The solution should be returned on October $5,2023$ at the start of class.

The soil is an undrained saturated clay soil under short term behavior. The appropriate strength parameter is the undrained cohesion $"$cu$".$ The overall goal is to find the $"$Nc$"$ bearing capacity factor for the two solutions: Upper bound and Lower bound, for the conditions indicated in the enclosed sketch. For the solution consider that $c_u=100$kPa.

Part One $-$ Upper Bound Solution

It is desired to develop an upper bound solution using the mechanism illustrated in the enclosed sketch. You need to draw the hodograph and calculate the energy dissipated within the soil mass, similar to the process indicated in the textbook. Please notice that the hodograph has to be plotted at scale. You can use drafting tools or cad. No xerox copies will be accepted as well as free hand drawings. You have to include all data retrieved from the sketch of the mechanism and the hodograph in tables showing all the calculations and intermediate steps.

Part Two $-$ Lower Bound Solution

It is desired to calculate and plot the state of principal stresses $($in the same seven soil wedges as used in the upper bound solution$)$ as the six frictional discontinuities are crossed. The plot should be done on the horizontal line at five meters depth. For this part, consider that $"o_q"$ is $50$kPa and it is desired to plot the principal stresses for the steps change across all the discontinuities. Please use a scale to plot all the principal stresses and show the angles of rotation of the principal stresses in each wedge. For this purpose, it is desired to plot the states of stress in each wedge at a depth of $5$ meters; that is$,$ the horizontal line where the vertical overburden pressure is $75$kPa.

If you have problems please stop by the office

No penalty for asking questions