Halliday, Resnick & Walker — Measurement: Problem 51

Density and liquefaction. A heavy object can sink into the ground during an earthquake if the shaking causes the ground to undergo liquefaction, in which the soil grains experience little friction as they slide over one another. The ground is then effectively quicksand. The possibility of liquefaction in sandy ground can be predicted in terms of the void ratio \( e \) for a sample of the ground: \( e = V_{voids}/V_{grains} \). Here, \( V_{grains} \) is the total volume of the sand grains in the sample and \( V_{voids} \) is the total volume between the grains (in the voids). If \( e \) exceeds a critical value of 0.80, liquefaction can occur during an earthquake. What is the corresponding sand density \( \rho_{sand} \)? Solid silicon dioxide (the primary component of sand) has a density of \( \rho_{SiO_2} = 2.600 \times 10^3 \text{ kg/m}^3 \).