The interaction of seismic waves with step-like slopes and its influence on landslide movements
Highlights
► Role of seismic-waves/slope-topography interaction to quantify landslide movements. ► Progressive-failure due to earthquakes depends on Arias-intensity and dip. ► Reactivation of landslide mainly depends on local amplification for low-dip slopes. ► Sliding-block methods underestimate co-seismic displacements for low-dip slopes. ► Far-field reactivation of landslides can be due to seismic amplification effects.
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 (kyg) and the acceleration time-history, assuming that sliding begins when kyg 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.
Section snippets
Analysis of amplification effects due to slope-topography
To evaluate the seismic amplification effects due to slopes in terms of both geometry and geological setting, preliminary numerical modelling was performed on nine different slope configurations, and different inputs were then applied to force them toward landslide processes. The considered soils are high-consistency clays and poorly cemented sands that outcrop at the base and at the top of the slope, respectively. In particular, all of the geometries were designed with a step-like slope
Seismically induced progressive failure in unsheared slopes
To test the strain effects induced by different seismic inputs on the nine selected step-like slope configurations for unsheared slopes, FDM numerical modelling using the code FLAC 6.0 (Itasca, 2008) was performed under dynamic conditions with the aim of predicting “first-time” landslides. The visco-plastic behaviour described above and the related parameter values (Table 1) were assumed for this modelling. In the case of a “first time” landslide, no sliding surface can be assumed but a
Seismically induced displacements of pre-existing landslide masses
To evaluate the displacements induced by different seismic inputs on step-like slope geometries with pre-existing landslide masses, FDM numerical modelling was performed under dynamic conditions using the code FLAC 6.0. In particular, the three slope configurations 2_15_50, 2_35_50 and 2_45_50 were selected for this modelling. A pre-existing landslide mass with a “finite-slope” roto-translational mechanism was modelled, based on evidence of progressive failure after dynamic shaking. In
Discussion
The numerical study presented here demonstrates that the step-like geometry of the slopes and their geological setting significantly control the local seismic response. This is because de-amplification along the slope increases with increasing dip, while the increasing thickness of the sandy upper stratum (from 0 to 50 m) corresponds to an increase of the amplification behind the crest of the slope. In the case of unsheared slopes, progressive failure can be regarded as being responsible for the
Conclusions
This numerical study on the influence of seismic wave interactions with step-like slopes in inducing landslide movements demonstrates that the progressive failure of unsheared slopes becomes more intense (up to failure conditions) with increasing slope dip and with increasing Arias intensity of the applied dynamic input. This finding agrees with the higher disequilibrium conditions that can be reached according to an ultimate-limit-state criterion (i.e., exceedance of a critical yielding
Aknowledgments
This research study was developed as part of the Cooperation Agreement between the Research Centre on Geological Risks CERI of the University or Rome (Italy) “Sapienza”, and the “French Institute of Science and Technology for Transport, Development and Networks (IFSTTAR)” (Paris, France) on the processing and analysis of seismic ground motions and the analysis of possible relationships between seismic records and local geological conditions (scientific supervisors: A. Prestininzi and J.
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2020, Engineering GeologyCitation Excerpt :The existing researches about the dynamic response of rock slopes were mostly based on the acceleration response of slopes in time domain (Yin et al., 2009; Liu et al., 2014a, 2014b; Song et al., 2018a). However, the existence of structural planes in rock mass will affect the dynamic mechanics of slope (Lenti and Martino, 2012; Fan et al., 2016), and result in the great change of frequency components of waves due to multiple wave refraction and reflection effects. The time domain analysis using PGA can not fully clarify the dynamic response of the slopes, hence, frequency domain analysis needs to further investigate the dynamic response of slopes, in particular, Fast Fourier transform (FFT) has been the most commonly used method in frequency domain analysis (Li et al., 2012; Fan et al., 2017b).