A residential block will be constructed on a clay deposit. The building will rest on a mat foundation at $2$ m depth and has $20m20m$ dimensions in plan. The clay deposit is $26$ m deep and overlies limestone$.$ The groundwater level is at $2$ m depth. The bulk unit weights are $18k\frac{N}{m^3}$ and $20k\frac{N}{m^3}$ above and below water table respectively. The clay has $c^{\text{'}}=5k\frac{N}{m^2},{}^{\text{'}}=20,c_u=48k\frac{N}{m^2},{}_u=0.$

The coefficient of volume compressibility is $1\mathrm{.}00{10}^{-4}\frac{m^2}{k}N$ at the ground surface and decreases with depth at a rate of $0\mathrm{.}02{10}^{-4}\frac{m^2}{k}N$ per meter. Use $\frac{E_u}{c_u}=$ constant $=1250$ and $I_s=1\mathrm{.}2$

$1\mathrm{.}1.$ Calculate ultimate bearing capacity of the foundation in the short term?

$1\mathrm{.}2.$ For the foundation described above what is the $($gross$)$ allowable bearing capacity? NOTE: For ${}_u=0$ case use Skempton values, use a safety factor of $3\mathrm{.}0$ against shear failure of the foundation.

$1\mathrm{.}3.$ Determine the immediate settlement under the foundation

$1\mathrm{.}4.$ Use sublayers to determine the expected primary consolidation settlement of the clay layer. Maximum allowable total settlement of the building is $15$ cm $.(8)$

$1\mathrm{.}5.$ Fill in the table below to indicate the changes in total stress, pore water pressure, effective stress and volume of soil which occur during application of load to a foundation on a clayey soil and as consolidation occurs. Insert the words "increase", "decrease" or $"$no change" in the appropriate block.

$\backslash$table$[[,$During load application,During consolidation$],[$Total stress,,$],[$Pore water pressure,,$],[$Effective stress,,$],[$Volume of soil,,$]]$

$1\mathrm{.}6.$ Name the three components of settlement on a saturated clay. Draw a graph of settlement versus time to illustrate your answer.

$[30$ marks$]$

Question $2$

A shallow spread footing is to be constructed on a layer of normally consolidated clay. Answer the following questions:

$2\mathrm{.}1.$ What type of failure would you expect $($drained or undrained$)?$

$2\mathrm{.}2.$ What bearing capacity theory $($name of Author$)$ would you use to evaluate bearing capacity?

$2\mathrm{.}3.$ Which soil strength parameter governs the bearing capacity?

$2\mathrm{.}4.$ If failure were to occur, when would you expect this to happen?

$2\mathrm{.}5.$ Name one field test and one laboratory test which could be used to determine the relevant soil strength parameter?

Question $3$

Calculate the maximum safe load $"$P$"($including weight of the footing$)$ that can be safely applied to the square footing shown below. Assume a factor of safety of $2,5.$ The soil is a silty sand and the water table is at founding level.

Saturated density of soil

Drained shear strength of soil

${}_{\text{s}\text{a}\text{t}}=22k\frac{N}{m^3}$

${}^{\text{'}}=26$

$c^{\text{'}}=10$kPa

Source: Basic Soil Mechanics, Whitlow, $3^{rd}$ edition

$[5$ marks$]$

Question $4$

$4\mathrm{.}1$ Design a bored concrete pile in stiff fissured clay to carry $3500$ kN $.$ The undrained shear strength $s_u=100$kPa at the surface increasing linearly to $400$ kPa at $30$ m $.$ Find the ultimate load capacity. Assume $=0\mathrm{.}45.$

$4\mathrm{.}2$ List any two advantages and disadvantages of bored and cast$-$in$-$place nondisplacement piles.

$[10$ marks$]$