Effects of spatial heterogeneity on pseudo-static stability of coal mine overburden dump slope,using random limit equilibrium and random finite element methods:A comparative study

Sudden and unforeseen seismic failures of coal mine overburden(OB)dump slopes interrupt mining operations,cause loss of lives and delay the production of coal.Consideration of the spatial heterogeneity of OB dump materials is imperative for an adequate evaluation of the seismic stability of OB dump slopes.In this study,pseudo-static seismic stability analyses are carried out for an OB dump slope by considering the material parameters obtained from an insitu field investigation.Spatial heterogeneity is simulated through use of the random finite element method(RFEM)and the random limit equilibrium method(RLEM)and a comparative study is presented.Combinations of horizontal and vertical spatial correlation lengths were considered for simulating isotropic and anisotropic random fields within the OB dump slope.Seismic performances of the slope have been reported through the probability of failure and reliability index.It was observed that the RLEM approach overestimates failure probability(P_(f))by considering seismic stability with spatial heterogeneity.The P_(f)was observed to increase with an increase in the coefficient of variation of friction angle of the dump materials.Further,it was inferred that the RLEM approach may not be adequately applicable for assessing the seismic stability of an OB dump slope for a horizontal seismic coefficient that is more than or equal to 0.1.

Influence of joint spacing and rock characteristics on the toppling stability of cut rock slope through a simplified limit equilibrium method

Toppling failure of rock mass/soil slope is an important geological and environmental problem.Clarifying its failure mechanism under different conditions has great significance in engineering.The toppling failure of a cutting slope occurred in a hydropower station in Kyushu,Japan illustrates that the joint characteristic played a significant role in the occurrence of rock slope tipping failure.Thus,in order to consider the mechanical properties of jointed rock mass and the influence of geometric conditions,a simplified analytical approach based on the limit equilibrium method for modeling the flexural toppling of cut rock slopes is proposed to consider the influence of the mechanical properties and geometry condition of jointed rock mass.The theoretical solution is compared with the numerical solution taking Kyushu Hydropower Station in Japan as one case,and it is found that the theoretical solution obtained by the simplified analysis method is consistent with the numerical analytical solution,thus verifying the accuracy of the simplified method.Meanwhile,the Goodman-Bray approach conventionally used in engineering practice is improved according to the analytical results.The results show that the allowable slope angle may be obtained by the improved Goodman-Bray approach considering the joint spacing,the joint frictional angle and the tensile strength of rock mass together.

A Generalized Limit Equilibrium Method for the Solution of Active Earth Pressure on a Retaining Wall

In this paper, a generalized limit equilibrium method of solving the active earth pressure problem behind a retaining wall is proposed.Differing from other limit equilibrium methods, an arbitrary slip surface shape without any assumptions of pre-defined shapes is needed in the current framework, which is verified to find the most probable failure slip surface. Based on the current computational framework, numerical comparisons with experiment, discrete element method and other methods are carried out. In addition, the influences of the inclination of the wall, the soil cohesion, the angle of the internal friction of the soil, the slope inclination of the backfill soil on the critical pressure coefficient of the soil, the point of application of the resultant earth pressure and the shape of the slip surface are also carefully investigated. The results demonstrate that limit equilibrium solution from predefined slip plane assumption, including Coulomb solution, is a special case of current computational framework. It is well illustrated that the current method is feasible to evaluate the characteristics of earth pressure problem.

A Method Combining Numerical Analysis and Limit Equilibrium Theory to Determine Potential Slip Surfaces in Soil Slopes

This paper describes a precise method combining numerical analysis and limit equilibrium theory to determine potential slip surfaces in soil slopes. In this method, the direction of the critical slip surface at any point in a slope is determined using the Coulomb’s strength principle and the extremum principle based on the ratio of the shear strength to the shear stress at that point. The ratio, which is considered as an analysis index, can be computed once the stress field of the soil slope is obtained. The critical slip direction at any point in the slope must be the tangential direction of a potential slip surface passing through the point. Therefore, starting from a point on the top of the slope surface or on the horizontal segment outside the slope toe, the increment with a small distance into the slope is used to choose another point and the corresponding slip direction at the point is computed. Connecting all the points used in the computation forms a potential slip surface exiting at the starting point. Then the factor of safety for any potential slip surface can be computed using limit equilibrium method like Spencer method. After factors of safety for all the potential slip surfaces are obtained, the minimum one is the factor of safety for the slope and the corresponding potential slip surface is the critical slip surface of the slope. The proposed method does not need to pre-assume the shape of potential slip surfaces. Thus it is suitable for any shape of slip surfaces. Moreover the method is very simple to be applied. Examples are presented in this paper to illustrate the feasibility of the proposed method programmed in ANSYS software by macro commands.

Lateral Bearing Capacity of Modified Suction Caissons Determined by Using the Limit Equilibrium Method

The modified suction caisson(MSC) adds a short-skirted structure around the regular suction caissons to increase the lateral bearing capacity and limit the deflection. The MSC is suitable for acting as the offshore wind turbine foundation subjected to larger lateral loads compared with the imposed vertical loads. Determination of the lateral bearing capacity is a key issue for the MSC design. The formula estimating the lateral bearing capacity of the MSC was proposed in terms of the limit equilibrium method and was verified by the test results. Parametric studies on the lateral bearing capacity were also carried out. It was found that the lateral bearing capacity of the MSC increases with the increasing length and radius of the external skirt, and the lateral bearing capacity increases linearly with the increasing coefficient of subgrade reaction. The maximum lateral bearing capacity of the MSC is attained when the ratio of the radii of the internal compartment to the external skirt equals 0.82 and the ratio of the lengths of the external skirt to the internal compartment equals 0.48, provided that the steel usage of the MSC is kept constant.

Comprehensive analysis of slope stability and determination of stable slopes in the Chador-Malu iron ore mine using numerical and limit equilibrium methods

One of the critical aspects in mine design is slope stability analysis and the determination of stable slopes. In the Chador- Malu iron ore mine, one of the most important iron ore mines in central Iran, it was considered vital to perform a comprehensive slope stability analysis. At first, we divided the existing rock hosting pit into six zones and a geotechnical map was prepared. Then, the value of MRMR （Mining Rock Mass Rating） was determined for each zone. Owing to the fact that the Chador-Malu iron ore mine is located in a highly tectonic area and the rock mass completely crushed, the Hoek-Brown failure criterion was found suitable to estimate geo-mechanical parameters. After that, the value of cohesion （c） and friction angle （tp） were calculated for different geotechnical zones and relative graphs and equations were derived as a function of slope height. The stability analyses using numerical and limit equilibrium methods showed that some instability problems might occur by increasing the slope height. Therefore, stable slopes for each geotechnical zone and prepared sections were calculated and presented as a function of slope height.

Overhanging rock slope by design:An integrated approach using rock mass strength characterisation,large-scale numerical modelling and limit equilibrium methods

Overhanging rock slopes(steeper than 90°) are typically avoided in rock engineering design, particularly where the scale of the slope exceeds the scale of fracturing present in the rock mass. This paper highlights an integrated approach of designing overhanging rock slopes where the relative dimensions of the slope exceed the scale of fracturing and the rock mass failure needs to be considered rather than kinematic release of individual blocks. The key to the method is a simplified limit equilibrium(LE) tool that was used for the support design and analysis of a multi-faceted overhanging rock slope. The overhanging slopes required complex geometries with constantly changing orientations. The overhanging rock varied in height from 30 m to 66 m. Geomechanical modelling combined with discrete fracture network(DFN)representation of the rock mass was used to validate the rock mass strength assumptions and the failure mechanism assumed in the LE model. The advantage of the simplified LE method is that buttress and support design iterations(along with sensitivity analysis of design parameters) can be completed for various cross-sections along the proposed overhanging rock sections in an efficient manner, compared to the more time-intensive, sophisticated methods that were used for the initial validation. The method described presents the development of this design tool and assumptions made for a specific overhanging rock slope design. Other locations will have different geological conditions that can control the potential behaviour of rock slopes, however, the approach presented can be applied as a general guiding design principle for overhanging rock cut slope.

Probabilistic Analysis of Slope Using Finite Element Approach and Limit Equilibrium Approach around Amalpata Landslide of West Central, Nepal

The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have different slope inclinations. The lower bench, located above the basement, consistently fails and sets others up for failure. The fluctuating water level of the slope, which travels down the slope masses, exacerbates the slide problem. The majority of these rocks are Amalpata landslide area experiences several structural disruptions. The area’s stability must be evaluated in order to prevent and control more harm from occurring to the nearby agricultural land and people living along the slope. The slopes’ failures increase the damages of house existing in nearby area and the erosion of the slope. Two modeling techniques the finite element approach and the limit equilibrium method were used to simulate the slope. The findings show that, in every case, the terrace above the basement is where the majority of the stress is concentrated, with a safety factor of near unity. Using probabilistic slope stability analysis, the failure probability was predicted to be between 98.90% and 100%.

A new double reduction method for slope stability analysis

The core of strength reduction method(SRM) involves finding a critical strength curve that happens to make the slope globally fail and a definition of factor of safety(FOS). A new double reduction method, including a detailed calculation procedure and a definition of FOS for slope stability was developed based on the understanding of SRM. When constructing the new definition of FOS, efforts were made to make sure that it has concise physical meanings and fully reflects the shear strength of the slope. Two examples, slopes A and B with the slope angles of 63° and 34° respectively, were given to verify the method presented. It is found that, for these two slopes, the FOSs from original strength reduction method are respectively 1.5% and 38% higher than those from double reduction method. It is also found that the double reduction method predicts a deeper potential slide line and a larger slide mass. These results show that on one hand, the double reduction method is comparative to the traditional methods and is reasonable, and on the other hand, the original strength reduction method may overestimate the safety of a slope. The method presented is advised to be considered as an additional option in the practical slope stability evaluations although more useful experience is required.

Seismic passive earth resistance using modified pseudo-dynamic method

In earthquake prone areas, understanding of the seismic passive earth resistance is very important for the design of different geotechnical earth retaining structures. In this study, the limit equilibrium method is used for estimation of critical seismic passive earth resistance for an inclined wall supporting horizontal cohesionless backfill. A composite failure surface is considered in the present analysis. Seismic forces are computed assuming the backfill soil as a viscoelastic material overlying a rigid stratum and the rigid stratum is subjected to a harmonic shaking. The present method satisfies the boundary conditions. The amplification of acceleration depends on the properties of the backfill soil and on the characteristics of the input motion. The acceleration distribution along the depth of the backfill is found to be nonlinear in nature. The present study shows that the horizontal and vertical acceleration distribution in the backfill soil is not always in-phase for the critical value of the seismic passive earth pressure coefficient. The effect of different parameters on the seismic passive earth pressure is studied in detail. A comparison of the present method with other theories is also presented, which shows the merits of the present study.

A new method for the stability analysis of geosynthetic-reinforced slopes

This paper is concerned with the stability analysis of reinforced slopes.A new approach based on the limit equilibrium principle is proposed to evaluate the stability of the reinforced slopes.The effect of reinforcement is modeled as an equivalent restoring force acting the bottom of the slice and added into the general limit equilibrium(GLE) method.The equations of force and moment equilibrium of the slice are derived and corresponding iterative solution methods are provided.The new method can satisfy both the force and the moment equilibrium and be applicable to the critical failure surface of arbitrary form.Furthermore,the results predicted by the proposed method are compared with the calculation examples of other researchers and the centrifuge model test results to validate its correctness and effectiveness.

Stability analysis of tunnel face reinforced with face bolts

Face bolting has been widely utilized to enhance the stability of tunnel face,particularly in soft soil tunnels.However,the influence of bolt reinforcement and its layout on tunnel face stability has not been systematically studied.Based on the theory of linear elastic mechanics,this study delved into the specific mechanisms of bolt reinforcement on the tunnel face in both horizontal and vertical dimensions.It also identified the primary failure types of bolts.Additionally,a design approach for tunnel face bolts that incorporates spatial layout was established using the limit equilibrium method to enhance the conventional wedge-prism model.The proposed model was subsequently validated through various means,and the specific influence of relevant bolt design parameters on tunnel face stability was analyzed.Furthermore,design principles for tunnel face bolts under different geological conditions were presented.The findings indicate that bolt failure can be categorized into three stages:tensile failure,pullout failure,and comprehensive failure.Increasing cohesion,internal friction angle,bolt density,and overlap length can effectively enhance tunnel face stability.Due to significant variations in stratum conditions,tailored design approaches based on specific failure stages are necessary for bolt design.

Classification and rating of disintegrated dolomite strata for slope stability analysis

Although disintegrated dolomite,widely distributed across the globe,has conventionally been a focus of research in underground engineering,the issue of slope stability issues in disintegrated dolomite strata is gaining increasing prominence.This is primarily due to their unique properties,including low strength and loose structure.Current methods for evaluating slope stability,such as basic quality(BQ)and slope stability probability classification(SSPC),do not adequately account for the poor integrity and structural fragmentation characteristic of disintegrated dolomite.To address this challenge,an analysis of the applicability of the limit equilibrium method(LEM),BQ,and SSPC methods was conducted on eight disintegrated dolomite slopes located in Baoshan,Southwest China.However,conflicting results were obtained.Therefore,this paper introduces a novel method,SMRDDS,to provide rapid and accurate assessment of disintegrated dolomite slope stability.This method incorporates parameters such as disintegrated grade,joint state,groundwater conditions,and excavation methods.The findings reveal that six slopes exhibit stability,while two are considered partially unstable.Notably,the proposed method demonstrates a closer match with the actual conditions and is more time-efficient compared with the BQ and SSPC methods.However,due to the limited research on disintegrated dolomite slopes,the results of the SMRDDS method tend to be conservative as a safety precaution.In conclusion,the SMRDDS method can quickly evaluate the current situation of disintegrated dolomite slopes in the field.This contributes significantly to disaster risk reduction for disintegrated dolomite slopes.

Comprehensive analysis of multiple machine learning techniques for rock slope failure prediction

In this study,twelve machine learning(ML)techniques are used to accurately estimate the safety factor of rock slopes(SFRS).The dataset used for developing these models consists of 344 rock slopes from various open-pit mines around Iran,evenly distributed between the training(80%)and testing(20%)datasets.The models are evaluated for accuracy using Janbu's limit equilibrium method(LEM)and commercial tool GeoStudio methods.Statistical assessment metrics show that the random forest model is the most accurate in estimating the SFRS(MSE=0.0182,R2=0.8319)and shows high agreement with the results from the LEM method.The results from the long-short-term memory(LSTM)model are the least accurate(MSE=0.037,R2=0.6618)of all the models tested.However,only the null space support vector regression(NuSVR)model performs accurately compared to the practice mode by altering the value of one parameter while maintaining the other parameters constant.It is suggested that this model would be the best one to use to calculate the SFRS.A graphical user interface for the proposed models is developed to further assist in the calculation of the SFRS for engineering difficulties.In this study,we attempt to bridge the gap between modern slope stability evaluation techniques and more conventional analysis methods.

An Improved Particle Swarm Optimization Algorithm with Harmony Strategy for the Location of Critical Slip Surface of Slopes

The determination of optimal values for three parameters required in the original particle swarm optimization algorithm is very difficult. It is proposed that two new parameters simulating the harmony search strategy can be adopted instead of the three parameters which are required in the original particle swarm optimization algorithm to update the positions of all the particles. The improved particle swarm optimization is used in the location of the critical slip surface of soil slope, and it is found that the improved particle swarm optimization algorithm is insensitive to the two parameters while the original particle swarm optimization algorithm can be sensitive to its three parameters.

Discontinuous flying particle swarm optimization algorithm and its application to slope stability analysis

A new version of particle swarm optimization(PSO) called discontinuous flying particle swarm optimization(DFPSO) was proposed,where not all of the particles refreshed their positions and velocities during each iteration step and the probability of each particle in refreshing its position and velocity was dependent on its objective function value.The effect of population size on the results was investigated.The results obtained by DFPSO have an average difference of 6% compared with those by PSO,whereas DFPSO consumes much less evaluations of objective function than PSO does.

A New Approach to the Determination of the Critical Slip Surfaces of Slopes

A new method for the determination of the critical slip surfaces of slopes is proposed in this paper. In this paper, the original critical slip field method is extended in terms of the total residual moment, values of residual work as well as the unbalanced thrust force at the exit point for a given non-circular slip surface. The most critical slip surface with the maximum representative value for a prescribed factor of safety will be optimized and located using the harmony search algorithm. The prescribed factor of safety is modified with certain tiny interval in order to find the critical slip surface where the maximum representative value is zero. The aforementioned approach to the location of the critical slip surface is greatly different from the traditional limit equilibrium procedure. Three typical soil slopes are evaluated by use of the proposed method, and the comparisons with the classical approaches have illustrated the applicability of the proposed method.

Hybrid method of limit equilibrium and finite element internal force for analysis of arch dam stability against sliding

A hybrid method of limit equilibrium and finite element internal force for analysis of arch dam stability against sliding is presented.The finite element internal force method(FEIFM) is used to provide more accurate thrust forces acting on the faces of a slip body,and the limit equilibrium method(LEM) is employed to evaluate the factor of safety of the slip body.The method presented can deal with a slip body with large amount of geometrically complex slip faces.In addition,compared with the traditional LEM,it can meet the balance condition of the forces in the slip faces.An example shows that the factor of safety obtained by the method presented agrees well with the theoretical solution.A practical example is also presented to demonstrate the application of the method in the stability analysis of an arch dam project.The results from the examples show that the method is promising in analysis of arch dam stability against sliding.

Slope stability analysis of Southern slope of Chengmenshan copper mine,China

The engineering geology and hydrogeology in the southern slope of Chengmenshan copper mine are very complicated,because there is a soft-weak layer between two kinds of sandstones.Field investigations demonstrate that some instability problems might occur in the slope.In this research,the southern slope,which is divided into six sections(I-0,I-1,I-2,II-0,II-1 and II-2),is selected for slope stability analysis using limit equilibrium and numerical method.Stability results show that the values of factor of safety(FOS) of sections I-0,I-1 and I-2 are very low and slope failure is likely to happen.Therefore reinforcement subjected to seismic,water and weak layer according to sections were carried out to increase the factor of safety of the three sections,two methods were used;grouting with hydration of cement and water to increase the cohesion(c) and pre-stressed anchor.Results of reinforcement showed that factor of safety increased more than 1.15.

Theoretical study on stability evolution of soft and hard interbedded bedding reservoir slopes

Soft and hard interbedded bedding rock slopes,which is prone to failure,are widely distributed in the Three Gorges Reservoir,China.Limit equilibrium method(LEM)is commonly used to analyze the stability of bedding rock slopes that have a single failure plane.However,this method cannot accurately estimate the stability of soft and hard interbedded bedding reservoir slopes because the strength parameters of a soft and hard interbedded rock mass vary spatially along the bedding plane and deteriorate with time due to periodic fluctuations of reservoir level.A modified LEM is proposed to evaluate the stability evolution of soft and hard interbedded bedding reservoir slopes considering the spatial variation and temporal deterioration of shear strength parameters of rock masses and bedding planes.In the modified LEM,the S-curve model is used to define the spatial variation of shear strength parameters,and general deterioration equations of shear strength parameters with the increasing number of wettingdrying cycles(WDC)are proposed to describe the temporal deterioration.Also,this method is applied to evaluate the stability evolution of a soft and hard interbedded bedding reservoir slope,located at the Three Gorges Reservoir.The results show that neglecting the spatial variation and temporal deterioration of shear strength parameters may overestimate slope stability.Finally,the modified LEM provides useful guidance to reasonably evaluate the long-term stability of soft and hard interbedded bedding reservoir slopes in reservoir area.