Question

A shallow strip footing of width 2 m is embedded at a depth of 1.5 m below the ground surface in a homogeneous pure clay with angle of internal friction equal to zero. The unit weight of soil is 20 kN/m³ and the undrained cohesion of soil is 20 kN/m². Due to a rise of the ground water table from far below the founding depth to the ground surface during the monsoon season, the magnitude of percentage change in the net ultimate bearing capacity of the footing as per Terzaghi's theory is ______ (rounded off to two decimal places).

Hint:

For \(\phi=0\) soils, Terzaghi's \(N_q=1\) makes the overburden term cancel exactly in the net bearing capacity, so \(q_u(\text{net})=cN_c\) regardless of the water table.

Answer 1

Correct Answer: 0

Step 1: Recall Terzaghi's bearing capacity equation for a strip footing.
\[ q_u = cN_c + qN_q + 0.5\gamma B N_\gamma \]
For a purely cohesive soil (\(\phi = 0\)), the bearing capacity factors take the special values \(N_c = 5.7\), \(N_q = 1\), and \(N_\gamma = 0\).

Step 2: Write the gross and net ultimate bearing capacity.
Here \(q = \gamma D_f\) is the effective overburden pressure at the footing base. Since \(N_\gamma = 0\), the width term vanishes entirely:
\[ q_u(\text{gross}) = cN_c + qN_q = cN_c + q \]
The net ultimate bearing capacity removes the overburden pressure that already existed in the ground before the footing was built:
\[ q_u(\text{net}) = q_u(\text{gross}) - q = cN_c + q(N_q-1) \]

Step 3: Substitute \(N_q = 1\).
Since \(N_q = 1\), the term \(q(N_q-1) = q(1-1) = 0\). So
\[ q_u(\text{net}) = cN_c \]
The net ultimate bearing capacity depends only on cohesion and \(N_c\); it contains no \(\gamma\), \(D_f\), or water table term at all.

Step 4: Apply this before and after the water table rise.
Before the rise, \(q_u(\text{net}) = cN_c = 20 \times 5.7 = 114\) kPa.
After the rise, the overburden pressure at the footing base would ordinarily be recomputed with the submerged unit weight, reducing \(q\). But since the net capacity formula has already cancelled the \(q\) term completely in Step 3, this change has zero effect on \(q_u(\text{net})\); it stays at 114 kPa.

Step 5: Compute the percentage change.
\[ \%\text{change} = \frac{114-114}{114}\times100=0 \]

Final Answer:
For a purely cohesive (\(\phi=0\)) soil, Terzaghi's net ultimate bearing capacity does not depend on unit weight or water table position, because \(N_\gamma=0\) removes the width/weight term and \(N_q=1\) makes the overburden term cancel exactly in the net definition.
\[ \boxed{\%\text{change} = 0.00\%} \]