$($ai$)$ What is 'negative skin friction'? how it is calculated for as single pile and a group of piles in clay?

$($b$)$ A $30m$ lone R$.$C$.$C pile is installed in cohesive soil. The lorizontal force acting on the pile is $45kN.$ The coeflicient of subgrnd. modulus of $5\mathrm{.}2M\frac{N}{m^3}.13$ of piles $3\mathrm{.}7{10}^{7}N*n^2.$ Calculate and plot the variation of the deflection and bending moment of pile for both freehead anc lixed$-$ head condition.

$4.($a$)$ When tension and laterally loaded piles are used? Mention the type of strictures and situations where batter piles are uscful.

$($b$)$ Design a friction pil$-$ group to carry a total load of $4000kN$ including the weiglt of pile cap at a sitc where the soil is uniform clay to a denth of $25m.$ underlain by hard strata. Average unconfine. compressive strength of clay is $75kN{m}^2*y^{2}19k\frac{N}{m^1}+C_0(1+c_0)=0\mathrm{.}08$A factor of safety of $2\mathrm{.}5$ is required against shear failurc. Negiect the beating and assume lise pile group. The perenissible sctlement of the pile group is $35mm.$ The lacation of ground water table is $1\mathrm{.}5m$ below ground level. Talke pore water correcion or consolidation ce rrection tuctor as $0\mathrm{.}65$ Take $E=600c_{11}$ and $=6\mathrm{.}5.$