Morgenstern-Price Method Research Articles

Slopes Analyses - Case Study, Slope Stability of Bypass Project

The scope of this study was to compare various stability evaluation methods. Accordingly, most common LE approaches were compared with the advanced LE (M‐P) method. Similarly, the differences in FOS computed from LE and FE analyses were compared based on a simple slope considering various load cases. In addition, two real slopes in a case study were analysed for the recorded minimum‐maximum GWT, pseudo‐static and dynamic conditions. Moreover, the stability evaluations of these slopes were based on both LE (M‐P) and FE (PLAXIS) calculation approaches, which both utilized shear strength parameters from advanced triaxle tests. Similarly, Mohr‐Coulomb model was applied in both approaches. The following conclusions are hence derived based on the reported work on both idealized and real slopes. To fulfil one of the aims of the study, the LE based methods are compared based on the factor of safety (FOS) obtained for various load combinations. The comparison is mainly based on simplified slope geometry and assumed input parameters. Among the LE methods, the Bishop simplified (BS), Janbu simplified (JS) and Janbu GPS methods are compared with the Morgenstern‐Price method (M‐PM). These LE methods are well established for many years, and thus some of them are still commonly used in practice for stability analysis. Moreover, the M‐PM has been compared with results from the FE analyses. Compared with theFE (PLAXIS) analyses, the LE (M‐PM) analyses may estimate 5 – 14percent higher FOS, depending on the conditions of a dry slope and a fully saturated slope with hydrostatic pore pressure distributions. For fully saturated conditions in the slope, inaccurate computation of stresses in LE methods may have resulted in larger difference in the computed FOS. Since, the FE software is based on stress‐strain relationship, stress redistributions are surely better computed even for a complicated problem. This has been found one of the advantages in FE simulations. A parameter study shows that the application of a positive dilatancy angle in FE analysis can significantly improve the FOS (4 ‐ 10percent). On contrast, the shear surface optimization in LE (M‐PM in SLOPE/W) analysis results in lower FOS, and thus minimizing the difference in FOS compared with FE analysis

The application of failure method probability for analyzing in pit dump stability at West Block ‘X’ pit PT Berau Coal - East Kalimantan

West Block 'X' pit is one of the coal mining locations operated by the Lati Mine Operation – PT Berau Coal. Administratively, the Lati Mine is located as part of Berau Regency – East Kalimantan. The study area is located at the north side of the concession, in a syncline fold structure zone. The disposal design in this area needs to special attention from slope stability aspect due it is located on the wing of a mega syncline with a certain slope and constituent of unconsolidated materials. The pit design needs to be stable. The purpose of this study is to determine the level of stability of the in-pit dump by analyzing the current in-pit dump stability based on the value of the safety factor (FS) and the probability of failure (PoF). The method used in this study is a probabilistic analysis of slope stability based on the Morgenstern-Price method to obtain the value of the safety factor and the probability of failure. The study results show that the slope is in the safe category (stable slope) in the range of PoF values 0 – 1%, marginal slope 1 – 12%, and unstable slope above 12%. Based on such as results, it is necessary to modify the slope geometry categorized as unstable to carry out mine operation safely underneath the toe of slope.

Comparison of factor of safety using different method of analysis for slope stability

Currently, the construction of slope is increasing, thus, the risk of slope to fail also increase. The series of landslide happen to the man-made slope has been recorded since in the early of 1993 until now. Many efforts such as treating the critical slope, redesigned the failed slope, and analyze the stability of the slope have been done. However, the landslide is still happening in Malaysia. The factor of safety (FOS) from the stability analysis that has been used might not be adequate to determine the safety of the slope in Malaysia. Therefore, in this study, the optimum factor of safety is obtained by using three methods of slice, Bishop’s Simplified method, Spencer method, and Morgenstern-Price method which have been used in many projects. A study place is selected in Ladang Balau, Semenyih, in Selangor and from the CIU test, the important soil parameter for slope is extracted for analysis of slope stability using SLOPE/W and manual calculation. The lambda for Spencer method and Morgenstern-Price method was generated for further discussion on the relationship between lambda and factor of safety. The data generated from both calculation method, from manual and software, were discussed and next the ideal method to achieve the optimum factor of safety determined. The factor of safety for every method basically are influenced by the interslice shear force presence but not Bishop’s Simplified method as moment equilibrium is insensitive towards interslice force function. For lambda, the factor that influenced the value is the function used; constant and half-sine function, however, for Bishop’s Simplified method, the lambda is equal to zero as the method ignored the interslice shear force. The Morgenstern-Price method has been chosen to be the best method to generate a good factor of safety.

Analysis and Evaluation of Landslide Failure and Using Different Techniques to the Mitigation

One of the most common natural catastrophic in the world is Landslides causing large casualties and large economic losses. In 1994, a landslide disaster struck a part of Nepal country along the llam road. This landslide caused devastation in the country at that time. In this paper, an evaluation of this landslide was conducted and deep study to mitigate the danger of these kinds of incidences. Preventing landslides is permanently significant to ensure a streamlined flow of traffic when there are roads on the area with a potential landslide incidence. The slope stability degree of the mass of landslide area is evaluated before and after preventing landslide to occur. Many slope stability methods are used such as ordinary sliced method, Bishop simplified method, Janbu simplified method, Spencer method, method of Corps of engineers and gle Morgenstern price method. The factor of safety calculated by these methods is varied by around 9 percent. The calculated factor of safety was less than one at the time of landslide incidence. In order to increase the factor of safety, various technique were suggested to mitigate Landslide such as lowering the water table, using high berm at the toe of the slope and using grouted tiebacks to support the soil mass. Lowering the water table only was not adequate to increase the factor of safety to 1.5 neither using high berm. The most active technique to increase the factor of safety was grouting tiebacks to support the soil mass at the landslide area. This technique contributed in increasing the factors of safety s more than 2 for static state and more than 1.1 for dynamic state. The software program, Rockscience slide 6.0, is used to verify the calculations and analyses from excel sheet for the ordinary and Bishop simplified method.

Analysis of Landslide Stability Based on the Morgenstern-Price Method

The landslide is a kind of natural disaster caused by slope instability. Due to its wide distribution, frequent occurrence, and damaging effects, many countries in the world suffer from it. Sichuan Province in China is a landslide-prone area since it locates in the seismic zone. In this paper, the Morgenstern-Price method is used to analyze the stability of a landslide in Sichuan Province, and heavy rainfall is also simulated to analyze the landslide stability under such conditions, which can provide assistance for geological disaster prevention in the future.

Optimal arrangement of geogrids in road embankment using different fill materials

Due to rapid growth of industrialization and urbanization, the slope stability of embankments constructed with locally available materials became the most important area for geotechnical engineers. The stability of these embankments can be improved by adopting geogrid reinforcement with native soil or by replacing the embankment with Pond Ash. The present study is on the slope stability analysis of a road embankment with crest width of 8 m, side slopes of 2H:1V and height 5 m resting on 10 m thick c-ϕ soil. The purpose of this study is to analyse the normal fill and pond ash embankments with reinforced and unreinforced conditions using Slope/w module in Geostudio 2021. The Mohr-coulomb material is used to model the soils and Morgenstern-Price method is used to find out the factor of safety (FOS) for a critical slip surface. Geogrids are placed at different layers in normal and pond ash embankments and the optimal arrangement is found out. It is found that the factor of safety is increased by 69.5% when the normal fill is replaced with pond ash as the angle of internal friction is higher for pond ash. The optimal arrangement of geogrid at 1st and 4th layers in combination with pond ash fill embankment gives a highest factor of safety of 2.928 and in case of normal fill, the highest factor of safety is 2.184.

Embankment Dam Seepage and Slope Stability Analysis: The Case of Arjo-dedessa Dam, Ethiopia

Dams have one of the greatest significant roles in operating water resources. Seepage and slope stability failures cause completely failure of embankment dams. Dam disasters not only hazard community safety, they also can cost our economy millions of dollars in compensations. The study area is found in Oromia regional state between East Wollega and Bunno Bedele Zone. The dam is located on Dedessa River, tributary of Blue Nile River. Analysis of seepage quantity was done by Darcy’s phreatic line, and SEEP/W software model for both homogeneous and zoned dam. The expected quantity of seepage estimated with the SEEP/W software model analysis that includes foundation seepage is 6.6*10^-6m³/sec. Slope stability study is to contribute to the safe and economic design of upstream and downstream slope of the dam. The factory of safety obtained by Morgenstern-Price method for end construction is (FOS=1.99), for steady state (FOS=2.03) and rapid drawdown (FOS=2.91). However, at the design document shell material hadn’t been designed properly. Finally the paper concluded that the likely corrective measures for seepage controls are impermeable blanket, grouting, and the downstream slope miscarriage by eliminating the pathetic zone and seal with like graded quantifiable, regular repairs and shield the downstream slope with grasses.

Inversion analysis of the shear strength parameters for a high loess slope in the limit state

It is difficult to obtain reliable shear strength parameters for the stability analysis and evaluation of high loess slopes. Hence, this paper determines slope elements and physical parameter of 79 slopes with heights of [40, 120] m based on the measured loess slopes in the Ganquan and Tonghuang subregions of northern Shaanxi Province, China. In the limit state of the loess slope (stability factor Fs is 1.0), a fitting equation for the slope height and width is established. Then, the model is developed by stability analysis software-SLOPE/W, and the comprehensive shear strength parameters corresponding to different slope heights of the high slope in the study area are obtained by inversion using the Morgenstern-Price method. The results show that when the height of the slope increases, the cohesion c increases in the soil, and the internal friction angle φ decreases. This change is consistent with the characteristics reflected in the composition and physical properties of the slopes, and the comprehensive strength parametric curves are very similar between the Ganquan subregion and the Tonghuang subregion. A landslide that occurred in Miaodian-zaitou of Jingyang County, Shaanxi Province, is selected to verify this inversion method, and the results show that the calculated shear strength parameters of the inversion are consistent with the measured value of the actual slope.

The expanded LE Morgenstern-Price method for slope stability analysis based on a force-displacement coupled mode

Slope displacement and factor of safety (FOS) of a slope are two aspects that reflect the stability of a slope. However, the traditional limit equilibrium (LE) methods only give the result of the slope FOS and cannot be used to solve for the slope displacement. Therefore, developing a LE method to obtain the results of the slope FOS and slope displacement has significance for engineering applications. Based on a force-displacement coupled mode, this work expands the LE Morgenstern-Price (M-P) method. Except for the mechanical equilibrium conditions of a sliding body adopted in the traditional M-P method, the present method introduces a nonlinear model of the shear stress and shear displacement. Moreover, the energy equation satisfied by a sliding body under a small slope displacement is also applied. Therefore, the double solutions of the slope FOS and horizontal slope displacement are established. Furthermore, the flow chart for the expanded LE M-P method is given. By comparisons and analyses of slope examples, the present method has close results with previous research and numerical simulation methods, thus verifying the feasibility of the present method. Thereafter, from the parametric analysis, the following conclusions are obtained: (1) the shear displacement parameters of the soil affect the horizontal slope displacement but have little effect on the slope FOS; and (2) the curves of the horizontal slope displacement vs. the minimum slope FOS could be fitted by a hyperbolic model, which would be beneficial to obtain the horizontal slope displacement for the slope in the critical state.

Application of Morgenstern-Price Method in Reversion Analysis of the Loess Strength Parameters

It is difficult to obtain reliable shear strength parameters for the stability analysis and evaluation of high loess slopes. Hence, this paper determines 17 slopes with a height of 40-120 m based on the measured loess slopes in Jingbian-Ansai subregion of northern Shaanxi, China. The model is established using the finite element method, and the comprehensive shear strength parameters of different slope heights of the high slope in the study area are obtained by inversion using the Morgenstern-Price method. The results show that when the height of the slope increases, the cohesion c in the soil increases, and the internal friction angle φ decreases. According to the calculation results, a comprehensive inversion curve of strength parameters under the slope height of 40 to 120 m is drawn, which can directly evaluate the stability of the loess high slope, which improves the work efficiency and also provides reliable data support in the high side Slope geometry design.

Effect of nail spacing on the global stability of soil nailed walls using limit equilibrium and finite element methods

The limit equilibrium method LEM is widely used for static and pseudo-static soil nailing designs. Soil nailed wall stability is usually evaluated based on a global factor of safety FSG under a predefined failure mechanism. When appropriate failure surfaces are adopted, FSG should reduce with the soil nailed wall inclination β for different nail geometries (length L, inclination α and diameter D), soil–nail strength rs, soil cohesion c’ and angle of friction ϕ’. However, nail spacing S can change this trend since FSG increases with β under certain combinations of β and S. In this study the nail spacing effect has been evaluated using LEM assuming a bilinear failure surface with two rigid blocks and the Morgenstern-Price method where the failure surface is neither linear nor circular. However, it was found that FSG increases with β for S < 2.00 m, which can lead to potentially unsafe designs. Alternatively, the finite element method FEM was chosen including the strength reduction factor SRF methodology which is equivalent to FSG under failure conditions. It was found that results from FEM represent a significant improvement respect to those from LEM because curves in a FSG-β-S plot follow a logical trend as with the other parameters (L, α, D, rs, c’ and ϕ’). Finally, it is recommended to choose FEM instead of LEM in soil nailing designs. In case of using LEM, results should be carefully assessed, in particular for steep walls and close nail spacing.

A novel method for locating the critical slip surface of a soil slope

Calculating the minimum slope safety factor or locating the critical slip surface of a soil slope is a complex optimization problem. This paper describes an improved whale optimization algorithm (IWOA) for locating the critical slip surface of a soil slope. Locating a critical slip surface is transformed into a three-dimensional problem from a high-dimensional optimization. Combined with the Morgenstern–Price method, IWOA is compared against other optimization techniques in an experimental study. Test results using 13 benchmark functions show that IWOA significantly outperforms the conventional whale optimization algorithm (WOA) and particle swarm optimization (PSO). The IWOA method is then used to search for the critical slip surfaces of four slopes. The results show that IWOA again performs better than WOA and PSO in locating the critical slip surface.

Estimating critical height of unsupported trenches in vadose zone

Workers are often required to enter unsupported trenches during the construction process, which may present serious risks. Trench failures can result in death or damage to adjacent properties; therefore, trenches should be excavated with extreme precaution. Critical height (i.e., maximum depth that can be excavated without failure) is the most important design consideration for ensuring the stability of unsupported trenches. Because excavation work is often done in the vadose zone, the influence of matric suction should be taken into account when estimating the critical height of an unsupported trench. In this study, an attempt was made to estimate the critical heights of unsupported trenches using three distinct approaches: (i) analytical method based on the extended Rankine earth pressure theory, (ii) finite element coupled stress – pore-water pressure analysis, and (iii) limit equilibrium method (i.e., Bishop’s simplified and Morgenstern–Price method). It was assumed that the trenches were excavated in an engineered sand (Unimin 7030) and Indian Head till, which represent cohesionless and cohesive soils, respectively, considering various practical scenarios. Geotechnical modeling software, GeoStudio (ver. 2016; SIGMA/W and SLOPE/W), was used for both finite element analysis and the limit equilibrium method.

Finite Element Analysis of Failure Characteristics of Structural Soil Slope under Different Rainfall Patterns

The slope model is established by Geo-Studio, and the deformation characteristics and stability of structural-soil slope in Zhanjiang area under different rainfall patterns are analyzed. The MK model was used basing on Morgenstern-price method. By setting monitoring points at the top, toe and slope surface of the slope, the variation rule of pore water pressure and displacement at the monitoring points under the four types of rainfall are gotten, and the shapes of different types of sliding surfaces are obtained. By the analysis of the most dangerous sliding surfaces, some suggestions are put forward. Those have important reference value for prevention or controlling the geological disasters such as landslides in Zhanjiang area.

Influence of stratum simplification on stability reliability index of loess slope

In the calculation of loess slope stability, most of the studies are based on the simplified calculation of the actual slope stratum, and it will affect the calculation results, so the influence of the simplified method of stratum on the slope stability analysis is discussed. Taking the stability analysis of the South Plateau of Jingyang as an example, the stability safety factor, the probability of failure and reliability index of the measured strata model (MSM) and three simplified models are calculated and analyzed based on the Morgenstern-Price method and Monte Carlo reliability analysis method. After comparing the calculation results, it is concluded that the simplification of the model will not have a great impact on the stability safety factor of the slope (in this example, the variation range is less than 0.026), but it has a significant impact on the failure probability and reliability index (in this example, the maximum difference of the failure probability between the simplified models and the MSM is 54.8%). The simplification method is an important factor affecting the calculation results, and unreasonable simplification will cause changes in the critical slip surface and large differences in reliability index.

A New Simplified Method for Calculating the Sliding Distance of the Rapid Long Run-out Loess Landslides

The area of loess in China is 640,000 km2, accounting for 6% of the total land area. Loess landslides occur frequently, causing economic losses of tens of millions of yuan per year. There is a close relationship between the hazard and the sliding distance of landslide. The study on the sliding distance of loess landslide can provide a scientific basis for the prediction of landslide risk. Based on the law of conservation of energy, a new simplified method for calculating the sliding distance of loess landslides is proposed in this paper. Based on the fact that the decrease of potential energy is equal to the energy consumed in the sliding process, the formula for calculating the sliding distance is obtained. Taking Dabuzi landslide in the Southern Jingyang Plateau (SJP) of Shaanxi Province as an example, considering the unsaturated property of soil, Morgenstern-Price method was used to calculate the slope stability of SJP and determine the most dangerous sliding surface and sliding body. According to the proposed formula, the calculated sliding distance is consistent with the actual one. The correctness of the proposed method is verified by case calculation.

Optimization of non-circular failure surface in slope based on particle swarm models

This article presents results of slope analyses employing a simple technique of generating segmented non-circular failure surfaces. The formulation of slope analysis is performed as an optimization problem with four constrained control variables characterizing the failure surface. In this study, different variants of particle swarm optimization (PSO) methods such as inertia weight equipped and contemporary standard PSO (CS-PSO) are utilized to obtain optimum control variables and associated critical failure surface. The factor of safety of the slope or the objective function of the constrained optimization problem is determined by Morgenstern–Price method. To explore the competence of proposed method with different PSO models, three benchmark problems are analysed for different maximum number of function evaluations such as 1000, 2500 and 5000. A series of sensitivity analyses are performed for various parameters such as swarm size with maximum iteration count of 100. The swarm diversity behaviour is also studied in relation with converged or promising global optimum solution. It is found that contemporary standard PSO (CS-PSO) with or without velocity clamping maintains better swarm diversity and preserves the balance between swarm “exploration” and “exploitation” efficiently. Velocity clamping and positional clamping are recommended as they prevent the solution/control variable from overflying the swarm best position.

Grey wolf optimization approach for searching critical failure surface in soil slopes

Detection of critical failure surface and associated minimum factor of safety (F) constitutes a constrained global optimization problem during the task of slope analysis. Morgenstern–Price method is an established limit equilibrium-based technique satisfying both moment and force equilibrium of all slices in the failure mass has been used to evaluate F against slope failure. The main objective of current study is to investigate the applicability and efficiency of grey wolf optimization (GWO) in solving slope stability problem. GWO is a nature inspired metaheuristic optimization method which mimics the social interaction between a pack of grey wolves in their endeavour to search, hunt and prey. The effectiveness of the recently developed GWO is examined by analyzing four different slope problems. Each soil slope model has been analysed for wolf pack size (NP) range 10–50 and maximum iteration count $$ (k_{\hbox{max} } ) $$ range 50–250. In effect, the number of evaluated functions (NFE) is found to lie in the range of 500–12,500. The results demonstrate that the GWO technique can detect the critical failure surface with very good accuracy. Furthermore, the statistical analysis is presented in terms of best $$ F_{\text{b}} $$, worst $$ F_{\text{w}} $$, mean $$ \overline{F} $$, standard deviation (SD) and % error (%E) of the optimum solutions i.e. factor of safety (F) from 10 independent runs. The effect of GWO parameters such as NP and $$ k_{\hbox{max} } $$ to obtain optimum solution are also presented. The $$ F_{\text{b}} , \, F_{\text{w}} , \, \overline{F} \;{\text{and}}\;{\text{SD}} $$ for 1st slope model are (1.7295, 1.7296, 1.7295, 0.000038) and they have been obtained for maximum NFE equal to 12,500. Similarly, for 2nd and 3rd slope model, the respective values are (1.4032, 1.4038, 1.4034, 0.000209) and (1.2530, 1.2546, 1.2537, 0.000741). The discrepancy or percentage error (%E) in best $$ F_{\text{b}} $$ from optimum (F) for NFE up to 500 are found to be equal to (0.0615, 0.2531, 0.8419) for studied slope models respectively. The evaluation of safety factor F for the fourth slope model has been studied for four different combinations of earthquake loadings and pore water pressures. The values of SD for all four cases are reported for maximum NFE equal to 12,500. It is found that uncertainty in reported F reduces if higher numbers of objective function evaluations are performed. This proves the excellent performance of GWO in evaluating minimum F of the slope.

Assessment of Optimum Location of Non-circular Failure Surface in Soil Slope Using Unified Particle Swarm Optimization

The solution of slope stability problems requires determination of critical failure surface and associated optimum/minimum factor of safety (FOS) value. Investigation of critical failure surface in any soil slope can be posed as a constrained global optimization problem. In this article, a simplified technique of generation of segmented non-circular failure surface is proposed. Unified particle swarm optimization (UPSO) method is utilized to search for the critical failure surface and associated minimum FOS of the slope. Limit equilibrium technique-based Morgenstern–Price method is used to evaluate the FOS value of the potential failure mass which satisfy both force as well as moment equilibrium. To demonstrate the performance of UPSO and its competence in yielding critical failure surface along with minimum FOS value, three benchmark problems with differing complexities are chosen from existing literatures. The results obtained are compared and are found to be in accord with the published literatures. The performance of UPSO as a solution algorithm for slope problems are established through convergence studies of various related parameters.

Features of modeling gabion retaining walls for engineering protection of roads on landslide slopes

During the construction of roads in mountainous areas, engineering protection of the highway from landslide processes is often required. Currently, there are many designs used to protect against landslides. However, the engineers are faced with the task of choosing the optimal structural solution both in terms of the boundaries of the field of application of the structures and in terms of economic efficiency. In addition, the problem arises of correct modeling of the predicted situation. The article discusses the engineering protection of the road under construction in Sochi, Krasnodar Territory. In the study of the territory on the site, three landslides were found that are in extreme condition, erosion processes, an elevated level of groundwater, planar flushing, and also weathering of bedrock when they are opened during the laying of the route. Two schemes of constructive solutions using gabion construction both on a natural basis and on a pile are considered. The choice of the type of protective structure is determined by the presence of both surface and ground waters, as well as by a technical and economic comparison (in comparison with a reinforced concrete retaining wall). The authors reviewed existing software systems used in the calculation of underground structures, and also analyzed the basic methods for calculating the slope stability and structural strength. As a result of the study, such geotechnical software systems as: Plaxis, GeoStudio, Geo5 were selected to simulate a landslide slope. Slope stability was determined both for the main combination of loads and for the special one (seismic of 8 points) using such methods as: Phi/c reduction, Morgenstern-Price method and Shahunyants method. The results obtained showed good convergence.