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.

A method to interpret fracture aperture of rock slope using adaptive shape and unmanned aerial vehicle multi-angle nap-of-the-object photogrammetry

The aperture of natural rock fractures significantly affects the deformation and strength properties of rock masses,as well as the hydrodynamic properties of fractured rock masses.The conventional measurement methods are inadequate for collecting data on high-steep rock slopes in complex mountainous regions.This study establishes a high-resolution three-dimensional model of a rock slope using unmanned aerial vehicle(UAV)multi-angle nap-of-the-object photogrammetry to obtain edge feature points of fractures.Fracture opening morphology is characterized using coordinate projection and transformation.Fracture central axis is determined using vertical measuring lines,allowing for the interpretation of aperture of adaptive fracture shape.The feasibility and reliability of the new method are verified at a construction site of a railway in southeast Tibet,China.The study shows that the fracture aperture has a significant interval effect and size effect.The optimal sampling length for fractures is approximately 0.5e1 m,and the optimal aperture interpretation results can be achieved when the measuring line spacing is 1%of the sampling length.Tensile fractures in the study area generally have larger apertures than shear fractures,and their tendency to increase with slope height is also greater than that of shear fractures.The aperture of tensile fractures is generally positively correlated with their trace length,while the correlation between the aperture of shear fractures and their trace length appears to be weak.Fractures of different orientations exhibit certain differences in their distribution of aperture,but generally follow the forms of normal,log-normal,and gamma distributions.This study provides essential data support for rock and slope stability evaluation,which is of significant practical importance.

Dynamic response and failure process of horizontal-layered fractured structure rock slope under strong earthquake

Rock slope with horizontal-layered fractured structure(HLFS)has high stability in its natural state.However,a strong earthquake can induce rock fissure expansion,ultimately leading to slope failure.In this study,the dynamic response,failure mode,and spectral characteristics of rock slope with HLFS under strong earthquake conditions were investigated based on the large-scale shaking table model test.On this basis,multiple sets of numerical calculation models were further established by UDEC discrete element program.Five influencing factors were considered in the parametric study of numerical simulations,including slope height,slope angle,bedding-plane spacing and secondary joint spacing as well as bedrock dip angle.The results showed that the failure process of rock slope with HLFS under earthquake action is mainly divided into four phases,i.e.,the tensile crack of the slope shoulder joints and shear dislocation at the top bedding plane,the extension of vertical joint cracks and increase of shear displacement,the formation of step-through sliding surfaces and the instability,and finally collapse of fractured rock mass.The acceleration response of slopes exhibits elevation amplification effect and surface effect.Numerical simulations indicate that the seismic stability of slopes with HLFS exhibits a negative correlation with slope height and angle,but a positive correlation with bedding-plane spacing,joint spacing,and bedrock dip angle.The results of this study can provide a reference for seismic stability evaluation of weathered rock slopes.

A semi-infinite beam theoretical model on predicting rock slope subsidence induced by underground mining

When the mining goaf is close to the cliff,rock slope subsidence induced by underground mining is significantly affected by its boundary conditions.In this study,an analytical method is proposed by considering the key strata as a semi-infinite Euler-Bernoulli beam rested on a Winkler foundation with a local subsidence area.The analytical solutions of deflection are derived by analyzing the boundary and continuity conditions of the cliff.Then,the analytical solutions are verified by the results from experimental tests,FEM and InSAR,respectively.After that,the influence of changing parameters on deflections is studied with sensitivity analysis.The results show that the distance between goaf and cliff significantly affects the deflection of semi-infinite beam.The response of semi-infinite beam is obviously determined by the length of goaf and the bending stiffness of beam.The comparisons between semi-infinite beam and infinite beam illustrate the ascendancy of the improved model in such problems.

An approach for determination of lateral limit angle in kinematic planar sliding analysis for rock slopes

Planar sliding is one of the frequently observed types of failure in rock slopes.Kinematic analysis is a classic and widely used method to examine the potential failure modes in rock masses.The accuracy of planar sliding kinematic analysis is significantly influenced by the value assigned to the lateral limit angleγlim.However,the assignment ofγlim is currently used generally based on an empirical criterion.This study aims to propose an approach for determining the value ofγlim in deterministic and probabilistic kinematic planar sliding analysis.A new perspective is presented to reveal thatγlim essentially influences the probability of forming a potential planar sliding block.The procedure to calculate this probability is introduced using the block theory method.It is found that the probability is correlated with the number of discontinuity sets presented in rock masses.Thus,different values ofγlim for rock masses with different sets of discontinuities are recommended in both probabilistic and deterministic planar sliding kinematic analyses;whereas a fixed value ofγlim is commonly assigned to different types of rock masses in traditional method.Finally,an engineering case was used to compare the proposed and traditional kinematic analysis methods.The error rates of the traditional method vary from 45%to 119%,while that of the proposed method ranges between 1%and 17%.Therefore,it is likely that the proposed method is superior to the traditional one.

Limit load and failure mechanisms of a vertical Hoek-Brown rock slope

The problem considered in this short note is the limit load determination of a vertical rock slope.The classical limit theorem is employed with the use of adaptive finite elements and nonlinear programming to determine upper and lower bound limit loads of a Hoek-Brown vertical rock slope.The objective function of the mathematical programming problem is such as to optimize a boundary load,which is known as the limit load,resembling the ultimate bearing capacity of a strip footing.While focusing on the vertical slope,parametric studies are carried out for several dimensionless ratios such as the dimensionless footing distance ratio,the dimensionless height ratio,and the dimensionless rock strength ratio.A comprehensive set of design charts is presented,and failure envelopes shown with the results explained in terms of three identified failure mechanisms,i.e.the face,the toe,and the Prandtl-type failures.These novel results can be used with great confidence in design practice,in particularly noting that the current industry-based design procedures for the presented problem are rarely found.

Stability of bedded rock slopes subjected to hydro-fluctuation and associated strength deterioration

Reservoir-induced earthquakes(RIEs)occur frequently in the Three Gorges Reservoir Area(TGRA)and the rock mass strength of the hydro-fluctuation belt(HFB)deteriorates severely due to the reservoirinduced seismic loads.Three models of typical bedded rock slopes(BRSs),i.e.gently(GIS),moderately(MIS),and steeply(SIS)inclined slopes,were proposed according to field investigations.The dynamic response mechanism and stability of the BRSs,affected by the rock mass deterioration of the HFB,were investigated by the shaking table test and the universal distinct element code(UDEC)simulation.Specifically,the amplification coefficient of the peak ground acceleration(PGA)of the slope was gradually attenuated under multiple seismic loads,and the acceleration response showed obvious“surface effect”and“elevation effect”in the horizontal and vertical directions,respectively.The“S-type”cubic function and“steep-rise type”exponential function were used to characterize the cumulative damage evolution of the slope caused by microseismic waves(low seismic waves)and high seismic waves,respectively.According to the dynamic responses of the acceleration,cumulative displacement,rock pressure,pore water pressure,damping ratio,natural frequency,stability coefficient,and sliding velocity of the slope,the typical evolution processes of the dynamic cumulative damage and instability failure of the slope were generalized,and the numerical and experimental results were compared.Considering the dynamic effects of the slope height(SH),slope angle(SA),bedding plane thickness(BPT),dip angle of the bedding plane(DABP),dynamic load amplitude(DLA),dynamic load frequency(DLF),height of water level of the hydro-fluctuation belt(HWLHFB),degradation range of the hydro-fluctuation belt(DRHFB),and degradation shape of the hydro-fluctuation belt(DSHFB),the sensitivity of factors influencing the slope dynamic stability using the orthogonal analysis method(OAM)was DLA>DRHFB>SA>SH>DLF>HWLHFB>DSHFB>DABP>BPT.

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.

Stability analysis of intermittently jointed rock slopes based on the stepped failure mode

In practical engineering,due to the noncontinuity characteristics of joints in rock slopes,in addition to plane failure,stepped sliding failure may occur for intermittently jointed rock slopes.Especially for intermittently bedding jointed rock slopes,the correlation and difference in strength parameters between joints and rock bridges,along with the various failure modes and intermittency of rock bridges,contribute to the complexity of stepped failure modes and the unpredictability of failure regions.Based on the upper-bound limit analysis method and multi-sliders step-path failure mode,considering the shear and tensile failure of rock bridges and the weakened relationship between the strength parameters of rock bridges and jointed surfaces,by introducing the modified M-C failure criterion and the formula for calculating the energy consumption of tensile failure of rock bridges,two failure mechanisms are constructed to obtain the safety factor(F_(s))of intermittently jointed rock slopes.The sequential quadratic programming method is used to obtain the optimal upper-bound solution for F_(s).The influence of multiple key parameters(slope height H,horizontal distance L,Slope angleβ,shear strength parameters of the rock bridgeφr and cr,Dimensionless parameter u,weakening coefficients of the internal friction angle and cohesion between the rock bridges and joint surfaces Kφand Kc)on the stability analysis of intermittently jointed rock slopes under the shear failure mode of rock bridges as well as under the tensile failure mode is also explored.The reliability of the failure mechanisms is verified by comparative analysis with theoretical results,numerical results,and landslide cases,and the variation rules of F_(s)with each key parameter are obtained.The results show that F_(s) varies linearly withφr and cr of the rock bridge and with K_(φ)and K_(c),whereas F_(s)changes nonlinearly with H and L.In particular,with the increase in Kφand Kc,Fs increases by approximately 52.78%and 171.02%on average,respectively.For rock bridge tensile failure,F_(s) shows a nonlinearly positive correlation withφr,cr,Kφand Kc.In particular,with the increase in Kφand Kc,Fs increases by approximately 13%and 61.69%on average,respectively.Fs decreases rapidly with increasing slope gradientβand decreasing dimensionless parameterμ.When Kφand Kc are both less than 1.0,the stepped sliding surface occurs more easily than the plane failure surface,especially in the case of tensile failure of the rock bridge.In addition,rock slopes with higher strength parameters,taller heights,and greater weakening coefficients are prone to rock bridge tension failure with lower Fs,and more attention should be given to the occurrence of such accidents in actual engineering.

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.

Model test and numerical simulation on the dynamic stability of the bedding rock slope under frequent microseisms

Shake table testing was performed to investigate the dynamic stability of a mid-dip bedding rock slope under frequent earthquakes. Then, numerical modelling was established to further study the slope dynamic stability under purely microseisms and the influence of five factors, including seismic amplitude, slope height, slope angle, strata inclination and strata thickness, were considered. The experimental results show that the natural frequency of the slope decreases and damping ratio increases as the earthquake loading times increase. The dynamic strength reduction method is adopted for the stability evaluation of the bedding rock slope in numerical simulation, and the slope stability decreases with the increase of seismic amplitude, increase of slope height, reduction of strata thickness and increase of slope angle. The failure mode of a mid-dip bedding rock slope in the shaking table test is integral slipping along the bedding surface with dipping tensile cracks at the slope rear edge going through the bedding surfaces. In the numerical simulation, the long-term stability of a mid-dip bedding slope is worst under frequent microseisms and the slope is at risk of integral sliding instability, whereas the slope rock mass is more broken than shown in the shaking table test. The research results are of practical significance to better understand the formation mechanism of reservoir landslides and prevent future landslide disasters.

Failure precursor of surrounding rock mass around cross tunnel in high-steep rock slope

The stability of the surrounding rock mass around cross tunnel in the right bank slope of Dagangshan hydropower station, in the southwestern China, was analyzed by microseismic monitoring as well as numerical simulations. The realistic failure process analysis code （abbreviated as RFPA3D） was employed to reproduce the initiation, propagation, coalescence and interactions of micro-fractures, the evolution of associated stress fields and acoustic emission （AE） activities during the whole failure processes of the surrounding rock mass around cross tunnel. Combined with microseismic activities by microseismic monitoring on the fight bank slope, the spatial-temporal evolution and the micro-fracture precursor characteristics during the complete process of progressive failure of the surrounding rock mass around cross tunnel were discussed and the energy release law of the surrounding rock mass around the cross tunnel was obtained. The result shows that the precursor characteristic of microfractures occurring in rock mass is an effective approach to early warn catastrophic damage of rock mass around cross tunnel. Moreover, the heterogeneity of rock mass is the source and internal cause of the failure precursor of rock mass.

Force analysis of pile foundation in rock slope based on upper-bound theorem of limit

Based on the characteristic that the potential sliding surfaces of rock slope are commonly in the shape of either line or fold line,analysis thought of conventional pile foundation in the flat ground under complex load condition was applied and the upper-bound theorem of limit analysis was used to compute thrust of rock layers with all possible distribution shapes. The interaction of slope and pile was considered design load in terms of slope thrust,and the finite difference method was derived to calculate inner-force and displacement of bridge pile foundation in rock slope under complex load condition. The result of example shows that the distribution model of slope thrust has certain impact on displacement and inner-force of bridge pile foundation. The maximum displacement growth rate reaches 54% and the maximum moment and shear growth rates reach only 15% and 20%,respectively,but the trends of inner-force and displacement of bridge pile foundation are basically the same as those of the conventional pile foundation in the flat ground. When the piles bear the same level lateral thrust,the distribution shapes of slope thrust have different influence on inner-force of pile foundation,especially the rectangle distribution,and the triangle thrust has the smallest displacement and inner-force of pile foundation.

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.

Influence of blasting on the properties of weak intercalation of a layered rock slope

A precondition for correctly analyzing the stability of a slope and designing its bracing structure is to study and determine the influence of excavation blasting on the properties of weak intercalation in the layered rock slope. On the basis of in-situ stratification-cracking blasting tests, the properties of weak intercalation were investigated using the LS-DYNA3D program. The displacement distribution and compactness of weak intercalation at different positions away from the charge center and their various laws are discussed. The critical displacement of stratification-cracking （0.1 mm） was obtained, and an approximate expression of compactness were deduced. Furthermore, through the simulation of a layered rock blasting under the same geological conditions, the stratification-cracking effect of deep-hole blasting on the properties of weak intercalation was compared with that of short-hole blasting, and the influencing differences, in addition to their causes, were analyzed. The results indicated that the blasting cavity of weak intercalation in short-hole blasting with a radius of 40 mm was nearly a circle, whose radius was about 28.7 cm; whereas in deep-hole blasting with a radius of 150 mm, the shape of the blasting cavity was different from that in short-hole blasting, the radius of the cavity behind the charge （89.1 cm） was further smaller than those of the other three （138.7 cm）, and there were sharp crinkles on the surface of weak intercalation. When the distance from the charge center （DCC） was less than 40 and 150 cm in short-hole and deep-hole blasting, respectively, the displacement of weak intercalation was reduced remarkably with the increase in DCC.

Microseismic monitoring and numerical simulation on the stability of high-steep rock slopes in hydropower engineering

For high-steep slopes in hydropower engineering, damage can be induced or accumulated due to a seriesof human or natural activities, including excavation, dam construction, earthquake, rainstorm, rapid riseor drop of water level in the service lifetime of slopes. According to the concept that the progressivedamage （microseismicity） of rock slope is the essence of the precursor of slope instability, a microseismicmonitoring system for high-steep rock slopes is established. Positioning accuracy of the monitoringsystem is tested by fixed-position blasting method. Based on waveform and cluster analyses of microseismicevents recorded during test, the tempo-spatial distribution of microseismic events is analyzed.The deformation zone in the deep rock masses induced by the microseismic events is preliminarilydelimited. Based on the physical information measured by in situ microseismic monitoring, an evaluationmethod for the dynamic stability of rock slopes is proposed and preliminarily implemented bycombining microseismic monitoring and numerical modeling. Based on the rock mass damage modelobtained by back analysis of microseismic information, the rock mass elements within the microseismicdamage zone are automatically searched by finite element program. Then the stiffness and strengthreductions are performed on these damaged elements accordingly. Attempts are made to establish thecorrelation between microseismic event, strength deterioration and slope dynamic instability, so as toquantitatively evaluate the dynamic stability of slope. The case studies about two practical slopes indicatethat the proposed method can reflect the factor of safety of rock slope more objectively. Numericalanalysis can help to understand the characteristics and modes of the monitored microseismic events inrock slopes. Microseismic monitoring data and simulation results can be used to mutually modify thesensitive rock parameters and calibrate the model. Combination of microseismic monitoring and numericalsimulation provides a more objective basis for the numerical model and parameters and a solidmechanical foundation for the microseismic monitoring.

Physical Modeling of Landslide Mechanism in Oblique Thick-Bedded Rock Slope: A Case Study

The Jiweishan landslide illustrates the failure pattern of an apparent dip slide of an oblique thick-bedded rockslide. Centrifugal modeling was performed using a model slope consisting of four sets of joints to investigate the landslide initiation mechanism. Crack strain gauges pasted between the slide blocks and the base failed in sequence from the rear to the front as the centrifugal acceleration increased. When the acceleration reached 16.3g, the instantaneous failure of the key block in the front triggered the apparent dip slide of all blocks. The physical modeling results and previous studies suggest that the strength reduction in the weak layer and the failure of the key block are the main reasons for the Jiweishan landslide. The centrifuge experiment validated the previously proposed driving-blocks-key-block model of apparent dip slide in oblique with inclined bedding rock slopes. In addition, the results from limit equilibrium method and centrifuge test suggest that even though the failure of the key block in the front is instantaneous, a progressive stable-unstable transition exists.

Experimental study on instability mechanism and critical intensity of rainfall of high-steep rock slopes under unsaturated conditions

Two critical factors,namely intense precipitation and intricate excavation,can trigger rock mass disasters in mining operations.In this study,an indoor rainfall system was developed to precisely regulate the flow and intensity of precipitation.A large-scale model experiment was conducted on a self-designed physical simulation experiment platform to investigate the failure and instability of high-steep rock slopes under unsaturated conditions.The real-time reproduction of the progressive failure process in high-steep rock slopes enabled the determination of the critical rainfall intensity and revealed the mechanism underlying slope instability.Experiment results indicated that rainfall may be the primary factor contributing to rock mass instability,while continuous pillar mining exacerbates the extent of rock mass failure.The critical failure stage of high-steep rock slopes occurs at a rainfall intensity of 40 mm/h,whereas a rainfall exceeding 50 mm can induce critical instability and precipitation reaching up to 60 mm will result in slope failure.The improved region growing segmentation method(IRGSM)was subsequently employed for image recognition of rock mass deformation in underground mines.Herein an error comparison with the simple linear iterative cluster(SLIC)superpixel method and the original region growing segmentation method(ORGSM)showed that the average identification error in the X and Y directions by the method was reduced significantly(1.82%and 1.80%in IRGSM;4.70%and 6.26%in SLIC;9.45%and 12.40%in ORGSM).Ultimately,the relationship between rainfall intensity and failure probability was analyzed using the Monte Carlo method.Moreover,the stability assessment criteria of rock slope under unsaturated condition were quantitatively and accurately evaluated.

Effect of the inclined weak interlayers on the rainfall response of a bedded rock slope

Engineering experience shows that outward dipping bedded rock slopes, especially including weak interlayers, are prone to slide under rainfall conditions. To investigate the effect of inclined weak interlayers at various levels of depth below the surface on the variation of displacements and stresses in bedded rock slopes, four geo- mechanical model tests with artificial rainfall have been conducted. Displacements, water content as well as earth pressure in the model were monitored by means of various FBG （Fiber Bragg Grating） sensors. The results showed that the amount of displacement of a slope with a weak interlayer is 2.8 to 6.2 times larger than that of a slope without a weak interlayer during one rainfall event. Furthermore, the position of the weak interlayer in terms of depth below the surface has a significant effect on the zone of deformation in the model. In the slope with a high position weak interlayer, the recorded deformation was larger in the superficial layer of the model and smaller in the frontal portion than in the slope with a low position weak interlayer. The slope with two weak interlayers has the largest deformation at all locations of all test slopes. The slope without a weak interlayer was only saturated in its superficial layer, while the displacement decreased with depth. That was different from all slopes with a weak interlayer in which the largest displacement shifted from the superficial layer to the weak interlayer when rainfall persisted. Plastic deformation of the weak interlayer promoted the formation of cracks which caused more water to flow into the slope, thus causing larger deformation in the slope with weak interlayers. In addition, the slide thrust pressure showed a vibration phenomenon o.5 to 1 hour ahead of an abrupt increase of the deformation, which was interpreted as a predictor for rainfall-induced failure of bedded rock slopes.

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.