Problem 1

A sheet pile wall system is built for construction of the foundation of a harbor structure (see below).

a) Using the flow net already drawn, determine the flow q underneath the wall system.

b) To maintain the excavation empty, a pump is used to remove the water entering the excavation. Assuming that the length of the wall system (into the page) is 50 meters and that you will use one pump only, determine the capacity (expressed in m3/sec) of the pump required.

c) Determine how high the water can rise on the left side of the sheet pile wall before a quick condition is reached at point A (elevation of 5 m from impervious layer). Don't worry if, as drawn, wall is not high enough.

d) What is the current factor of safety against a quick condition at A‘? (The FS is defined as the ratio of the critical gradient to the existing gradient).

e) Calculate the total and effective stresses (both vertical and horizontal) at point B. Assume K@=0.52.

Note: Place your datum plane at bottom impervious boundary. Elevations of Points A and B are 5m and 3m, respectively.

Problem 2

Consider the soil layer shown in the Figure and assume hydrostatic groundwater conditions with the phreatic surface at depth, -1 m below ground surface. Taking into account capillary rise above the phreatic surface (if it is significant), determine stresses and pore pressure, σ_v, µ and σ_v in function of depth across the layer for two cases (a) soil is sand and (b) soil is clay.

Then, for each case (a) and (b) determine the horizontal effective stresses 0|,' and horizontal total stresses 0|, across the layer. Use for both case K0 = 0.4.

Plot all your results in function of depth from the ground surface.

Note: For both cases the saturated unit weight is 18 kN/m3 as indicated in the Figure. Additional data of void ratio and specific gravity of solids are available for the sand: e=0.6 and GS=2.7

Problem 3

For the soil profile shown in the figure, assuming the sand below water table and the clay are saturated (sand above groundwater table is assumed to be dry), determine at points A, B, C and D:

- The vertical total stress

- The pore pressure

- The vertical effective stress

- The horizontal effective stress

- The horizontal total stress

Use for the at-rest coefficient of lateral stress in sand K4, = 0.45 and in the clay layer Kn = 0.60

Plot these stresses and pore pressure in function of depth.

Problem 4

Construction at a site includes a 100m x 100m building that will host a factory and a separate immediately adjacent mechanical building (15m x 15m).

Distributed loads:

- Over area of large building: q=20O kPa

- Over area of small building: q=3O0 kPa

Calculate the vertical total stress increase Δσ_v due to these combined loads below Points A and B, at depths -5m, -10m and -50m below ground surface.

Hint: When the stress increase in the soil is smaller than 5% of the applied pressure q, consider it is neglectable. According to this criterion does the soil below Point A "feel" the load of the small building?