According to Bekker's classical terramechanics equation for pressure-sinkage of a rigid plate on agricultural soil: $p = \left(\frac{k_c}{b} + k_\phi\right) z^n$. For a soil with cohesive modulus $k_c = 40\text{ kPa}\cdot\text{m}^{n-1}$, frictional modulus $k_\phi = 1600\text{ kPa}\cdot\text{m}^{n-1}$, and sinkage exponent $n = 1.0$. A footing plate of width $b = 0.20\text{ m}$ sinks to a depth of $z = 0.05\text{ m}$. The contact pressure $p$ in $\text{kPa}$ is ________ (round off to integer).
Answer Key:
90
Step-by-Step Solution & Explanation
```
Bekker Pressure-Sinkage Model:
p = (k_c / b + k_phi) * z^n
k_c = 40, b = 0.20 m, k_phi = 1600, n = 1.0, z = 0.05 m
```
**Step-by-step Calculation:**
1. Modulus bracket calculation:
$\frac{k_c}{b} = \frac{40}{0.20} = 200\text{ kPa/m}$
$\frac{k_c}{b} + k_\phi = 200 + 1600 = 1800\text{ kPa/m}$
2. Calculating contact pressure with $z = 0.05\text{ m}$ and $n = 1.0$:
$p = 1800 \times (0.05)^1 = 90\text{ kPa}$