Permanent Displacement Of Slope Research Articles

Impact of Soil Properties’ Spatial Correlation Lengths and Inclination on Permanent Slope Displacements Due to Earthquake Excitation

Natural disasters, when and where they occur, often cause serious social and economic consequences, which require an urgent solution to the problem. In particular, Greece, which is characterized by a complex geological structure and intense tectonic stress, has suffered and continues to suffer the consequences of such catastrophic phenomena. Among the various destructive phenomena recorded on the Earth’s surface, two of the most important problems are landslides and land subsidence. The above phenomena may cause, in addition to the serious case of loss of human life, a threat to the social and economic fabric affecting sustainability in general, i.e., the quality of life of an area (destruction of property, filling of reservoirs, blockage of streams and rivers, etc.). In fact, landslides are a phenomenon with enormous social and economic consequences, since apart from the financial burden due to the collapse of a technical project or the interruption of transportation, they are accompanied by the loss of human life. This research examines the stochastic characteristics of a slopes’ stability to investigate the variation range of permanent earthquake movements. More specifically, the influence of inclination as well as the lengths of the spatial correlation of ground are investigated. The method in the present study follows the development of arbitrary fields of soil properties, which follow the Gaussian distribution characterized by autocorrelation lengths lx and ly in the horizontal and vertical directions, respectively, mean value μ, standard deviation σ, and cross-correlation coefficients ρij. The estimation of permanent displacements is performed by the combination of the Local Average Subdivision algorithm and the FLAC software (Fast Lagrangian Analysis of Continua) used in the parametric investigation of this work. The results of this research showed that the spatial correlation of the properties has an important impact on the permanent displacements of slopes caused by strong earthquake excitations.

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.

Predictive models for the run-out distance of clay slopes based on material point method

This paper aims to propose run-out distance predictive models for clay slopes using the material point method (MPM), which can simulate the progressive failure process of slopes considering the strain softening effect of soils. A suite of 100 ground motions is selected from the NGA-West2 database and then scaled for conducting the dynamic analysis of slopes. The permanent slope displacements (D) can be classified into two categories, namely the “un-failure” category with D smaller than 0.4 m and the “failure” category with D in the range of 10 m to 15 m. It is found that peak ground velocity (PGV) exhibits the highest correlation with D for the “un-failure” category, whereas all ground-motion intensity measures (e.g., PGV, peak ground acceleration) are less correlated with D for the “failure” category. Therefore, the run-out distance of collapsed clay slopes is more related to the failure model rather than the triggering shaking intensities. Moreover, thousands of slope models with various slope angles, slope heights (H), soil densities, and peak and residual strength parameters are developed based on MPM. The run-out distances for the slopes being collapsed are then collected. Predictive models for different slope angles are proposed, which predict the run-out distance as a function of H, unit weight, residual cohesion, and residual friction angle. The proposed models are applicable for clay slopes with slope angles in the range of 30° to 45° and H in the range of 10 m to 30 m.

A probabilistic framework for the stability analysis of slopes considering the coupling influence of random ground motion and conditional random field

The uncertainty of the input parameters can have a significant influence on the evaluation of the slope stability. A simple probabilistic framework is presented in this paper to quantify the influence of the uncertainties of the stochastic ground motion coupled with the spatial variability of soil parameters. The robust quasi–Monte Carlo simulation in the proposed framework is employed to estimate the failure probability of slopes. The conditional random field (CRF) is manipulated to simulate the spatial variability of soil properties with the sample points where the soil parameters are determined, and the spectral representation of stochastic process is applied to generate the horizontal and vertical stochastic ground motions. In each run of the Quasi–Monte Carlo simulation, a modified Newmark method based on an infinite slope failure model is applied to determine the permanent displacement of slopes under horizontal and vertical ground motions. The originality and significance of this proposed probabilistic framework are validated by a real slope case. The results of the case show that the uncertainty affecting the stability of the slope can decrease when CRF is used in a random field simulation to incorporate the real values of soil parameters at sample points, and the failure probability of slopes can be underestimated without considering stochastic vertical ground motion. Moreover, the correlated distance and critical permanent displacement are significant in predicting the failure probability of slopes.

Permanent displacement reliability analysis of soil slopes subjected to mainshock-aftershock sequences

It is of great significance for disaster prevention to study the influence of mainshock-aftershock sequences on reliability of the soil slope. Considering the uncertainty of the mainshock-aftershock sequences, a new analysis method is proposed for the random dynamic response analysis and permanent displacements reliability evaluation of soil slopes under the action of mainshock-aftershock sequences. Firstly, a simulation method of random seismic sequence based on Copula function considering the correlation between mainshock and aftershock is introduced in this paper. Then, the permanent displacement of soil layered slope under 86 randomly generated mainshock-aftershock sequences and single mainshocks is calculated based on Newmark method. And the influence of aftershocks on the permanent displacement of slope is analyzed through the mean value. Besides, the influence of peak ground acceleration (PGA) on the permanent displacement and sliding surface of slope is also discussed. Finally, based on the probability density evolution method (PDEM), the influence of aftershocks on the permanent displacement reliability of slope is explained from the perspective of probability for the first time. The results show that the randomly generated mainshock-aftershock sequence can meet the needs of random dynamic analysis and probability analysis of soil slope by comparing with the target value. Based on the random dynamic calculation results, compared with single mainshocks, the soil slope has larger permanent displacement under the mainshock-aftershock sequences. However, there are obvious uncertainties in the permanent displacement and the position of the most dangerous sliding surface according to the different soil layer distributions and ground motions. It is very necessary to study the influence of mainshock-aftershock sequence on slope reliability from the perspective of probability. When the threshold is 1 m, the reliability of the slope will be reduced by 2 %∼15 % by aftershocks.

Predicting permanent slope displacements due to multidirectional earthquake shaking from unidirectional shaking analyses

The current state-of-practice for time-domain modelling of seismic slope stability is to apply a single horizontal ground motion component in the downslope direction. However, several numerical and experimental studies have demonstrated the importance of multidirectional shaking on seismically induced permanent displacements. To understand better the effect of multidirectional shaking on seismically induced permanent slope displacements, we performed 28,100 three-dimensional finite element slope stability analyses using 230 ground motion record pairs, 48 soil profiles, and four different combinations of ground motion components. We then performed traditional regression analyses and applied machine learning techniques to develop simplified models that estimate the permanent displacements due to multidirectional shaking from the results of analyses where only one component of the ground motion is applied downslope. The simplified model has R2 = 0.91 and uses the displacement from a unidirectional shaking analysis as its only input variable. The standard deviation decreases as the predicted unidirectional shaking displacements increase.

Effects of spatial variability of soil properties and ground motion characteristics on permanent displacements of slopes

The seismic performance of earth slopes is a problem of great importance in geotechnical earthquake engineering associated with various sources of uncertainty. This research investigates the effects of two important causes of such uncertainty: (a) the spatial variability of soil properties and (b) the variability of the temporal and frequency characteristics of the earthquake excitation. The former is investigated based on a series of detailed dynamic numerical simulations using stationary random fields of both cross-correlated and spatially autocorrelated soil properties. The latter is explored by conducting incremental dynamic analysis at various levels of excitation intensity using (a) a total of forty historic earthquake and synthetic records, modified to match the Eurocode 8 design spectra for rock sites, and (b) thirty original historic earthquake records. The results demonstrate the significant effect of the spatial variability of soil properties on the permanent slope displacements. Moreover, they show that the effect of the uncertainty associated with the variability in the temporal and frequency characteristics of excitations is more important compared to the effect of the spatial variability of soil properties.

Dynamic Analysis of the Seismo-Dynamic Response of Anti-Dip Bedding Rock Slopes Using a Three-Dimensional Discrete-Element Method

Earthquakes are a major external factor that induce landslides. In order to systematically study the dynamic effects and failure mechanism of anti-dip bedding rock slopes (the slope trend is the same as the joint trend, while the slope dip direction is opposite to the joint dip direction) under seismic action (as well as the spatial effects of the structural planes in the anti-dip bedding rock slopes), three-dimensional (3D) discrete-element numerical calculations were performed to analyze anti-dip bedding rock slopes with different slope angles, joint angles, and joint trends subjected to the action of natural seismic and sinusoidal waves. The results were analyzed to investigate the amplification effect, change in Fourier spectrum, failure mechanism, and permanent displacement of the slope under the applied seismic action. The permanent displacement of the slope was calculated using Newmark’s method and the results obtained were discussed and compared with those obtained from a dynamic analysis performed using the 3D discrete-element method. The results showed that the regularity of the spatial distribution of the amplification effect was less clear than that encountered in the planar problem (unidirectional or bidirectional dynamical loading), and this leads to the effect of having an overall rhythmical nature. The seismic wave decays in the high-frequency part from the bottom up of the slope, while the dominant frequency of the seismic wave decreases. The value of the permanent displacement obtained using Newmark’s method is much smaller than that obtained using the dynamic 3D discrete-element analysis approach. The angle between the joint and slope trends has a significant effect on the amplification effect, failure mode, permanent displacement, and stability of slopes subjected to seismic action.

Performance-based assessment of permanent displacement of soil slopes using two-dimensional dynamic analysis

ABSTRACT In this paper, a performance-based method is suggested to assess the permanent displacement of a slope using two-dimensional dynamic analysis considering both uncertainties in ground motions and basic soil parameters. In the suggested method, the statistics of the permanent displacement is first analyzed at different peak ground acceleration levels through uncertainty propagation analysis, and regression analysis is then used to derive the fragility curve. A seven-step procedure is suggested to implement the suggested method, and a numerical example is used to illustrate the suggested method. For the slope examined in this paper, the performance-based assessment based on one-dimensional model underestimates the mean of the permanent displacement, and the performance-based assessment based on the empirical model overestimates the uncertainty in the permanent displacement. The uncertainty in soil properties can contribute up to 40% to the uncertainty in the permanent displacement at low peak ground acceleration level.

Probabilistic assessment of permanent displacement of soil slopes: how many ground motions are needed?

As the occurrence of earthquakes is highly uncertain, the permanent displacement of a slope during a given exposure time is also uncertain. Probabilistic analysis can be used to assess the effect of uncertainty in the ground motions on the permanent displacement. However, the number of ground motions to be considered in a probabilistic assessment of permanent displacement of a slope is still not clearly defined. In this paper, a numerical study is conducted to investigate the effect of number of ground motions on the variability of fragility curves and the hazard curve of the permanent displacement. It is found that for the slope study in this paper, the median fragility curve and hazard curve are not sensitive to the number of ground motions. The width of the confidence interval of the fragility curve can be reduced by half when the number of ground motions is increased by four times. It can be learned from the COV of the hazard curve of permanent displacement that the determination of the number of ground motion records should be based on a concerned critical permanent displacement.

Towards the vulnerability assessment of low-code RC frame buildings at precarious slopes subjected to rainfall induced landslide hazard

The presence of capillary pressure in unsaturated soils may, under certain circumstances, significantly affect the stability of a slope and the safety of a structure standing in the vicinity of its crest. More specifically, the change in saturation induced by a rainfall event may directly influence the value of apparent soil cohesion potentially resulting in excessive permanent slope displacements and subsequent structural damages for the structure standing on it. Under these considerations, this study aims at the vulnerability assessment of typical reinforced concrete (RC) buildings on precarious slopes subjected to rainfall induced landslide hazard. The proposed methodology is based on a two-step numerical analysis procedure. First, the permanent absolute and differential ground displacement time histories at the assumed building location within the landslide zone are evaluated performing coupled mechanical-flow analysis of a generic initially unsaturated natural slope configuration considering the employment of different rainfall events of increased intensity at the surface of the slope model. Different soil properties of the surface layer are considered to represent silty and soft clayey soil material. Appropriate analytical relationships between the rainfall intensity and its duration and the computed permanent displacements are extracted. Then, a series of nonlinear static time history analyses are performed for reference low and mid-rise, low-code RC bare and infilled frame buildings located next to the slope's crest to assess their fragility. The buildings’ response assessed using appropriate engineering demand parameters (EDPs) to account for both the global flexural and local shear demand are statistically correlated with predefined damage limit states to construct the fragility functions. To facilitate the applicability of the proposed methodology within a quantitative landslide risk assessment framework, vulnerability curves are finally developed to quantify the expected direct losses in normalised cost terms.

Probabilistic assessment of seismic-induced slope displacements: an application in Italy

Earthquake-induced slope instability is one of the most important hazards related to ground shaking, causing damages to the environment and, often, casualties. Therefore, it is important to assess the seismic performance of slopes, especially in the near fault regions, evaluating the permanent displacements induced by seismic loading. This paper applies a probabilistic approach to evaluate the seismic performance of slopes using an updated database of ground motions recorded during the earthquakes occurred in Italy. The main advantage of this approach is that of accounting for the aleatory variability of both ground motions and prediction of seismic-induced displacements of slopes. The results are presented in terms of hazard curves, showing the annual rate of exceedance of permanent slope displacement evaluated using ground motion data provided by a standard probabilistic hazard analysis and a series of semi-empirical relationships linking the permanent displacements of slopes to one or more ground motion parameters. The procedure has been implemented on a regional scale to produce seismic landslide hazard maps for the Irpinia district, in Southern Italy, characterised by a severe seismic hazard. Seismic landslide hazard maps represent a useful tool for practitioners and government agencies for a regional planning to identify and monitor zones that are potentially susceptible to earthquake-induced slope instability, thus requiring further detailed, site-specific studies.

A generalized seismic sliding model of slopes with multiple slip surfaces

AbstractEarthquake‐induced permanent displacements of slopes are generally evaluated through the simplified sliding block analyses of a singular coherent mass on a predefined failure plane. However, coseismic landslides may exhibit multiple slip surfaces as a result of earthquake shaking. This study presents a generalized seismic sliding analysis using a column of sliding blocks to model seismic slope failures with multiple slip surfaces. The formulation of the sliding mode equations of the block system is obtained by a rigorous theoretical derivation. Both a rigid soil column associated with an acceleration–time series that is constant with depth, and a flexible soil column considering an acceleration–time series that varies throughout the sliding mass is presented. The conditional yield accelerations and the equivalent seismic accelerations are defined to characterize the complex interplay of the sliding block assemblies. The approach is applied to model the seismic sliding behavior of layered slopes in which failures would likely occur at the interfaces between soil layers with different shear strengths. The effects of input ground motions and soil deposits on the sliding patterns of slopes are investigated. The developed generalized model provides a promising means for evaluating the seismic slope stability by combining a number of seismic failure locations within slopes.

Influence of ground motion duration on the seismic performance of earth slopes based on numerical analysis

Assessing the dynamic stability of earth slopes is an important topic in geotechnical engineering field. In this study, the duration effect on the seismic performance of a multi-layer earth slope is quantitatively investigated, using two pairs of ground-motion suites selected matching a scenario-based response spectrum and a design spectrum, respectively. The four ground-motion suites are selected from the NGA-West2 database, with each pair of suites exhibiting a consistent distribution of response spectra yet different distributions of significant duration. Numerical analyses using the selected ground-motion suites as input are then conducted for the earth slope implemented in FLAC. Comparative results indicate that as compared to the shorter-duration suites, using the longer-duration ground-motion suites generally yields similar topographic acceleration-amplifications but an enlarged distribution of permanent slope displacements. Therefore, the influence of ground-motion duration on seismic-wave amplifications is insignificant; such influence on the earthquake-induced slope displacements is, however, significant. Using the selected longer-duration ground-motion suites, the slope (moderate) damage and failure probabilities exceeding specific displacement thresholds are increased by up to 20% and 50%, respectively. Therefore, when assessing the seismic performance of earth slopes in applications, one should pay adequate attention to the ground-motion duration effect, and input motions shall be selected in such a way that the duration characteristics of ground-motion records are properly constrained.

Investigation and mechanism analysis of disasters under Hokkaido Eastern Iburi earthquake

An Mw6.6 earthquake occurred at 3a.m. on September 6, 2018, in the eastern part of Iburi, Hokkaido. This earthquake killed 41 people, caused a series of service interruptions in Sapporo city. Soil liquefaction and approximately 6000 landslides were triggered. A field investigation was conducted on liquefaction and typical landslides during September 18 to 24, 2018. The liquefaction disaster exhibited soil flow, subgrade collapse, uneven settlement, earthquake subsidence, and deformation of buildings. After investigation of typical landslides, it was found that owing to the continuous heavy rainfall and typhoon, the surface soil had a high-water content. A layered loam of approximately 2 m below ground surface developed into a weak surface. Based on the analysis of sliding morphology, the landslides were classified into translational earth slides and earth flow. To clarify the mechanism of regional landslides, the stability and permanent displacement of slopes considering effect of continuous heavy rainfall and seismic motion was analyzed. Limit equilibrium analysis was applied based on the pseudo-static method. Then Newmark displacement calculation was conducted based on the seismic acceleration record. The distribution range of analysis results showed agreement with actual landslides disasters. The results verified the contribution of continuous rainfall and strong motion to the failure of regional slopes.

Displacement hazard curves derived from slope-specific predictive models of earthquake-induced displacement

Probabilistic hazard curves for earthquake-induced permanent slope displacements incorporate the important variabilities associated with predictions of slope movements, such that a rational assessment of slope performance can be obtained. To date, displacements estimated from sliding block analyses predominantly have been used to compute displacement hazard curves, despite the fact that nonlinear finite element analysis is becoming the preferred method to evaluate the performance of slopes. This paper extends the probabilistic approach for use with displacements from finite element analyses. We develop slope-specific displacement prediction models using displacements computed by nonlinear finite element analyses. Various models are developed that utilize different ground motion intensity measures and each model is used to compute a displacement hazard curve for a site in Northern California. The computed hazard curves reveal that the different models generate a large range of epistemic uncertainty, and the model with the smallest standard deviation does not necessarily predict the smallest displacement hazard due to the influence of the shape of the ground motion hazard curve and of the displacement model. As a result, multiple displacement models that incorporate different intensity measures should be considered in any assessment of the seismic performance of slopes, in the same way that multiple ground motion models are incorporated into ground motion hazard analyses.

Coupled analysis of earthquake-induced permanent deformations at shallow and deep failure planes of slopes

The seismic performance of slopes is commonly evaluated by simplified sliding block analyses. In this paper, an extended sliding block model is developed to compute the earthquake-induced deformations at both shallow and deep failure planes of slopes. The coupled analytical model captures simultaneously the stick-stick, stick-slip and slip-slip behaviors of the lumped mass system of soil profile. The complex interactions between the dynamic response of the soil and the slip episodes at shallow and deep slide planes are revealed. The proposed sliding model is compared to the conventional single base-sliding analyses, and the influence of the presence of shallow failure sliding is emphasized. Then, the dynamic response and permanent displacement of slopes with different locations of the shallow sliding plane and different yield accelerations of shallow and deep sliding planes are examined. The comparisons are also performed for permanent displacements determined from the developed coupled multi-sliding procedure and from the seismic sliding model with multiple rigid blocks. Finally, an example is presented to demonstrate the procedure in the application and the differences of the results from the traditional coupled approach. The coupled model in this study provides a rigorous procedure to combine the shallow and deep failure modes for the assessment of the co-seismic landslide hazard.

A methodology for uncertainty analysis of landslides triggered by an earthquake

Strong earthquakes lead to slopes instability in mountainous regions and subsequently trigger landslides. Landslides may cause serious damage to infrastructure such as roads and railways, and may also lead to human injuries and death. The severity of the direct and indirect consequences of damage caused by landslides is inevitable and needs a more reliable approach for risk analysis associated with this phenomenon. In this paper, a novel methodology is employed to estimate the probability of permanent displacement of slopes in mountainous regions. This methodology is developed by using Bayesian network and probabilistic modeling of Newmark displacement. As a part of this methodology, the static safety factor is determined considering uncertain effective parameters. An uncertainty analysis is then performed to estimate the permanent displacement of soil block affected by critical and peak ground accelerations. To demonstrate the application of the developed methodology, slope stability in the Alborz Mountains was considered as a case study. The results highlight that in the absence of the earthquake, instability of the slope is unlikely in the Alborz Mountains. However, with occurrence of an earthquake, it is possible to observe the permanent displacement for the slopes of between 0.2 cm and 5 cm. It was also found that displacements of most probable permanent slope (probability of 19%) occurred in the range of between 1 and 1.5 cm.

Effect of Earthquake Motion on The Permanent Displacement of Embankment Slopes

Permanent displacement of slopes is key data for designing the slope in performance-based seismic design. To estimate the permanent displacement of a slope, empirical as well as numerical methods should be adopted. However, the results of these methods are highly dependent on both stationary and nonstationary ground-motion characteristics. This paper aims to find the most influential nonstationary characteristics of earthquakes on the permanent displacement of slopes. Two different numerical methods, Newmark’s sliding-block and response-history analysis, are used for a total of 47 real earthquake records. The records are classified into three groups based on their event characteristics. They are spectrally matched before analysis to the target spectrum to eliminate the effect of stationary characteristics. The amount of permanent displacement obtained from the analyses is different for varying input motions. The intensity-based parameters, destructiveness potential factor, Arias intensity, and characteristic intensity play an important role on the permanent displacement of the slope. The results of this study are expected to yield judgment criteria for designers to select appropriate ground motion to evaluate the permanent displacement of slopes under seismic loading.

Spatial distribution of yield accelerations and permanent displacements: A diagnostic tool for assessing seismic slope stability

Seismically-induced permanent displacements of slopes are commonly evaluated using the Newmark sliding block approach. The conventional Newmark approach, while convenient in application, is often applied to a singular potential failure mechanism, omits consideration of the spatial distribution of potential failure mechanisms, neglects complex yet realistic failure geometry, and does not consider the temporal evolution of the critical mechanism. The proposed diagnostic tool applies the Newmark approach within a rigorous limit equilibrium framework to produce spatial distributions of yield accelerations and seismically-induced permanent displacements, or yield maps and surface-associated displacement maps, respectively. In this study, the application and utility of these diagnostic tools are demonstrated through a sensitivity analysis considering various soil strength parameters, horizontal and vertical motions, and complex slope and failure geometries. Additionally, it is shown that the proposed diagnostic tool reasonably estimates post-seismic geometry, shown by a comparison to an experimental shake table study. Using yield and displacement maps, both coseismic displacement and the range of potentially unstable geometry may be constrained. Moreover, the spatial and temporal evolution of possible seismically-induced displacements may be considered. This tool provides a rational means of applying sliding block approaches that reduces the need to assume the surface of maximum displacement a priori while retaining the simplicity that has facilitated the application of the sliding block approach versus more complex numerical models. The proposed diagnostic tools also provide a framework for future potential analyses, as it can be modified to incorporate other slope stability methods or seismic analyses.