a) Sheet pile coffer dam

a) Sheet pile coffer dam. Figure 1 shows the flow nets for seepage through a homogeneous, isotropic, permeable, fully saturated foundation rock beneath a sheet pile coffer dam. The water depths in the dam and on the downstream side of the dam are 10m and 2m, respectively. The hydraulic conductivity of the permeable foundation rock is K = 10^-5 m/s. For simplicity, take fluid density to be p = 1000kg/m? and the gravitational acceleration to be g = 10m/s2 in all calculations.

impermeable rock

Fig. 1. Cross-section of the dam with a grout curtain. To scale.

Using the flow nets drawn in Fig. 1,

i) Calculate the pressure at point d (the bottom of the sheet pile wall). {4 marks]

ii) Determine the seepage loss under the dam. {2 marks]

Iii) Calculate the exit velocity in units of mm/s at the three points where the flow lines intersect the equipotential line h1. {6 marks]

iv} Do you anticipate piping? Justify your answer in one or two sentences. {2 marks]

b. Flow nets. Consider seepage under an impermeable concrete dam through a homogeneous, isotropic, permeable, fully saturated foundation rock (Fig. 2).

7 &

open .

waler air

permeable

layer

impermeable layer

Fig. 2. Cross-section of the dam. To scale.

A larger version of Fig. 2 is provided on the next page. Draw a quantitatively accurate flow net, with nm = 5 stream tubes, on it. Draw arrows to indicate direction of flow.

b) Describe the effect of cracks on slopes in cohesive soils. Use sketches to support your answer. [4 marks]

c) Using Bishop’s simplified method of slices determine the factor of safety in terms of effective stress for the trial circle in the slope as shown in Figure 4 (QS). The properties of the sandy soil are as follows: » = 20 kN/m? and ¢# = 30°. Divide the slope cut into at least four slices. Show your values for the heights of the slices and for a, the inclination of the base to the horizontal both graphically and in a table with the additional information that you need to make the calculation for the factor of safety. Do full calculation for at least two slices.

F= | x [(w-ub) tan Gore /

> sinaw | ( cosa +( tang’, sin a/Fs)