The interaction of seismic waves with step-like slopes and its influence on landslide movements

Abstract

The interaction of seismic waves with slopes is a major factor influencing landslide movements that involve slope stability, local site seismic amplification and topographic effects affecting ground motion. The results of a numerical study of landslide movements induced by the interaction of seismic waves with step-like slopes are presented here. To investigate this input–slope interaction, a dynamic analysis was performed using the finite difference stress-strain numerical code FLAC 6.0 under visco-plastic conditions. The dynamic signals were selected to be representative of different peak ground accelerations (PGAs), Arias intensities and frequency contents, and they were used in a parametric study of different step-like slopes with different geometrical configurations in terms of dip, height and thickness of geological strata. The derived outputs were processed for a seismic amplification analysis and to evaluate the induced stress-strain effects in terms of progressive failure and resulting displacements.

The obtained results: i) describe a fundamental role of topography in amplifying or de-amplifying the seismic ground motion; ii) demonstrate that the progressive failure of unsheared slopes influences the seismic amplification; iii) show that the strain effects on unsheared slopes, in terms of progressive failure, are more intense with increasing Arias intensity and slope dip; iv) prove that amplification or de-amplification processes can justify the values of displacements involving pre-existing landslide masses, which are significantly different with respect to those expected on the basis of sliding block approaches (i.e., Newmark's and flexible sliding block methods); v) highlight that, in the geological setting considered here, the seismically induced displacements arising from the reactivation of pre-existing landslide masses can be significantly underestimated by sliding block approaches in the case of low-angle slopes characterised by high K values, i.e. the ratios between the critical pseudostatic threshold (k_y) of the landslide and PGAs of the applied seismic input.

Introduction

Seismically induced slope instabilities are often responsible for the greatest damage and losses during earthquakes (Bird and Bommer, 2004). Empirical correlations have been proposed (Keefer, 1984, Rodriguez et al., 1999) between the epicentral distance of the earthquake from the landslides and the magnitudes of the triggering earthquakes. However, these correlations may be altered by local site conditions (tectonic features, stratigraphic conditions, morphology) that modify the seismic ground motion. The possible interactions between seismic waves and slopes have recently been analysed to predict seismically induced landslide movements (Martino and Scarascia Mugnozza, 2005, Sepulveda et al., 2005a, Sepulveda et al., 2005b, Del Gaudio and Wasowski, 2007, Bozzano et al., 2008c, Bourdeau and Havenith, 2008, Danneels et al., 2008, Barani et al., 2010, Bozzano et al., 2011, Ohashi and Sugito, 2010) to show how both the landslide mechanisms and the triggering conditions depend on seismic input properties such as energy, frequency content, directivity and peak ground acceleration (PGA). In particular, some case studies have indicated the role of a “self-excitation” process (sensu Bozzano et al., 2011) due to seismic amplification effects in triggering far-field pre-existing large landslides, which represent outliers (Delgado et al., 2011) with respect to the predictive curves proposed by Rodriguez et al. (1999).

The effects of seismic amplification due to specific topography types, such as ridges and canyons, have been studied since the 1970s by different authors (Sanchez-Sesma and Rosenblueth, 1979, Geli et al., 1988, Athanasopoulos et al., 1999, Zaslavsky and Shapira, 2000, Kamalian et al., 2008, Bakavoli and Hagshenhas, 2010) on the basis of instrumental data from strong earthquakes (i.e., the 1909 Angot (France) earthquake; the 1976 Friuli (Italy) earthquake; the 1980 Irpinia (Italy) earthquake; the 1985 Chile earthquake). These studies suggested that surface topography modifies seismic ground motion. Nevertheless, the effects of step-like slope topography on seismic ground motion have only recently been studied (Ashford et al., 1997, Bouckovalas and Papadimitriou, 2005, Nguyen and Gatmiri, 2007, Papadimitriou and Chaloulos, 2010) using numerical modelling because reliable field measurements are difficult to obtain since wave scattering due to step-like slope geometries require an unrealistically dense distribution of recording stations. These studies demonstrated that step-like slope topographies may lead to intense amplification and de-amplification irregularly along the slope, depending on its geometry. The topographic aggravation of the horizontal ground motion varies with the distance from the crest of the slope, with alternating amplification and de-amplification within very short distances as a function of the normalised height H/λ (where H = height of the slope and λ = wavelength).

The interaction of seismic waves with a slope can also influence the nonlinear induced deformation in the cases of unsheared slopes, which have not yet been affected by landslide processes, and pre-existing landslide masses, i.e., “first-time slides” and “slides on pre-existing shears” (sensu Hutchinson, 1988), respectively.

Often, for a given acceleration time-history, the expected co-seismic displacements in slopes are evaluated by applying Newmark's sliding block method (Newmark, 1965). The Newmark procedure models the sliding mass as a rigid block and uses the yield pseudostatic acceleration (k_yg) and the acceleration time-history, assuming that sliding begins when k_yg is exceeded; this method has been widely reviewed and improved (Sarma, 1981, Wilson and Keefer, 1983). In particular, the sliding block displacement methodology has been extended to account for the deformable response of deeper sliding masses in earth structures using a decoupled analysis in which the deformable response of the earth structure is computed, ignoring the potential for sliding (Makdisi and Seed, 1978, Bray and Rathje, 1998). More recently, the sliding block displacement methodology was improved to account for the coupled interaction between sliding and dynamic responses by an analytical procedure to simultaneously estimate the seismically induced permanent displacements due to stick-slip events of sliding and the 1D deformable dynamic response of the structure, which exhibits significantly nonlinear behaviour (Rathje and Bray, 2000, Rathje and Antonakos, 2010). In these latter studies, the coupled analyses indicate that the accelerations within the sliding mass often exceed the yield acceleration at its base due to the dynamic response of the sliding mass.

Many relationships between seismic ground-motion parameters (i.e., magnitude, Arias intensity and PGA) and computed landslide displacements have been proposed to obtain scenarios of seismically induced effects and to predict the probability of exceeding the fixed values of co-seismic landslide displacements calculated by Newmark's method (Jibson, 1993, Romeo, 2000, Assimaki et al., 2005, Saygili and Rathje, 2008, Peng et al., 2009, Cvetanovska and Sesòv, 2010, Kaynia et al., 2010). Nevertheless, the ultimate-limit-state criterion at the basis of the Newmark method does not quantify strain effects on unsheared slopes (i.e., in the case of “first-time landslides”) or take into account the interaction between slopes and seismic inputs in terms of local ground motion amplification/de-amplification due to the topography of the slope and the geological setting. In contrast, stress-strain numerical analysis performed under dynamic conditions can contribute to this topic and quantify the expected strain effects due to seismic shaking (Meunier et al., 2008).

In this regard, the numerical study presented here is focused on the interaction between seismic inputs and slopes to evaluate the possible role of seismic amplification in seismically induced landslide movements and to quantify the induced strain effects.