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# Some important considerations in analysis of earthquake-induced landslides

- Brian Carlton
^{1}Email author, - Amir M. Kaynia
^{1}and - Farrokh Nadim
^{1}

**Received:**14 October 2015**Accepted:**12 May 2016**Published:**20 May 2016

## Abstract

### Background

The frequency of landslide disasters is increasing as a result of exploitation of natural resources, deforestation, and greater population vulnerability due to growing urbanization and uncontrolled land-use. Earthquakes are a major triggering factor of landslides, and earthquake-induced landslides pose a major threat to infrastructure and human life. This paper presents the effects of slope angle, soil sensitivity, ground motion orientation, and multidirectional shaking on the results of seismic slope stability analyses.

### Results

The results show that permanent shear stresses due to sloping ground, strain softening and sensitivity, ground motion orientation, and multidirectional shaking all have a large influence on the permanent displacements estimated from earthquake-induced landslide hazard analyses. Multidirectional shaking also predicts larger excess pore pressures in deep layers than unidirectional shaking.

### Conclusions

It is important that site investigations provide adequate information to model the correct slope angle and soil sensitivity. The ground motion orientation should be considered and chosen based on the specific needs of a project. Analyses with only one ground motion component could give unconservative results.

## Keywords

- Slope stability
- Earthquake
- Soil sensitivity
- Strain softening
- Multidirectional shaking

## Background

Earthquakes are a major triggering factor of landslides. This was highlighted by the 25 April 2015 Gorkha, Nepal earthquake sequence. The earthquake and its aftershocks killed nearly 9,000 people and triggered thousands of landslides. The landslides were responsible for hundreds of those deaths, blocked vital road and lifeline routes to villages, and created temporary dams across several rivers that were a major concern for villages located downstream. The earthquake-induced landslides continue to pose an immediate and long-term hazard to people and infrastructure within central Nepal (Collins and Jibson, 2015).

This event and similar recent earthquakes, such as the Wenchuan earthquake of 12 May 2008 and the Kashmir earthquake of 8 October 2005, have underscored the threat that earthquake-induced landslides represent to human life, property, built environment and infrastructure in mountainous and hilly regions of the world. The frequency of landslide disasters is increasing as a result of exploitation of natural resources, deforestation, and greater population vulnerability due to growing urbanization and uncontrolled land-use. For example, traditionally uninhabited areas such as mountains are increasingly used for recreation and transportation purposes, and new technologies for resource extraction are pushing the borders further into more hazardous areas. This has stimulated more research on earthquake-induced landslides and methods of prediction, mapping and mitigation.

Traditionally, geotechnical engineers have assessed the seismic stability of slopes by pseudo-static analysis where the inertial force caused by ground acceleration is applied as an effective static load equal to the mass of the soil times the peak or effective acceleration. However, the duration of the peak earthquake load is very short and in most situations the main effects of the ground shaking are accumulation of down-slope displacements accompanied by a moderate cyclic degradation of soil strength. This means that the focus of seismic slope stability assessments should be on estimating the earthquake-induced deformations, rather than computing a pseudo-static safety factor. This idea was first put forward by Newmark (1965), who proposed a simple sliding block model as the analogue for the downslope movement of the soil mass during an earthquake. With this model, one can estimate the permanent earthquake-induced displacements and assess whether or not they are acceptable.

Nadim et al. (2007) proposed a more rigorous approach for seismic slope stability assessment of clay slopes on the basis of nonlinear, dynamic response analysis. The approach was developed for the evaluation of stability of submarine slopes under earthquake loading, which is one of the most challenging issues in offshore geohazard studies. They recommended that three scenarios should be evaluated and analysed: 1) Failure occurring during the earthquake, where the excess pore pressures generated by the cyclic stresses degrade the shear strength to a level that the slope is not able to carry the static shear stresses; 2) Post-earthquake failure due to an increase in excess pore pressure at critical locations caused by seepage from deeper layers; and 3) Post-earthquake failure due to creep. The advanced numerical methods used for dynamic response analysis provide a reliable picture of the response of a slope during an earthquake, but require detailed information about the geometry, stratification and mechanical properties of the slope.

This paper examines the importance of the effect of permanent shear stresses due to sloping ground, strain softening and sensitivity, ground motion orientation, and the effect of multidirectional shaking on dynamic slope stability analyses. The earthquake-induced permanent shear strains and deformations are used as the metric describing the seismic behaviour of the slope.

## Methods

### Effect of permanent shear stresses and strain softening

_{n}) in the direction normal to the slope, and a consolidation shear stress (τ

_{c}) acting in the plane of the slope parallel to the dip. The dynamic equation of motion for each node of the system is combined into the global equation of motion, which QUIVER solves in the time domain using the constant acceleration Newmark β method (Newmark, 1959). This is an implicit and unconditionally stable integration algorithm method.

_{w}= 7.5). It is representative of a design ground motion for sites in active crustal regions. In Fig. 2 the positive direction is applied in the downslope direction and the negative corresponds to the upslope direction. Based on the recommendations of Stewart et al. (2008), we performed the dynamic slope stability analyses in QUIVER using the input motion as recorded, with no deconvolution, and with an elastic half-space underlying the soil profile. We scaled the record to a peak ground acceleration (PGA) of 0.2 g.

_{max,i}= V

_{s,i}/(4 × H

_{i}), where f

_{max,i}is the maximum period that layer i can propagate, V

_{s,i}is the shear wave velocity of layer i, and H

_{i}is the height of layer i. Frequencies greater than f

_{max}will not be propagated though the soil layer. We adjusted the thickness of the soil layers so that the maximum frequency propagated through the site was 15 Hz.

The constitutive model implemented in QUIVER consists of a visco-elastic linear loading/unloading response together with strain softening and a kinematic hardening yield function post peak strength. The advantage of QUIVER over other 1D codes is the inclusion of strain softening in the nonlinear soil model. Damping in the loading/unloading cycles is simulated by conventional Rayleigh damping, defined as C = α × M + β × K where C is the damping matrix, M is the mass matrix, K is the stiffness matrix, and α and β are scalar values selected to obtain given damping values for two target frequencies. As recommended by Stewart et al. (2008), we selected the target frequencies as the elastic site frequency, and five times the elastic site frequency. QUIVER was validated against results from 2-dimensional analyses with PLAXIS (PLAXIS 2D Version 9.0, 2009).

### Effect of multidirectional shaking

To investigate the effect of multidirectional shaking on dynamic slope stability analyses, Anantanavanich et al. (2012a) developed the constitutive model MSimpleDSS and implemented it in AMPLE2D, which is an improved version of the finite element code AMPLE2000 (Pestana and Nadim, 2000). The MSimpleDSS model is an effective stress model that includes anisotropy, strain rate adjustable parameters, and allows redistribution of shear stresses, strains, and pore pressures between two directions. The model parameters were estimated from laboratory tests on normally consolidated Young Bay Mud from the San Francisco Bay, which is representative of medium plasticity soft clay.

## Results and discussion

### Permanent shear stresses due to sloping ground

The most important information about the slope geometry is the slope angle. When the ground is sloping a static shear stress develops in the soil. This stress causes the deformations to accumulate in the downhill direction. Biscontin (2001) conducted a series of direct simple shear tests on Young Bay Mud from San Francisco Bay. She observed that the effect of a slope (i.e., a consolidation shear stress) increased the strength of the soil when shearing downslope, but reduced the factor of safety (FoS) for the slope by decreasing the difference between the permanent stress and the soil strength.

### Strain softening/sensitivity

Strain softening is the reduction of shear strength as the shear strain increases past the shear strain value where the peak shear strength occurs. Sensitivity (S_{t}) is defined as the ratio of peak shear strength to the residual shear strength. Soils that have strong strain softening characteristics and high sensitivity are most susceptible to complete failure during earthquake shaking. Strain softening is found for many soils, however, highly sensitive soils are usually clays at high water content (>0.9 × liquid limit). The most sensitive soils are commonly found in Eastern Canada and Scandinavia. In addition, marine clays may be highly sensitive due to leaching of salt from the pore water, which reduces interparticle bonding. These types of clays are commonly called quick clays.

_{u}) for a given soil layer, then remain flat until a shear strain of 2 % before reducing to the residual strength at a shear strain of 20 %. In all of the sensitivity analyses we used the acceleration time series shown in Fig. 2, the site profile shown in Fig. 3, and slope angles of 0, 5, 10, and 15 degrees.

### Orientation of acceleration time series

Ground motions are often recorded in three orthogonal directions, such as north, east, and up. However, when applying only one of the horizontal components, changing the orientation can change the intensity and frequency content of the acceleration time series. Therefore, an important consideration when performing dynamic slope stability analyses is the orientation of the acceleration time series with respect to the slope.

In the prior analyses, we applied the north oriented component (azimuth = 0°) of the ground motion recorded during the 1999 Kocaeli Earthquake at the Bursa Tofas station. To investigate the effect of the orientation of the acceleration time series, we combined and rotated the two horizontal components to the orientation with the maximum peak ground acceleration (PGA), the orientation with the maximum spectral acceleration value at a period of one second (Sa(T=1)), and the opposite orientation (azimuth = 180°). We then conducted dynamic slope stability analyses in QUIVER using the same site conditions and slope angles as the prior analyses for soil with no sensitivity (S_{t} = 1).

_{t}= 1. If the opposite orientation is applied (i.e. the negative direction in Fig. 2 is downslope and positive is upslope), then the calculated permanent displacements are larger. This is because the ground motion has larger displacements in the negative direction than the positive direction, as shown in Fig. 2. Applying the orientation with the maximum PGA gives permanent displacements between those predicted using the given and opposite orientation. The orientation with the maximum spectral acceleration at a period of one second gives the largest permanent displacements for slope angles of 5, 10 and 15 degrees. This is because longer periods are more correlated with displacements than shorter periods, such as PGA.

### Multidirectional shaking

One-dimensional models provide a good approximation of the seismic behaviour of slopes for depths that are relatively small compared to the slope length. This is often the case for offshore submarine landslides, where the ratio between thickness and length of the sliding mass is relatively small. However, for more complicated offshore scarps or for onshore mountainous regions, deep seated failures often develop along curved surfaces, and the top and bottom slope boundaries have a significant effect. Slopes with level top and bottom boundaries will have smaller permanent displacements than their corresponding 1D infinite slope approximation due to the reduced consolidation shear stresses on the level ground boundaries and because the bottom boundary will act as a buffer. In addition, slope failures along curved sliding surfaces in 2D models require more energy than flat surfaces predicted in 1D models, which leads to smaller permanent displacements. For complicated topographies, 3D analyses may even be necessary due to wave refraction at the edges and wave interferences.

Even when modelled in 2D or 3D, most seismic slope stability analyses only consider one component of the ground motion, when in reality ground shaking occurs in all directions. Kammerer et al. (2005) performed extensive laboratory stress-controlled cyclic tests on granular soil, and found that the soil response under multidirectional shearing tended to generate pore pressure faster than that of unidirectional shearing. Su and Li (2003) applied both unidirectional and multidirectional shaking to level saturated sand deposits in a centrifuge and found that the maximum pore pressure at great depths for multidirectional shaking was about 20 % larger than that in one-directional shaking and the difference reduced to about 10 % near the surface.

Using the MSimpleDSS model in AMPLE2D, Anantanavanich et al. (2012b) performed nonlinear dynamic slope stability analyses for two generic soft clay sites with depths of 20 m and 100 m, and four sets of ground motions. They compared the estimated permanent displacements and excess pore pressures generated from applying one or both horizontal components of a ground motion at the same time for different slope angles.

## Conclusions

The numerical results from the site response analysis programs QUIVER and AMPLE2D show that permanent shear stresses due to sloping ground, strain softening and sensitivity, ground motion orientation, and multidirectional shaking all have a large influence on the permanent displacements estimated from earthquake-induced landslide hazard analyses.

For the analyses conducted in this investigation, increasing the slope angle by 10 degrees or increasing the sensitivity from 1 to 4 for non-zero slopes resulted in an order of magnitude difference in the predicted permanent displacements. Changing the orientation of the ground motion from the as given orientation to the orientation with the maximum spectral acceleration value at a period of 1 second increased the estimated permanent displacements by 50 cm or more for all non-zero slopes. Applying two horizontal ground motion components instead of only one resulted in 10-40 % larger permanent displacements than unidirectional shaking near the soil surface. In addition, multidirectional shaking also predicted larger excess pore pressures than unidirectional shaking.

We also found that as the slope angle increases, the energy in the response spectra predicted at the soil surface shifts to longer periods and the overall amplitude decreases. However, soil sensitivity has a negligible effect on the response spectra calculated at the soil surface.

The results from this investigation show that it is important for site investigations to provide adequate information to model the correct slope angle and soil sensitivity. In addition, project managers should consider the ground motion orientation when selecting acceleration time series for analysis. Finally, analyses with only one ground motion component may give unconservative results, therefore, multidirectional analyses should be conducted when possible.

## Declarations

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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