Due $29/03,$ Friday, $23$:$59,$ Late submissions will not be accepted under any clrctumstance.

To be stibmitted in digital form, via odtuclass.

CE$364$ Spring'$24$ Soll Mechanics Homework$-2$

State all assumptions clearly. For all questions, take ${}_v=1\frac{g}{c}c,g=9\mathrm{.}8\frac{m}{s^2},{}_w=9\mathrm{.}8k\frac{N}{m^3}$

The tabulated water content data was obtained from samples taken from a

borehole in a clay layer. You can assume data from each depth represents

$+-1m$ vicinity $($assume $w=18\%$ between $z=1-3m,w=38\%$ between $z=3-5m,$

etc.$).$ Groundwater level is at the depth of $8m.$

In addition, Gs of this clay is measured as $2\mathrm{.}75.$ This clay can sustain a

capillary rise of $5$ meters. Its shrinkage limit is $SL=30\%($assume the soil is

saturated if its water content is higher than SL$,$ assume its volume

therefore void ratio is constant if the water content is below SL$).$

a$)$ Calculate the void ratio, bulk unit weight of soil and degree of saturation at each listed

depth. $($You don't have to show all calculations at every depth; it is enough if you devise

equations, and then use a spreadsheet software to get results as additional columns to this

table$)$

b$)$ Calculating stresses using unit weights at each depth $($as in part a$)$ would be too much

detail. Instead simplify the problem into an idealized soil profile, by taking average values of

soil's unit weight, separately for the saturated and non$-$saturated parts. Then, calculate the

total vertical stress, pore water pressure and vertical effective stress at the depths of $3,5,8,16$

meters. Plot variation of these stresses with depth.

c$)$ Top $5$ meters of this soil is rapidly excavated. Calculate the total vertical stress, pore water

pressure and vertical effective stress at the depths of $5,8$ and $16$ meters, immediately after the

excavation. $($very large negative pore pressures may develop, that's of as far as physics is

concerned$)$

d$)$ Immediately after the excavation, a large building is erected in the excavated area. The

building applies $120$kPa foundation pressure onto the soil $($at the foundation level of $5m)$ due

to its own weight. Calculate the total vertical stress, pore water pressure and vertical effective

stress at the depths of $5,8$ and $16$ meters, a long time after the building is completed.