Sliding Block Model Research Articles

Directionality of earthquake-induced slope displacements from numerical analysis and sliding block approaches

Earthquake ground shaking intensity differs at different azimuthal orientations (ground motion directionality), which could also result in orientational variations in earthquake-induced slope displacements. Therefore, the range of seismic displacements (e.g., the median and maximum values over all orientations) that may occur by considering the directions of downslope movement and strong shaking is important to evaluate seismic landslide hazard of site-specific slopes. This study performs comprehensive directionality analyses of seismic slope displacement based on two-dimensional numerical and sliding-block approaches. Four slope models with clay and sand soil layers and slope angle of 30° and 40° are analyzed using 75 ground motion records rotated over all orientations. Different sliding-block models are considered, including rigid-block analysis and two coupled flexible-block representations of one-dimensional soil columns with only sliding mass and full site respectively. The results indicate that the orientation variation of slope displacements is much larger than the ground motion parameters. The directionality characteristics of seismic slope displacement from numerical calculation can be well captured by the sliding-block analyses, although significant differences in the computed displacement values are observed. A procedure is proposed to obtain the maximum and median values of seismic slope displacement over all orientations from advanced numerical analysis at low computational cost.

Seismically induced deformations of layered slopes with non-unique and non-planar slip surfaces

Earthquake-induced deformation is prevalently used to evaluate the seismic performance of slopes, often assumed to occur along a predefined single slip surface. This paper presents a new limit equilibrium method combining with Newmark sliding block analysis for calculating the seismic displacement of layered slopes with non-unique and non-planar slip surfaces. The determination of the most and subsequent critical slip surfaces during the earthquake shaking is discussed with an emphasis on the coupling effects between the shallow and deep failures. The approach is validated by the results from numerical simulation and the shaking table model test of layered slopes. Comparison analyses are also performed for the predictions of seismic displacement from the developed and previous sliding-block models. It is found that the seismic sliding deformation at the first slip surface significantly affects the evolution and sliding deformation of the subsequent slip surface. For the considered example of layered slope, a second slip surface at deeper location passing through the slope toe is identified, and a coupled variation is observed for the sliding displacement along the two slip surfaces. These features are not well predicted from the available sliding-block models. The developed model can capture the interaction between the non-unique slip surfaces and the geometry effect of the non-planar slip surfaces.

Investigation of seismic displacements in bedding rock slopes by an extended Newmark sliding block model

Investigation of seismic displacements in bedding rock slopes by an extended Newmark sliding block model

Reliability Analysis of Seismic Slope Incorporating Interactions among Multiple Sliding Blocks Using Imbalance Thrust Force Method in Primary Sliding Direction

This paper proposes a methodology for reliability analysis of seismic slope stability that incorporates interactions among multiple sliding blocks. The primary sliding direction is first determined using the vector sum method and then the imbalance thrust force along the primary sliding direction is calculated using the slice-wise strategy and, finally, the double integration strategy is adopted to calculate the accumulated sliding displacement within the earthquake duration. The interactions among multiple sliding blocks are incorporated by checking the potential of occurrence for each of the multiple sliding modes. The proposed method is applied to a soil slope with two sliding surfaces. The comparative studies demonstrate that the mean and standard deviation of the sliding displacement considering the interaction of multiple sliding blocks are approximately three times larger than that of a single sliding mode, and the COV (mean value divided by standard deviation) of the two are slightly different. For the single sliding mode, the mean and standard deviation of the sliding displacement calculated using the proposed method are about 1/2 of the traditional Newmark sliding block model, and the failure probability obtained by the proposed method is lower than that from the traditional Newmark sliding block model owing to the difference in the sliding direction. The Peak Ground Acceleration (PGA) exhibits a significant effect on the statistics of 10,000 sliding displacements. The interactions among multiple sliding blocks and the PGA are required to be properly considered in seismic slope reliability analysis.

Seismic reliability analysis of soil slope based on Newmark sliding block model with representative slip surfaces and response surfaces

AbstractThis paper presents a framework combining Monte Carlo Simulation (MCS) and the Newmark sliding block model with representative slip surfaces (RSS) (model II) and multiple response surfaces method (MRSM) to conduct seismic reliability analysis and risk assessment of soil slopes. An empirical threshold is introduced to define the limit state function to identify the failure samples in MCS and the sliding area and Newmark sliding displacement are multiplied to quantify the failure consequence. The proposed methodology is illustrated through a soil slope with multiple layers. The calculation results demonstrate that traditional Newmark sliding block model (model I) tend to underestimate the variations of yield acceleration. Both the failure probability and landslide risk exhibit decreasing trends with the increase of threshold. Significant discrepancy in failure probability and landslide risk between two models is found even for a small threshold. Therefore, the proposed methodology is highly recommended in seismic reliability analysis and risk assessment. The contributions of RSSs to the failure probability and landslide risk are insensitive to the variation of displacement thresholds.

Performance-based seismic assessment of slope systems

The calculated seismic slope displacement provides a valuable index of the seismic performance of earth embankments and natural slopes. Sliding block models are often employed. The specific features of each sliding block method determine its reliability. Rigid sliding block models should not be used except for the limited case when the sliding mass is rigid. A coupled nonlinear deformable stick-slip sliding block model calculates reasonable seismic slope displacements. The primary source of uncertainty in assessing the seismic performance of an earth slope is the input ground motion. Hence, many ground motion records for each tectonic setting should be employed. Seismic slope displacement depends primarily on the earth structure's yield coefficient and the earthquake ground motion's spectral acceleration at the effective fundamental period of the sliding mass. Coupled nonlinear sliding block models enable the sensitivity of the seismic slope displacement and its uncertainty to key input parameters to be assessed. These procedures can be implemented within a performance-based design framework to estimate the seismic slope displacement hazard, which is a more rational approach.

Stability Analysis of Shield Excavation Surface with Curved Body Model

Currently, the limit equilibrium method of wedge shape is generally adopted for the stability of the excavation surface in shield tunnel construction. In this method, the sliding surface is approximated by a plane, and the lateral friction force of the sliding surface is estimated and assumed to be a known quantity to derive the equilibrium equation and calculate the support force of the excavation surface. However, it is difficult to accurately estimate the lateral friction force of the sliding surface because of many factors that affect such friction, for example, soil arching. In this paper, a sliding block model of curved surface body composed of a semicircular platform and a partial sphere is proposed for the stability of the excavation surface in shield tunnel construction. By using the symmetry of the surface body model, there is no need for estimating the friction force of the sliding surface during the stability analysis of the excavation surface, and the calculation accuracy of the limit support pressure is improved. Furthermore, the force analysis of the semi-circular platform surface model above the tunnel vault is carried out. Considering the variation of the lateral pressure coefficient caused by the deflection of the principal stress under the soil arch effect, the analytical solution of the vertical stress in the soil is derived when the sliding crack surface is curved. Finally, we present a sensitivity analysis of various parameters affecting the support force of the excavation face through the study of examples. The influencing factors and changing rules related to the support force of the excavation face are also discussed.

Effect of Excitation-Applied Manners on Permanent Displacements of Planar Slopes Using Dynamic Sliding Blocks Analysis

The sliding block model is widely used to evaluate the stability of slopes under earthquakes. In this model, the horizontal ground motion is usually applied to the parallel to the slope, whereas the vertical ground motion is commonly ignored. This study investigated the effects of different excitation-applied methods (EAMs) on slope permanent displacements (PDs) using a general sliding block model. For this purpose, three types of ground motion records selected from the NGA-West2 database were applied with six different EAMs to a series of gentle/steep slope sliding systems whose critical accelerations ac ranges from 0.01 to 0.40g. Comparison of the PDs obtained from the two-dimensional (2D) EAM and the other five systems reveal the following: (1) the common practice of applying a one-dimensional (1D) input motion excessively underestimates the PDs of sliding systems, particularly for those with large slope angles and large critical accelerations; and (2) the effects of the vertical component on the arithmetic mean of PDs are ignorable although the impact can reach several times for some cases in which the slopes are located in near-fault areas and affected by pulse-like ground motions. Besides, it is demonstrated in this study that applying the horizontal and vertical base motions simultaneously to the slope can be the most suitable excitation-applied manner for seismic slope stability analysis in the near-fault zone.

Investigation of permanent displacements of near-fault seismic slopes by a general sliding block model

Investigation of permanent displacements of near-fault seismic slopes by a general sliding block model

Rapid Terrain Assessment for Earthquake-Triggered Landslide Susceptibility With High-Resolution DEM and Critical Acceleration

Earthquake ground motion often triggers landslides in mountainous areas. A simple, robust method to quickly evaluate the terrain’s susceptibility of specific locations to earthquake-triggered landslides is important for planning field reconnaissance and rescues after earthquakes. Different approaches have been used to estimate coseismic landslide susceptibility using Newmark’s sliding block model. This model requires an estimate of the landslide depth or thickness, which is a difficult parameter to estimate. We illustrate the use of Newmark sliding block’s critical acceleration for a glaciated valley affected by the 2015 Gorkha earthquake in Nepal. The landslide data came from comparing high-resolution pre- and post-earthquake digital elevation models (DEMs) derived from Spot 6/7 images. The areas where changes were detected provided an inventory of all the landslides triggered by the earthquake. The landslide susceptibility was modeled in a GIS environment using as inputs the pre-earthquake terrain and slope angles, the peak ground acceleration from the 2015 Gorkha earthquake, and a geological map. We exploit the depth information for the landslides (obtained by DEM difference) to apply the critical acceleration model. The spatial distribution of the predicted earthquake-triggered landslides matched the actual landslides when the assumed landslide thickness in the model is close to the median value of the actual landslide thickness (2.6 m in this case). The landslide predictions generated a map of landslide locations close to those observed and demonstrated the applicability of critical acceleration for rapidly creating a map of earthquake-triggered landslides.

Clay landslide movement triggered by artificial vibrations: new insights from monitoring data

Slope stability is influenced by a number of factors that modify the resisting/acting force ratio control landslide initiation and movement velocity. Among these, artificial vibrations have been identified as an important degrading factor for soil strength, but it is not fully clear if they can trigger or modulate movements of clay landslides. To contribute to a better understanding of the potential effect of vibrations on landslide movement, also in terms of boundary conditions, we analyzed monitoring data acquired at the toe of the Pietrafitta landslide in southern Italy. This landslide adjoins the SS87 national road that suffered periodic closure due to landslide activity and in April 2016 operates daytime only for risk mitigation purpose. This condition promoted a better identification of a potential cause-effect relation between traffic vibration and landslide movement. Results from data analysis and landslide modeling suggest that in condition of incipient movement, artificial vibrations, also of limited amplitude, are able to directly initiate clay landslide movement that due to the viscous nature of the involved material exhibit a specific displacement pattern that is not consistent with a sliding block model.

A Hybrid Approach Calculating Lateral Spreading Induced by Seismic Liquefaction

Liquefaction-induced lateral spreading has caused severe damages to the infrastructures. To predict the liquefaction-induced lateral spreading, a hybrid approach was proposed based on the Newmark sliding-block model. One-dimensional effective stress analysis based on the borehole investigation of the site was conducted to obtain the triggering time of liquefaction and acceleration time history. Shear wave velocity of the liquefiable soil was used to estimate the residual shear strength of liquefiable soil. The limit equilibrium analysis was conducted to determine the yield acceleration corresponding with the residual shear strength of liquefied soil. The liquefaction-induced lateral spreading was calculated based on the Newmark sliding-block model. A case study based on Wildlife Site Array during the 1987 Superstition Hills earthquake was conducted to evaluate the performance of the hybrid approach. The results showed that the hybrid approach was capable of predicting liquefaction-induced lateral spreading and the calculated lateral spreading was 1.5 times the observed displacement in terms of Wildlife Site Array. Numerical simulations with two other constitutive models of liquefiable sand were conducted in terms of effective stress analyses to reproduce the change of lateral spreading and excess pore water ratio over the dynamic time of Wildlife Site Array. Results of numerical simulations indicated that the lateral spreading varied with the triggering time of liquefaction when different constitutive models were used. The simulations using PM4sand and UBC3D-PLM constitutive models predicted 5.2 times and 4 times the observed lateral spreading, respectively. To obtain the site response, the motions recorded at and below the ground surface were analyzed using the Hilbert–Huang transform. The low-frequency content of the motion below the ground surface was amplified at the ground surface, and the liquefaction effect resulted in a shift of the frequency content. By comparing the response spectra of the entire ground surface motion and the ground surface motion from the beginning to the triggering time of liquefaction, the liquefaction effect at the site was confirmed.

Probabilistic investigation of the seismic displacement of earth slopes under stochastic ground motion: a rotational sliding block analysis

Earthquakes frequently induce landslides and other natural disasters that would have a huge impact on human life and properties. In geotechnical engineering, evaluation of the seismic stability of earth slopes has been attracting a substantial amount of research interest. In this regard, the Newmark permanent displacement provides a simple yet effective index of slope co-seismic performance. The traditional Newmark method involves many assumptions and the displacement results thereby calculated are subject to various degrees of uncertainty. In this paper, a modified rotational sliding block model considering depth-dependent shear strength and dynamic yield acceleration is established. The seismic critical slip surface is analysed through a pseudo-static approach, where the failure volume is larger than that in the static condition. The dynamic yield acceleration is updated by considering the instantaneous movement of the sliding mass in each time-step. The parametric sensitivity of soil shear strength, slope geometry, and Arias intensity to the seismic displacement is also analysed. Results show that the internal friction angle and the cohesion have equal effects on the permanent displacement. On a logarithmic scale, the displacement approximately linearly correlates with Arias intensity. Furthermore, the underlying uncertainty of the ground motion is introduced to obtain the probabilistic distribution of the seismic slope displacement. The uncertainty of earthquake time history details has considerable influence on the permanent displacement results. Under the specific allowable displacement, the probability of failure increases exponentially with seismic intensity.

Mineralogical Analysis of Selective Melting in Partially Coherent Rockslides: Bridging Solid and Molten Friction

AbstractFrictional shearing along the basal slip surface is the main energy dissipation mechanism in coherent landslides, which undergo little internal deformation during runout. Most landslide bodies, however, deform and break down more or less extensively; thus, only a portion of their potential energy is dissipated through basal shearing. The mineral components of rocks and soils have individual melting temperatures. Therefore, as temperature increases, selective melting will occur in a defined sequence. The product of such melting is termed frictionite. Here, we exploited a sliding block model to investigate the role of selective melting in the evolution of the frictional resistance (and hence mobility) of partially coherent landslides. We recognized three frictional stages, characterized by weakening, strengthening, and melt lubrication. As melting proceeds, a gradual transition from solid friction to viscous flow occurs, which can be modeled in terms of the molten mineral fraction. The chemical composition also evolves and so does its viscosity. Rocks with different mineral proportions (e.g., mafic vs. felsic rocks) will exhibit different frictional evolutions. Our model results are consistent with the recognized role of landslide thickness in defining its mobility. Moreover, the frictional strengthening stage is shown to become irrelevant under high confinement, thereby facilitating higher mobility, or sometimes shifting slip surface if weak layer exists. We also discussed the relevance of some strengthening‐upon‐melting behavior observed at the experimental scale, pointing out the role of the energy conversion coefficient, which is a proxy for landslide coherence.

A MODEL FOR ASSESSMENT OF TREE STABILITY AND ENTRAINMENT OF WOODY DEBRIS BY FLOW SLIDES AND SHALLOW SLOPE FAILURE

The effect of trees on the stability of soil slopes is widely studied. Tree roots can reinforce the soil slope by increasing its shear strength; moreover, trees may reduce soil moisture content through the transpiration process, which may reduce the pore-water pressure, improving the shear strength of the soil slope. Nevertheless, trees can also be felled by landslides and flow slides. Fallen trees create woody debris, which is a serious hazard precipitated by landslides, slope failures, and flow slides that increases the magnitude of the destruction caused to infrastructure and housing. The processes of tree instability and the entrainment of woody debris are important mechanisms in the study of the behaviour of woody debris in the ecosystem. Therefore, the purpose of this study is to propose a model to describe the mechanism of tree instability caused by shallow slope failures and flow slides, including the entrainment of woody debris by flow slides or debris flows. The proposed model combines a rainfall-induced shallow slope failure model, a sliding block model for flow slides runout analysis, and a tree stability model.

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.

Bayesian calibration of an avalanche model from autocorrelated measurements along the flow: application to velocities extracted from photogrammetric images

AbstractPhysically-based avalanche propagation models must still be locally calibrated to provide robust predictions, e.g. in long-term forecasting and subsequent risk assessment. Friction parameters cannot be measured directly and need to be estimated from observations. Rich and diverse data are now increasingly available from test-sites, but for measurements made along flow propagation, potential autocorrelation should be explicitly accounted for. To this aim, this work proposes a comprehensive Bayesian calibration and statistical model selection framework. As a proof of concept, the framework was applied to an avalanche sliding block model with the standard Voellmy friction law and high rate photogrammetric images. An avalanche released at the Lautaret test-site and a synthetic data set based on the avalanche are used to test the approach and to illustrate its benefits. Results demonstrate (1) the efficiency of the proposed calibration scheme, and (2) that including autocorrelation in the statistical modelling definitely improves the accuracy of both parameter estimation and velocity predictions. Our approach could be extended without loss of generality to the calibration of any avalanche dynamics model from any type of measurement stemming from the same avalanche flow.

Prediction of amount of earthquake-induced slope displacement by using Newmark method

Landslides are one of the most important results of earthquakes. Estimation of the earthquake-triggered landslide displacement is a major topic for engineering because the amount of ground displacement is significant for seismic hazard assessment. Newmark sliding block model is a method commonly used to estimate earthquake-induced ground displacements. Based on this method some regression analyses have been carried out and different equations have been obtained. In this study, primarily, previous studies have been updated according to significant world wide earthquake records (2307 strong ground motion records belonging to 26 earthquakes). Then, in scope of this paper, a new regression equation has been obtained and the results have been examined. In consequence of the comparisons, it has been determined that the new formula has more appropriate results in terms of the regression parameters (R2 and standard deviation). All of these regression equations are suitable for a general approximation to the topic. These equations are useful to predict the amount of displacement for regionalscale seismic landslide hazard but they are not proposed for spesific design.

Seismic landslides hazard zoning based on the modified Newmark model: a case study from the Lushan earthquake, China

Seismically triggered landslides can cause great damage to the road construction in mountainous areas. The permanent displacement analysis based on Newmark sliding-block model can evaluate risk of these landslides from the perspective of deformation damage and overall failure probability of slopes. However, the sliding-block model does not consider the attenuation effect of the shear strength on the sliding surface during earthquake, causing the calculated value of Jibson method to be less than the actual value. Therefore, the Newmark model was modified by adding attenuation coefficients to the effective internal friction angle and the effective cohesion of geologic units. The landslide areal density was proposed for hazard zoning with the Wenchuan earthquake data. The results showed that the predicted values agreed well with the real distribution of the landslides triggered by the Lushan earthquake. The proposed hazard zoning method in this paper can predict the severity of seismic landslides in consideration of the environmental changes in mountainous regions after the earthquake and provide support for the site selection in highly seismic areas.

Assessment of sliding block methods performance considering energy-representative parameters

In this research, permanent deformation of ten real earth dams were estimated using all the sliding block models and then, the errors between calculated deformations by each model and observed deformations of earth dams were presented and discussed in detail. The applied motion for estimating displacement of each dam was the recorded acceleration in the dam site. It was indicated that, conservative and non-conservative estimations of each model can be separated by Specific Energy Density and Response Ratio parameters in the time and frequency domains, respectively. It was also shown that, there is a logical relationship between the occurred earthquake-induced displacements and the specific energy density.