In a soil specimen, the total stress, effective stress, hydraulic gradient, and critical hydraulic gradient are σ, σ’, i and i _c, respectively. For initiation of quicksand condition, which one of the following statements is TRUE?

Question

Prepp Team · Accepted Answer

The question asks to identify the correct statement for the initiation of quicksand condition in a soil specimen, considering total stress (\(\sigma\)), effective stress (\(\sigma'\)), hydraulic gradient (\(i\)), and critical hydraulic gradient (\(i_c\)).

Quicksand Condition: An Overview

The quicksand condition, often referred to as boiling, is a phenomenon that occurs in saturated cohesionless soils, such as sands and silts. It happens when the upward flow of water exerts enough pressure to counteract the submerged weight of the soil particles. When this balance is reached, the soil loses its shear strength and behaves like a viscous liquid, making it unable to support any load. This situation is extremely dangerous in construction, especially during excavation work below the water table.

Effective Stress and Quicksand Initiation

Effective stress (\(\sigma'\)) is a fundamental concept in soil mechanics. It represents the stress transferred through the soil skeleton, i.e., the force carried by the solid particles at their contact points. It is defined by Terzaghi's principle as:

\(\sigma' = \sigma - u\)

Where:

\(\sigma\) is the total stress (total load per unit area).
\(u\) is the pore water pressure.

For the initiation of quicksand condition, the most critical requirement is that the effective stress (\(\sigma'\)) within the soil specimen becomes zero. When effective stress is zero, the soil particles lose their inter-granular contact, and the soil loses all its shear strength, effectively becoming suspended in water.

Critical Hydraulic Gradient Explained

The hydraulic gradient (\(i\)) is a measure of the rate of change of hydraulic head per unit length in the direction of flow. In the case of upward seepage, a higher hydraulic gradient means a stronger upward flow force.

The critical hydraulic gradient (\(i_c\)) is the specific value of the hydraulic gradient at which the quicksand condition initiates. At this point, the upward seepage force per unit volume of soil becomes exactly equal to the submerged weight per unit volume of the soil. The formula for the critical hydraulic gradient is:

\(i_c = \frac{\gamma_{sub}}{\gamma_w} = \frac{(G-1)\gamma_w / (1+e)}{\gamma_w} = \frac{G-1}{1+e}\)

Where:

\(\gamma_{sub}\) is the submerged unit weight of the soil.
\(\gamma_w\) is the unit weight of water.
\(G\) is the specific gravity of soil solids.
\(e\) is the void ratio of the soil.

The quicksand condition begins precisely when the upward hydraulic gradient (\(i\)) reaches the critical hydraulic gradient (\(i_c\)), i.e., \(i = i_c\).

Analyzing Quicksand Conditions

To summarize, for the initiation of quicksand condition in a soil specimen, two conditions must be met simultaneously:

The effective stress (\(\sigma'\)) must become zero. This indicates that the soil particles are no longer pressing against each other and have lost their frictional resistance.
The hydraulic gradient (\(i\)) must be equal to the critical hydraulic gradient (\(i_c\)). This signifies that the upward seepage force balances the effective weight of the soil.

Thus, the correct statement for the initiation of quicksand condition is \(\sigma' = 0 \text{ and } i = i_c\).

Evaluating the Statements for Quicksand

Statement	Analysis for Quicksand Condition
`\(\sigma' = 0 \text{ and } i = i_c\)`	This statement accurately defines the conditions for the initiation of quicksand condition. When the hydraulic gradient reaches its critical hydraulic gradient, the upward seepage force becomes equal to the submerged weight of the soil, leading to zero effective stress.
`\(\sigma = 0 \text{ and } i = i_c\)`	This statement is incorrect. Total stress (`\(\sigma\)`) is the sum of effective stress and pore water pressure. In a soil mass under gravity, total stress cannot be zero. It is the effective stress that reduces to zero during quicksand, not the total stress.
`\(\sigma' \ne 0 \text{ and } i = i_c\)`	This statement is incorrect. If the hydraulic gradient is equal to the critical hydraulic gradient, by definition, the upward seepage force exactly balances the submerged weight of the soil. This leads directly to a condition where the effective stress becomes zero. Therefore, `\(\sigma'\)` must be zero if `\(i = i_c\)` for quicksand.
`\(\sigma' \ne 0 \text{ and } i \ne i_c\)`	This statement describes a stable soil condition where quicksand is not occurring. The effective stress is not zero, meaning the soil retains its strength, and the hydraulic gradient is not at its critical value.

Conclusion on Quicksand Initiation

In summary, the initiation of quicksand condition is characterized by a state where the soil loses its shear strength entirely. This occurs precisely when the effective stress in the soil specimen becomes zero, which is a direct consequence of the hydraulic gradient reaching its critical hydraulic gradient. These two conditions are interdependent and define the onset of quicksand.