A Parametric Study on the Effect of Drainage on Sand Liquefaction under High Overburden Pressure

The effect of high overburden pressure above 1 atm on sand liquefaction potential is typically evaluated based on cyclic undrained testing, with the overburden pressure correction factor, $K_{\sigma }<1.0$ and $K_{\sigma }$ decreasing as the pressure increases. Recent centrifuge experiments of a prototype 5 m-thick clean sand layer having a permeability $1.2\times {10}^{-4}\mathrm{m}/\mathrm{s}$, with free drainage at the top and subjected to 1 and 6 atm overburden pressures, show that a high overburden pressure may increase partial drainage. As a result, the measured field overburden pressure factor, $(K_{\sigma }{)}_{\mathrm{field}}$ was estimated to be >1.0 instead of $<1.0$ in these centrifuge tests. A parametric study is presented here that extends the centrifuge results for a relative density, $D_{\mathrm{r}}=45\%$ and free top drainage, utilizing a high-fidelity, calibrated numerical model (P2Psand in FLAC 3D). A stepped acceleration base input is used that ensures a uniform cyclic shear stress amplitude at the elevation of maximum pore pressure ratio. The main parameters varied in the numerical study are overburden pressure, ${\sigma }_{\mathrm{v}0}^{\prime }$ (1-12 atm); sand permeability, $k$ (${10}^{-6}$ to ${10}^{-3}\mathrm{m}/\mathrm{s}$); and sand layer thickness, $H$ (2-10 m). A new drainage factor, $K_{\mathrm{dr}}\ge 1.0$, is proposed to separate the usual undrained $K_{\sigma }$ from the effect of partial drainage. The recommendation is to evaluate the overburden pressure factor to be used in liquefaction charts, $(K_{\sigma }{)}_{\mathrm{field}}$, as the product of two factors, $(K_{\sigma }{)}_{\mathrm{field}}=K_{\sigma }\times K_{\mathrm{dr}}$. The study shows that for constant ${\sigma }_{\mathrm{v}0}^{\prime }=6$ atm, $K_{\mathrm{dr}}\approx 1.4–1.7$ when $k={10}^{-4}$ to ${10}^{-5}\mathrm{m}/\mathrm{s}$, even for a very thick sand layer of $H=10\mathrm{m}$. Still for a constant ${\sigma }_{\mathrm{v}0}^{\prime }=6$ atm, $K_{\mathrm{dr}}$ decreases considerably to values close to 1.0 for a low $k\approx {10}^{-5}\mathrm{m}/\mathrm{s}$, when the layer thickness is $H=7$ or 8m or greater. And for constant $k\approx {10}^{-4}\mathrm{m}/\mathrm{s}$ and ${\sigma }_{\mathrm{v}0}^{\prime }=12$ atm, $K_{\mathrm{dr}}\approx 1.4$ if $H=5–10\mathrm{m}$, increasing to $K_{\mathrm{dr}}\approx 1.8$ if the layer thickness decreases to $H=2\mathrm{m}$. The parametric study provides insight on when the current State-of-Practice of using only undrained $K_{\sigma }$ becomes too conservative and should be supplemented with consideration of partial drainage through use of factor $K_{\mathrm{dr}}$. Ready-to-use charts are provided to evaluate $K_{\mathrm{dr}}$ and $(K_{\sigma }{)}_{\mathrm{field}}$ for a $D_{\mathrm{r}}=45\%$ sand layer with free top drainage.

This research challenges conventional notions of sand liquefaction risk assessment. Traditionally, higher overburden pressures were thought to increase this risk, as indicated by the factor $K_{\sigma }<1.0$. However, recent findings, supported by centrifuge experiments and advanced numerical modeling, reveal a more nuanced reality. Under specific field conditions, especially with elevated overburden pressures, partial drainage in clean sand deposits can enhance the layer stability, resulting in $(K_{\sigma }{)}_{\mathrm{field}}$ values greater than 1.0. This means that high overburden pressures may not necessarily lead to increased liquefaction vulnerability, contrary to previous assumptions. To better guide practical applications, a novel drainage factor, $K_{\mathrm{dr}}$, is introduced. When combined with $K_{\sigma }$, it provides a more accurate assessment of liquefaction potential. For engineers and practitioners, this means considering both $K_{\sigma }$ and $K_{\mathrm{dr}}$ when evaluating the liquefaction potential of loose sand layers with at least one drainage boundary. This study supplies valuable insights into when the current practice of relying solely on undrained $K_{\sigma }<1.0$ may be overly conservative. It offers ready-to-use charts to assess $K_{\mathrm{dr}}$ and $(K_{\sigma }{)}_{\mathrm{field}}$, empowering practitioners to make more informed decisions regarding liquefaction risk. It must be noted that an actual field case history is expected to require some engineering judgment due to soil stratigraphy and the usual spatial variability associated with field deposits.