Square footing, B = 2 m, sandy soil, γ = 18 kN/m³, φ = 30°, Df = 1.5 m, c = 0. Find ultimate bearing capacity.

 Square footing, B = 2 m, sandy soil, γ = 18 kN/m³, φ = 30°, Df = 1.5 m, c = 0. Find ultimate bearing capacity.

Solution:

$$q_u = \gamma Df N_q + 0.4 \gamma B N_\gamma$$

• $N_q \approx 18.4, N_\gamma \approx 22.4$

$$q_u = 18 \cdot 1.5 \cdot 18.4 + 0.4 \cdot 18 \cdot 2 \cdot 22.4 = 858.7 \text{ kPa}$$

Answer: 0.859 MPa

A clay layer of thickness 4 m is subjected to a uniform load of 100 kPa. Coefficient of volume compressibility m v = 0.0004 m²/kN mv​=0.0004 m²/kN. Find the immediate consolidation settlement.

 A clay layer of thickness 4 m is subjected to a uniform load of 100 kPa. Coefficient of volume compressibility 

$m_v = 0.0004 \text{ m²/kN}$. Find the immediate consolidation settlement.

Solution:

Step 1: Settlement formula

$$S = m_v \cdot \sigma \cdot H$$

Where:

• $S$ = settlement

• $m_v$ = coefficient of volume compressibility

• $\sigma$ = applied pressure

• $H$ = thickness of layer

Step 2: Substitute values

$$S = 0.0004 \cdot 100 \cdot 4 = 0.16 \text{ m} = 160 \text{ mm}$$

✅ Answer: Settlement = 160 mm