A $3$X$3$ pile group was driven into clayey soil to support a compressive

load of $1600$ kN$.$ The undrained shear strength of the soil increases

with soil depth as cu$=20+4$z kPa, z is the depth of the soil in meters.

The diameter of the pile is $0\mathrm{.}5$m$.$ Check if a penetration length of $9$

meters is adequate. A safety factor of $3$ is required.