3D Limit Equilibrium Method Research Articles

Influence of 3D subsurface flow on slope stability for unsaturated soils

The occurrence of rainfall-induced slope failures has become more frequent due to the effect of climate change. Hence, various studies have been conducted to analyse the effect of rainfall infiltration on slope stability. Physically-based hydrological models have been commonly used with slope stability models such as the infinite slope model to develop slope susceptibility maps. However, a combination of three-dimensional (3D) water balance model with 3D limit equilibrium method (LEM) has not been commonly used. Hence, in this study, a water balance model, GEOtop was used to investigate the influence of subsurface flow in unsaturated soil under extreme rainfall conditions on regional slope stability in 3D directions. The results from the GEOtop model were used as inputs for 3D LEM slope stability analysis performed using the Scoops3D software to obtain the factor of safety (FOS) map for the region. Four slopes within the region were then selected to be modelled in the two-dimensional (2D) seepage and slope stability analyses, SEEP/W and SLOPE/W. Results from the detailed study showed that the pore-water pressures (PWPs) from the 3D water balance analyses were found to be higher than the 2D seepage analyses. Under similar PWP conditions, the FOS from the 2D slope stability analysis was observed to be lower than the 3D analysis for two out of the four slopes. However, the combined 3D water balance and slope stability analyses produced lower FOS compared to the 2D seepage and slope stability analyses due to the higher PWPs in the 3D water balance analyses. Therefore, this study highlights the importance of considering the 3D subsurface flow in unsaturated soil given that it has a significant influence on the FOS of slopes.

A pseudo-3D methodology for regional-scale back-analysis of earthquake-induced landslides

Major earthquakes can cause hundreds to thousands of landslides in mountainous areas, but the methods for regional earthquake-induced landslide analyses are currently not well developed. This paper proposes an algorithm for back-analyzing earthquake-induced landslide inventories. The result of the back-analysis (or “inversion”) is a modeled three-dimensional (3D) “best-matching” landslide for each mapped landslide in an inventory as well as an estimate of average shear strength along the landslide failure plane. The algorithm leverages seismic displacement models to detect the triggering location (i.e., triggering grid cell) of modeled landslides. The triggering grid cell is then projected to form a 3D cone-shape failure surface for each modeled landslide using geomorphic characteristics, i.e., flow direction and flow accumulation, and a geometric rule, a procedure termed here as pseudo-three-dimensional (pseudo-3D). The inversion algorithm uses the landslide location, area, and volume (if available) of each mapped landslide to find a modeled landslide that minimizes the “mismatch” between the two, expressed as total error, and outputs an associated triggering depth, landslide geometry, and strength. The estimate of strength for each individual landslide can then, if needed, be aggregated using a geospatial methodology (e.g., geologic unit information or a K-means clustering method) to derive regional-scale Mohr-Coulomb shear strength parameters. The potential bias of the proposed pseudo-3D methodology on the strength estimate is assessed against synthetic landslide inventories generated using a 3D limit equilibrium method. The back-calculated friction angles agree well with 3D results, while the cohesions are lower than the estimated cohesions from 3D slope stability analysis. In addition, the effect of different seismic displacement models on the results of the back-calculated strengths is investigated. The proposed methodology is implemented to the 2015 Lefkada earthquake event in Greece, which triggered more than 700 landslides, with the goal to demonstrate the efficiency in the inversion of many landslides and the generation of regional estimates of strength parameters. For this study region, the spatial distribution of the shear strength results indicates that areas with fewer landslides have higher shear strength while areas with more landslides have lower shear strength.

Mechanical properties and acoustic emission response of carbonate fault breccias: a study from Greece

The present study aims to investigate the mechanical properties and acoustic emission (AE) response of carbonate fault rocks in Lefkada Island, Greece. In the aforementioned region, tectonic processes have resulted in the formation of fault breccias with poor mechanical properties and complex behaviour. In these weak formations, conventional laboratory testing methods are restricted due to disintegration during sampling and specimen preparation. A novel sample preparation and laboratory testing technique are used jointly with a back-analysis of a co-seismic landslide that occurred during a M w 6.5 earthquake in 2015. These two approaches are employed to characterize and predict the mechanical behaviour of these formations. The uniaxial compressive strength (UCS) of the fault breccias, determined in the laboratory, has a wide range due primarily to the complex nature of the material. The back-analysis, using a 3D limit equilibrium method, proves that the shear strength of the in situ material is significantly lower than that determined in the laboratory. Finally, the acoustic emission response of fault breccias was different compared to that of brittle rocks. Both b -value analysis and the damage variable evolution indicate that the accumulated damage within fault breccias is higher than expected, and thus they are more prone to fatigue. Thematic collection: This article is part of the Leading to Innovative Engineering Geology Practices collection available at: https://www.lyellcollection.org/topic/collections/leading-to-innovative-engineering-geology-practices

New Green-Ampt model based on fractional derivative and its application in 3D slope stability analysis

The infiltration process in slopes is an essential issue in geotechnical engineering. A new Green-Ampt model for describing the two-stage infiltration in slopes based on fractional derivatives was proposed in this paper. The Green and Ampt (1911)’s model, and Chen and Young (2006)’s model are two special cases of the proposed model. A 1D loess soil column test in the literature as well as a laboratory rainfall test of loess slope were used to validate the proposed model. The travel curve of wetting front obtained by the proposed model was obviously closer to the actual test value than that obtained by the Chen and Young’s model, indicating that the performance of the proposed model is superior to the Chen and Young’s model due to the use of fractional derivatives. The proposed Green-Ampt model was combined with a rigorous 3D limit equilibrium method to obtain the real-time safety factor of the slope during rainfall. The calculated failure time of the loess slope by the proposed method is close to the actual failure time of the laboratory test, while the corresponding of Chen and Young’s model is obviously shorter than the actual status. Six parameters are included in the proposed model, and sensitivity analysis shows that the fractional derivative has the most significant impact on the wetting front depth, followed by the permeability coefficient, moisture content difference, suction head, rainfall intensity, and slope angle.

Application of cuckoo search method in 3D slope stability analysis for limestone quarry mine

The Cuckoo Search (CS) is a very fast and efficient global optimization method to locating the slip surface which carried out by iteration. However, the Grid Search (conventional method) method in 3D slope stability analysis takes longer than this method on the computation process. Slope stability analysis was performed using the 3D limit equilibrium method “Bishop” with Cuckoo Search of slip surface by maximizing iteration of the simulation and columns in X or Y. To ensure that the slip surface within the global minimum slip surface, the maximum iteration in CS was also specified from 40 to 1200. Based on maximum columns in X or Y, the safety factor value of the 3D CS results was then compared to the Grid Search results to determine the final 3D safety factor and the estimated volume of potential failure. The final 3D safety factor obtained from the average 3D safety factor (with maximum iteration 400, 800, 1000, and 1200) is about 2,01 with the average estimated volume of slope failure of 190.000 m3 that located at the north of the pit.

Optimisation on plane arrangement of stabilising piles subjected to spatial distributed lateral load in landslides with multilayer sliding masses

The paper develops an analytical method to design the plane arrangement of stabilising piles under spatial lateral load of 3D colluvial landslides with multilayer sliding masses. Firstly, an approach based on the geological map and binary Lagrange Interpolation method was presented to establish 3D landslide calculation models. The improved 3D limit equilibrium method was then proposed to calculate the stability coefficient and spatial distributed lateral load of landslide with multilayer sliding masses. And main sliding direction of 3D multilayer landslide can be determined by the developed principle of minimum potential energy. Moreover, through assuming the piles and soil as elastic transversely isotropic continuum medium, analytical approach was employed to accurately calculate the stress distribution of soil between adjacent piles; and the maximum pile spacing can be calculated. Finally, the reasonable arrangement of stabilising piles can be determined based on Monte-Carlo method and cost of all piles. The finite difference method was employed to validate the theoretical results through the case study of Bazimen landslide. And it is found that the proposed method for the design of piles' arrangement is economically beneficial compared with the traditional method on the premise of ensuring safety.

The influence of number of grid points and radius increments in determining safety factor and estimated sliding volume on three-dimensional slope stability analysis

The existence of geometric complexity in the longitudinal direction makes 3D Limit Equilibrium Method (LEM) able to depict conditions in the field well and obtain Safety Factor (SF) that is more representative than the 2D limit equilibrium method. Safety factor calculations are not only influenced by the Direction of Sliding (DoS), but also by the location of the slip surface. Therefore, determining the location of the slip surface is important in the 3D limit equilibrium method. In this study, the method used for generating slip surfaces is a grid search where variations are made on the number of grid points and the radius increments to determine the effect of these two variables on the determination of safety factor and estimated sliding volume. Based on the results of the study, it can be stated that the greater the number of grid points and the radius increments, the estimated sliding volume will be more precise, while the calculation of safety factor is only affected by the number of grid points where the greater the number of grid points, the search of critical slip surface will be more accurate.

Three-dimensional (3D) slope stability analysis using stability charts

Stability of slopes is a very serious issue in the field of geotechnical engineering. The analysis and design of failing slopes requires a thorough knowledge of the failure mechanism in order to choose the right slope stability analysis method. The two-dimensional (2D) slope stability methods are very common to the engineers because of the simplicity in their assumptions. As a result the analysis results vary greatly between the different analysis methods. The importance of three-dimensional (3D) slope stability analysis greatly increased where the geometry of the problem becomes complex which makes it very difficult to solve using 2D analysis. A lot many 2D slope stability methods were extended to 3D methods since 1970s based on limit equilibrium (LE) and finite element approaches. In this paper, slopes were analysed using 3D limit equilibrium method (LEM) using SLIDE3 software having different geometry and soil parameters and finally stability charts were prepared to calculate the FOS of the slopes. It is found that the slope stability factor can be read from the stability charts without the need for iterations.

Lava delta deformation as a proxy for submarine slope instability

The instability of lava deltas is a recurrent phenomenon affecting volcanic islands, which can potentially cause secondary events such as littoral explosions (due to interactions between hot lava and seawater) and tsunamis. It has been shown that Interferometric Synthetic Aperture Radar (InSAR) is a powerful technique to forecast the collapse of newly emplaced lava deltas. This work goes further, demonstrating that the monitoring of lava deltas is a successful strategy by which to observe the long-term deformation of subaerial–submarine landslide systems on unstable volcanic flanks. In this paper, displacement measurements derived from Synthetic Aperture Radar (SAR) imagery were used to detect lava delta instability at Stromboli volcano (Italy). Recent flank eruptions (2002–2003, 2007 and 2014) affected the Sciara del Fuoco (SdF) depression, created a “stacked” lava delta, which overlies a pre-existing scar produced by a submarine–subaerial tsunamigenic landslide that occurred on 30 December 2002. Space-borne X-band COSMO-SkyMED (CSK) and C-band SENTINEL-1A (SNT) SAR data collected between February 2010 and October 2016 were processed using the SqueeSAR algorithm. The obtained ground displacement maps revealed the differential ground motion of the lava delta in both CSK and SNT datasets, identifying a stable area (characterized by less than 2 mm/y in both datasets) within the northern sector of the SdF and an unstable area (characterized by velocity fields on the order of 30 mm/y and 160 mm/y in the CSK and SNT datasets, respectively) in the central sector of the SdF. The slope stability of the offshore part of the SdF, as reconstructed based on a recently performed multibeam bathymetric survey, was evaluated using a 3D Limit Equilibrium Method (LEM). In all the simulations, Factor of Safety (F) values between 0.9 and 1.1 always characterized the submarine slope between the coastline and −250 m a.s.l. The critical surfaces for all the search volumes corresponded to the 30 December 2002 landslide, which involved the lava delta and its surrounding areas. InSAR data provided the post-effusive deformation field after the 2007 and 2014 flank eruptions, whereas LEM results highlighted that the accumulation of lava flows on the prone-to-failure SdF submarine slope is the main cause of the detected lava delta deformation. Lava delta instability, measured also at Pico Island (Azores) and Kilauea volcano (Hawaii), is evidence of the broader spectrum of instability phenomena that take place in the coastal or submarine area of the flanks of the volcanoes. At Kilauea, past lava deltas have moved faster than the surrounding slope and the recorded movements relate only to the collapses of the deltas themselves, producing rapid mass wasting near the coasts. In contrast, at Stromboli and Pico, lava deltas move at the same velocity as the surrounding slope. In these cases, the displacement at lava deltas can be considered as a proxy for the deformation of submarine slides. There are very few studies dealing with lava delta deformation, thus, the analysis presented in this work will benefit the monitoring of submarine slopes in other prone-to-failure coastal or island volcanic systems which have the potential to generate tsunamis.

Safety monitoring and stability analysis of left bank high slope at Jinping-I hydropower station

At the Jinping-I hydropower station the excavation height on the slope of the left bank is about 530 m. The stability of the excavated slope is very important because of the complicated geological conditions. To analyse the process of deformation evolution of the left abutment slope during construction, a comprehensive monitoring system was employed, which combined surface deformation observations, multi-point extensometers and graphite rod extensometers. This paper describes this monitoring system and analyses the deformation development with slope excavation. We also established a 3D numerical model of the slope and simulated the whole process of excavation using the finite-difference method. Results from both monitoring and numerical simulation show that the deformation depth in the left bank slope of the Jingping-I hydropower station is over 150 m owing to large-scale excavation unloading, far greater than that of general engineering slopes. The 3D limit equilibrium method and the strength reduction method are applied to evaluate the stability of the excavated slope. The calculated factors of safety indicate that the left abutment slope is stable and safe as a whole, which is in agreement with the deformation monitoring results.

Numerical limit analysis of three-dimensional slope stability problems in catchment areas

Risk analysis of existing slopes in catchment areas requires quantification of their stability. This quantification becomes particularly difficult when dealing with larger areas under 3D conditions and including saturated and unsaturated water flow. This paper proposes the use of an effective numerical procedure to solve three-dimensional slope stability problems in large areas subjected to pore pressure effects. This numerical approach, numerical limit analysis, utilizes the finite element method and mathematical programming techniques. Mathematical programming is needed because the basic plasticity theorems for limit analysis can be cast as optimization problems. The generated optimization problem is formulated under a second-order cone programming framework, which is known to solve large-scale problems with great computational efficiency. The main objective of this work was to determine the slope safety factor and the collapse mechanism of soils governed by the Drucker–Prager yield criterion for large-scale 3D problems including pore pressure effects. This approach is applied to an experimental catchment in the Oregon Coast Range that failed after an intense rainfall. The results were compared with a previous stability analysis of the area available in the literature that used a novel 3D limit equilibrium method.

3D stability analysis of gravity dams on sloped rock foundations using the limit equilibrium method

A convenient approach to performing stability analysis of concrete gravity dams is the so-called two-dimensional “gravity method.” However, concrete gravity dams located in valleys with sloped rock foundation abutments behave as three-dimensional (3D) structures and are often able to share compressive and shear loads between adjacent monoliths, especially when shear keys are present. A general 3D limit equilibrium method was developed in this study to compute global sliding safety factors (SSFg) by considering sequential load redistribution among adjacent monoliths when individual monoliths have mobilized their sliding strength. Two validation examples of the sliding safety assessment of existing dams are presented to illustrate the accuracy and efficiency of the proposed approach compared to that of the full 3D numerical analyses conducted using the distinct element method. It is shown that gravity dams may be formed by individual monoliths on sloped rock foundations that will slide if considered as isolated structures but will constitute a stable assembly when the load-sharing capabilities of monoliths are recognized in the analysis.

Hazard assessment by 3D stability analysis of landslides due to reservoir impounding

The Yudonghe landslide is located in a upcoming reservoir region of a 233-m-high Shuibuya rockfill dam, 2,300 m away from the dam site. It consists of a massive landslide with upper and lower segments and two secondary slides, i.e. an eastern secondary slide and a western secondary slide. In this paper, values of factor of safety (FS) for various masses were calculated in a scenario of reservoir impounding-induced increase in groundwater levels, using a method of three-dimensional (3D) limit equilibrium. Results showed that the smallest value of FS for the massive landslide is 1.12 computed on the presupposition of reactivating along a bottom slide zone in case of an earthquake. The smallest FS value of the lower slide mass is 1.12 in a possible direction, given earthquake occurrence and a groundwater level of 225 m above the sea level. This FS value shows that the lower slide mass is stable in case of groundwater increasing. In addition, by the calculation of the 3D limit equilibrium method, the FS value of the east secondary slide is approximately 1.0 in different groundwater levels under consideration of earthquake occurrence, which reflects that this mass is prone to reactivate when external factors are taken into effect.