c and b$,$ kbc$,$ according to the relationship kac $=4$kbc$.$ a$)$ Sketch the variation of elevation, pressure head and total head along the soil

sample, labelling points a$,$ c and b$.$ Label the elevation, pressure and total head

values at points a and b$.$

b$)$ Calculate the total head at point c$.$

c$)$

i$.$ Calculate the pore water pressure at the midpoint of a and c$.$

ii$.$ Calculate the pore water pressure at the midpoint of c and b$.$

d$)$

i$.$ Find the average hydraulic gradient in the soil from a to c$.$

ii$.$ Find the average hydraulic gradient in the soil from c to b