$13\mathrm{.}1$ The following data are given for a direct shear test conducted on dry silty sand:

Specimen dimensions: $63mm63mm25mm($height$)$

Normal stress: $105k\frac{N}{m^2}$

Shear force at failure: $300N$

a$.$ Determine the angle of friction, ${}^{\text{'}}.$

Answer:

$35\mathrm{.}5$

b$.$ For a normal stress of $180k\frac{N}{m^2},$ what shear force is required to cause failure?

Answer:

$509\mathrm{.}5N$