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.

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.

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.

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 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.

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.

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.

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.

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.

Slope Stability Evaluations by Limit Equilibrium and Finite Element Methods Applied to a Railway in the Moroccan Rif

Since 1930, the analysis of slope stability is done according to the limit equilibrium approach. Several methods were developed of which certain remain applicable because of their simplicity. However, major disadvantages of these methods are (1) they do not take into account the soil behavior and (2) the complex cases cannot be studied with precision. The use of the finite elements in calculations of stability has to overcome the weakness of the traditional methods. An analysis of stability was applied to a slope, of complex geometry, composed of alternating sandstone and marls using finite elements and limit equilibrium methods. The calculation of the safety factors did not note any significant difference between the two approaches. Various calculations carried out illustrate perfectly benefits that can be gained from modeling the behavior by the finite elements method. In the finite elements analysis, the shape of deformations localization in the slope is nearly circular and confirms the shape of the failure line which constitutes the basic assumption of the analytical methods. The integration of the constitutive laws of soils and the use of field’s results tests in finite elements models predict the failure mode, to better approach the real behavior of slope soil formations and to optimize its reinforcement.

An Artificial Neural Network-Based Response Surface Method for Reliability Analyses of c-φ Slopes with Spatially Variable Soil

This paper presents an artificial neural network（ANN）-based response surface method that can be used to predict the failure probability of c-φslopes with spatially variable soil.In this method,the Latin hypercube sampling technique is adopted to generate input datasets for establishing an ANN model;the random finite element method is then utilized to calculate the corresponding output datasets considering the spatial variability of soil properties;and finally,an ANN model is trained to construct the response surface of failure probability and obtain an approximate function that incorporates the relevant variables.The results of the illustrated example indicate that the proposed method provides credible and accurate estimations of failure probability.As a result,the obtained approximate function can be used as an alternative to the specific analysis process in c-φslope reliability analyses.

Evolution of economic linkage network of the cities and counties on the northern slope of the Tianshan Mountains,China

The exchanges between cities and counties in the northern slope economic belt of Tianshan Mountains(NSEBTM)are increasingly frequent and the economic linkages are increasingly close,but the spatial distribution of economic development and linkages among the cities and counties within NSEBTM is uneven.Therefore,it is of great significance to study the evolution of spatial-temporal pattern of the economic linkage network of cities and counties on NSEBTM to promote the coordinated and integrated development of the regional economy on NSEBTM.In this study,we used the modified gravity model and social network analysis method to analyze the spatio-temporal evolution characteristics of the economic linkage network structure of cities and counties on NSEBTM in 2000,2010,and 2020.The results showed that the comprehensive development quality level of cities and counties on NSEBTM increased from 2000 to 2020,its growth rate also increased,and its gap between cities and counties continued expanding.Both the spatial distribution patterns of the comprehensive development quality level of cities and counties on NSEBTM in 2000 and 2010 were presented as“high in the middle and low at both ends”,while the spatial distribution pattern of 2020 was exhibited as“high value and low value staggered”.The total amount of external economic linkages of cities and counties on NSEBTM showed an obvious upward trend,and its gap between cities and counties continued expanding,presenting a pattern of“a strong middle section and weak ends”.The direction of economic linkages of NSEBTM existed obvious central orientation and geographical proximity.The density of economic linkage network of NSEBTM increased from 2000 to 2020,and the structure of economic linkage network changed from single-core structure centered with Urumqi City to multicore structure centered with Urumqi City,Karamay City,Shihezi City,and Changji City,shifting from unbalanced development to balanced development.In the future,we should accelerate the construction of urban agglomeration on NSEBTM,cultivate a modern Urumqi metropolitan area,improve comprehensive development quality of the cities and counties at the eastern and western ends,strengthen the intensity of economic linkages between cities and counties,optimize the economic linkage network,and promote the coordinated and integrated development of regional economy.

Fe-Al-V三元系富铁角热力学优化

采用CALPHAD方法对Fe-Al-V三元系富铁角进行热力学优化,并首次提出采用三亚点阵模型描述三元金属间化合物L21相,即(Fe)2(Al,Fe)1(Fe,V)1。基于可靠的边界二元系热力学描述,结合Fe-Al-V三元系富铁角试验数据,通过优化获得了一套自洽准确的热力学模型参数。优化的模型参数可较满意地重现Fe-Al-V三元系富铁角的相平衡关系,弥补了商业数据库无法对其进行描述的不足,为钒微合金化轻质钢的设计开发提供可靠的理论基础。

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 (φ) 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.

3D stability analysis method of concave slope based on the Bishop method

In order to study the stability control mechanism of a concave slope with circular landslide, and remove the influence of differences in shape on slope stability, the limit analysis method of a simplified Bishop method was employed. The sliding body was divided into strips in a three-dimensional model, and the lateral earth pressure was put into mechanical analysis and the three-dimensional stability analysis methods applicable for circular sliding in concave slope were deduced. Based on geometric structure and the geological parameters of a concave slope, the influence rule of curvature radius and the top and bottom arch height on the concave slope stability were analyzed. The results show that the stability coefficient decreases after growth, first in the transition stage of slope shape from flat to concave, and it has been confirmed that there is a best size to make the slope stability factor reach a maximum. By contrast with average slope, the stability of a concave slope features a smaller range of ascension with slope height increase, which indicates that the enhancing effect of a concave slope is apparent only with lower slope heights.

Strategies for Advancing Road Construction Slope Stability: Unveiling Innovative Techniques for Managing Unstable Terrain

This comprehensive review paper explores various aspects of geotechnical engineering, with a focus on the management of unstable terrains, numerical methods for solving complex soil and consolidation problems, rheological analysis of suspensions and muddy soils, and stability analysis of slopes. It begins by examining the unique physicochemical properties of cohesive sediments, including cohesion and specific surface area. The temporal evolution of deposit concentration and average bed concentration in unstable terrains is discussed, along with settling behavior of isolated particles and hindered settling using empirical equations. Key sedimentation theories, such as Kynch’s theory, and geotechnical consolidation theories, including Terzaghi’s consolidation equation and Gibson’s theory, are presented. The investigation interrelates these theories and principles to offer a holistic view of managing unstable terrains. It also addresses the challenges associated with experimental determination of constitutive relationships and presents alternative simplification methods proposed by researchers. Additionally, it delves into numerical methods for solving nonlinear partial differential equations governing soil behavior, emphasizing the need for numerical frameworks and discussing various techniques and associated challenges. The rheological analysis section covers material flow behavior, rheological behavior models, and the rheological properties of water and cohesive sediment mixtures. Fundamental geotechnical calculations, constitutive laws, and failure criteria are explained, highlighting their relevance in geotechnical engineering applications. This paper provides a multidimensional perspective on geotechnical engineering, offering valuable insights into soil properties, consolidation processes, numerical methods, rheological analysis, and slope stability assessment for professionals in the field.

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.

Slope analysis based on local strength reduction method and variable-modulus elasto-plastic model

Employing an ideal elasto-plastic model,the typically used strength reduction method reduced the strength of all soil elements of a slope.Therefore,this method was called the global strength reduction method(GSRM).However,the deformation field obtained by GSRM could not reflect the real deformation of a slope when the slope became unstable.For most slopes,failure occurs once the strength of some regional soil is sufficiently weakened; thus,the local strength reduction method(LSRM)was proposed to analyze slope stability.In contrast with GSRM,LSRM only reduces the strength of local soil,while the strength of other soil remains unchanged.Therefore,deformation by LSRM is more reasonable than that by GSRM.In addition,the accuracy of the slope's deformation depends on the constitutive model to a large degree,and the variable-modulus elasto-plastic model was thus adopted.This constitutive model was an improvement of the Duncan–Chang model,which modified soil's deformation modulus according to stress level,and it thus better reflected the plastic feature of soil.Most importantly,the parameters of the variable-modulus elasto-plastic model could be determined through in-situ tests,and parameters determination by plate loading test and pressuremeter test were introduced.Therefore,it is easy to put this model into practice.Finally,LSRM and the variable-modulus elasto-plastic model were used to analyze Egongdai ancient landslide.Safety factor,deformation field,and optimal reinforcement measures for Egongdai ancient landslide were obtained based on the proposed method.

Time-variant reliability analysis of three-dimensional slopes based on Support Vector Machine method

In the reliability analysis of slope, the performance functions derived from the most available stability analysis procedures of slopes are usually implicit and cannot be solved by first-order second-moment approach. A new reliability analysis approach was presented based on three-dimensional Morgenstern-Price method to investigate three-dimensional effect of landslide in stability analyses. To obtain the reliability index, Support Vector Machine (SVM) was applied to approximate the performance function. The time-consuming of this approach is only 0.028% of that using Monte-Carlo method at the same computation accuracy. Also, the influence of time effect of shearing strength parameters of slope soils on the long-term reliability of three-dimensional slopes was investigated by this new approach. It is found that the reliability index of the slope would decrease by 52.54% and the failure probability would increase from 0.000 705% to 1.966%. In the end, the impact of variation coefficients of c and f on reliability index of slopes was taken into discussion and the changing trend was observed.

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%.