Calculate frictional component of required jacking force using $2$ methods. Method $2$ is a hybrid of two of the methods discussed in class.

a$.$ Rule of thumb with $0\mathrm{.}06$ tons$/$sq ft of frictional resistance acting on circumferential pipe area.

b$.$ More optimistic case, assuming that $2000\text{'}$ of tunnel is in stable rock that does not close in around pipe, resulting in jacking force being proportional to buoyant weight of pipe and friction factor.$$Assume that $500\text{'}$ of tunnel does partially collapse around pipe, resulting in frictional resistance being proportional to residual soil friction angle and normal confining stress proportional to diameter of bore $(48").$ Use arching factor, Ca$,$ of $1\mathrm{.}0,$ i$.$e$.$ normal stress $=1\mathrm{.}0$ x bore diameter of $48"$ and an effective rock unit weight of $90$ pcf and friction factor of $0\mathrm{.}67$ multiplied by an assumed residual friction angle of $33$ degrees.