Question Bank • QB_SWCE_GATE_004 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Soil Mechanics

Subtopic: Engineering properties of soils

Question Statement:

A stratified soil deposit consists of three horizontal layers of thickness $1.0\text{ m}, 2.0\text{ m}$, and $3.0\text{ m}$ with hydraulic conductivities of $2 \times 10^{-4}\text{ cm/s}, 4 \times 10^{-4}\text{ cm/s}$, and $6 \times 10^{-4}\text{ cm/s}$, respectively. The equivalent horizontal hydraulic conductivity ($K_h$) parallel to the bedding planes is ________ $\times 10^{-4}\text{ cm/s}$ (round off to 2 decimal places).

Answer Key:

4.67

Step-by-Step Solution & Explanation

Equivalent Horizontal Conductivity: $K_h = \frac{(2 \times 1.0) + (4 \times 2.0) + (6 \times 3.0)}{1.0 + 2.0 + 3.0} = \frac{2 + 8 + 18}{6.0} = \frac{28}{6.0} \approx 4.6667 \times 10^{-4}\text{ cm/s}$ Rounding to 2 decimal places: **4.67**.
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