Cyclic Shear Strain Needed for Liquefaction Triggering and Assessment of Overburden Pressure Factor $K_{\sigma }$

This paper has two objectives. The first is to evaluate the cyclic shear strain needed to trigger liquefaction, ${\gamma }_{cl}$, in clean and silty sands in the field during earthquakes as an alternative to the currently used cyclic resistance ratio (CRR). The second objective is to explore the effect of a high effective overburden pressure, ${\sigma }_{v0}^{\prime }$, on the value of CRR. The first objective is accomplished mainly by using an equation relating ${\gamma }_{cl}$ and CRR valid for shear wave velocity–based liquefaction charts. This equation is supplemented with laboratory results from undrained cyclic strain-controlled tests as well as large-scale and centrifuge model shaking experiments. It is shown that for recent uncompacted clean and silty sand deposits and earthquake magnitude $M_w=7.5$, ${\gamma }_{cl}\approx 0.03\%$, with this value increasing to ${\gamma }_{cl}\approx 0.3\%$ (in some cases to 0.6%) in denser and overconsolidated, preshaken, and compacted sands. These small values of ${\gamma }_{cl}$ in the field are controlled by two factors: excess pore pressure buildup in the soil due to the cyclic straining and the redistribution of excess pore pressures and upward water flow that occurs during shaking. The available evidence suggests that ${\gamma }_{cl}$ is either constant with ${\sigma }_{v0}^{\prime }$ or increases slowly with it. Therefore, in the second objective the simplest assumption is made in the paper that the small ${\gamma }_{cl}$, valid for the low confining pressures covered by the liquefaction charts [${\sigma }_{v0}^{\prime }<200\mathrm{kPa}$ ($\approx 2\mathrm{atm}$)] can be extrapolated without change to confining pressures as high as ${\sigma }_{v0}^{\prime }=800$ or 1,000 kPa ($\approx 8\mathrm{or}10\mathrm{atm}$). This assumption allows derivation of a simple expression for the overburden pressure factor, $K_{\sigma }$. The expression predicts a decrease in $K_{\sigma }$ with confining pressure that is very similar to some curves of $K_{\sigma }$ versus ${\sigma }_{v0}^{\prime }$ proposed in the literature. $K_{\sigma }$ curves are also calculated assuming that ${\gamma }_{cl}$ is proportional to ${({\sigma }_{v0}^{\prime })}^{\beta }$, where $0\le \beta \le 0.5$. Additional experimental research is needed to establish the exact variation of ${\gamma }_{cl}$ with ${\sigma }_{v0}^{\prime }$ for different sands and different parts of the liquefaction charts and to clarify some of the remaining discrepancies between the different approaches.