Some laboratory testing returned the parameters:

 • Poisson's ratio for the sand and clay is 0.3

 • Young's modulus of the sand is 10 MPa 

• Coefficient of compressibility of clay is 0.8 MPa-1

 • Void ratio of clay = 0.9, coefficient of consolidation = 12 m2 /y, coefficient of creep = 0.02

 

Figure 1 shows a cross section of a coal loading facility on a port. Embankments (1), (2) and (4) support railway tracks on which a coal stacker reclaimer can travel. In Figure 1, the coal stacker reclaimer is on embankment (2) on which it imposes two line loads (L1 and L2), and the coal stockpile (3) is located in between embankments (2) and (4). It is assumed that the loading geometry of Figure 1 does not change. 

The soil profile under the ground surface (at elevation = 0m) consists of 3m of loose sand overlying 17 m of silty clay on an impermeable rock stratum. The water table is.at a depth of 1m (not shown on the figure).

 

Q1. The coal in the stockpile has a specific gravity of 1.5, a porosity of 45% and a volumetric water content of 14.5%. What is the bulk unit weight of the coal stockpile? Use 9.8 kN/m3 for unit weight of water. 

 

Q2. Plot the distribution of additional vertical stress and horizontal stress (in both directions) with depth (from the surface indicated by the black horizontal line in the figures, to a depth of 20m, in 0.5 m increments), at the location indicated by the blue dashed line due to the relevant surface load, for:

 a. Embankment (2) (Figure 2a)

 b. Coal stockpile (3) (Figure 2b) - if you have not answered Question 1, assume assume the bulk unit weight is 12 kN/m^3

c. Embankment (1) (Figure 2d)

 d. Line load L2 (Figure 2c) - assume that load on embankment is equivalent to load on infinite half space

 e. Line load L1 (Figure 2e) - - assume that load on embankment is equivalent to load on infinite half space

 

Q3. Using the principle of superposition, plot the distribution of additional vertical stress and horizontal stress (in both directions) with depth (from the surface indicated by the black horizontal line in the figures, to a depth of 20m, in 0.5 m increments), under the centreline of embankment (2) for the loading case of Figure 1. Show two example calculations (one at depth 0m and one at 10 m) and plot the rest of the results.

 

Q4. Compute the settlement of the sand layer under the centreline of the embankment for the loads shown in Figure 1, assuming that all the loads in Figure 1 are applied instantaneously. Justify your choice of settlement model

 

Q5. Compute the settlement associated to full dissipation of excess pore pressure under the centreline of the embankment, assuming that all the loads shown in Figure 1 are applied instantaneously and never removed. Discretise the silty clay layer into sublayers of 1m thickness and compute stresses at the relevant depth. Provide an example of calculation for the first clay sublayer. Justify your choice of settlement model.

 

Q6. Compute the amount of creep settlement under the centreline of the embankment at 30 years of service.
 

Elevation -30m 0 3m (1) Embankments (1), (2), (4): - Height: 3m - Base (toe to toe): 22m - Batter slopes: 2H:1V - Bulk unit weight: 18 kN/m Coal stockpile (3): Height: 30m - Base (toe to toe): 80m -Bulk unit weight: TBD Line loads on (2): - L1 = 250 kN/m - L2 = 400 kN/m -Each load applied at 3.5 m from centre line CL (2) L2 (3) (4) 10m Depth 80m 80m Figure 1: Cross section of site showing embankments (1), (2) and (4) on which a coal stacker and reclaimer operates. The toes of the coal stockpile (3) coincide with the toes of embankments (2) and (4). CL: centreline. - Height: 3m -Base (toe to toe): 22m - Batter slopes: 2H:1V -Bulk unit weight: 18 kN/m 1 Coal stockpile: - Height: 30m - Base (toe to toe): 80m - Bulk unit weight: TBD K 11m (a) Blue line at centre of embankment Load L2 = 400 kN/m, applied at 3.5 m from dashed line Embankment: - Height: 3m -Base (toe to toe): 22m - Batter slopes: 2H:1V - Bulk unit weight: 18 kN/m (c) 91m (b) (d) Load L1 250 kN/m, applied at 3.5 m from dashed line L1 Figure 2: Elements of Figure 1 and their characteristics, presented separately. (e)