Numerical Simulation of the Effect of High Confining Pressure on Drainage Behavior of Liquefiable Clean Sand

This article presents numerical simulations investigating pore pressure buildup of a sand layer with a free drainage boundary at the top under both low and high overburden pressures and subjected to earthquake base excitation. The numerical runs simulate two centrifuge experiments previously conducted and reported. In these tests, a 5-m layer of clean Ottawa sand with relative density $D_r=45\%$ was tested under overburden pressures of ∼100 and ∼600 kPa (1 and 6 atm). The simulations were performed using Dmod2000, a nonlinear effective stress numerical one-dimensional (1D) site response analysis code. The tests revealed that the response was partially drained rather than undrained, with much more partial drainage at ∼600 kPa (6 atm) compared to ∼100 kPa (1 atm). The simulations correctly modeled this behavior, with very good agreement between simulated and measured centrifuge excess pore pressures. A key aspect of this good accord in the simulations was the correct selection in the simulations of the 1D drained volumetric stiffness of the sand, $M^{\prime }=1/m_v$, because the coefficient of consolidation, $c_v$, is proportional to $M^{\prime }$. Both $c_v$ and $M^{\prime }$ were 2.5–3 times greater at ∼600 kPa (6 atm) than at ∼100 kPa (1 atm) in both centrifuge tests and simulations. Any future simulation of pore pressure response of sand under field drainage conditions needs to consider this large increase in volumetric stiffness at high overburden pressure. Good agreement was found between values of $M^{\prime }$ back-calculated from the centrifuge tests and from a consolidometer test on a different sand reported in the literature. The value of $M^{\prime }$ seems to increase approximately with the root square of the overburden pressure, and future simulations for high overburden and realistic field drainage conditions should account for this increase. The proper high-pressure correction factor, $K_{\sigma }$, to be used in conjunction with liquefaction charts may be higher than 1 for some realistic field drainage conditions due to this substantial decrease of sand compressibility under high overburden pressure.