Efficient slope reliability and sensitivity analysis using quantile-based first-order second-moment method

This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.

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 Calculation Method of Double Strength Reduction for Layered Slope Based on the Reduction of Water Content Intensity

The calculation of the factor of safety(FOS)is an important means of slope evaluation.This paper proposed an improved double strength reductionmethod(DRM)to analyze the safety of layered slopes.The physical properties of different soil layers of the slopes are different,so the single coefficient strength reduction method(SRM)is not enough to reflect the actual critical state of the slopes.Considering that the water content of the soil in the natural state is the main factor for the strength of the soil,the attenuation law of shear strength of clayey soil changing with water content is fitted.This paper also establishes the functional relationship between different reduction coefficients.Then,a USDFLD subroutine is programmed using the secondary development function of finite element software.Controlling the relationship between field variables and calculation time realizes double strength reduction applicable to the layered slope.Finally,by comparing the calculation results of different examples,it is proved that the stress and displacement distribution of the critical slope state obtained by the improved method is more realistic,and the calculated safety factor is more reliable.The newly proposedmethod considers the difference of intensity attenuation between different soil layers under natural conditions and avoids the disadvantage of the strength reduction method with uniform parameters,which provides a new idea and method for stability analysis of layered and complex slopes.

A vector sum analysis method for stability evolution of expansive soil slope considering shear zone damage softening

Slope stability analysis is a classical mechanical problem in geotechnical engineering and engineering geology.It is of great significance to study the stability evolution of expansive soil slopes for engineering construction in expansive soil areas.Most of the existing studies evaluate the slope stability by analyzing the limit equilibrium state of the slope,and the analysis method for the stability evolution considering the damage softening of the shear zone is lacking.In this study,the large deformation shear mechanical behavior of expansive soil was investigated by ring shear test.The damage softening characteristic of expansive soil in the shear zone was analyzed,and a shear damage model reflecting the damage softening behavior of expansive soil was derived based on the damage theory.Finally,by skillfully combining the vector sum method and the shear damage model,an analysis method for the stability evolution of the expansive soil slope considering the shear zone damage softening was proposed.The results show that the shear zone subjected to large displacement shear deformation exhibits an obvious damage softening phenomenon.The damage variable equation based on the logistic function can be well used to describe the shear damage characteristics of expansive soil,and the proposed shear damage model is in good agreement with the ring shear test results.The vector sum method considering the damage softening behavior of the shear zone can be well applied to analyze the stability evolution characteristics of the expansive soil slope.The stability factor of the expansive soil slope decreases with the increase of shear displacement,showing an obvious progressive failure behavior.

Investigation of the block toppling evolution of a layered model slope by centrifuge test and discrete element modeling

Primary toppling usually occurs in layered rock slopes with large anti-dip angles.In this paper,the block toppling evolution was explored using a large-scale centrifuge system.Each block column in the layered model slope was made of cement mortar.Some artificial cracks perpendicular to the block column were prefabricated.Strain gages,displacement gages,and high-speed camera measurements were employed to monitor the deformation and failure processes of the model slope.The centrifuge test results show that the block toppling evolution can be divided into seven stages,i.e.layer compression,formation of major tensile crack,reverse bending of the block column,closure of major tensile crack,strong bending of the block column,formation of failure zone,and complete failure.Block toppling is characterized by sudden large deformation and occurs in stages.The wedge-shaped cracks in the model incline towards the slope.Experimental observations show that block toppling is mainly caused by bending failure rather than by shear failure.The tensile strength also plays a key factor in the evolution of block toppling.The simulation results from discrete element method(DEM)is in line with the testing results.Tensile stress exists at the backside of rock column during toppling deformation.Stress concentration results in the fragmented rock column and its degree is the most significant at the slope toe.

Numerical analysis of downward progressive landslides in long natural slopes with sensitive clay

Landslides occurring in sensitive clay often result in widespread destruction,posing a significant risk to human lives and property due to the substantial decrease in undrained shear strength during deformation.Assessing the consequences of these landslides is challenging and necessitates robust numerical methods to comprehensively investigate their failure mechanisms.While studies have extensively explored upward progressive landslides in sensitive clays,understanding downward progressive cases remains limited.In this study,we utilised the nodal integration-based particle finite element method(NPFEM)with a nonlinear strain-softening model to analyse downward progressive landslides in sensitive clay on elongated slopes,induced by surcharge loads near the crest.We focused on elucidating the underlying failure mechanisms and evaluating the effects of different soil parameters and strainsoftening characteristics.The simulation results revealed the typical pattern for downward landslides,which typically start with a localised failure in proximity to the surcharge loads,followed by a combination of different types of failure mechanisms,including single flow slides,translational progressive landslides,progressive flow slides,and spread failures.Additionally,inclined shear bands occur within spread failures,often adopting distinctive ploughing patterns characterised by triangular shapes.The sensitive clay thickness at the base,the clay strength gradient,the sensitivity,and the softening rate significantly influence the failure mechanisms and the extent of diffused displacement.Remarkably,some of these effects mirror those observed in upward progressive landslides,underscoring the interconnectedness of these phenomena.This study contributes valuable insights into the complex dynamics of sensitive clay landslides,shedding light on the intricate interplay of factors governing their behaviour and progression.

Comprehensive Analysis Method of Slope Stability Based on the Limit Equilibrium and Finite Element Methods and Its Application

To study the safety and stability of large slopes, taking the right side slope of the Yuxi’an tunnel of the Yuchu Expressway Bridge in Yunnan Province as an example, limit equilibrium and finite element analysis were applied to engineering examples to calculate the stability coefficient of the slope before and after excavation in the natural state. After comparative analysis, it was concluded that the former had a clear mechanical model and concept, which could quickly provide stability results;the latter could accurately determine the sliding surface of the slope and simulate the stress state changes of the rock and soil mass. The stability coefficients calculated by the two methods were within the stable range, but their values were different. On this basis, combined with the calculation principles, advantages and disadvantages of the two methods, a comprehensive analysis method of slope stability based on the limit equilibrium and finite element methods was proposed, and the rationality of the stability coefficient calculated by this method was judged for a slope case.

Failure evaluation and control factor analysis of slope block instability along traffic corridor in Southeastern Tibet

The instability of slope blocks occurred frequently along traffic corridor in Southeastern Tibet(TCST),which was primarily controlled by the rock mass structures.A rapid method evaluating the control effects of rock mass structures was proposed through field statistics of the slopes and rock mass structures along TCST,which combined the stereographic projection method,modified M-JCS model,and limit equilibrium theory.The instabilities of slope blocks along TCST were then evaluated rapidly,and the different control factors of instability were analyzed.Results showed that the probabilities of toppling(5.31%),planar(16.15%),and wedge(35.37%)failure of slope blocks along TCST increased sequentially.These instability modes were respectively controlled by the anti-dip joint,the joint parallel to slope surface with a dip angle smaller than the slope angle(singlejoint),and two groups of joints inclined out of the slope(double-joints).Regarding the control effects on slope block instability,the stabilization ability of doublejoints(72.7%),anti-dip joint(67.4%),and single-joint(57.6%)decreased sequentially,resulting in different probabilities of slope block instability.Additionally,nearby regional faults significantly influenced the joints,leading to spatial heterogeneity and segmental clustering in the stabilization ability provided by joints to the slope blocks.Consequently,the stability of slope blocks gradually weakened as they approached the fault zones.This paper can provide guidance and assistance for investigating the development characteristics of rock mass structures and the stability of slope blocks.

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.

Optimal mining sequence for coal faces under a bedding slope:insight from landslide prevention

Repetitive mining beneath bedding slopes is identified as a critical factor in geomorphic disturbances, especially landslides and surface subsidence. Prior research has largely concentrated on surface deformation in plains due to multi-seam coal mining and the instability of natural bedding slopes, yet the cumulative impact of different mining sequences on bedding slopes has been less explored. This study combines drone surveys and geological data to construct a comprehensive three-dimensional model of bedding slopes. Utilizing FLAC3D and PFC2D models, derived from laboratory experiments, it simulates stress, deformation, and failure dynamics of slopes under various mining sequences. Incorporating fractal dimension analysis, the research evaluates the stability of slopes in relation to different mining sequences. The findings reveal that mining in an upslope direction minimizes disruption to overlying strata. Initiating extraction from lower segments increases tensile-shear stress in coal pillar overburdens, resulting in greater creep deformation towards the downslope than when starting from upper segments, potentially leading to localized landslides and widespread creep deformation in mined-out areas. The downslope upward mining sequence exhibits the least fractal dimensions, indicating minimal disturbance to both strata and surface. While all five mining scenarios maintain good slope stability under normal conditions, recalibrated stability assessments based on fractal dimensions suggest that downslope upward mining offers the highest stability under rainfall, contrasting with the lower stability and potential instability risks of upslope downward mining. These insights are pivotal for mining operations and geological hazard mitigation in multi-seam coal exploitation on bedding 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.

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%.

Slope stability analysis under seismic load by vector sum analysis method

The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method （DFEM）. Combining with the DFEM, the vector sum analysis method （VSAM） is employed in seismic stability analysis of a slope in this paper. Different from other conventional methods, the VSAM is proposed based on the vector characteristic of force and current stress state of the slope. The dynamic stress state of the slope at any moment under seismic load can he obtained by the DFEM, thus the factor of safety of the slope at any moment during earthquake can be easily obtained with the VSAM in consideration of the DFEM. Then, the global stability of the slope can be estimated on the basis of time-history curve of factor of safety and reliability theory. The VSAM is applied to a homogeneous slope under seismic load. The factor of safety of the slope is 1.30 under gravity only and the dynamic factor of safety under seismic load is 1.21. The calculating results show that the dynamic characteristics and stability state of the slope with input ground motion can be actually analyzed. It is believed that the VSAM is a feasible and practical approach to estimate the dynamic stability of slopes under seismic load.

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.

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.

Q-factor estimation in CMP gather and the continuous spectral ratio slope method

The attenuation factor or quality factor(Q-factor or Q) has been used to measure the energy attenuation of seismic waves propagating in underground media. Many methods are used to estimate the Q-factor. We propose a method to calculate the Q-factor based on the prestack Q-factor inversion and the generalized S-transform. The proposed method specifies a standard primary wavelet and calculates the cumulative Q-factors; then, it finds the interlaminar Q-factors using the relation between Q and offset(QVO) and the Dix formula. The proposed method is alternative to methods that calculate interlaminar Q-factors after horizon picking. Because the frequency spectrum of each horizon can be extracted continuously on a 2D time–frequency spectrum, the method is called the continuous spectral ratio slope(CSRS) method. Compared with the other Q-inversion methods, the method offers nearly effortless computations and stability, and has mathematical and physical significance. We use numerical modeling to verify the feasibility of the method and apply it to real data from an oilfield in Ahdeb, Iraq. The results suggest that the resolution and spatial stability of the Q-profile are optimal and contain abundant interlaminar information that is extremely helpful in making lithology and fluid predictions.

Stability assessment of landslide-prone road cut rock slopes in Himalayan terrain:A finite element method based approach

Large-scale slope destabilization could be aggravated due to swift urbanization and ever-rising demands of geoengineering projects such as dams,tunnels,bridges and widening roads.National Highway-58 connects Delhi to Badrinath in India,which passes through complex geomorphological and geological terrain and often encounters cut slopes susceptible to slope failures.In the present investigation,a detailed geotechnical appraisal is conducted along the road cut slopes from Rishikesh to Devprayag in the Himalayas.Twenty vulnerable road cut slopes were demarcated for detailed slope stability analysis using Phase2D finite element modeling simulator.Nonlinear generalized Hoek-Brown(GHB)criterion was adopted for stability analyses.Out of 20 slopes,five slopes(S6,S7,S18,S19 and S20)are unstable with factor of safety(FoS)less than or equal to 1,and thus needs immediate attention.The FoS values of four slopes(S2,S9,S13 and S17)lie between 1 and 1.3,i.e.marginally stable,and slopes S1,S3,S4,S5,S8,S10,Sll,S12,S14,S15 and S16 are stable.Mohr-Coulomb(MC)criterion was also adopted to compare the slope stability analysis with GHB criterion.The FoS calculated from GHB criterion is close to that using MC criterion for lower values of FoS whereas for higher values,the difference is marked.For the jointed rock in the Himalayan region,the nonlinear GHB criterion gives better results as compared to MC criterion and matches with the prevailing field conditions.Accordingly,some suggestions are proposed to strengthen the stability of cut slopes.

Efficient Elliptic Solver for the Mild Slope Equation Using BI-CGSTAB Method

The elliptic mild slope equation is used to simulate linear wave propagation over variable sea bed topography with mild slopes. The governing equation is discretized by the finite difference method. Based on the BI-CGSTAB technique, an attractive variant bf BI-Conjugate Gradients (BI-CG) method, the obtained linear algebraic system of equations is solved. Numerical experiments show that the BI-CGSTAB method is efficient for solving the elliptic mild slope equation. The results obtained by the BI-CGSTAB-Based method are much the same as those obtained by other authors with different solution methods, but the convergence rate is much faster than that of other methods.

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.

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.