Question $1[22$ marks$]$

Stresses in the ground at a location along a proposed roading embankment need to be calculated. At the site, there

is a $7$ m thick layer of sand followed by a $5$ m thick layer of clay. The water table was found to be at $3$ m below

the ground surface. A diagram of the soil profile at the location is shown below with relevant soil parameters

included. Assume hydrostatic water conditions, that each soil is homogeneous, and that the soils are dry above

the water table and saturated below the water table.

a$)$ Calculate the relevant unit weights of the Sand and Clay soils. $($Round unit weights to $1$ decimal place

for subsequent calculations.$)$

b$)$ Calculate the vertical total stress $({}_v),$ pore water pressure $(u_w),$ vertical effective stress $({}_v^{\text{'}}),$ horizontal

effective stress $({}_h^{\text{'}}),$ and horizontal total stress $({}_h)$ at locations A$,$ B and C $(3,7$ and $12$ m below the

ground surface, respectively$).$

c$)$ Plot the variation of ${}_v,u_w,{}_v^{\text{'}},{}_h^{\text{'}}$ and ${}_h$ from $0$ to $12$ m depth $($by hand, on paper or digitally$).$ You

should plot each separately on the graph templates provided on Page $3$ of this assignment handout. Mark

relevant values on the plots.

d$)$ Briefly in approximately $1-2$ sentences each, explain qualitatively $($i$.$e$.$ without numbers$)$ what you would

expect to happen to ${}_v,u_w,{}_v^{\text{'}},$ and ${}_h^{\text{'}}$ at location $C(12m)$ if the water table were to drop $2$ m $($i$.$e$.$ to a

depth of $5$ m below the ground surface$).$ Provide reasoning for your answers.