Understanding Quick Sand Condition

A quick sand condition, also known as boiling sand, occurs when the upward flow of water through a soil strata creates a buoyant force that counteracts the gravitational force on the soil particles. This results in a loss of effective stress, causing the soil to behave like a liquid.

The condition is reached when the hydraulic gradient ($i$) equals the critical hydraulic gradient ($i_c$). The critical hydraulic gradient is the minimum gradient required to initiate the quick sand condition.

Calculating Critical Hydraulic Gradient ($i_c$)

The critical hydraulic gradient depends on the soil's properties, specifically the specific gravity of the solids ($G_s$) and the void ratio ($e$). The formula is:

$i_c = \frac{(G_s - 1)}{(1 + e)}$

Given:

• Specific gravity ($G_s$) = 2.5
• Void ratio ($e$) = 0.5

Substituting the values:

$i_c = \frac{(2.5 - 1)}{(1 + 0.5)} = \frac{1.5}{1.5} = 1$

So, the critical hydraulic gradient is 1.

Determining Required Head (h)

The relationship between the hydraulic gradient ($i$), the head loss ($h$), and the length of the flow path ($H$) is given by $i = \frac{h}{H}$. For the quick sand condition to develop, the actual gradient must equal the critical gradient ($i = i_c$).

Given:

• Strata thickness ($H$) = 3 m
• Critical hydraulic gradient ($i_c$) = 1

We need to find the head ($h$) required for $i_c = \frac{h}{H}$:

$1 = \frac{h}{3 \text{ m}}$

Solving for $h$:

$h = 1 \times 3 \text{ m} = 3 \text{ m}$

Therefore, a head of 3 m is required for a quick sand condition to develop.