You are required to analyse a slope stability problem using the Swedish method for failure along the slip surface as shown in the figure below. The slope is inclined at an angle of 30° to the horizontal and has a height of 10 m. The ground water table (GWT) is located at a depth of 5.1 m below the crest. It goes along the slope and reaches at the toe level as shown in the figure. Soil investigation revealed that the site consists of a layer of silty clay overlying a layer of sand. Assume c = (40 + 2x) kPa and ϕ = 10° for the silty clay, and c = 0 and ϕ = (30 + x)° for the sand layer; where x is the last digit of your student ID (e.g., if your student ID is 5746189, x = 9). All slices have equal width (b = 2.89 m) and the slices are numbered 1‒6 from left to right. The coordinates of the midpoint of the bases (M , M , M , M , M , M ) of the slices are shown on the right side of the figure. The weights of slices 1‒6 are as follows (in kN/m): W1 = 53.5, W2 = 141.3, W3 = 199.6, W4= 224.8, W5= 206.3, W6 = 108.2. Assume γ = 10 kN/m3 . a) Calculate the average cohesion (c1 , c 2, c3 , c 4, c5 , c6 ) and friction angle (ϕ 1, ϕ2 , ϕ 3, ϕ4 , ϕ5 , ϕ 6) for the 6 slices. b) Calculate the pore pressures acting at the bases of the slices: u1 , u2, u3 , u4, u5 , u6 . c) Calculate the resisting moment and the disturbing moment. (d) Estimate the factor of safety and comment on the stability of the slope. Note: Make approximations wherever necessary. Mention proper units in your calculations.
You are required to analyse a slope stability problem using the Swedish method for failure along the slip surface as shown in the figure below. The slope is inclined at an angle of 30° to the horizontal and has a height of 10 m. The ground water table (GWT) is located at a depth of 5.1 m below the crest. It goes along the slope and reaches at the toe level as shown in the figure.
Soil investigation revealed that the site consists of a layer of silty clay overlying a layer of sand. Assume c = (40 + 2x) kPa and ϕ = 10° for the silty clay, and c = 0 and ϕ = (30 + x)° for the sand layer; where x is the last digit of your student ID (e.g., if your student ID is 5746189, x = 9). All slices have equal width (b = 2.89 m) and the slices are numbered 1‒6 from left to right. The coordinates of the midpoint of the bases (M , M , M , M , M , M ) of the slices are shown on the right side of the figure. The weights of slices 1‒6 are as follows (in kN/m): W1 = 53.5, W2 = 141.3, W3 = 199.6, W4= 224.8, W5= 206.3, W6 = 108.2. Assume γ = 10 kN/m3 .
a) Calculate the average cohesion (c1 , c 2, c3 , c 4, c5 , c6 ) and friction angle (ϕ 1, ϕ2 , ϕ 3, ϕ4 , ϕ5 , ϕ 6) for the 6 slices.
b) Calculate the pore pressures acting at the bases of the slices: u1 , u2, u3 , u4, u5 , u6 .
c) Calculate the resisting moment and the disturbing moment.
(d) Estimate the factor of safety and comment on the stability of the slope.
Note: Make approximations wherever necessary. Mention proper units in your calculations.
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