With water table at ground surface, which unit weight is used?

gamma' = gamma_sat - gamma_w = 9.81 kN/m3

2081 Bhadra · 6 marks

Rectangular footing size, 6000 kN

Short answer

Using Terzaghi’s equation for rectangular footing with water table at ground surface (γ' = 9.81 kN/m³), qu = qNq + 0.5(1–0.2B/L)γ'BNγ. Solving for B from safe load 6000 kN with FS=3 gives B=3.2 m, so footing size 3.2 m × 4.8 m.

An RCC column footing rectangular in shape ( $L/B = 1.5/1$ ) rests 1.5 m below the ground surface. The total load to be transmitted including the weight of column and footing is 6000 kN. If the saturated density of sand be 2.0 g/cc for $\phi = 34^\circ$ , $N_q = 41.4$ , $N_\gamma = 42.4$ , find the suitable size of foundation considering the rise of water table to the ground surface. Use FoS = 3. (Values of $N_q$ , $N_\gamma$ as read from the scan.)

Given: $L/B = 1.5$ , $D_f = 1.5$ m, $Q = 6000$ kN, $\phi = 34^\circ$ , $N_q = 41.4$ , $N_\gamma = 42.4$ , $c = 0$ , $\gamma_{sat} = 2.0\ \text{g/cc} = 19.62$ kN/m³, FS = 3, water table at ground surface (worst case). Use $\gamma_w = 9.81$ kN/m³.

Assumptions: Terzaghi's equation for a rectangular footing with $B/L = 1/1.5 = 0.667$ . The load of 6000 kN includes the weights of column and footing, so the gross allowable pressure is $q_u/F$ .

\begin{aligned} \gamma' &= 19.62 - 9.81 = 9.81\ \text{kN/m}^3 \\ q &= \gamma' D_f = 9.81 \times 1.5 = 14.715\ \text{kN/m}^2 \\ q_u &= qN_q + 0.5\left(1 - 0.2\tfrac{B}{L}\right)\gamma' B N_\gamma \\ &= 14.715 \times 41.4 + 0.5(1 - 0.133)(9.81)(42.4)B \\ &= 609.2 + 180.3\,B\ \text{kN/m}^2 \end{aligned}

Load capacity: $Q = \dfrac{q_u}{3} \times B \times L = \dfrac{609.2 + 180.3B}{3} \times 1.5B^2 = 6000$

Solving for $B$ by trial and error gives $B = 3.185$ m.

$B$ (m)	$L = 1.5B$ (m)	$q_u$ (kN/m²)	Safe load $= q_uBL/3$ (kN)
3.0	4.5	1149.9	5174.7
3.2	4.8	1186.0	6072.2
3.3	4.95	1204.0	6555.8

Answer: provide a rectangular footing of 3.2 m × 4.8 m (safe load 6072 kN > 6000 kN).

✓ Answer checked by Claude Sonnet 5.5

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