TASK $3(30$ points$)$

The subsurface conditions of a site are shown below. A $\backslash (5\backslash$mathrm$\{$ft$\}\backslash$times $4\backslash$mathrm$\{$ft$\}\backslash ).$ footing is placed at a depth of $2\backslash (\backslash$mathrm$\{$ft$\}\backslash ).$ to support a structural load. Soil collected from the field was tested in the laboratory.

Part $1$

Draw the distribution of the effective stress.

Part $2$

You performed direct shear tests on three specimens collected from the middle of the sandy$/$silty clay each having an equal density of $\backslash (118\backslash$mathrm$\{$lbs$\}/\backslash$mathrm$\{$ft$\}^\{3\}\backslash ),$ but the vertical normal stresses used were $5$ psi $,20$ psi and $35$ psi $.$ The corresponding $\backslash (\backslash$tau$\_\{$f f$\}\backslash )$ values were $\backslash (8\backslash$mathrm$\{$psi$\},15\backslash$mathrm$\{$psi$\}\backslash ),$ and $22$ psi respectively. From this information determine the following:

$1.$ Find the shear strength of a soil element located at the middle of the layer.

$2.$ Draw the Mohr's Circle for the third test.

$3.$ What are the major and minor principal stresses?

$4.$ Find the pole. Show all steps.

$5.$ What are the inclinations of the major and minor principal planes?

$6.$ What is the failure shear stress and what is the maximum possible shear stress?

Part $3$

You prepared a cylindrical specimen out of the clay: $2$ inches in diameter, $4$ inches in length. Then performed an unconfined compression test. The specimen failed at a load of $65$ pounds.

$1.$ What is the compressive strength of the specimen?

$2.$ Draw the Mohr's circle.

$3.$ Show the pole

$4.$ What is the shear strength?

$5.$ What is the major principal stress?