Test: Soil Mechanics- 7 - Civil Engineering (CE) MCQ

The Rankine's theory assumes that there is no wall friction, the ground and failure surfaces are straight planes, and that the resultant force acts parallel to the backfill slope.

The soil mass is homogeneous and semi-infinite and retaining wall yields about the base.

In case of retaining structures, the earth retained may be filled up earth or natural soil. These backfill materials may exert certain lateral pressure on the wall.

For the retaining with supporting backfill of cohesionless soil having an angle of internal friction ϕ and inclined at an angle β with the horizontal. Active Earth Pressure (P_a) acts at a height H/3 from the base of the wall and at an angle β with the horizontal

The actual shape of a slip surface in the case of finite slopes is curvilinear. The assumption of a circular slip surface and its application for stability analysis was developed in Sweden. The method is known as the Swedish circle method or method of slices. This method neglects the effect of forces acting on the sides of the vertical strips. The error due to this is on safe side. i.e. the factor of safety obtained is generally less than that obtained from more accurate methods such as Bishop’s method which also consider the forces on the sides of vertical strips.

ϕ_T = 0 means that friction is not mobilized. In the actual case the resistance to shear will be due to friction and cohesion both thus exact value of factor of safety cannot be obtained for ϕ_T = 0.

Total active earth pressure at 2m below the Ground level = k_aγ×2

Active thrust:
P_a1 = 12 × k_a × γ × 2 × 2 = 
P_a1 = 9.756 kN/m
Total active earth pressure at 5m below the Ground level:

= k_a × γ ×2 + k_aγ¹×3 + γ_ω × 3

= 0.271 × 18 × 2 + 0.271 × [20 – 10] × 3 + 10 × 3

= 47.88 kN/m²

Active thrust:-

P_a = 9.756 + 29.27 + 12.195 + 45

P_a = 96.221 kN/m

Concept: Stability Number is given by:

C_m = mobilised cohesion

γ = unit weight of the soil

H = Depth of vertical cut

S_n = Stability No.

Factor of Safety w.r.t. cohesion

C = Cohesion of soil

Stability factor = 1/ Stability Number

Calculation:

C = 50 kN/m²

γ = 22 kN/m³

H = 8.30 m

F_c = 2

FOS = 1.5

If there is seepage parallel to the slope

β = 11.095°

The slip will occur when shear stress is greater than shear strength.

Assumption 1

z₁ ≤ 4m

Hence assumption wrong.

Assumption 2

Z > 4m

Hence depth of slip = 4 + 4.13 = 8.13 m

Active earth Pressure coefficient (k_a)

Active earth Pressure at Point P is

H₁ = 4m

γ₁ = 19 kN/m³
Active earth Pressure at Point Q is


 

P_V = total vertical pressure at point Q

P_V = 19 × 4 + 18 × 4 = 148 kN/m²

K_a3=1

C₃ = 30 kN/m³

K_a = (1 – sin φ)/ (1 + sin φ) = 0.33

At z = 0, σ’_v = 0

p_a = σ_v k_a – 2c √ka = – 2 × 5 × √0.33

= – 5.77 kPa

Depth of tension crack

(z_v) = 2c/(r √ka) = (2 × 5)/(17.5 × √0.33) = 0.99m

At bottom,

σ'_v = (17.55 x 5) = 87.5 kPa

P_a = 87.5 × 0.33 – 5.77 = 23.392 kPa

After formation of tension crack = 1/2 × 23.393 × 4.01 = 46.9 kN/m