following data are available:

$B=3m,D_f=1\mathrm{.}5m\frac{,}{b}ar(b)=2m,H=8m,=30,=18\mathrm{.}5k\frac{N}{m^3},=0$ and

$c=75k\frac{N}{m^2}$

Determine the ultimate bearing capacity of the footing

Determine the damping of a system if its amplitude of motion for the first

cycle is $20$ times than that of $6$ th cycle under free vibration.

$($a$)$ A square pile group of $9$ piles passes through a recently filled up soil layer.

The depth of fill is $3$ m from G$.$L$.$ The cohesion and the unit weight of the

filled$-$up soil are $50k\frac{N}{m^2}$ and $16k\frac{N}{m^3}$ respectively. Diameter of each pile

is $30$ cm and they are spaced at $90$ cm centre to centre distance apart.

Compute the maximum probable negative friction load on the pile group due

to the consolidation of the filled$-$up soil layer.

$($b$)$ Derive the expression for depth of embedment of cantilever sheet pile wall

in cohesionless soil when the water table is at great depth

A steel pipe pile of $600$ mm outside diameter with a wall thickness of $25$ mm

is driven into saturated cohesive soil to a depth of $20$ m $.$ The submerged unit

weight of the soil is $9\mathrm{.}7k\frac{N}{m^3}$ and the undrained cohesive strength $(c_u)$ is $85$

kPa $.$ The $EI$ value of the pile is $4\mathrm{.}35{10}^{2}MN-m^2.$ Compute the ultimate

lateral resistance of the free head pile by Broms' method with the load

applied at ground level. The section molulus of pile is $\frac{}{64r_o}[d_o^4-d_i^4].$

Yeild strength of the pile material is $2800k\frac{g}{c}{m}^2.$ Refer Fig$-2.$

Determine the depth of embedment and the force in the tie rod of the

anchored bulkhead shown in the Fig$-3.$ The backfill above the dredge line is

sand, having the following properties

sand, having the following propertes

$G_s=2\mathrm{.}67,{}_{\text{s}\text{a}\text{t}}=18k\frac{N}{m^3},{}_d=13k\frac{N}{m^3}$ and $=30$

The soil below dredge line is clay having

The soil below dredge

$c=50k\frac{N}{m^2},G_s=2\mathrm{.}67,{}_{\text{s}\text{a}\text{t}}=19k\frac{N}{m^3}$

Solve the problem by the free$-$earth support method. Assume the backfill

above the water table remains dry.

$($a$)$ Explain with neat sketches the behaviour of a system under forced damped

vibration.