Morgenstern-Price Method Research Articles

Slope stability analysis using recent metaheuristic techniques: a comprehensive survey

In the framework of designing civil engineering structures such as dams and road embankments, slope stability assessment is essential. Many slope stability assessment methods based on swarm intelligence algorithms and artificial intelligence techniques have been developed in the past decade. Therefore, this paper aims to provide an up-to-date overview of slope stability by summarizing the review of applications of several metaheuristics in this field with their advantages and limitations. In this study, we present recent swarm intelligence methods and machine learning techniques used for assessing the stability of slopes and compare them with the antlion optimiser (ALO) technique. The factor of safety related to every slip surface searched was computed using Morgenstern-Price method. The performance of the proposed ALO is evaluated and validated for four slope examples against recent metaheuristics. Finally, the work carried out will help practitioners as they can now have all swarm intelligence approaches combined in one paper and will help in choosing them the right technique based on their application.

Probabilistic Risk Assessment of unsaturated Slope Failure Considering Spatial Variability of Hydraulic Parameters

Probabilistic risk assessment of slope failure evaluates the slope safety in a quantitative manner, which considers the failure probability and failure consequence simultaneously. However, risk assessment of unsaturated slope accounting for spatially variable soil-water characteristic curve (SWCC) model parameter and saturated hydraulic conductivity has been rarely reported. A probabilistic risk assessment approach is proposed in current study for rationally quantifying the unsaturated slope failure risk with the aid of Monte Carlo (MC) simulation. The SEEP/W and SLOPE/W modules contained in Geostudio software are applied to carry out deterministic analysis, where factor of safety (FS) of the unsaturated slope is calculated by Morgenstern–Price method. The spatially variable hydraulic parameters are characterized by their respective random fields that are transferred from the random void ratio field in this study, rather than generating them separately. The proposed approach is subsequently employed to an unsaturated slope example for exploring the influences of spatially variable void ratio. Results show that the unsaturated slope failure risk is considerably affected by the spatially variable void ratio, and the single exponential autocorrelation function (ACF) popularized in geotechnical engineering tends to underestimate the failure risk in the unsaturated slope risk assessment.

Summary of Modelling Safety Factors of Slope Stability in A Tar-Sand Quarry: A Case Study

This research studies the importance of slope stability during open-pit mining of tar sand within the Dahomey basin, Southwest Nigeria. It involved the geotechnical characterization of the layers of Laterites and Alluvium which it underlies. In addition, SLOPE/W software of the GeoStudio package was utilized for deducing and modeling the bench face angles which had higher safety factors, through the Morgenstern Price method of slices. It was discovered that the lateritic soil layer possessed higher values of unit weight, cohesion and internal frictional angle than those of the Alluvial Sand layer. Factors of safety were generated for bench face angles ranging from 10o to 90o at 1m, 4m and above 40m groundwater levels; over a 10m bench width and 6m bench height. However, for heavy equipment, a bench width of 20m and height of 6m were assumed. This resulted in factors of safety varying between 3.58 and 1.73 for bench face angles between 10o and 30o during higher precipitation (and water tables). Thus, this suggests that stable slopes predominate at bench face angles of 10o to 30o. This can be further enhanced when sufficient drainage systems are constructed.Â

Numerical Analysis of Soil Slope Stabilization by Soil Nailing Technique

Slope instability may be a result of change in stress conditions, rise in groundwater table and rainfall. Similarly, many slopes that have been stable for several years can abruptly fail due to changes in geometry, weak soil shear strength or as the effect of an external force. Debris flows (i.e. slope failures) take place without any warning and can have devastating results. So, it is vital to understand the slope failure mechanism and adopt safety prevention measures. Soil nailing is one of the widely used stabilization techniques for soil slopes. In this study, soil nail technique is proposed to upgrade the existing slope in clay. A parametric study was conducted to understand the effects of different nail diameter (i.e. 25mm and 40mm) and nail inclination (i.e. 200, 250, 300, 350 and 400) on slope stability. Morgenstern-Price (i.e. limit equilibrium) method was used to determine the factor of safety of the slope. It was found that the factor of safety of the existing slope improved significantly with three rows of 40mm diameter nail at an inclination of 400.

Influence of Water Level Rise on the Bank of Reservoir on Slope Stability: A Case Study of Dagangshan Hydropower Project

This paper considers stability of slope under varying water level for the right bank of reservoir of Dagangshan hydropower project. SEEP/W and SLOPE/W are used for numerical analysis. Morgenstern-Price method is used for stability analysis. Change in Factor of Safety with the rise in water level is obtained. Three cases of water level rise are studied as fast, medium and slow. It is found out that, when water level rises, the water table also rises correspondingly hence changing the properties of the rock mass in slope and its behavior to different situations and stresses. With the change in the water table line, the property like permeability changes, which is a significant property for slope stability and affects directly the strength of rock mass. Also due to change in water table within the slope, the situation of saturated and unsaturated portions in the slope also changes which is a complex phenomenon to deal with. So it has to be considered as an important factor. The changing pattern of the factor of safety with the elevation is similar for the cases of slow and medium but it is different for fast case. There is difference in factor of safety for the same elevation for different cases so the speed of the rise in water level also influences the impact on the stability. The comparison of fast and medium cases show that the difference in factor of safety is low but while comparing the cases- slow and fast the difference is high.

An Approach to Assess the Stability of Unsaturated Multilayered Coastal-Embankment Slope during Rainfall Infiltration

This study aims to develop a simple but effective approach to investigate the stability of an unsaturated and multilayered coastal-embankment slope during the rainfall, in which a Random Search Algorithm (RSA) based on the random sampling idea of the Monte Carlo method was employed to obtain the most dangerous circular sliding surface, whereas the safety factor of the unsaturated slope was calculated by the modified Morgenstern–Price method. Firstly, two typical distributions of matric suction were illustrated and the associated methods for determining the strength parameters of unsaturated soil were developed. Based on this, the Morgenstern–Price method was further modified to calculate the safety factor, and RSA was adopted to locate the most dangerous sliding surface of the unsaturated multilayered coastal-embankment slope. Finally, the slope breaking process under rainfall infiltration was simulated through continuously searching the critical slip surfaces under different groundwater levels by RSA. The results indicated that the stability of the unsaturated embankment slope was gradually deteriorated with the increase of rainfall infiltration. It was also found that both of the distributions of the matrix suction (ua-uw) and the suction angle (φb) had significant effects on the safety factor of the embankment slope. Basically, linear distribution of (ua-uw) along the depth and linear relationship between φb and (ua-uw) should be adopted in assessing the stability of the unsaturated multilayered coastal-embankment slope.

Reliability Analysis of Grillage Flexible Slope Supporting Structure with Anchors Considering Fuzzy Transitional Interval and Fuzzy Randomness of Soil Parameters

Reliability analysis of grillage flexible slope supporting structures with anchors does not consider fuzzy randomness of slopes; thus, this paper proposes a method for the reliability analysis of grillage flexible slope supporting structures with anchors by considering both the fuzzy randomness of soil parameters and the fuzzy transitional interval. This paper converts random variables of soil parameters into fuzzy random variables with the fuzzy random processing method of sample mechanics parameters and establishes a fuzzy random limit state equation based on the fuzzy transitional interval of the slope. The upper and lower boundaries of classical sets of different cut sets are obtained by transforming a fuzzy set into a classical set with the decomposition theorem of fuzzy sets. At the same time, the slope slip surface is determined using the Morgenstern–Price method. Applying the reliability calculation formula of grillage flexible slope supporting structures with anchors deduced from this paper, the fuzzy random reliability of reinforced slope is obtained by weighting. Finally, comparing the calculation result of this paper and the reliability calculated by Monte Carlo simulation, it can be concluded that when the failure probability calculated by the Monte Carlo simulation is zero, the failure probability of the slope considering the fuzzy randomness of the slope is 6.4538%. The results show that the reliability analysis of the reinforced slope considering the ambiguity of the slope can better reflect the actual state of the slope.

Evaluation of Slope Stability Considering the Preservation of the General Patrimonial Cemetery of Guayaquil, Ecuador

Inefficient blasting techniques and poor closure management of the old quarry that existed during the 1970s in the area of the actual General Patrimonial Cemetery of Guayaquil resulted in an almost vertical slope of approximately 50 m in height and an intense induced fracturing that weakened the rock mass. This led to the loss of stability and increased material detachment, which damaged the infrastructure of the graveyard representing a risk to visitors and workers. The aim of this research is to evaluate the slope stability through a geotechnical analysis that allows decision-making to recover and preserve the safety of the area. In this work, we used structural measurements and observations made in the field, as well as a three-dimensional model of the slant generated by photographs taken by a drone. Slope Mass Rating (SMR) and Chinese Slope Mass Rating (CSMR) rankings were used to evaluate stability, susceptibility to rockfall was determined using a theoretical–practical procedure, and the safety factor was calculated using the Morgenstern–Price method. The analysis of the geomechanical classifications yielded a low stability value of the slope, which was in accordance with the high susceptibility to rockfall and with the low safety factor. Based on these results, we recommend the application of systematic bolt and shotcrete for stabilization.

Robust design of siphon drainage method for stabilizing rainfall-induced landslides

Drainage is a critical and cost-effective method to stabilize rainfall-induced landslide. In order to improve the efficiency and sustainability of drainage system, a new siphon drainage method is presented in this paper. Factor of safety (FOS) under the action of a given siphon drainage design, computed using Morgenstern-Price method, was used to evaluate the design effectiveness. A guidance for the design of this new siphon drainage method was established based on the robust design concept. Signal-to-noise ratio, which is a function of mean and standard deviation of FOS and related to the uncertainty of shear strength parameters of slip surface, is used as a measure of the design robustness. A framework based on the concept of robust design is proposed for determining the most optimal siphon drainage design considering multiple objectives including safety, cost, design robustness, and drain effectiveness. This framework is illustrated with a case study, the Hongpucun landslide in Zhejiang Province, China. Based on the outcome of this study, the optimal siphon drainage design is obtained.

Improved finite element–based limit equilibrium method for slope stability analysis by considering nonlinear strength criteria and its application in assessing the anchoring effect

SummaryThe shear strength envelope of most geotechnical materials is nonlinear. In this study, the finite element–based limit equilibrium method (FELE) is improved to assess the stability of a prescribed slip surface that obeys a nonlinear failure criterion. Two nonlinear failure criteria, namely, the Barton criterion and the generalized Hoek‐Brown (GHB) criterion, are implemented. A power curve model that can perfectly fit the envelope of the GHB criterion is proposed to explicitly express the shear strength from the normal stress. The algorithm of the improved FELE, which includes a nonlinear criterion, is explained in detail, and the fast convergence of the method is checked by evaluating examples. The numerical examples show that, for a smooth slip surface, FELE can calculate a greater factor of safety (FOS) than that calculated using the Morgenstern‐Price (MP) method when the strength criterion of slip surface is nonlinear. In addition, FELE can determine the bell‐shaped distribution of the increase in normal stress caused by anchoring measures, which cannot be considered in the MP method.

Stability analysis of the Zhangmu multi-layer landslide using the vector sum method in Tibet, China

The Zhangmu landslide is located on the China–Nepal border in Tibet, China, which has recently become a serious threat to the lives and properties of local people. In order to efficiently quantify the stability of the Zhangmu landslide, a new method named the vector sum method (VSM) is proposed. Differing from conventional slope-stability analysis methods, the VSM considers both the magnitude, the direction of force and the strength-reserving definition of the safety factor based on the actual stress field of slope achieved from finite element analysis. Moreover, the global sliding direction of potential landslides was theoretically deduced by the principle of minimum potential energy, while the safety factor can be directly computed by not only the force limit equilibrium of the whole sliding body in the global sliding direction but also the moment limit equilibrium at the moment center. Finally, stability analysis of the Zhangmu landslide was performed by the proposed method, and verified against the rigorous Morgenstern–Price method.

Mechanics of Reinforcement–Slope Interactions

Steepening of slopes for construction of rail/road embankments or for widening with geosynthetics for other civil engineering structures is a necessity for development. The present paper details a kinematic analysis to optimize the length of geosynthetic reinforcement from the face or near end of the slope with respect to its location to obtain the desired minimum factor of safety. Unreinforced and reinforced slopes are analyzed using Morgenstern–Price method to obtain critical factors of safety. The effect of providing geosynthetic reinforcement layer in shifting the critical slip circle has been identified and quantified. The length of the reinforcement is optimized by curtailing the superfluous length from face end but maintaining the required factor of safety.

Slope stability evaluation of iron ore fines during marine transport in bulk carriers

A commodity, such as iron ore fines, shifting in the hold of a bulk carrier can lead to the vessel listing or capsizing. The objective of this study is to investigate the factors of safety pertaining to slope failure for both untrimmed and trimmed cargoes of iron ore fines during marine transportation. To determine the shear strength parameters needed to perform this analysis, triaxial testing was performed on samples of iron ore fines under varying densities and moisture contents. Using the shear strength parameters of the material, the Morgenstern–Price method of slices and infinite slope analysis, referred to as rotational and translational slope stability analyses, were used to determine the factors of safety against slope failure. The study concludes that, considering a factor of safety of 1.5, an untrimmed cargo of iron ore fines is unstable at angles of heel that bulk carriers are expected to experience during a typical voyage. If the cargo is trimmed it is shown to be significantly more stable. Results support the recommendation that it become mandatory for cargoes of iron ore fines to undergo trimming to reduce the chance of slope failure occurring, which may result in the loss of human life and industry assets.

Investigating the critical slip surface of soil slope based on an improved black hole algorithm

Analysing the stability of soil slopes and investigating critical slip surfaces present an important and very complicated optimisation problem. In this paper, we solve this problem by introducing and modifying a new global optimisation (black hole algorithm) technique to form a new global optimisation algorithm for continuous optimisation (the improved black hole algorithm). By combination with typical mature limit equilibrium analysis (the Spencer method and the Morgenstern-Price method), the improved black hole algorithm was used to find the critical slip surface of soil slope. Thus, this paper proposed a new method for finding the critical slip surface of soil slope. Finally, the proposed method was verified through two typical numerical soil slope cases and was compared with the black hole algorithm and other extant studies. The results indicated that the applicability, validity and effectiveness of the improved black hole algorithm showed an improvement over previous studies and over the black hole algorithm. Moreover, the proposed method was applied for one highway landslide, and the determined critical slip surface was well agreement with the real one.

Locating Global Critical Slip Surface Using the Morgenstern-Price Method and Simulated Annealing Algorithm

The paper presents a new limit equilibrium method to locate the global critical slip surface for slope profiles with complex geology. In this method, noncircular slip surface is assumed to calculate the factor of safety with the Morgenstern-Price method. And the simulated annealing algorithm is introduced to search for the global critical slip surface. For the given slope profile with high complexity, the search strategy can locate the global critical slip surface regardless of the initial slip surface location. Compared to the slope profile evaluated by the commercial software Geo-Studio 2007, the calculation result of the algorithm coded by Fortran and Matlab is approved to have good precision.

Limit equilibrium method for slope stability based on assumed stress on slip surface

In the limit equilibrium framework, two- and three-dimensional slope stabilities can be solved according to the overall force and moment equilibrium conditions of a sliding body. In this work, based on Mohr-Coulomb (M-C) strength criterion and the initial normal stress without considering the inter-slice (or inter-column) forces, the normal and shear stresses on the slip surface are assumed using some dimensionless variables, and these variables have the same numbers with the force and moment equilibrium equations of a sliding body to establish easily the linear equation groups for solving them. After these variables are determined, the normal stresses, shear stresses, and slope safety factor are also obtained using the stresses assumptions and M-C strength criterion. In the case of a three-dimensional slope stability analysis, three calculation methods, namely, a non-strict method, quasi-strict method, and strict method, can be obtained by satisfying different force and moment equilibrium conditions. Results of the comparison in the classic two- and three-dimensional slope examples show that the slope safety factors calculated using the current method and the other limit equilibrium methods are approximately equal to each other, indicating the feasibility of the current method; further, the following conclusions are obtained: 1) The current method better amends the initial normal and shear stresses acting on the slip surface, and has the identical results with using simplified Bishop method, Spencer method, and Morgenstern-Price (M-P) method; however, the stress curve of the current method is smoother than that obtained using the three abovementioned methods. 2) The current method is suitable for analyzing the two- and three-dimensional slope stability. 3) In the three-dimensional asymmetric sliding body, the non-strict method yields safer solutions, and the results of the quasi-strict method are relatively reasonable and close to those of the strict method, indicating that the quasi-strict method can be used to obtain a reliable slope safety factor.

Limit equilibrium stability analysis of slopes under external loads

Two calculation modes for the effect of external load on slope stability, i.e., mode I in which the external load is thought to act on slope surface, and mode II in which the external load is thought to act on slip surface along the force action line, were considered. Meanwhile, four basic distribution patterns of external load were used, of which complex external loads could be composed. In analysis process, several limit equilibrium methods, such as Swedish method, simplified Bishop method, simplified Janbu method, Spencer method, Morgenstern-Price (M-P) method, Sarma method, and unbalanced thrust method, were also adopted to contrast their differences in slope stability under the external load. According to parametric analysis, some conclusions can be obtained as follows: (1) The external load, with the large magnitude, small inclination angle, and acting position close to the slope toe, has more positive effect on slope stability; (2) The results calculated using modes I and II of external load are similar, indicating that the calculation mode of external load has little influence on slope stability; (3) If different patterns of external loads are equivalent to each other, their slope stability under these external loads are the same, and if not, the external load leads to the better slope stability, as action position of the resultant force for external load is closer to the lower sliding point of slip surface.

A global procedure for stability analysis of slopes based on the Morgenstern-Price assumption and its applications

By combining the numerical stability of the global analysis method and the flexibility of the Morgenstern-Price method, a global procedure for the stability analysis of slopes is developed. Firstly, based on the Morgenstern-Price assumption of inter-slice forces, an expression for the distribution of normal stress on the sliding surface is derived. Then, the equilibrium equations of the sliding body are built. Finally, three different expressions for the distribution of normal stress on the sliding surface are proposed, followed by the comparison of their effects and the stability analysis of a large-scale landslide exposed during the construction of a hydropower project.

Prediction of landslide run-out distance based on slope stability analysis and center of mass approach

Mitigation of landslide hazard requires the knowledge of landslide run-out distance. This paper presents the application of slope stability analysis and center of mass approach to predict the run-out distance of a rotational landslide model with different soil types. The Morgenstern-Price method was used to estimate the potential sliding zone and volume of landslide material. The center of mass approach used a simple Coulomb friction model to determine the run-out distance. Results of the slope stability analysis showed that the soil unit weight can influence the depth of sliding zone, and the volume of unstable material. The slope model of silty sand and gravel would have the largest volume of unstable mass. From the Coulomb friction analysis, this slope model has higher run-out distance and velocity than other slope models. Thus, the run-out distance will be influenced by soil type and the dimension of unstable soil mass.

Stability Analysis of Slope under Different Soil Nailing Parameters Based on the GeoStudio

In order to investigate the influence of different soil nailing parameters on the safety factor of a slope, the slope stability is analyzed by the GeoStudio software with different analysis methods. Soil nailing parameters (such as nail inclination, nail horizontal space, nail diameter and length) that influence the slope stability are analyzed by the Morgenstern-Price method. As the results show, the slope has the highest safety factor when the obliquity of soil nailing is about 15°, the safety factor decreases with the increase of soil-nail horizontal space with an evident acceptable space range of 2 m or less and increases linearly with the increase of soil-nail diameter and length. However when the soil-nail length equals approximately the height of the slope, the safety factor increases slowly. These results can provide a design base for field engineers.