Morgenstern Price Research Articles

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.

Optimization Model for Determining Safety Factor and Thrust Line in Landslide Assessments

AbstractWhen the limit-equilibrium method is employed in the stability assessment of complicated landslides, some eccentric results are often encountered with the use of rigorous methods. These eccentric results may be attributable to irrationally assumed interslice forces. Furthermore, engineers should verify the rationality of the thrust-line position in a landslide after the safety factor of the landslide is solved with the use of such rigorous methods. In this paper, a new global analysis method is proposed based on the Morgenstern–Price assumption for interslice forces. The global equilibrium equations, normal stresses on the sliding surface, and position of the thrust line were employed as constraint conditions to construct an optimization model. The relationships between the constraint conditions and the safety factors and thrust line were investigated through the analysis of some typical landslides with some interesting results.

Predictive analysis of slope stability of internal dumps in Tamnava–West field mine after flooding

The article reports the results of estimation of internal dump slope stability in flooded open pit coal mine Tamnava–West Field. The geostatic analysis of stability used methods by Bishop and Morgenstern–Price. The studies confirm that slopes of internal dump are sufficiently stable and sustain stability after drainage of the open pit.

Slope stability analysis based on immunised evolutionary programming

The key task in analyzing slope stability is determining its critical slip surface. To solve this problem, a new critical slip surface search method based on an immunised evolutionary programming is proposed. From application of the improved adaptive mutation operation and improved selection operation based on thickness adjustment of artificial immune system into evolutionary programming, a new immunised evolutionary programming for continuous optimisation is proposed. Then, combined with typical mature limit equilibrium analysis (the Spencer method and the Morgenstern–Price method), the immunised evolutionary programming is used to analyze the stability of the slope. Finally, the proposed method is verified through four typical numerical examples and is compared with the evolutionary programming and previous studies in the literature. The results indicate that the applicability, validity and effectiveness of the immunised evolutionary programming are all improved over previous studies and over the evolutionary programming.

A three‐dimensional rigorous method for stability analysis of landslides

In the stability analysis of landslides based on limit equilibrium methods, the “rigorous” methods that satisfy complete equilibrium conditions are more reliable and are preferred. For two‐dimensional analyses, the rigorous methods of slices are becoming mature in both theory and practice. However, the attempts to realize their three‐dimensional rigorous counterparts have not yet been realized. Introducing the Morgenstern–Price (M‐P) assumption on the internal forces of the slip body, this study presents the three‐dimensional version of the M‐P method, which is rigorous and applicable to failure surfaces of complex shape. In the formulation, meanwhile, the volume integrals over the slip body are transformed into the boundary integrals, rendering column‐partitioning unnecessary. The methodology developed in this study can be utilized to extend those two‐dimensional rigorous methods of slices to their three‐dimensional rigorous versions.

Locating the general failure surface of earth slope using particle swarm optimisation

In this study, a new particle swarm optimisation (PSO) approach is proposed for evaluating the factor of safety (FS) in a slope stability analysis based on the limit equilibrium method. The safety factors of the general slip surfaces are calculated using a concise algorithm of the Morgenstern–Price method, which satisfies both the force and the moment equilibriums. Each new slip surface is randomly generated by a straight-line technique. The performance of the proposed algorithm is evaluated using a set of three benchmark functions and three slope stability problems from the literature. The results indicate that the new method can provide high-quality, accurate and efficient solutions for computing the FS. Moreover, this method can predict a more critical failure mechanism of earth slope and outperform both the other methods in the literature and the standard PSO.

Effects of Soil Properties Uncertainty on Reliability Index of Slope

A probabilistic analysis procedure and related algorithms were based on the Monte Carlo simulation method that considers the variability of soil properties in this paper. A homogenous slope example provide insight into the effects of uncertainty due to the variability of soil properties on slope stability .Taking soil parameters cohesion c, friction angle, gravity γ as the basic random variables, the reliability index are calculated using Monte Carlo simulation method taking into account the uncertainties of these basic random variables. The calculated results are compared for four recognized methods of slope stability, which are Ordinary method, simplified Bishop method, simplified Janbu method and Morgenstern Price method. And the influence of soil parameters’ probability distribution model (i.e. the normal distribution and the log–normal distribution), variation coefficient, mean value, correlation between parameters on the reliability index of slope is discussed. The study shows that different soil properties have different influence degree on the reliability index with regard to the slope reliability analysis.

Debris slope stability analysis using three-dimensional finite element method based on maximum shear stress theory

How to evaluate debris slope stability reasonably is yet an urgent problem. The paper presents an applied method evaluating debris slope stability, using three-dimensional (3D) finite element contact algorithm based on the maximum shear stress theory. The Guanjia debris slope is located between K9 + 940 and K10 + 200 of Longli First-class Highway in Zhejiang, China. On its left slope, some cracks appeared at the end of 2002 and these were immediately backfilled, overlying a plastic membrane. However, many new cracks appeared on the slope during the rainfall in April 2003. Meanwhile, some small collapses and springs occurred in the front of the slope, and many cracks appeared on the middle part. The stability of the Guanjia debris slope was analyzed using the method proposed in the paper, the strength reduction finite element method, the imbalance thrust force method, Fellenius method, Janbu simplified method, Spencer’s method, Morgenstern–Price method and generalized limit equilibrium (GLE) method. The results show that: (1) the safety factors of the debris slope obtained using the imbalance thrust force method is the minimum in all limit equilibrium methods; (2) 1.07 and 1.06 are the safety factors of Section CC′ and DD′ (the middle part of this slope) of the Guanjia debris slope obtained using the method proposed (FEM with shear strength reduction technique based on the maximum shear stress theory) in this study, respectively, which reflect the slope actual condition in critical failure status; (3) the method proposed in this study may take into account the spatial effect of the debris slope, which makes the results of slope stability analysis more reasonable and reliable than other methods that can be used as a reference for the evaluation of stability of the same type of debris slope; and (3) further study should be done to confirm whether the proposed method in this study is suitable for other types of slopes.

Determination of the critical failure surface for slope stability analysis using ant colony optimization

Slope stability analysis of any natural or artificial slope aims at determining the factor of safety of the slip surface that possesses the lowest factor of safety. In this study, an ant colony optimization (ACO) algorithm is developed to solve this factor-of-safety minimization problem. Factors of safety of slip surfaces are found by using the Morgenstern–Price method, which satisfies both force and moment equilibrium. Nonlinear equations from the Morgenstern–Price method are solved numerically by the Newton–Raphson method. In the proposed ACO algorithm, the initiation point and the shape of the slip surface are treated as the search variables. The proposed heuristic algorithm represents slip surfaces as piecewise-linear curves and solves for the optimal curve yielding the minimum factor of safety. To demonstrate its applicability and to investigate the validity and effectiveness of the algorithm, four examples with varying complexity are presented. The obtained results are compared with the available literature and are found to be in agreement.

Three-Dimensional Asymmetrical Slope Stability Analysis Extension of Bishop’s, Janbu’s, and Morgenstern–Price’s Techniques

Most existing three-dimensional (3D) slope stability analysis methods are based on simple extensions of corresponding two-dimensional (2D) methods of analysis and a plane of symmetry or direction of slide is implicitly assumed. In this paper, 3D asymmetric slope stability models based on extensions of Bishop’s simplified, Janbu’s simplified, and Morgenstern–Price’s methods are developed. Under these new formulations, the direction of slide is unique and is determined from 3D force/moment equilibrium. Results from the new formulations are similar to the classical methods in normal cases but are numerically stable under transverse load. Further, the writers demonstrate that the present formulation is actually equivalent to the axes rotation formulation by Jiang and Yamagami but is much more convenient to be used for general problems. The writers have also discovered some inherent limitations of 3D limit equilibrium analysis which are absent in the corresponding 2D analysis.

Simple genetic algorithm search for critical non-circular failure surface in slope stability analysis

Soil slope stability problems in engineering works are usually analysed using limit equilibrium methods. A number of existing methods are based on finding the critical circular failure surface for homogeneous soils, but failure surfaces tend to be non-circular for layered slopes. A simple genetic algorithm is presented to search the critical non-circular failure surface in slope stability analysis and is used to solve the Morgenstern–Price method to find the factor of safety. The pseudo-static horizontal and vertical forces due to earthquake and surcharge load due to existing buildings and structures on natural slopes are included in the analysis.

A concise algorithm for computing the factor of safety using the Morgenstern–Price method

A concise algorithm is proposed in this paper for the calculation of the factor of safety of a slope using the Morgenstern–Price method. Based on force and moment equilibrium considerations, two expressions are derived for the factor of safety Fs and the scaling factor λ, respectively, both in relatively simple forms. With this algorithm and assumed initial values of Fs and λ, the solutions for Fs and λ are found to converge within a few iterations. Compared to other procedures, the present algorithm possesses the advantages of simplicity and high efficiency in application. It is rather straightforward to implement this algorithm into a computer program.Key words: slope, stability, factor of safety, limit equilibrium method.

Explicit limit equilibrium solution for slope stability

AbstractConventional methods of slices used for slope stability analysis satisfying all equilibrium conditions involves generally solving two highly non‐linear equations with respect to two unknowns, i.e. the factor of safety and the associated scaling parameter. To solve these two equations, complicated numerical iterations are required with non‐convergence occasionally occurring. This paper presents an alternative procedure to derive the three equilibrium equations (horizontal and vertical forces equations and moment equation) based on an assumption regarding the normal stress distribution along the slip surface. Combination of these equations results in a single cubic equation in terms of the factor of safety, which is explicitly solved. Theoretical testing demonstrates that the proposed method yields a factor of safety in reasonable agreement with a closed‐form solution based on the theory of plasticity. Example studies show that the difference in values of factor of safety between the proposed method, the Spencer method and the Morgenstern–Price method is within 5%. Application of the proposed method to practical slope engineering problems is rather straightforward, but its solution is of the same precision as those given by the conventional rigorous methods of slices since it is still within the rigorous context. Copyright © 2002 John Wiley & Sons, Ltd.

Failure mechanisms and pore water pressure conditions: analysis of a riverbank along the Arno River (Central Italy)

Mechanisms of failure occurring in two portions of a riverbank along the Arno River (Central Italy), are investigated in detail starting by a series of periodic field observations and bank profile measurements. Two dominant mechanisms involving the silty sand portion of the bank have been observed: (a) alcove-shaped failure in the middle portion of the bank; (b) slab failure involving the middle–upper bank. A portion of the riverbank was subject to laboratory (grain size analysis; phase relationship analysis; triaxial tests) and in situ tests (borehole shear tests (BSTs)) to characterise the geotechnical properties of the overbank deposits. Two different procedures of bank stability analysis have been performed: (1) a complete analysis, coupling seepage analysis with the limit equilibrium method; (2) two simplified analyses, through the limit equilibrium method with simple assumptions on pore water pressures distribution. For the complete analysis, saturated/unsaturated flow within the riverbank was modelled by finite element seepage analysis in transient conditions, using as boundary conditions eight hydrographs with increasing water stage. Riverbank stability analyses have been conducted by the Morgenstern–Price rigorous method, dividing each of the eight hydrographs in 21 time steps and calculating the safety factor for each step. The analysis revealed the occurrence of two possible mechanisms of failure (slab-type and alcove-shaped sliding failures), according to the field observations, related to different river stages and pore water pressures within the riverbank: alcove failures are likely to occur with moderate flow events, while slab failures are favoured by flow events with higher peak river stage. A first type of simplified analysis, representing critical conditions reached during a rapid flow event, was based on the main hypothesis of the occurrence of a zero pore water pressures zone within the portion of the bank between the low-water stage and the peak stage reached. A second type of simplified analysis was applied in order to represent rapid drawdown conditions following a prolonged flow event (worst case), with the main assumption of total saturation of the material up to the same elevation of the peak river stage. The first simplified analysis has given similar results to the complete seepage/stability analysis, confirming slab-type and alcove-shaped failure as the two main mechanisms of instability, while the second type of simplified analysis has conducted to too conservative results compared to the other previous analyses. Field observations regarding different characteristic bank geometries in adjacent sub-reaches have been summarised in a conceptual cyclic sketch, that include all the possible paths of bank evolution depending on the succession of river stages reached during flow events and related pore pressure conditions.

Usage, requirements and features of slope stability computer software (Canada, 1977)

A survey of Canadian universities and consulting engineering firms was conducted to ascertain the present status of slope stability software usage in Canada. The results indicate that most universities have access to at least one slope stability computer program. However, there is limited usage of computer programs as a teaching tool at the undergraduate or graduate level. In general, the programs are poorly documented and not distributed. Consulting engineering firms indicate that more education on the relationship between the various methods of slices, on available software and its application to practical problems would be beneficial. The most commonly used procedures are the simplified Bishop method for circular failure surfaces and the Morgenstern–Price method for noncircular failure surfaces.Several well-documented slope stability computer programs are available to the geotechnical engineer at the cost of reproduction. The source for obtaining the programs is listed in the paper. Computer programs are available for all the commonly used methods of slices and the features of each program are also summarized in the paper.

Comparison of slope stability methods of analysis

The paper compares six methods of slices commonly used for slope stability analysis. The factor of safety equations are written in the same form, recognizing whether moment and (or) force equilibrium is explicitly satisfied. The normal force equation is of the same form for all methods with the exception of the ordinary method. The method of handling the interslice forces differentiates the normal force equations.A new derivation for the Morgenstern–Price method is presented and is called the 'best-fit regression' solution. It involves the independent solution of the force and moment equilibrium factors of safety for various values of λ. The best-fit regression solution gives the same factor of safety as the 'Newton–Raphson' solution. The best-fit regression solution is readily comprehended, giving a complete understanding of the variation of the factor of safety with λ.