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.

A stability evaluation method for deep-seated toppling in the upper Lancang river,Southwestern China

Deep-seated toppling in the upper reaches of the Lancang River,southwest China involves deformations exceeding 100 m in depth.The slope deformation is initiated by river downcutting and evolves distinctive characteristics with a depth of river incision.In this study,we propose a system for evaluating the stability of deep-seated toppled slopes in different evolutionary stages.This system contains identification criteria for each evolutionary stage and provides the corresponding stability evaluation methods.Based on the mechanical and kinematic analysis of slope blocks,the specific stage of slope movement can be identified in the field through outcrop mapping,in situ tests,surface displacement monitoring,and adit and borehole explorations.The stability evaluation methods are established based on the limiting equilibrium theory and the strain compatibility between the undisturbed zone and the toppled zone.Finally,several sample slopes in different evolution stages have been investigated to verify the applicability and accuracy of the proposed stability evaluation system.The results indicate that intense tectonic activity and rapid river incision lead to a maximum principal stress ratio exceeding 10 near the slope surface,thus triggering widespread toppling deformations along the river valley.When considering the losses of joint cohesion during the further rotation process,the safety factor of the slope drops by 7%e28%.The self-stabilization of toppling deformation can be recognized by the layer symmetry configuration after the free rotation of the deflected layers.Intensely toppled rock blocks mainly suffer sliding failures beyond the layer symmetry condition.The factor of safety of the K73 rockslide decreased from 1.17 to 0.87 by considering the development of the potential sliding surface and the toesaturated zone.

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.

Evaluation of toppling rock slopes using a composite cloud model with DEMATEL–CRITIC method

Safety evaluation of toppling rock slopes developing in reservoir areas is crucial. To reduce the uncertainty of safety evaluation, this study developed a composite cloud model, which improved the combination weights of the decision-making trial and evaluation laboratory (DEMATEL) and criteria importance through intercriteria correlation (CRITIC) methods. A safety evaluation system was developed according to in situ monitoring data. The backward cloud generator was used to calculate the numerical characteristics of a cloud model of quantitative indices, and different virtual clouds were used to synthesize some clouds into a generalized one. The synthesized numerical characteristics were calculated to comprehensively evaluate the safety of toppling rock slopes. A case study of a toppling rock slope near the Huangdeng Hydropower Station in China was conducted using monitoring data collected since operation of the hydropower project began. The results indicated that the toppling rock slope was moderately safe with a low safety margin. The composite cloud model considers the fuzziness and randomness of safety evaluation and enables interchange between qualitative and quantitative knowledge. This study provides a new theoretical method for evaluating the safety of toppling rock slopes. It can aid in the predication, control, and even prevention of disasters.

Deformation characteristics and mechanism of an impoundment-induced toppling landslide in Baihetan Reservoir based on multi-source remote sensing

Impoundment and water level fluctuations in reservoirs can induce landslides,especially during initial filling and drawdown.Since the initial impoundment in April 2021,multiple landslides have occurred within the Baihetan(BHT) reservoir,which is located at the boundary of Sichuan and Yunnan province in southeast China.However,due to the complex terrain conditions of reservoir banks,traditional landslide research methods,such as surveys,deformation monitoring,and geotechnical experiments,cannot be effectively conducted in a timely manner.In recent years,the development of remote sensing technology has addressed the shortcomings of traditional landslide research methods that may not be promptly carried out.In particular,interferometric synthetic aperture radar(InSAR) technology,capable of measuring subtle deformations,and portable small unmanned aerial vehicles(UAVs) have played a significant role.This study integrates multiple remote sensing data sources,including InSAR results,optical remote sensing images,digital elevation model(DEM),and UAV imagery,to investigate and elucidate the deformation characteristics and mechanisms of the Xiaomidi(XMD) landslide developed on the left bank of Jinsha River,about 100 km from the BHT hydropower dam site.The spatial deformation distribution of the landslide before and after impoundment and the deformation time series during filling were examined.Monitoring water level variation and analysing the deformation process of the landslide were achieved by employing continuous synthetic aperture radar(SAR) intensity images and DEM.UAV photography was utilized to assist in the verification of ground deformation.The findings suggest that the weak strength of the reversed bedding strata structure and the steep slope eroded by the Jinsha River are inherent factors that contribute to the development of the landslide.The rise in the water level leads to softening of the rock mass at the slope toe,thereby directly facilitating the acceleration of landslide deformation.The toppling deformation of the lower rock mass initiates the formation of surface cracks and localized uneven subsidence in the overlying colluvial deposits.

A two-dimensional limit equilibrium computer code for analysis of complex toppling slope failures

Evaluation of blocky or layered rock slopes against toppling failures has remained of great concern for engineers in various rock mechanics projects.Several step-by-step analytical solutions have been developed for analyzing these types of slope failures.However,manual application of these analytical solutions for real case studies can be time-consuming,complicated,and in certain cases even impossible.This study will first examine existing methods for toppling failure analyses that are reviewed,modified and generalized to consider the effects of a wide range of external and dead loads on slope stability.Next,based on the generalized presented formulae,a Windows form computer code is programmed using Visual C#for analysis of common types of toppling failures.Input parameters,including slope geometry,joint sets parameters,rock and soil properties,ground water level,dynamic loads,support anchor loads as well as magnitudes and forms of external forces,are first loaded into the code.The input data are then saved and used to graphically draw the slope model.This is followed by automatic identification of the toppling failure mode and a deterministic analysis of the slope stability against this failure mode.The results are presented using a graphical approach.The developed code allows probabilistic introduction of the input parameters via probability distribution functions(PDFs)and thus a probabilistic analysis of the toppling failure modes using Monte-Carlo simulation technique.This allows calculation of the probability of slope failure.Finally,several published case studies and typical examples are analyzed with the developed code.The outcomes are compared with those of the main references to assess the performance and robustness of the developed computer code.The comparisons demonstrate good agreement between the results.

Mechanism of toppling and deformation in hard rock slope: a case of bank slope of Hydropower Station, Qinghai Province, China

Recently, various toppling slopes have emerged with the development of hydropower projects in the western mountainous regions of China. The slope on the right bank of the Laxiwa Hydropower Station, located on the mainstream of the Yellow River in the Qinghai Province of Northwest China, is a typical hard rock slope. Further, its deformation characteristics are different from those of common natural hard rock toppling. Because this slope is located close to the dam of the hydropower station, its deformation mechanism has a practical significance. Based on detailed geological engineering surveys, four stages of deformation have been identified using discrete element numerical software and geological engineering analysis methods, including toppling creep, initial toppling deformation, intensified toppling deformation, and current slope formation. The spatial and time-related deformation of this site also exhibited four stages, including initial toppling, toppling development, intensification of toppling, and disintegration and collapse. Subsequently, the mechanism of toppling and deformation of the bank slope were studied. The results of this study exhibit important reference value for developing the prevention–control design of toppling and for ensuring operational safety in the hydropower reservoir area.

Toppling and sliding in volcanic bimrocks around Bayrakli(Izmir, Turkey)

Discontinuities have significant role on the behavior of rock masses with respect to several types of instabilities. Excavability, deformability, bearing capacity and slope stability of the rock masses should be investigated considering the discontinuity characteristics with particular emphasis on the geomechanical properties. Kinematic analyses mostly provide an insight to the instabilities, however the dimensions of the blocks bounded by discontinuities, their geomechanical properties and the geometry of the slope should also to be taken into account. The study area is in the abandoned stone quarry in Bayrakl? district of ?zmir residential area. Due to the excavations and discontinuity orientations, instabilities have occured. Miocene aged andesites and altered agglomerates of Yamanlar Volcanics form the bimrock mass. The study area is located within a sheared zone, bounded by strike slip fault zone. Intact andesite blocks were encountered in altered agglomerate matrix, forming a volcanic bimrock. Wedge and planar sliding and block toppling were observed within the area. Detailed discontinuity surveying was conducted, combined with core drillings. Several typical locations were detected where prismatic blocks of andesites are bound to experience block toppling. Such locations are nearby the top of the steep slopes. Agglomerates are subjected to mainly sliding and the blocks have been formed not by gravity but by peculiarities of thevolcanic sedimentation and, probably by subsequent tectonics. In order to determine the mechanism of the sliding and toppling in more details, the relation of the blocks and the slope geometry were investigated. Bimrock type volcanic rock masses sometimes do not tend to accommodate the general rules of toppling and sliding due to their anisotropic settings.

Deep-seated large-scale toppling failure in metamorphic rocks：a case study of the Erguxi slope in southwest China

Deep-seated large-scale toppling failure presents unique challenges in the study of natural slope deformation process in mountainous regions.An active deep-seated toppling process was identified in the Erguxi slope located in southwest China,which affected a large area and damaged critical transportation infrastructure with the volume of the deforming rock mass exceeding 24×10~6 m^3.It poses significant risks to the downstream Shiziping Hydropower Station by damming the Zagunao River.Field investigation and monitoring results indicate that the deformation of the Erguxi slope is in the advanced stage of deep-seated toppling process,with the formation of a disturbed belt but no identifiable master failure surface.It was postulated that the alternating tensile and shear strength associated with the hard/soft laminated rock strata of metasandstone and phyllite layers preclude the development of either a tensile or shear failure surface,which resulted in the continuous deformation and displacement without a catastrophic mass movement.The slope movement is in close association with the unfavorable geological conditions of the study area in addition to the construction of transportation infrastructure and the increase of the reservoir level.On the basis of the mechanism and intensity of the ongoing toppling deformation,a qualitative grading system was proposed to describe the toppling process and toevaluate the slope stability.This paper summarized the field observation and monitoring data on the toppling deformation for better characterizing its effect on the stability of the Erguxi slope.The qualitative grading system intends to provide a basis for quantitative study of large-scale deep-seated toppling process in metamorphic rocks.

Boundary effect of toppling failure based on three-dimensional mechanical model

Previous researches on the mechanical model of toppling failure mainly concentrated on twodimensional mechanical model(TwDM) analysis. The TwDM analysis assumes the width of the slab beam is unit width without considering the lateral constraint force. The assumed conditions are obviously different from the site conditions, thus there is a certain difference between the calculated results and the field work. A three-dimensional mechanical model(ThDM)of toppling failure was established, considering that the slab beam was mainly subject to self-weight, the frictional resistance of interlayer and lateral constraint force. Due to the progressive characteristics of toppling failure, the concept and the formula of the first fracture depth(FFD) of toppling was raised and constructed. The case study indicates that the ThDM is more effective and can be accurately used to calculate the toppling fracture depth of the slab beam. The FFD decreases proportionally with the increase of slab beam width. FFD grows fast when the slab beam width is less than 2.0 m and it tends to be stable when the slab beam width is above 2.0 m. The FFD decreases with the increase of the lateral constraint coefficient, indicating that the boundary condition of the free space is positively correlated with the stability and depth of toppling. This is a good explanation of the free space effect. This study provides a reference for the stability evaluation and prevention-control design of toppling slope in the future.

A Method for Evaluating the Maximum Bending Degree of Flexural Toppling Rock Masses Based on the Rock Tensile Strain-Softening Model

Flexural toppling occurs when a series of layered rock masses bend towards their free face.It is important to evaluate the maximum bending degree and the requirement of supports of flexural toppling rock mass to prevent rock mass cracking and even failure leading to a landslide.Based on the rock tensile strain-softening model,this study proposes a method for calculating the maximum curvature(C_(ppmax))of flexural toppling rock masses.By applying this method to calculate Cppmax of 9 types of rock masses with different hardness and rock layer thickness,some conclusions are drawn:(1)the internal key factors affecting C_(ppmax)are E^(⋆)(E^(⋆)=E_(ss)/E_(0),where E_(0)and E_(ss)are the mean deformation moduli of the rock before and after reaching its peak tensile strength,respectively),the strainεt corresponding to the tensile strength of rock,and the thickness(h)of rock layers;(2)hard rock layers are more likely to develop into block toppling than soft rock layers;and(3)thin rock layers are more likely to remain in flexural toppling state than thick rock layers.In addition,it is found that C_(ppmax)for flexural toppling rock masses composed of bedded rocks such as gneiss is related to the tensile direction.

Weight Analysis of Impact Factors of Interbedded Anti-Inclined Slopes Block-Flexure Toppling Based on Support Vector Regression

Block-flexure toppling failure is frequently encountered in interbedded anti-inclined rock(IAR)slopes,and seriously threatens the construction of hydropower infrastructure.In this study,we first investigated the Lean Reservoir area’s geological setting and the Linda landslide’s characteristics.Then,uniform design and random design were used to design 110 training datasets and 31 testing datasets,respectively.Afterwards,the toppling response was obtained by using the discrete element code.Finally,support vector regression was used to obtain the influence weights of 21 impact factors.The results show that the influence weight of the slope angle and rock formation dip angle on the toppling deformation among tertiary impact factors is 25.96%and 17.28%,respectively,which are much greater than the other 19 impact factors within the research range.For the primary impact factors,the influence weight is sorted from large to small as slope geometry parameters,joints parameters,and rock mechanics parameters.Joints parameters,especially the geometric parameters,cannot be ignored when evaluating the stability of IAR slopes.Through numerical simulation,it was qualitatively determined that failure surfaces of slopes were controlled by cross joints and that the rocks in the slope toe play a role in preventing slope deformation.

Dynamic Stability and Fuzzy Reliability Analysis of Toppling Perilous Rock Under Seismic Excitation

To predict the occurrence of the collapse disaster in toppling perilous rock under the action of bidirectional earthquakes,the dynamic stability and fuzzy reliability calculation method of toppling perilous rock under the action of bidirectional earthquakes is proposed.First,the mass viscoelasticity model is used to simulate two main control surfaces of toppling perilous rock,the seismic dynamic response model and motion equation of toppling perilous rock are established based on the D'Alembert principle,and the Newmark-β method is used to solve the dynamic motion equation.Then,the instability event of toppling perilous rock is considered a fuzzy event,the membership function expression of the stability coefficient of toppling perilous rock is determined based on the fuzzy failure criterion,the calculation equations of the toppling perilous rock dynamic stability coefficient and fuzzy reliability are established,and the fuzzy reliability evaluation method based on the probability distribution of reliability is proposed.Finally,the influence of different superposition modes of seismic excitation on the fuzzy reliability of toppling perilous rock is analyzed.The calculation results of toppling perilous rock in the engineering case show that the fuzzy reliability calculated after considering the fuzzy failure criterion is reduced by 10.73% to 25.66% compared with the classical reliability.Considering the bidirectional seismic excitation,the fuzzy reliability of toppling perilous rock is reduced by 5.46% to 14.89%.Compared with using the acceleration peak time encounter mode to superpose the seismic excitation,the fuzzy reliability of toppling perilous rock is reduced by 3.4% when the maximum action effect time encounter mode is adopted.

Numerical and theoretical study of large-scale failure of strata overlying sublevel caving mines with steeply dipping discontinuities

The deformation and fracture evolution mechanisms of the strata overlying mines mined using sublevel caving were studied via numerical simulations.Moreover,an expression for the normal force acting on the side face of a steeply dipping superimposed cantilever beam in the surrounding rock was deduced based on limit equilibrium theory.The results show the following:(1)surface displacement above metal mines with steeply dipping discontinuities shows significant step characteristics,and(2)the behavior of the strata as they fail exhibits superimposition characteristics.Generally,failure first occurs in certain superimposed strata slightly far from the goaf.Subsequently,with the constant downward excavation of the orebody,the superimposed strata become damaged both upwards away from and downwards toward the goaf.This process continues until the deep part of the steeply dipping superimposed strata forms a large-scale deep fracture plane that connects with the goaf.The deep fracture plane generally makes an angle of 12°-20°with the normal to the steeply dipping discontinuities.The effect of the constant outward transfer of strata movement due to the constant outward failure of the superimposed strata in the metal mines with steeply dipping discontinuities causes the scope of the strata movement in these mines to be larger than expected.The strata in the metal mines with steeply dipping discontinuities mainly show flexural toppling failure.However,the steeply dipping structural strata near the goaf mainly exhibit shear slipping failure,in which case the mechanical model used to describe them can be simplified by treating them as steeply dipping superimposed cantilever beams.By taking the steeply dipping superimposed cantilever beam that first experiences failure as the key stratum,the failure scope of the strata(and criteria for the stability of metal mines with steeply dipping discontinuities mined using sublevel caving)can be obtained via iterative computations from the key stratum,moving downward toward and upwards away from the goaf.

Comparisons between centrifuge and numerical modeling results for slope toppling failure

This paper presents series studies on the toppling mechanism by centrifuge tests and numerical simulations. Two different discrete element methods, i.e., the continuum-based discrete element method(CDEM) and the discontinuous deformation analysis(DDA), are adopted. The modeling results show that both the methods can accurately capture the failure modes of the centrifuge tests, including three distinct zones and two failure surfaces. Comparisons are made between the physical test and numerical simulation results. The critical inclination angle of the tilting table where the slope models are fixed on can be moderately predicted by the two methods, with different degrees of precision. The error between the test results and the simulated results is within 1% for the slope models without rock-bridges by both CDEM and DDA. However, it is amplified for the staggered-joint models that simulate the rock-bridges. With DDA, the average error is about 5%, and the maximum error is up to 17%. While with CDEM, the errors for the aligned-joint models are ranged from 1% to 6%, and it is from 10% to 29% for the staggered-joint models. The two numerical methods show the capability in simulating toppling failure of blocky rock mass with and without rock-bridges. The model with rock-bridges which provides a certain bending resistance is more stable than the one without any rock-bridge. In addition, the two failure surfaces were observed, which is different from the common understanding that only one failure surface appears.

Integrated simulation and monitoring to analyze failure mechanism of the anti-dip layered slope with soft and hard rock interbedding

The significant difference between the mechanical properties of soft rock and hard rock results in the complexity of the failure mode of the anti-dip layered slope with soft and hard rock interbedding.In order to reveal the landslide mechanism,taking the north slope of Fushun West Open-pit Mine as an example,this paper analyzed the failure mechanism of different landslides with monitoring and field surveys,and simulated the evolution of landslides.The study indicated that when the green mudstone(hard rock)of the anti-dip slope contains siltized intercalations(soft rock),the existence of weak layers not only aggravates the toppling deformation of anti-dip layered slope with high dip,but also causes the shear failure of anti-dip layered slope with stable low dip.The shear failure including subsidence induced sliding and wedge failure mainly exists in the unloading zone of the slope.Its failure depth and failure time were far less than that of toppling failure.In terms of the development characteristics of deformation,toppling deformation has the long-term and progressive characteristics,but shear failure deformation has the abrupt and transient characteristics.This study has deepened the understanding of such slope landslide mechanism,and can provide reference for similar engineering.

Smart and fast reinforcement design for anti-dip bedding rock slopes

Rock slopes are usually reinforced by a number of rock bolts due to the high efficiency and low price.However,where should the rock bolts be installed is still a troublesome issue.For anti-dip bedding rock slopes(ABRSs),the installation position of rock bolts is a controlling factor that determines the reinforcement effect.In this work,a theoretical method is firstly proposed for assessing the stability of ABRSs reinforced by rock bolts using a limit equilibrium model.A comparison of theoretical calculations and numerical results was conducted to test the correctness of the theoretical method.Based on the stability assessment of ABRSs,we introduce adaptive moment estimation method(Adam)to optimize the installation location of rock bolts.Using Adam optimizer,the optimal layout of rock bolts with the maximum factor of safety can be determined,and the factor of safety of the slope increases by about 25%using the same amount of rock bolts but with different installation locations.The proposed method enables the fast stability analysis and supporting design for reinforced ABRSs,which paves the way to smart supporting design of slopes.

Deformation and failure of a high-steep slope induced by multi-layer coal mining

During underground mining,accurate revelation on the deformation and failure mechanisms of a high-steep slope under multi-layer mining conditions facilitates the prevention and control of geological disasters in mines.Numerical simulation based on discrete element theory can be used to explore the characteristics and mechanism of action of deformation and failure of a slope under complex geological and multi-layer mining conditions.By utilising PFC2 D(particle flow code) software,the deformation and failure characteristics of a high-steep slope in Faer Coal Mine in Guizhou Province,China were investigated.Additionally,the mechanism of influence of different numbers of mining layers on the deformation and failure of the high and steep slope was elucidated.The result showed that after the goaf passed by the slope toe,multi-layer mining aggravated the subsidence and deformation of the slope toe:the slope toppled forward as it sank.The toppling of the slope changed the slope structures:the strata in the front of the slope were transformed from anti-dip to down-dip features.Extruded by collapsedtoppled rock mass,the slope toe and the rock mass located in the lower part of the slope toe generally exhibited a locking effect on the slope.Multi-layer mining degraded the overall stability of the slope,in that the total displacement of the slope was much greater than the total mining thickness of the coal seams.Based on the aforementioned research,ideas for preventing and controlling geological disasters during mining operations under a high-steep slope were proposed.

Design of a Mobile Mechanism for Missing Miner Search Robots in Underground Mines

A mobile mechanism with four tracked-units for a missing miner search robot (MMSR) is presented, with a design based on the terrain features and atrocious environment of an underground mine. Its structure and working prin- ciple is discussed. The four tracked-units are controlled independently and driven cooperatively. By means of two DC motors being controlled respectively, one tracked-unit can accomplish two types of driving mode: tracked travel and in- tegral unit legged rotation (IULR), forming a track-legged compound function mechanism. Its capabilities of surmount- ing obstacles and its toppling stability in underground mines have also been analyzed. The results show that the mobile mechanism can directly surmount an obstacle of the height less than the length of one tracked-unit and get across a raceway with a span less than the length of one tracked-unit by using tracked travel and IULR. Its unstable slope angle is 51.3°. Toppling stability is determined by its structural size, moving direction and slope angle. IULR of four tracked-units can adjust the robot’s posture and then enhance toppling stability or assist in surmounting obstacles. Its track-legged compound function mechanism makes it suitable for working in underground mines.

To Topple Trees for Subways or Not?

The tall trees in Nanjing,capital city of east China’s Jiangsu Province,are an amenity local people boast about.In1928,in order to commemorate Sun Yat-sen,founder o the Kuomintang,hundreds