Refer to Figure 15.50. Given that β = 55°, γ = 19 kN/m3, ϕ′ = 17°, c′ = 57.4 kN/m2, and H = 13.7 m, determine the factor of safety with respect to sliding. Assume that the critical sliding surface is a plane.

7. A long slope is formed in a soil with shear strength parameters: c' = 0 and '= 34°. A firm stratum lies below the slope and it is assumed that the water table may occasionally rise to the surface, with seepage taking place parallel to the slope. Use Ysat = 18 kN/m³ and y = 10 kN/m³. The Yw maximum slope angle (in degrees) to ensure a factor of safety of 1.5, assuming a potential failure surface parallel to the slope, would be

Please solve with steps

1. Considering the figure and table below, if you know that H' = 7.158 m, Ph = 158.75 kN/m, Pp = 215 kN/m, k₁ =k2=0.67. Determine the factor of safety against Sliding and overturning. 15m-D T -18 kN/m dj-M7 5=0 Section Area Weight/unit length Moment arm H,-0.458 m from point C no. (m²) (kN/m) (m) Moment (kN-m/m) 1 6 x 0.5-3 70.74 1.15 81.35 2 (0.2)60.6 14.15 0.833 11.79 3 4 x 0.7 = 2.8 66.02 2.0 132.04 4 6 x 2.6 = 15.6 280.80 2.7 758.16 H.-6m 5 (2.6)(0.458) = 0.595 10.71 3.13 33.52 P 10 P₁ = 28.0 ΣΕ = 470.42 4.0 112.0 1128.86 = EMR H,=0.7 m C 07f0.72.6m 12-19 kN/m³ -20° -40 kN/m² 2. Considering the figure and table below, if you know that H' = 7.158 m, Ph = 158.75 kN/m, Pp = 215 kN/m, k₁ = k2 = 0.67, e = 0.406 m. Find q heel 0.5m 1.5 m = D 0.7m H,-0.458 m Section no." Area (m²) Weight/unit length (kN/m) Moment arm from point C (m) Moment (kN-m/m) 7-18 kN/m 4;=30 6 x 0.5=3 70.74 1.15 81.35 -0 2 (0.2)6 = 0.6 14.15 0.833 11.79 H-6m 3 4 x 0.7 = 2.8 66.02 2.0 132.04 P 4 10 6 x 2.6 = 15.6…