Displacements from the 2014 Iquique $M8.2$ Earthquake and $M7.7$ Aftershock Added to a Sliding Displacement Model

There are many empirical relations for estimating sliding displacements caused by seismic excitation of a mass resting on a rigid plane. Usually the accelerograms from a suite of earthquakes are input to a Newmark sliding block analysis, and regression analysis of the displacements against a set of parameters gives the empirical relation. When the relations are applied to accelerograms from events not in the original database, the accuracy of the predictions varies considerably (Urzúa and Christian 2013). Combining an analytical expression for the Arias intensity of a sinusoid with the sliding block displacement for sinusoidal input, Urzúa and Christian (2013) obtained the following estimate of displacements:where $D_R$ = sliding displacement (meters or centimeters); $D_N$ = normalized displacement; $a_c$ = critical horizontal acceleration at which sliding starts; $a_{\max }$ = maximum acceleration in the accelerogram; ${\beta }_0$ and ${\beta }_1$ = parameters found by linear regression; $I_a$ = Arias intensity of the ground motion (meters per second or centimeters per second); $T$ = fundamental period of the ground motion (seconds); and $K_a$ = peak acceleration (gravitational force). Urzúa and Christian (2013) developed values of ${\beta }_0$ and ${\beta }_1$ on the basis of accelerograms from three large Chilean earthquakes: the 1985 $M=7.8$ earthquake in the Valparaiso region, the 2007 $M=7.7$ earthquake in the Tocopilla region, and the 2010 $M=8.8$ earthquake in the Maule region. The analysis for each record (1) selected a value of $a_c/a_{\max }$ between 0.05 and 0.50 in intervals of 0.05; (2) chose one of the time histories; (3) performed the sliding block analysis for that combination of time history and $a_c/a_{\max }$; and (4) repeated Steps 1–3 for all the other values of $a_c/a_{\max }$ and time histories. Linear regression analyses ($R^2=0.892$) gave the dashed lines in Fig. 1. The same analysis on records from the 1999 $M=7.6$ Chi Chi and 1994 $M=6.7$ Northridge earthquakes gave similar results, indicating that the model applies to events with other source mechanisms.

The accelerograms from the 2014 $M=8.2$ Iquique earthquake and a major aftershock with $M=7.7$ have become available. Applying the same algorithms to 46 records from the main shock and 28 from the aftershock provides the solid lines in Fig. 1. The normalized displacements are slightly larger than those for the original suite and have slightly greater scatter. Nevertheless, the results are close and support the basic soundness of the model.

How close the new results are to those predicted by the earlier lines can be appreciated by considering the estimated displacements in centimeters. A report for a site in Chile proposes that the maximum credible earthquake has $I_a=\mathrm{2,000}\hspace{0.17em}\text{cm}/\text{s}$, $T=0.13$, and $K_a=0.8g$. When these parameters and the original ${\beta }_0$ and ${\beta }_1$ values are used in Eq. (1) for a slope with critical acceleration $a_c=0.2g$, the median computed sliding displacement is 50 cm. The ${\beta }_0$ and ${\beta }_1$ values from the 2014 Iquique earthquakes give 58 cm. In view of the many recognized limitations of the sliding block model, these results are remarkably close.