ss we mentioned that some geologic features can give us information as to the stress conditions that existed
during their formation. For example, stylolites from by dissolution of material in a plane whose normal is oriented
parallel to 1. Also, other features such as tension veins tend to open in the direction of 3 on a plane parallel to 1.
The figure below shows a hypothetical outcrop that incorporates these data and a set of through-going fractures. Use
this figure to answer the following:
(a)Draw the orientation of 1 on the figure.
(b) Assuming that the fracture formed at the same time as the stylolites and tension veins, and that the normal stress
and shear stress required for failure were: n=240 MPa and s=320 MPa, calculate the magnitude of the principal
stresses 1 and3 during their formation.
(c) What type of faults are shown on the schematic figure? Justify by drawing the motion arrows on the faults on the
schematic outcrop figure.
Question 2: A reservoir is arranged as shown in Figure 2, with a side wall inclined at an angle of 8 = 50 to the horizontal . A triangular gate of width w = 2m, has its top ho = 6m below the water surface. The gate, of mass 300kg is hinged along its top edge, and kept closed by a horizontal force P, acting at the tip of the gate as shown. Air at atmospheric pressure surrounds the external side of the gate. The vertical distance from the top of the gate to the bottom of the gate, is hy = 3m. You should assume water density to be pw = 1000kg m-, and the value for gravitational acceleration to be g = 9,8 ms? Side view Water w hi gate hinge h P Figure 2 a) Draw a free body diagram to represent the forces acting the gate, clearly labeling the forces and any relevant dimensions. [3 marks) b) Calculate the force on the gate due to the water. (5 marks] c) Calculate the distance between the centre of pressure and the centre of gravity of the gate. [3 marks] d) Take moments about the hinge to find the force P needed to keep the gate closed where P is applied at the tip of the triangular gate as shown in the diagram [5 marks]
Q1) A 4 m thick clay layer is drained at the top and bottom. Its characteristics are Cvr=Cv (for vertical drains)=0.0040m2/day, rw=20 cm and de= 1.8 m. Estimate the degree of consolidation of the clay layer caused by combination of vertical and radial; drainage at t=0.2, 0.4, 0.8 and 1 year. 1
Q.1. A steel bar, 70 mm long is struck at one end by a heavy mass travelling at 20 m/s.
The impact causes a compression wave to travel along the bar until it reaches the other
end, which is kept fixed. The bar has a density of 7900 kg/m3 and a Youngs modulus of
a. What are the boundary conditions at the two ends? You may assume that the
heavy mass is a rigid body that does not decelerate when it hits the bar, i.e. the
initial velocity of the impacted end is the same as the heavy mass.
b. Construct a spreadsheet to solve this problem, using an explicit FD scheme with
6 computational nodes (8 nodes including boundary conditions) and a timestep
∆t = 1 × 10−6
s. Plot the results for the displacement w at times t = 1 × 10−5
and t = 2 × 10−5
s. Please submit your spreadsheet and graphs (on paper!) – and
please use scientific notation and appropriate decimal places where necessary to
make it easy to read.
c. Replot the results from part b for a timestep of ∆t = 3 × 10−6
s. What is the
critical value of CL∆t/∆z for stability?
d. Revise the spreadsheet to use 13 computational points (15 including boundaries).
Plot the stress at the mid-point of the bar as a function of time.
e. Using the 15 node simulation again, plot the velocity of the mid-point of the bar
as a function of time. At what time does the bar lose contact with the impacting
mass? What boundary condition should you use at the impacted end once this
Q.2. Use the von Neumann stability analysis to find an expression for the error growth
factor G for this algorithm (you can leave this as a quadratic). Show that the scheme is
unstable for a value of CL∆t/∆z =√2
A number of cells that are simultaneously selected is called a