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 an angle of internal friction zero. Consider unit weight of soil as 20 kN/m³ and undrained cohesion of soil as 20 kN/m². Due to rise of ground water table from far below the founding depth to the ground surface in monsoon season, the magnitude of percentage change in the net ultimate bearing capacity as per Terzaghi’s theory is_________ (rounded off to two decimal places).

The correct answer is 0.

Step-by-Step Explanation:

According to Terzaghi's bearing capacity theory, the ultimate bearing capacity ($q_u$) of a shallow strip footing is given by the equation:
$$q_u=c{N}_c+q{N}_q+0.5\gamma B{N}_{\gamma }$$
where:
- $c$ is the cohesion of the soil ($20\text{kN/m}{2}^{}$)
- $q=\gamma D_f$ is the effective overburden pressure at the founding depth
- $\gamma$ is the unit weight of the soil
- $B$ is the width of the footing ($2\text{m}$)
- $D_f$ is the depth of the footing ($1.5\text{m}$)
- $N_c,N_q,N_{\gamma }$ are Terzaghi's bearing capacity factors

For a homogeneous pure clay with an angle of internal friction $\phi =0$, Terzaghi's bearing capacity factors are:
$$N_c=5.7$$
$$N_q=1.0$$
$$N_{\gamma }=0$$

Substituting these factor values into Terzaghi's equation gives:
$$q_u=c{N}_c+\gamma D_f\left(1\right)+0.5\gamma B\left(0\right)=c{N}_c+\gamma D_f$$

The net ultimate bearing capacity ($q_{\mathrm{nu}}$) is defined as the ultimate bearing capacity minus the overburden pressure ($\gamma D_f$):
$$q_{\mathrm{nu}}=q_u-\gamma D_f$$
$$q_{\mathrm{nu}}=(c{N}_c+\gamma D_f)-\gamma D_f=c{N}_c$$

Since the net ultimate bearing capacity of pure clay is simplified to $q_{\mathrm{nu}}=c{N}_c$, it is entirely independent of the unit weight of the soil ($\gamma$) and the surcharge pressure. Consequently, the position of the ground water table has no effect on $q_{\mathrm{nu}}$ because the terms affected by the water table (the unit weight in the overburden and the weight of the soil block below the footing) cancel out or are zero when $\phi =0$ ($N_{\gamma }=0$ and $N_q=1$).

Therefore, the percentage change in the net ultimate bearing capacity due to the rise of the ground water table is 0%.