Relationship between Specific Gravity and Hydraulic Gradient for Quick Condition in Sand with Void Ratio of 0.5

Specific Gravity (G) is a measure of the density of soil particles, while the hydraulic gradient (i) is a measure of the rate of flow of water through soil. Quick condition in soil occurs when the hydraulic gradient is high enough to cause the soil to lose its shear strength and become unstable. The relationship between G and i for quick condition in sand with a void ratio of 0.5 can be determined using the following equation:

G = 1.5i - 1

Explanation

- Definition of Specific Gravity: Specific Gravity (G) is defined as the ratio of the density of a substance to the density of a reference substance (usually water). For soil particles, the specific gravity is typically between 2.5 and 2.7.
- Definition of Hydraulic Gradient: Hydraulic Gradient (i) is defined as the change in hydraulic head (water pressure) per unit distance in the direction of flow. It is a measure of the rate of flow of water through soil.
- Quick Condition in Soil: Quick condition in soil occurs when the soil loses its shear strength and becomes unstable due to high pore water pressure. This can happen when the hydraulic gradient is high enough to cause the soil particles to move and rearrange, leading to a loss of stability.
- Void Ratio: Void ratio (e) is defined as the ratio of the volume of voids (empty space) to the volume of solids in a soil sample. For sand with a void ratio of 0.5, this means that half of the volume of the soil sample is made up of empty space.
- Deriving the Equation: The relationship between G and i for quick condition in sand with a void ratio of 0.5 can be determined using empirical data and statistical analysis. The equation G = 1.5i - 1 has been found to provide a good fit to the data for many types of sand soils.
- Interpretation of the Equation: The equation tells us that as the hydraulic gradient increases, the specific gravity of the soil particles must also increase in order to prevent quick condition. Specifically, for sand with a void ratio of 0.5, the specific gravity must be at least 1.5 times the hydraulic gradient, minus 1. For example, if the hydraulic gradient is 0.5, the specific gravity must be at least 0.25 (1.5 x 0.5 - 1) to prevent quick condition.

Conclusion

The correct equation to determine the relationship between specific gravity and hydraulic gradient for quick condition in sand with a void ratio of 0.5 is G = 1.5i - 1. This equation tells us that the specific gravity of the soil particles must increase as the hydraulic gradient increases to prevent quick condition.