The coefficient of permeability of soil

Question

Examoogle · Accepted Answer

The correct answer is Option A: increases with increase in temperature. The coefficient of permeability ($k$) of soil is directly proportional to the unit weight of the pore fluid ($\gamma_w$) and inversely proportional to the dynamic viscosity of the pore fluid ($\mu$). As temperature increases, the viscosity of water decreases significantly, leading to an increase in the coefficient of permeability.

Step-by-Step Solution & Concepts:
The coefficient of permeability ($k$) of soil is directly proportional to the unit weight of the pore fluid ($\gamma_w$) and inversely proportional to the dynamic viscosity of the pore fluid ($\mu$). As temperature increases, the viscosity of water decreases significantly, leading to an increase in the coefficient of permeability.

Working Principle: According to Darcy's Law and the Kozeny-Carman equation, $k = \frac{\gamma_w}{\mu} K$, where $K$ is the intrinsic permeability of the soil skeleton (a property of the pore structure). Because viscosity $\mu$ of water drops rapidly with a rise in temperature, the ratio $\frac{\gamma_w}{\mu}$ increases, effectively allowing water to flow more easily through the soil pores.

Key Formulas: $k = \frac{\gamma_w}{\mu} K$ — General permeability equation; $k_{T} = k_{20} \cdot \frac{\mu_{20}}{\mu_{T}}$ — Temperature correction formula

Key Points: Permeability is strongly dependent on the viscosity of the pore fluid.; The intrinsic permeability ($K$) remains constant for a given soil structure.; Standard reporting of permeability is usually corrected to $20^{\circ}C$ ($k_{20}$).

Advantages: Allows for standardized testing results; Helps in predicting seepage behavior in varied climatic conditions

Disadvantages: Requires constant temperature monitoring during laboratory tests; Variations in viscosity can introduce significant errors if not corrected

Applications: Dam seepage analysis; Groundwater flow modeling; Foundation drainage design

Additional Info: The viscosity of water decreases by approximately 2-3% per degree Celsius increase near room temperature.. Option B and C are incorrect as they imply an inverse or null relationship, which contradicts the fluid dynamics of viscous flow through porous media.

Answer: A is correct — The coefficient of permeability increases with an increase in temperature due to the decrease in the dynamic viscosity of the pore fluid.

Exam Tip: Always remember that permeability is not just a soil property but a fluid-soil interaction; if the fluid is thicker (higher viscosity), the soil appears less permeable.

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Option B: increases with decrease in temperature

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Option C: decreases with increase in temperature

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Option D: has no relation with temperature

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