Deterministic Slope Stability Analyses Research Articles

Assessing the stability of the reservoir rim in moraine deposits for a mega RCC dam

<abstract> <p>Diamer Basha Dam is an under-construction, 272-meter-high, roller compacted concrete (RCC) dam on the Indus River in Pakistan. Once constructed, it will be the world's highest RCC gravity dam with a 105-kilometer-long reservoir. Most of the reservoir lies in unstable moraine deposits with steep slopes. Events like saturation during reservoir filling, alternate wetting, drawdown during reservoir operation, or a seismic event could trigger a large mass movement of these slopes into the reservoir to disrupt the dam functionality. This work identified the 15 most vulnerable slide areas using digital slope maps, elevation maps, and satellite imagery. Deterministic slope stability analysis was carried out on the identified sections under various stages of reservoir operation for static and seismic loading, using pseudo-static and dynamic analysis approaches. Probabilistic analysis was then performed using Monte Carlo simulation. The findings showed that most moraine deposits would collapse under reservoir filling, rapid drawdown, or seismic activity. Following the assessments, landslide susceptibility maps were generated, and an assessment of potential impacts, including the generation of dynamic waves, reservoir blockage, increased sediment loads, and reduced reservoir storage capacity, was also performed.</p> </abstract>

Probabilistic analysis of width‐limited 3D slope in spatially variable soils: UBLA enhanced with efficiency‐improved discretization of horn‐like failure mechanism

AbstractReliability analysis of earth slopes considering soil spatial variability has garnered significant attention from researchers. However, previous studies have predominantly focused on long slopes with infinite or ample width, such as dams and subgrades, but rare research was dedicated to slopes with width restricted by boundary constraints. In this regard, this paper proposes an efficient reliability framework suitable for width‐limited slopes in spatially variable soils. The proposed framework employed spatial discretization‐based upper bound limit analysis (UBLA) to conduct the deterministic slope stability analysis. The established failure mechanism can well capture the width‐limited three‐dimensional slip surface characteristics and satisfies the kinematically admissible conditions in spatially variable soils. Two innovative strategies are proposed to boost the efficiency of the discretized mechanism. They reduce the computational time to determine safety factors from over 20 min to less than 2 min. For the uncertainty modeling and slope reliability computing procedure, the Sparse Polynomial Chaos Expansion (SPCE) and Monte Carlo Simulation (MCS) methods are combined to generate the distribution of safety factors and failure probabilities. This combination addresses the high‐dimensional stochastic problem arising from 3D spatial variability. Using the proposed framework, a parametric analysis of a 3D spatially variable slope is conducted to investigate the impact of various factors. The findings of this paper are beneficial to the risk evolution of width‐limited slopes, and the efficiency enhancement strategies have the potential to expedite the limit analysis of other geo‐structures, such as tunnels, retaining walls, and foundations.

Hydrologic-geotechnical modelling of shallow landslide and flood hazards caused by heavy rainfall

Landslides and flooding are two of the most common hazards associated with heavy rainfall. Most studies, however, tackle the occurrence of these hazards separately or independently. Therefore, this study introduces a catchment-scale, multihazard approach that unifies the assessment of both phenomena through a combination of hydrological and geotechnical principles. By incorporating surface flow, infiltration, and slope stability analyses, the spatio-temporal response of both landslides and flooding during intense or heavy rainfall is characterized. To improve computational efficiency, a hybrid approach, consisting of the zero- and local-inertia flow models, is introduced to approximate the surface flow. Additionally, rainfall infiltration is estimated using the one-dimensional Green-Ampt model, and the results are incorporated in a deterministic slope stability analysis whose failure mechanism is generated from the forces arising from the effects of surface flow and the downward propagation of water along the assumed failure surface. The model is applied in the catchment of Marumori Town, Japan which suffered numerous landslide and flooding disasters during Typhoon Hagibis in 2019. The results indicate that the proposed model successfully simulates the hydrologic and geotechnical response of the catchment showing the distribution of both unstable slopes and inundated areas indicative of landslide and flooding hazards. The model’s capability to identify the timing and location of potential landslide and flood-prone areas could provide a practical framework for a unified early warning system, enhancing emergency planning and response efforts during heavy rainfall.

Efficient reliability‐based design of slope angles in spatially variable soils with field data

AbstractDeterministic single factor of safety method cannot explicitly account for the influences of various sources of uncertainties (e.g., spatial variability of geomaterials, measurement and transformation uncertainties) in stability design of slopes. Many probabilistic methods have been applied to the reliability‐based design (RBD) of slopes, but they typically require performing numerous deterministic slope stability analyses. In this paper, an efficient reliability‐based design method for spatially varying slopes based on field data is proposed. Here, the RBD of a slope angle is concerned. Reliability‐based design is implemented using an inverse First Order Reliability Method (inverse FORM ‐ IFORM). A sandy slope and a cohesive slope are investigated as examples, respectively, to illustrate the proposed method. The results indicate that the proposed method can quickly obtain rational design schemes of slope angles accounting for the spatial variability of soil properties, measurement and transformation uncertainties based on the field data. It can act as a practical and effective tool for the RBD of slopes in two‐dimensional spatially variable soils. Additionally, it is found that the random field mesh size affects the RBD results significantly, while the probability distribution and horizontal autocorrelation of soil parameters have slight influences on the RBD results.

Reliability of an engineered slope considering the Regression Kriging (RK)-based conditional random field

Many attempts have been made to apply random field theory to the slope reliability analysis in recent decades. However, there are only a few studies that consider real landslide cases by incorporating actual soil data in the probabilistic slope stability analysis with spatially variable soils. In this paper, an engineered slope located in Hong Kong was investigated using the probabilistic approach considering the Regression Kriging (RK)-based conditional random field. The slope had been assessed and considered to be safe by classical deterministic slope stability analyses but failed eventually. In this study, both deterministic slope stability analyses and probabilistic slope stability analyses were conducted, and the comparison was made between the probabilistic approach adopting RK-based conditional random field and that adopting Ordinary Kriging (OK)-based approach. The results show that the deterministic factor of safety (FS) for a slope may not be an adequate indicator of the safety margin. In particular, a slope with a higher deterministic FS may not always represent a lower probability of failure under the framework of probabilistic assessment, where the spatial variability of soil properties is explicitly considered. Besides, the critical portion of the slope could not be found using the OK-based approach that considers a constant trend structure.

Probabilistic landslide susceptibility analysis in tropical mountainous terrain using the physically based r.slope.stability model

Abstract. Landslides triggered by rainfall are very common phenomena in complex tropical environments such as the Colombian Andes, one of the regions of South America most affected by landslides every year. Currently in Colombia, physically based methods for landslide hazard mapping are mandatory for land use planning in urban areas. In this work, we perform probabilistic analyses with r.slope.stability, a spatially distributed, physically based model for landslide susceptibility analysis, available as an open-source tool coupled to GRASS GIS. This model considers alternatively the infinite slope stability model or the 2.5-D geometry of shallow planar and deep-seated landslides with ellipsoidal or truncated failure surfaces. We test the model in the La Arenosa catchment, northern Colombian Andes. The results are compared to those yielded with the corresponding deterministic analyses and with other physically based models applied in the same catchment. Finally, the model results are evaluated against a landslide inventory using a confusion matrix and receiver operating characteristic (ROC) analysis. The model performs reasonably well, the infinite slope stability model showing a better performance. The outcomes are, however, rather conservative, pointing to possible challenges with regard to the geotechnical and geo-hydraulic parameterization. The results also highlight the importance to perform probabilistic instead of – or in addition to – deterministic slope stability analyses.

Tropical storm-induced landslide-dammed lakes and debris flow hazards at Ocotepeque, Western Honduras

One of the deadliest tropical storms on record in Central America is the 1934 tropical storm that resulted in over 3000 fatalities; the majority of fatalities caused by floods, debris flows, and landslides. The hardest hit region was in western Honduras near the city of Ocotepeque, where 64 cm of rain fell on June 4, 1934. The rainfall caused a rock landslide forming a natural dam in a mountain valley above Ocotepeque. The dam failed 3 days later on June 7. The ensuing debris flow destroyed Ocotepeque killing an estimated 486 people, over 10% of the city’s population. There was little to no reporting of this disaster due to the city’s remote location and lack of adequate communications. Following this event, the city was relocated 4 km north of Ocotepeque and renamed Nueva Ocotepeque. Over time, however, the old location, Ocotepeque, was resettled and called Antigua Ocotepeque. In this study, we examine the 1934 event and the effects of a similar recurrence on both Antigua Ocotepeque and Nueva Ocotepeque. Landslide hazard maps of the area (for shallow landslides) were generated and used to investigate the possibility of landslide dams forming. The potential debris flow inundation areas were predicted, and the effects of potential debris flows were investigated. Deterministic slope stability analyses conducted on the new location indicated that potential landslides could be more significant than suggested by the current hazard maps.

Stability analysis of “Kukovi” landslide

AbstractThis paper presents conducted stability analysis for landslide „Kukovi”, Bosnia and Herzegovina. As all geological cross sections are formed of rock mass that lies under upper layers of soil cover, analysis have been run by using Hoek Brown failure criterion and Mohr‐Coulomb failure criterion respectively. Data on geotechnical parameters were determined by statistical analysis of results from laboratory experiments, field tests and literature data. Values of safety factor are obtained by deterministic slope stability analysis using characteristic values of parameters from statistical distributions. Sensitivity analysis for safety factors has been completed and Monte‐Carlo probability analysis adopted distribution curves for parameters.

Effect of spatial variability of shear strength parameters on critical slip surfaces of slopes

Critical slip surface (CSS) of slopes is useful information in system reliability analyses and risk assessments of slopes. This paper investigates the effect of spatial variability of shear strength parameters on the CSS distribution of a two-dimensional slope using a finite element stress-based slope stability method. The failure mechanics for typical CSSs in a heterogeneous slope are analyzed and distributions of CSS for various combinations of horizontal and vertical scales of fluctuation (SOFs) are evaluated. The results show that local failures may occur in statistically homogeneous slopes, which cannot be observed in deterministic slope stability analyses. The distribution range of CSS first increases and then decreases with an increasing scale of fluctuation. As the ratio of horizontal SOF to vertical SOF is large, local failures have entry points located at the top of a slope. By contrast, as the ratio of horizontal SOF to vertical SOF is relatively small, local failures have entry points located either at the top of a slope or on the slope surface. The findings facilitate a more accurate evaluation of the system reliabilities or risks of slopes.

Efficient system reliability analysis of rock slopes based on Subset simulation

How to efficiently assess the system reliability of rock slopes is still challenging. This is because when the probability of failure is low, a large number of deterministic slope stability analyses are required. Based on Subset simulation, this paper proposes an efficient approach for the system reliability analysis of rock slopes. The correlations among multiple potential failure modes are properly accounted for with the aid of the “max” and “min” functions. A benchmark rock slope and a real engineered rock slope with multiple correlated failure modes are used to demonstrate the effectiveness of the proposed approach.

Hydrologically complemented deterministic slope stability analysis in part of Indian Lesser Himalaya

ABSTRACTThis study uses a deterministic approach to evaluate the factor of safety (FS) of the terrain for different hydrological conditions, in part of Indian Lesser Himalaya. The results indicate sudden increase in the percentage unstable area from 7.5% to 13.8% for rainfall intensity variation from 50 to 100 mm/day. For the rainfall intensity of 15 August 2007 which caused many landslides in the study area, 18.5% of the total area was unstable and it increases to 21.7%, 23.5% and 24.7%, respectively, for rainfall intensities corresponding to 10, 25 and 50 year return periods. This increment stagnates at about 260 mm/day, making about 25% of the area unstable. Higher rainfall intensities make progressively gentler slopes unstable, but limited to 25 degrees of slope in this area. The area underlain by granitic gneiss showed 23.1% of area as unstable for 135 mm/day of rainfall intensity, and was followed by those areas underlain by amphibolite (16%), limestone (13.7%) and quartzite (10.4%). Receiver operating characteristic (ROC) curve analysis has given 84.2% accuracy for the model. Conversion of FS to failure probability through Z scores enables identification unstable or marginally unstable areas, for planning selective slope stabilization measures.

Short-Term Stability Evaluation of an Embankment Constructed on Marine Clay Foundation at Kobe Airport

This article introduces the application of a stability analysis method that accounts for strength anisotropy on the embankment constructed at the Kobe airport. Shear strength anisotropy is induced by the in-situ state of stress along a potential slip surface of the embankment. In addition, the effects of the shearing rate on the undrained shear strength of the marine clay are examined in detail based on the results of a series of constant-volume direct shear box (DSB), triaxial compression (TC), and triaxial extension (TE) tests varying shearing rates. The most critical slip surface was selected from the deterministic slope stability analysis using unconfined compression tests of undisturbed clay samples from the field. For the most critical slip surface, the potential factor of safety of the embankment is estimated to be within the range of 1.21 to 1.28, as indicated by the results of the stability analyses using the strengths obtained from the DSB, TC, and TE tests and varying shearing rates.

System probabilistic stability analysis of soil slopes using Gaussian process regression with Latin hypercube sampling

This paper presents a system probabilistic stability evaluation method for slopes based on Gaussian process regression (GPR) and Latin hypercube sampling. The analysis is composed of three parts. Firstly, Latin hypercube sampling is adopted to generate samples for constructing the response surface. Then, based on the samples, Gaussian process regression, which is a popular machine learning technique for nonlinear system modeling, is used for establishing the response surface to approximate the limit state function. Finally, Monte Carlo simulation is performed via the GPR response surface to estimate the system failure probability of slopes. Five case examples were examined to verify the effectiveness of the proposed methodology. Computer simulation results show that the proposed system reliability analysis method can accurately give the system failure probability with a relatively small number of deterministic slope stability analyses.

Role of Probabilistic Methods in Sustainable Geotechnical Slope Stability Analysis

Sustainable stable slope for flood protection systems are of continuing interest, especially among developers of recommended practices and design standards for geotechnical engineers. The Factor-of-Safety, used in conventional deterministic slope stability analyses, is the ratio of the capacity (force, stress, deformation, displacement) of a structure to the demand imposed on or induced in the structure. Such index is clearly evaluated without regard to the degree of uncertainty involved in its calculation that is for instance particularly large for levee slope stability design. This paper advances reliability based slope stability approaches and strategies that address such uncertainties. Probabilistic methods have been successfully applied taking into account two primary categories of uncertainties: natural variabilities and modeling uncertainties.

Extension of Hassan and Wolff method for system reliability analysis of soil slopes

While a soil slope may have a large number of potential slip surfaces, its system failure probability is usually governed by a few representative slip surfaces due to the high correlation between factors of safety (FOS) of different slip surfaces. This paper shows that, despite its embedded empiricism, the Hassan and Wolff method can identify with reasonable accuracy not only the most critical slip surface, but also representative slip surface for system reliability analysis. In the Hassan and Wolff method, the assumed distribution of FOS has important effect on the calculated failure probability and it is not appropriate to always assume FOS is lognormally distributed. Whether the system effect in a slope reliability analysis is obvious can be judged easily by comparing the values of reliability index of different representative slip surfaces. Combined with the response surface method, the Hassan and Wolff method can be extended into a practical tool for system reliability analysis utilizing existing deterministic slope stability analysis programs. A simple equation is provided to estimate the bounds of system failure probability based on the most critical slip surface.

Modeling 2-D spatial variation in slope reliability analysis using interpolated autocorrelations

This paper deals with slope reliability analysis incorporating two-dimensional spatial variation. Two methods, namely the method of autocorrelated slices and the method of interpolated autocorrelations, are proposed for this purpose. Investigations are carried out based on the limit equilibrium method of slices. First-order-reliability-method (FORM) is coupled with deterministic slope stability analysis using the constrained optimization approach. Systematic search for the probabilistic critical slip surface has been carried out in this study. It is shown that both methods work well in modeling 2-D spatial variation. The results of slope reliability analysis are validated by Monte Carlo simulations. Failure probabilities obtained by FORM agree well with simulation results. It is found that 2-D spatial variation significantly influences the reliability analysis, and that the reliability index is more sensitive to vertical autocorrelation distance than to horizontal autocorrelation distance. Based on this study, failure probability is found significantly overestimated when spatial variation is ignored. Finally, the possible use of the method of interpolated autocorrelations in a probabilistic finite element analysis is suggested.

Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet

This paper develops a Monte Carlo simulation (MCS)-based reliability analysis approach for slope stability problems and utilizes an advanced MCS method called “subset simulation” for improving efficiency and resolution of the MCS at relatively small probability levels. Reliability analysis is operationally decoupled from deterministic slope stability analysis and implemented using a commonly available spreadsheet software, Microsoft Excel. The reliability analysis spreadsheet package is validated through comparison with other reliability analysis methods and commercial software. The spreadsheet package is then used to explore the effect of spatial variability of the soil properties and critical slip surface. It is found that, when spatial variability of soil properties is ignored by assuming perfect correlation, the variance of the factor of safety (FS) is overestimated, which may result in either over (conservative) or under (unconservative) estimation of the probability of failure (Pf = P(FS < 1)). When the spatial variability of soil properties is considered, the critical slip surface varies spatially and such spatial variability should be properly accounted for. Otherwise, the probability of failure can be significantly underestimated and unconservative.

A study to incorporate engineering probability techniques into deterministic slope stability methods

It is very difficult to provide reasonable solutions with respect to the uncertainties of soil parameters in general slope stability analyses based on deterministic nature. In order to identify the effects of these uncertainties on searching a critical slip surface, probabilistic approaches should be employed in the rational engineering manner. In this study, the efforts to incorporate couples of engineering probabilistic techniques into existing deterministic slope stability analysis methods were conducted. Using UTEXAS 3, a slope stability analysis computer program developed by U.S. Army Corps of Engineers (U.S. COE), this study provides the results of these probabilistic slope stability analyses in terms of probability of failure or reliability index. The effects of different deterministic methods and probabilistic methods on quantifying slope reliability are comprehensively investigated through the inspection of a proje ct embankement slope stability. Probabilistic methods for slope stability analysis appears to allow more comprehensive comparisons of slope reliability than does deterministic methods with safety factors alone.

Probabilistic slope analysis using Janbu's generalized procedure of slices

Abstract Practical spreadsheet techniques are proposed for the deterministic slope stability analysis based on Janbu's generalized procedure of slices (GPS) and a probabilistic analysis that obtains the same reliability index as the first order reliability method (FORM). The equilibrium equations of slices are solved automatically. An intuitive ellipsoid perspective greatly simplifies the reliability analysis. A search for the deterministic critical slip surface and the reliability-based critical slip surface is automatic, despite the fact that the factor-of-safety expressions and the performance function are non-explicit. The conceptual simplicity, ease of implementation, and practical versatility of the proposed perspectives and methods are emphasized.

Landslide susceptibility mapping of the slopes in the residual soils of the Mengen region (Turkey) by deterministic stability analyses and image processing techniques

The aim of the present study is to prepare a landslide susceptibility map of a region of about 120 km 2, between Gökcesu and Pazarköy (around Mengen, NW Turkey) at approximately 10 km north of the North Anatolian Fault Zone, where frequent landslides occur. For this purpose, mechanisms of the landslides were studied by two-dimensional stability analyses together with field observations, and the parameters controlling the development of such slides were identified. Field observations indicated that the failures generally developed within the unconsolidated and/or semiconsolidated soil units in forms of rotational, successive shallow landslides within the weathered zone in Mengen, Cukurca and Sazlar formations. Although consisting of residual soils, Capak and Gökdag formations do not exhibit landslides as the natural slopes formed on these, do not exceed the critical slope angles. Statistical evaluations and distribution of the landslides on the topographical map showed that such parameters as cohesion, angle of internal friction, slope, relative height, orientation of slopes, proximity to drainage pattern, vegetation cover and proximity to major faults were the common features on the landslides. Digital images were obtained to represent all these parameters on gray scale on the SPOT image and on the digital elevation model (DEM) of the area using image processing techniques. Soil mechanics tests were carried out on 36 representative samples collected from different units, and parameters were determined for two-dimensional stability analyses basing on “sensitivity approach” and for the preparation of digital shear strength map. In order to determine the critical slope angle values for the residual soils, a series of sensitivity analyses were realized by using two-dimensional deterministic slope stability analyses techniques for varying values of cohesion, angle of internal friction and slope height along with varying saturation conditions. According to the results of the sensitivity analyses, the Mengen formation was found to be most susceptible unit to landslides, covering about 33.5% of the region studied in terms of surface area. The distribution of the critical slopes were determined by superimposing the critical slope values from sensitivity analyses on slope map of the study area. On the other hand, iso-cohesion and iso-friction maps were produced by locating the values of cohesion and internal friction angles in a geographic coordinate system such that they coincide with sample locations on the DEM and by further interpolation of the values concerned. The pixel values were evaluated in gray scale from 0 to 255, 0 representing the lowest pixel value and 255 representing the highest. Sensitivity analyses on cohesion and angle of internal friction to investigate the effects of these parameters only on stability, revealed that cohesion was effective at a rate of 70% by itself, while angle of internal friction alone controlled the stability by a rate of 30%. The iso-cohesion and iso-friction maps previously obtained were digitally combined in these rates and a “shear strength map” was prepared. The geographic setting of the study area is such that northern slopes usually receive dense precipitation. In relation to this fact, about 42% of the landslides are due north. Thus, a slope orientation map was prepared using the DEM, and slopes facing north were evaluated as being more susceptible to sliding. Proximity to the drainage pattern was another important factor in the evaluation, as streams could adversely affect the stability by either eroding the toe or saturating the slope, or both. When considered together, in conjunction with the field observations, faults and landslides showed a close association. In the area, about 88% of the landslides were detected within an area closer than 250 m to major faults, therefore, a main discontinuity map was produced using the SPOT image of the region, and “proximity to major faults” was evaluated as a parameter as most of the landslides developed in areas where the vegetation was rather sparse. A vegetation cover map was therefore obtained from the SPOT image, and the areas with denser vegetation were considered to be less susceptible to sliding with respect to the areas with less or no vegetation. Having prepared the maps accounting for the distribution of critical slopes, shear strength properties, relative height, slope angle, orientation of the slopes, vegetation cover, proximity to the drainage pattern, geographic corrections were carried on each of these, and a potential failure map was obtained for the residual soils by superimposing all these maps. Next, a classification was performed on the final map and five relative zones of susceptibility were defined. When compared with this map, all of the landslides identified in the field were found to be located in the most susceptible zone. The performance of the method used in processing the images appears to be quite high, the zones determined on the map being the zones of relative susceptibility.