JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech IV Year ADVANCED STRUCTURAL DESIGN Previous Question Paper (July/August - 2022 - R18)

To design a counterfort retaining wall for a height of 4 m, we first determine the earth pressure coefficients using Rankine's theory.

• Earth Pressure Coefficient: Given φ = 30°, the active earth pressure coefficient is:
  K_a = (1 - sin 30°) / (1 + sin 30°) = 1/3
• Design Parameters: Height (H) = 4 m. Density of soil (γ) = 18 kN/m³. Safe Bearing Capacity (SBC) = 160 kN/m².
• Stability Check: The base width (B) is typically taken as 0.6H to 0.7H. Assuming B = 2.5 m. The total active thrust (P_a) per meter length is:
  P_a = 0.5 × γ × H² × K_a = 0.5 × 18 × 4² × (1/3) = 48 kN/m
• Structural Components:
  • Stem: Designed as a continuous slab spanning horizontally between counterforts. The maximum bending moment at the base is calculated using the span of 2 m c/c.
  • Heel Slab: Designed as a continuous slab spanning between counterforts, subjected to downward earth pressure and upward soil reaction.
  • Counterforts: Designed as T-beams acting as vertical cantilevers. The reinforcement is provided to resist the tension generated by the earth pressure acting on the stem.
• Reinforcement Details: Using M25 concrete and Fe500 steel, the effective depth is calculated based on the bending moment. Provide minimum reinforcement as per IS 456:2000 requirements for temperature and shrinkage.
• Safety Checks: Ensure the factor of safety against sliding (F_s = μΣV / ΣH) is ≥ 1.5 and against overturning (F_o = ΣM_R / ΣM_O) is ≥ 1.5.

To design a cantilever retaining wall for a height H = 3 m above ground level, we assume a total height including embedment depth D. Assuming a foundation depth of 1.0 m, total height H_t = 4.0 m.

• Design Constants: Angle of internal friction φ = 25°. Coefficient of active earth pressure K_a = (1 - sin φ) / (1 + sin φ) = (1 - 0.4226) / (1 + 0.4226) ≈ 0.406.
• Earth Pressure: Total horizontal force P_a = 0.5 × γ × K_a × H_t².
P_a = 0.5 × 18 × 0.406 × 4.0² = 58.46 kN/m
• Stability Checks: The wall must be checked for overturning and sliding. The factor of safety against sliding is FOS_s = μ × ΣW / P_a. Given μ = 0.5, the weight of the wall and soil surcharge must be sufficient to ensure FOS_s ≥ 1.5.
• Stem Design: The stem acts as a cantilever beam fixed at the base. The maximum bending moment at the base is M_u = 1.5 × (P_a × H_t / 6).
M_u = 1.5 × (58.46 × 4.0 / 6) = 58.46 kNm/m
• Reinforcement: Using M30 concrete and Fe500 steel, the effective depth d is calculated using the limiting moment of resistance formula:
M_u,lim = 0.133 × f_ck × b × d²
• Assuming a base thickness of 400 mm and stem thickness tapering from 300 mm at base to 200 mm at top, calculate required steel area A_st using M_u = 0.87 × f_y × A_st × d × (1 - (A_st × f_y) / (b × d × f_ck)). Provide main vertical reinforcement on the back face of the stem.
• Base Slab: Design the heel and toe slabs as cantilevers. The heel slab is subjected to downward soil pressure and upward soil reaction, while the toe slab is subjected to upward soil pressure. Ensure the base width is sufficient to keep maximum soil pressure below 180 kN/m².