✨ VIPSolutions

Let's break down the problem step by step for each scenario: --- ### **Given Data** - **Silty Sand (above 2.5 m):** - γ' (Effective unit weight) = 1.92 g/cm³ = 19.2 kN/m³ - **Clay (below 2.5 m):** - γ_s (unit weight of solids) = 2.67 g/cm³ (not used directly unless porosity, water content, etc.) - **Depths:** - Surface to 2.5 m: Silty Sand - 2.5 m to 5.5 m: Clay **Assume:** - Unit weight of water, γ_w = 9.81 kN/m³ --- ### **Formulas** 1. **Total Stress (σ):** \[ \sigma = \sum (\text{unit weight} \times \text{thickness above point}) \] 2. **Pore Water Pressure (u):** \[ u = \gamma_w \times (\text{depth below GWT}) \] 3. **Effective Stress (σ'):** \[ \sigma' = \sigma - u \] --- ## **a) GWT at 1-1 Level (Ground Surface)** **Here, the whole soil profile is saturated. Use saturated unit weights.** #### **At 1-1 (0 m):** - σ = 0 - u = 0 - σ' = 0 #### **At 2-2 (2.5 m):** - σ = 2.5 m × 19.2 kN/m³ = **48 kPa** - u = 2.5 m × 9.81 kN/m³ = **24.53 kPa** - σ' = 48 - 24.53 = **23.47 kPa** #### **At 3-3 (5.5 m):** - Silty Sand: 2.5 m × 19.2 = 48 kPa - Clay (assume γ_sat ≈ γ_s; if not provided, use the same): 3.0 m × 26.7 kN/m³ = 80.1 kPa - σ = 48 + 80.1 = **128.1 kPa** - u = 5.5 m × 9.81 = **53.96 kPa** - σ' = 128.1 - 53.96 = **74.14 kPa** --- ## **b) GWT at 2-2 Level (2.5 m)** **Above GWT: use moist/dry weight. Below GWT: use saturated weight.** #### **At 1-1 (0 m):** - σ = 0 - u = 0 - σ' = 0 #### **At 2-2 (2.5 m):** - σ = 2.5 m × 19.2 kN/m³ = **48 kPa** - u = 0 (since it’s at GWT) - σ' = 48 - 0 = **48 kPa** #### **At 3-3 (5.5 m):** - Silty Sand: 2.5 m × 19.2 = 48 kPa - Clay (below GWT, use γ_sat ≈ 26.7 kN/m³): 3.0 m × 26.7 = 80.1 kPa - σ = 48 + 80.1 = **128.1 kPa** - u = (5.5 - 2.5) × 9.81 = 3.0 × 9.81 = **29.43 kPa** - σ' = 128.1 - 29.43 = **98.67 kPa** --- ## **c) GWT at 3-3 Level (5.5 m, soil dry above GWT)** **All soil above 5.5 m is dry, use dry unit weight.** #### **At 1-1 (0 m):** - σ = 0 - u = 0 - σ' = 0 #### **At 2-2 (2.5 m):** - σ = 2.5 m × 19.2 = **48 kPa** - u = 0 (above GWT) - σ' = 48 - 0 = **48 kPa** #### **At 3-3 (5.5 m):** - Silty Sand: 2.5 m × 19.2 = 48 kPa - Clay: 3.0 m × 26.7 = 80.1 kPa - σ = 48 + 80.1 = **128.1 kPa** - u = 0 (at GWT) - σ' = 128.1 - 0 = **128.1 kPa** --- ### **Summary Table** | Point | Depth (m) | Total Stress σ (kPa) | Pore Water Pressure u (kPa) | Effective Stress σ' (kPa) | |-------|-----------|----------------------|-----------------------------|---------------------------| | **Case a:** GWT at 0 m | | 1-1 | 0 | 0 | 0 | 0 | | 2-2 | 2.5 | 48 | 24.53 | 23.47 | | 3-3 | 5.5 | 128.1 | 53.96 | 74.14 | | **Case b:** GWT at 2.5 m | | 1-1 | 0 | 0 | 0 | 0 | | 2-2 | 2.5 | 48 | 0 | 48 | | 3-3 | 5.5 | 128.1 | 29.43 | 98.67 | | **Case c:** GWT at 5.5 m (dry above) | | 1-1 | 0 | 0 | 0 | 0 | | 2-2 | 2.5 | 48 | 0 | 48 | | 3-3 | 5.5 | 128.1 | 0 | 128.1 | --- If you need the calculations for each layer in more detail, or with different assumptions for unit weights, let me know!