Permanent Seismic Displacement Research Articles

Updated Predictive Models for Permanent Seismic Displacement of Slopes for Greece and Their Effect on Probabilistic Landslide Hazard Assessment

Earthquake-triggered landslides have been widely recognized as a catastrophic hazard in mountainous regions. They may lead to direct consequences, such as property losses and casualties, as well as indirect consequences, such as disruption of the operation of lifeline infrastructures and delays in emergency response actions after earthquakes. Regional landslide hazard assessment is a useful tool to identify areas that are vulnerable to earthquake-induced slope instabilities and design prioritization schemes towards more detailed site-specific slope stability analyses. A widely used method to assess the seismic performance of slopes is by calculating the permanent downslope sliding displacement that is expected during ground shaking. Nathan M. Newmark was the first to propose a method to estimate the permanent displacement of a rigid body sliding on an inclined plane in 1965. The expected permanent displacement for a slope using the sliding block method is implemented by either selecting a suite of representative earthquake ground motions and computing the mean and standard deviation of the displacement or by using analytical equations that correlate the permanent displacement with ground motion intensity measures, the slope’s yield acceleration and seismological characteristics. Increased interest has been observed in the development of such empirical models using strong motion databases over the last decades. It has been almost a decade since the development of the latest empirical model for the prediction of permanent ground displacement for Greece. Since then, a significant amount of strong motion data have been collected. In the present study, several nonlinear regression-based empirical models are developed for the prediction of the permanent seismic displacements of slopes, including various ground motion intensity measures. Moreover, single-hidden layer Artificial Neural Network (ANN) models are developed to demonstrate their capability of simplifying the construction of empirical models. Finally, implementation of the produced modes based on Probabilistic Landslide Hazard Assessment is undertaken, and their effect on the resulting hazard curves is demonstrated and discussed.

A modified Newmark block method for determining the seismic displacement of a slope reinforced by prestressed anchors

The seismic permanent displacement is an essential aspect to evaluate the seismic stability of slope. The conventional Newmark block method commonly adopts a constant yield acceleration to determine the seismic permanent displacement of slope. In order to reflect a more realistic behavior of seismic displacement, the dynamic kinetic failure mechanism and the instant displacement model of slope reinforced by prestressed anchors in infinitesimal time are established. The time-dependent formula for dynamic yield acceleration is deduced based on upper bound method. A modified method is proposed to determine the seismic permanent displacement within the framework of Newmark block theory. The results are compared with the existing work with regard to the yield acceleration and seismic permanent displacement. Three typical seismic ground motions are performed to study the responses of the anchor force, the dynamic yield acceleration and the seismic permanent displacement. Results show that the anchor force, the dynamic yield acceleration and the seismic displacement all increase continuously during the excitation of seismic ground motion. The anchor causes the yield acceleration to increase, and the seismic permanent displacement to decrease significantly. The conventional method adopting a constant yield acceleration greatly overestimates the seismic permanent displacement.

Centrifuge and theoretical study of the seismic response of anchored steel sheet pile walls in dry sand

Displacement-based approaches have been proven to be effective for the seismic design of gravity retaining structures. However, application of these methods to embedded flexible walls, such as anchored steel sheet pile (ASSP) walls, is still an open issue, as the factors affecting the accumulation of permanent displacements of these systems are not fully understood. This paper presents the results of four dynamic centrifuge tests on small-scale models of ASSP walls in uniform dry sand. The experimental results showed that ASSP walls can experience different failure mechanisms depending on their geometry and on the magnitude of accumulated displacements. During the earthquake, the system exhibits an overall increase of its seismic capacity, caused by: (a) progressive mobilisation of the soil passive strength; (b) sand densification; (c) rotation of the walls; and (d) reduction of the retained height. Accounting for these effects in pseudo-static limit equilibrium solutions improved the predictions of both the critical failure mechanism and the maximum internal forces in the structural members. Moreover, it allowed development of an efficient analytical tool for the prediction of the seismic permanent displacements of these systems, based on Newmark's sliding block approach.

Effect of spatial variability of soil properties on permanent seismic displacements of slopes with uniform load

The purpose of this study is to investigate the development of permanent displacements of earth slopes, with spatially varying properties and a uniform surface load, subjected to a strong seismic excitation. The uncertainties associated with the determination of the mechanical properties of the slopes and the intensity of the seismic excitation, make the use of stochastic methods very attractive. As opposed to deterministic methods, stochastic methods allow an acceptable risk level based on the specifications of each project. Recent research described the spatial variability of soil parameters using the Random Field Theory. Apart from the prescribed statistical characteristics and cross-correlation of the various soil properties, the generated random field variables exhibit autocorrelation, a trend in which the soil properties of a point appear to be correlated with the soil properties of neighbouring points. Among the various random field algorithms, a particularly effective one is the Local Average Subdivision (LAS) method by Fenton and Vanmarcke [1]. To this end, a large number of random fields of soil properties is generated for a natural slope, having prescribed mean value μ, standard deviation σ, cross-correlation coefficients pij of properties i and j, and spatial autocorrelation lengths lx and ly for the vertical and horizontal directions, respectively. The numerical simulations are achieved using an automated procedure, based on collaboration of Mathematica, the incorporated LAS algorithm, and the finite difference program FLAC. The studied slope is loaded with a uniform load and subjected to a seismic shaking of various intensities using a series of acceleration records obtained from the five different earthquakes. The paper focuses mainly on the development of permanent seismic displacements of the slope at the end of ground shaking. It is demonstrated that the spatial variability of soil properties has a significant effect on the values of permanent displacements, resulting to a wide range of displacement variation.

Practical seismic fragility estimation of unreinforced and reinforced embankments in Japan

The seismic fragility of an embankment can be calculated considering the permanent seismic displacement obtained through the Newmark's sliding block analysis implemented using a Monte Carlo simulat...

Yield acceleration of reinforced soil slopes using the modified pseudo-dynamic method

This study presents the yield acceleration of reinforced soil slopes using the horizontal slice approach. Yield acceleration plays a key role in calculating the permanent seismic displacement of slopes. The modified pseudo-dynamic method, in conjunction with the equivalent linear site response analysis, is used. Unlike the pseudo-static analysis, the pseudo-dynamic method takes into account the effects of time and phase difference of waves propagation. The developed computer code is used to compute the yield acceleration. Using the planar and log-spiral slip surfaces, this code considers the distribution of reinforcement layers as uniform and variable spacing. The effect of surcharge pressure is also considered. According to the results, the modified pseudo-dynamic method using the equivalent linear ground response analysis led to more critical results than other methods.

Effect of vertical seismic coefficient on cohesive-frictional soil slope under generalised seismic conditions

ABSTRACT In the present work, seismic performance parameters have been reviewed by considering the possible combined action of vertical and horizontal seismic loadings of the ground motion during the earthquakes. Analytical expressions of factor of safety, yield seismic coefficient and permanent seismic displacement of a cohesive-frictional soil slope have been developed by following deterministic sliding block approach in a two-dimensional pseudo-static framework. The slope with a planar failure surface is assumed to follow the Mohr-Coulomb criterion by considering a slice of unit thickness through the slope. For a given range of slope geometrical and soil parameters, the role of vertical seismic coefficient has been analysed in the presence of cohesion to investigate its effect on factor of safety, yield seismic coefficient, and consequently on the permanent seismic displacement of the slope through a set of graphical presentations. The results show that avoidance of vertical seismic component of the ground motion in the stability analysis may lead to severe slope failures. The general expressions proposed herein can be used to carry out a quantitative stability assessment of cohesive- frictional soil slopes during earthquakes in real-life projects.

Real-Time Seismic Waveforms Estimation of the 2019 MW = 6.4 and Mw = 7.1 California Earthquakes With High-Rate Multi-GNSS Observations

Global Navigation Satellite System (GNSS) is recognized as an effective tool to retrieve high-precision seismic displacements, which has been widely used in earthquake early warning systems such as magnitude estimation and fault slip inversion. In this study, we present two multi-GNSS positioning models for rapidly capturing real-time coseismic displacements using the raw pseudorange, carrier phase and Doppler measurements, called constant velocity (CV) and constant acceleration (CA) dynamic precise point positioning (PPP) models, respectively. The proposed methods are validated with the datasets collected during the 2019 July 4 Mw 6.4 and July 6 Mw 7.1 earthquakes in real-time scenarios. Results show that the two models can provide accurate displacement waveforms with the accuracy of few centimeters. Besides, the multi-GNSS integration can significantly improve the model performances compared with GPS-only solutions in both time- and frequency- domains. The dynamic PPP models can also reliably recover the moment magnitudes and permanent seismic displacements, indicating that the methods have the potential to benefit for earthquake early warning and rapid geohazard assessment.

Prediction of large seismic sliding movement of slopes using a 2-body non-linear dynamic model with a rotating stick-slip element

In the present work a new cost-effective dynamic method predicting large seismic displacement along slip surfaces is proposed. For this purpose, the 1-D propagation of horizontal shear waves on a soil stratum with a horizontal stick-slip element at some depth is considered. State-of-the-art equations modeling (a) the coupled 1-dimesional dynamic response of soils with slippage both above and below the slip element, (b) the rotation of the sliding mass with displacement effect and (c) the non-linear soil response for both the dry and saturated cases are combined in a unique manner. No other cost-effective dynamic method was found in the bibliography that simulates all the above effects. The new method is applied for some particular geometries for both the linear and non-linear cases. In the linear case the effects of the stiffness of the soil layers both above and below the slip element and of the rotation of the sliding mass on the permanent seismic displacement are illustrated and interpreted. Likewise, in the non-linear case, the effects of (i) the shear modulus degradation in dry soil profiles and (ii) the additional effect of excess pore pressure build-up in saturated soil profiles on the permanent seismic displacement are illustrated and interpreted.

Regional landslide susceptibility following the 2016 Kumamoto earthquake using back-calculated geomaterial strength parameters

The 2016 Kumamoto earthquake first occurred on April 14, 2016 with magnitude 6.5 in Kumamoto, Japan as a foreshock. Subsequently, after 28 h, an even larger earthquake occurred with magnitude 7.3 as the main shock on April 16, 2016. These earthquakes were caused by two active faults: the Futagawa and Hinagu faults. This paper proposes a landslide susceptibility calculation method that considers the geomaterial strength reduction from peak to residual state and ground motion directivity. Although there is a lack of information regarding the strength parameters of geomaterials in the slopes, a parametric analysis with various strength parameters of friction angle and cohesion was carried out. To simulate the actual landslides triggered by the 2016 Kumamoto earthquake, the best combination of friction angle and cohesion in each lithology was optimized by a proposed weighted prediction rate. Based on the calculated permanent seismic displacement, a landslide susceptibility map was produced to show the degree of susceptibility over a wide area comprising 100 km2. The proposed regional landslide susceptibility map will be valuable for estimating the locations of possible slope failures and the extent of damage, as well as for planning field reconnaissance and preventing secondary disasters immediately after earthquakes.

A multi-block sliding approach to calculate the permanent seismic displacement of slopes

The Newmark sliding block method is widely used to assess the seismic performance of earth slopes by calculating the permanent displacement of the simplified sliding mass. The conventional Newmark method models the potential landslide mass as a single rigid block sliding on a well-defined slip surface. In this study, a multi-block approach to calculate the sliding displacement of slopes is presented. The dynamic equation of a series of rigid blocks in different sliding conditions is established and the complex interactions within the slip episodes of rigid block assemblies are explicitly resolved. The results show that the original Newmark single block method may produce unconservative estimates of permanent displacement of the shallow sliding mass when the deep-seated sliding subsequently occurs during the earthquake. The predicted displacement of the upper sliding mass, which is simplified as a summation of the Newmark displacement of each single sliding mass, may either overestimate or underestimate the computed displacement including the coupling of sliding of multiple soil masses. The developed approach extends the well-accepted Newmark sliding block method, and can serve as an alternative to predict the seismic slope displacement in which multiple failure surfaces are expected during earthquakes.

Predicting seismic permanent displacement of soil walls under surcharge based on limit analysis approach

Seismic permanent displacement of the soil walls plays an important role in design of these structures. Due to the increase in growth of urban areas and the limitations in use of flat grounds, many structures are built near slopes and retaining walls. During earthquakes, these structures can apply an additional surcharge on the wall. The intensity and location of the surcharge is of considerable importance on the seismic displacements of the soil wall. In this study, by using the limit analysis and upper bound theorem, seismic permanent displacement of the soil wall under surcharge has been analyzed. Thus, a formulation is presented for calculating the yield acceleration and seismic displacement for different surcharge conditions. The effect of seismic acceleration, surcharge intensity, its location and soil properties is investigated. A parameter called the “displacement coefficient” is proposed, and is a potential modification for Newmark’s sliding-block method.

Discussion on ‘‘Seismic displacement along a log-spiral failure surface with crack using rock Hoek–Brown failure criterion’’

This discussion is based on the paper by Zhao et al. [4] (hereafter identified as “the authors” or “the original paper”). In the original paper, the authors presented a numerical model to calculate the seismic displacement for rock slopes with cracks using the Hoek-Brown yield criterion. For the proposed numerical model, the upper bound limit analysis and rigid block displacement technique were employed in which the actual horizontal and vertical earthquake ground motion records were utilized in the analyses. This discussion addresses the theoretical issues of the computed permanent seismic displacements in conjunction with the upper bound limit analysis using the rigid block displacement technique. In addition, the discussion comments on some issues related to the assumption of using the factor of safety being less than 1 for a calculation of induced seismic displacement under an actual time history of horizontal and vertical accelerations, and the use of fixed crack depth ratios of 0.1 and 0.2 in the parametric studies of the original paper.

Application of a Probabilistic Assessment of the Permanent Seismic Displacement of a Slope

AbstractPredicting the seismic performance of slopes involves an assessment of the expected permanent sliding displacement induced by ground shaking. Often, this analysis uses a deterministic appro...

Yield acceleration of reinforced soil slopes

Calculation of permanent seismic displacement of reinforced soil slopes plays a very important role in proper and optimal design of these structures in earthquake-prone regions. In the Newmark’s sliding block method, yield acceleration is required to calculate the permanent displacement. Pseudo-Static (PS) is an approximation method to compute yield acceleration. Unlike PS method, the pseudo-dynamic method considers the time and phase shift of P and S waves propagated in the soil. In this study, the yield acceleration of reinforced soil slopes is calculated using PS, Conventional Pseudo-Dynamic and Modified Pseudo-Dynamic (MPD) methods and the results are compared. The limit equilibrium analyses are conducted using the horizontal slice method by satisfying the equilibrium of the horizontal and vertical forces as well as moments. A program is written that is able to calculate the yield acceleration coefficient for all three mentioned methods for the uniform and variable spacing between reinforcements. The results show that, in general, the obtained value for the yield acceleration using MPD method is smaller than that in the PS method.

Regional landslide susceptibility following the Mid NIIGATA prefecture earthquake in 2004 with NEWMARK’S sliding block analysis

This study proposes a calculation method for regional earthquake-induced landslide susceptibility that applies the permanent seismic displacement calculated using Newmark’s sliding block analysis with estimated vertical and horizontal seismic motions. The proposed method takes into account the direction of slope failure based on the specified slope azimuth. The study results reveal the importance of predominant slope failure direction using a simple infinite slope model subjected to earthquakes. The target area for the earthquake-induced landslide susceptibility analysis constituted a region of more than 2000 km2 surrounding the epicenter of the Mid Niigata prefecture earthquake in 2004. An earthquake-induced landslide susceptibility map was created based on the proposed method with a specific combination of friction angle and cohesion, and the resulting data were compared to the landslide inventory map produced from aerial photographs following the Mid Niigata prefecture earthquake in 2004. To create the susceptibility map, geomaterial cohesion values for the slope were back-calculated to satisfy the minimum safety factor in the static state. This study also proposes a calculation method for the prediction rate and determines the back-calculated strength parameters of geomaterials. The proposed regional landslide susceptibility map will be useful for understanding potential slope failure locations and magnitude of damage, as well as for planning field investigation and preventing secondary disasters immediately after earthquakes.

Effect of the vertical earthquake component on permanent seismic displacement of soil slopes based on the nonlinear Mohr–Coulomb failure criterion

In the present study, a model is developed to calculate the upper bound of the seismic displacement of a slope based on the sliding rigid block model. In this model, it is assumed that the geotechnical materials satisfy the nonlinear Mohr–Coulomb (M–C) failure criterion, and the instantaneous shear strength parameters are introduced by the “external tangent method”. A sequential quadratic program, based on the nonlinear iteration procedure, is also employed to obtain the optimal solution for the objective function. Using the upper bound method and the Newmark sliding rigid block model, the effect of the vertical earthquake component on the permanent displacement of slopes is studied under the following two conditions: (1) It is assumed that the vertical acceleration is in phase with the horizontal acceleration; (2) Actual vertical ground motion records are used (i.e., the vertical and horizontal accelerations are mutually independent). The results show that the nonlinear parameter m significantly affects the permanent displacement of slopes, and that the effect of the vertical earthquake component on permanent displacement cannot be ignored. The impact of the vertical earthquake component on slope stability will be overestimated if the vertical acceleration is in phase with the horizontal acceleration.

Simplified Procedure for Coupled Seismic Sliding Movement of Slopes Using Displacement-Based Critical Acceleration

Downward movement of sliding soil mass in earthquake-induced earth slopes may gradually improve the system's stability. Hence, significant change in critical (or yield) acceleration of the slope is anticipated. The existing simplified coupled procedures, however, assume a constant critical acceleration in stick-slip sliding analysis. Fully coupled sliding block analyses with continuously increased critical acceleration were conducted to estimate earthquake-induced permanent displacement of earth slopes. The sliding mass was assumed as a flexible chain moving along the planes with gradually gentler inclinations. The measured data of a slope failure test in a shaking table were used to validate performance of the model. The proposed approach was compared with the previous procedures, which ignored critical acceleration changes due to downward movement of the sliding mass. Accordingly, earth slopes with smaller slip length were more influenced by the downward movement modification, especially in small amounts of initial yield acceleration. A semi-empirical equation is presented based on more than 425,000 modified-coupled analyses of several hundred strong ground motion records. An equation was then developed as a function of acceleration ratio, period ratio, slip length, peak ground velocity, Arias intensity, and earthquake magnitude. Predictions of the developed equation were compared with the available equations, which ignore the role of increased critical acceleration. It is shown that a majority of the previous models predict conservative estimates of seismic permanent displacements compared with that of new equation. The proposed semi-empirical model can be used as an alternative equation of seismic displacement for deterministic and probabilistic evaluations of earthquake-induced landslide hazard.

Displacement – based parametric study on the seismic response of gravity earth-retaining walls

The essence of performance-based design of gravity earth-retaining structures lies in the estimation of the residual (i.e. permanent) displacements after a seismic event. The accomplishment of this task however can be very complicated due to two interacting phenomena: the coupled sliding and tilting rigid body motion of the wall on an inelastic base and the formation of failure surfaces in the soil backfill. In this study a large number of fully non-linear, time-history analyses of gravity retaining walls (GRW) were performed using advanced numerical modelling. Different types of soil parameters and varying wall geometry within a practical range were investigated. The influence of different ground motion parameters was discussed and the results were compared with some of the most common limit equilibrium Newmark׳s sliding block procedures, including the recommendations by Eurocode 8, Part 5 [20]. Lastly, some recommendations for fast preliminary assessment of the seismic permanent displacements of GRW were provided.

Prediction of seismic displacement of dry mountain slopes composed of a soft thin uniform layer

In this paper, the earthquake-induced permanent seismic displacement of dry mountain slopes is calculated from a series of two-dimensional dynamic nonlinear finite difference analyses. The mountain slopes considered are composed of a thin, soft, uniform soil layer underlain by an inclined bedrock parallel to the slope. The material properties of the soil, thickness of the soil layer, and slope inclination angles are varied. Equivalent acceleration time histories are calculated at potential sliding surfaces to derive amplification factors, and a Newmark sliding block analysis is used to calculate the seismic displacements. The calculated seismic displacements of the mountain slopes are compared with those predicted by empirical displacement models. The results show that mountain slopes composed of soft soil layers with a shear wave velocity less than or equal to 200m/s cannot be modeled as a rigid block because the displacement under strong ground motions will be greatly overestimated. The displacement prediction is significantly enhanced if the slope is modeled as a flexible sliding mass and the amplification characteristics are accounted for. A new flexible sliding block model, which uses multiple ground motion parameters, is shown to provide a reliable estimate of the sliding displacement. The success rate of the model to predict the landslide hazard category ranges from 52 to 88.3%.