A methodology was proposed for the design of micropiles to increase earth slopes stability. An analytic model based on bearn-colurnn equation and an existing P-y curve method was set up and used to find the shear capa...A methodology was proposed for the design of micropiles to increase earth slopes stability. An analytic model based on bearn-colurnn equation and an existing P-y curve method was set up and used to find the shear capacity of the micropile. Then, a step-by-step design procedure for stabilization of earth slope with rnicropiles was introduced, involving six main steps： 1） Choosing a location for the rnicropiles within the existing slope; 2） Selecting micropile cross section; 3） Estimating length of rnicropile; 4） Evaluating shear capacity of mieropiles; 5） Calculating spacing required to provide force to stabilize the slope; 6） Designing the concrete cap beam. The application of the method to an embankment landslide in Qinghai Province was described in detail. In the final design, three rows of rnicropiles were adopted as a group and a total of 126 rnicropiles with 0.23 m in diameter were used. The micropile length ranged between 15 and 18 m, with the spacing 1.5 m at in-row direction. The monitoring data indicate that slope movement has been effectively controlled as a result of the slope stabilization measure, which verifies the reasonability of the design method.展开更多
The discrete fracture system of a rock mass plays a crucial role in controlling the stability of rock slopes.To fully account for the geometric shape and distribution characteristics of jointed rock masses,terrestrial...The discrete fracture system of a rock mass plays a crucial role in controlling the stability of rock slopes.To fully account for the geometric shape and distribution characteristics of jointed rock masses,terrestrial laser scanning(TLS)was employed to acquire high-resolution point-cloud data,and a developed automatic discontinuity-identification technology was coupled to automatically interpret and characterize geometric information such as orientation,trace length,spacing,and set number of the discontinuities.The discrete element method(DEM)was applied to study the influence of the geometric morphology and distribution characteristics of discontinuities on slope stability by generating a discrete fracture network(DFN)with the same statistical characteristics as the actual discontinuities.Based on slope data from the Yebatan Hydropower Station,a simulation was conducted to verify the applicability of the automatic discontinuity identification technology and the discrete fracture network-discrete element method(DFN-DEM).Various geological parameters,including trace length,persistence,and density,were examined to investigate the morphological evolution and response characteristics of rock slope excavation under different joint combination conditions through simulation.The simulation results indicate that joint parameters affect slope stability,with density having the most significant impact.The impact of joint parameters on stability is relatively small within a reasonable range but becomes significant beyond a certain threshold,further validating that the accuracy of field geological surveys is critical for simulation.This study provides a scientific basis for the construction of complex rock slope models,engineering assessments,and disaster prevention and mitigation,which is of great value in both theory and engineering applications.展开更多
Landslides triggered by high gas pressure represent a distinct geotechnical hazard,especially in scenarios without significant rainfall.Recent studies have revealed that high-pressure gas accumulation within slopes ca...Landslides triggered by high gas pressure represent a distinct geotechnical hazard,especially in scenarios without significant rainfall.Recent studies have revealed that high-pressure gas accumulation within slopes can be a dominant trigger for large-scale failures although the processes behind this remain not well understood.This study examines how unsaturated soil slopes fail under high gas pressure using a combination of laboratory experiments and numerical simulations.A key discovery is that gas pressure changes slope stability by redistributing pore fluids and altering effective stress,with distinct depthdependent effects.Moreover,a novel concept of critical stable gas pressure(P_(ac))is proposed as a practical threshold for stability assessment,which is depthdependent,with extreme values at shallow and intermediate depths,reflecting the interplay between gas diffusion and overburden resistance.This study advances the mechanistic understanding of gasinduced slope instability and offers actionable benchmarks for managing related risks in engineering projects including waste landfill management and shale gas operations.展开更多
The network of Himalayan roadways and highways connects some remote regions of valleys or hill slopes,which is vital for India’s socio-economic growth.Due to natural and artificial factors,frequency of slope instabil...The network of Himalayan roadways and highways connects some remote regions of valleys or hill slopes,which is vital for India’s socio-economic growth.Due to natural and artificial factors,frequency of slope instabilities along the networks has been increasing over last few decades.Assessment of stability of natural and artificial slopes due to construction of these connecting road networks is significant in safely executing these roads throughout the year.Several rock mass classification methods are generally used to assess the strength and deformability of rock mass.This study assesses slope stability along the NH-1A of Ramban district of North Western Himalayas.Various structurally and non-structurally controlled rock mass classification systems have been applied to assess the stability conditions of 14 slopes.For evaluating the stability of these slopes,kinematic analysis was performed along with geological strength index(GSI),rock mass rating(RMR),continuous slope mass rating(CoSMR),slope mass rating(SMR),and Q-slope in the present study.The SMR gives three slopes as completely unstable while CoSMR suggests four slopes as completely unstable.The stability of all slopes was also analyzed using a design chart under dynamic and static conditions by slope stability rating(SSR)for the factor of safety(FoS)of 1.2 and 1 respectively.Q-slope with probability of failure(PoF)1%gives two slopes as stable slopes.Stable slope angle has been determined based on the Q-slope safe angle equation and SSR design chart based on the FoS.The value ranges given by different empirical classifications were RMR(37-74),GSI(27.3-58.5),SMR(11-59),and CoSMR(3.39-74.56).Good relationship was found among RMR&SSR and RMR&GSI with correlation coefficient(R 2)value of 0.815 and 0.6866,respectively.Lastly,a comparative stability of all these slopes based on the above classification has been performed to identify the most critical slope along this road.展开更多
The high and steep slopes along a high-speed railway in the mountainous area of Southwest China are mostly composed of loose accumulations of debris with large internal pores and poor stability,which can easily induce...The high and steep slopes along a high-speed railway in the mountainous area of Southwest China are mostly composed of loose accumulations of debris with large internal pores and poor stability,which can easily induce adverse geological disasters under rainfall conditions.To ensure the smooth construction of the high-speed railway and the subsequent safe operation,it is necessary to master the stability evolution process of the loose accumulation slope under rainfall.This article simulates rainfall using the finite element analysis software’s hydromechanical coupling module.The slope stability under various rainfall situations is calculated and analysed based on the strength reduction method.To validate the simulation results,a field monitoring system is established to study the deformation characteristics of the slope under rainfall.The results show that rainfall duration is the key factor affecting slope stability.Given a constant amount of rainfall,the stability of the slope decreases with increasing duration of rainfall.Moreover,when the amount and duration of rainfall are constant,continuous rainfall has a greater impact on slope stability than intermittent rainfall.The setting of the field retaining structures has a significant role in improving slope stability.The field monitoring data show that the slope is in the initial deformation stage and has good stability,which verifies the rationality of the numerical simulation method.The research results can provide some references for understanding the influence of rainfall on the stability of loose accumulation slopes along high-speed railways and establishing a monitoring system.展开更多
Assessing the stability of slopes is one of the crucial tasks of geotechnical engineering for assessing and managing risks related to natural hazards,directly affecting safety and sustainable development.This study pr...Assessing the stability of slopes is one of the crucial tasks of geotechnical engineering for assessing and managing risks related to natural hazards,directly affecting safety and sustainable development.This study primarily focuses on developing robust and practical hybrid models to predict the slope stability status of circular failure mode.For this purpose,three robust models were developed using a database including 627 case histories of slope stability status.The models were developed using the random forest(RF),support vector machine(SVM),and extreme gradient boosting(XGB)techniques,employing 5-fold cross validation approach.To enhance the performance of models,this study employs Bayesian optimizer(BO)to fine-tuning their hyperparameters.The results indicate that the performance order of the three developed models is RF-BO>SVM-BO>XGB-BO.Furthermore,comparing the developed models with previous models,it was found that the RF-BO model can effectively determine the slope stability status with outstanding performance.This implies that the RF-BO model could serve as a dependable tool for project managers,assisting in the evaluation of slope stability during both the design and operational phases of projects,despite the inherent challenges in this domain.The results regarding the importance of influencing parameters indicate that cohesion,friction angle,and slope height exert the most significant impact on slope stability status.This suggests that concentrating on these parameters and employing the RF-BO model can effectively mitigate the severity of geohazards in the short-term and contribute to the attainment of long-term sustainable development objectives.展开更多
The hydro-mechanical responses of vegetated deposited slopes are complex and far from clear.On one hand,the soils in deposited slopes are typically poorly consolidated and widely graded,making them vulnerable to inter...The hydro-mechanical responses of vegetated deposited slopes are complex and far from clear.On one hand,the soils in deposited slopes are typically poorly consolidated and widely graded,making them vulnerable to internal erosion during rainfall infiltration.On the other hand,vegetation plays a significant role in influencing the hydro-mechanical properties of the soil at the slope surface.This paper presents a coupled seepage-erosion model to investigate the rainfall-induced internal erosion process within vegetated deposited slopes and its impact on slope stability.The detailed seepage-erosion coupling processes were simulated for a series of 1D rooted soil columns with varying root distributions,as well as 2D vegetated layered slopes under both light and heavy rainfall conditions.The numerical results reveal that roots can significantly mitigate rainfall-induced internal erosion,even with shallow root lengths.However,their protective effect on the slope increases as the root density in the superficial soil layer increases.Transpiration can rapidly restore matric suction in the shallow soil during rain intervals,slowing the rainfall-induced seepage-erosion process and thereby increasing slope stability.However,in the absence of transpiration,roots may either accelerate or inhibit the seepage-erosion process,depending on the specific rainfall conditions.展开更多
The prediction of slope stability is a complex nonlinear problem.This paper proposes a new method based on the random forest(RF)algorithm to study the rocky slopes stability.Taking the Bukit Merah,Perak and Twin Peak(...The prediction of slope stability is a complex nonlinear problem.This paper proposes a new method based on the random forest(RF)algorithm to study the rocky slopes stability.Taking the Bukit Merah,Perak and Twin Peak(Kuala Lumpur)as the study area,the slope characteristics of geometrical parameters are obtained from a multidisciplinary approach(consisting of geological,geotechnical,and remote sensing analyses).18 factors,including rock strength,rock quality designation(RQD),joint spacing,continuity,openness,roughness,filling,weathering,water seepage,temperature,vegetation index,water index,and orientation,are selected to construct model input variables while the factor of safety(FOS)functions as an output.The area under the curve(AUC)value of the receiver operating characteristic(ROC)curve is obtained with precision and accuracy and used to analyse the predictive model ability.With a large training set and predicted parameters,an area under the ROC curve(the AUC)of 0.95 is achieved.A precision score of 0.88 is obtained,indicating that the model has a low false positive rate and correctly identifies a substantial number of true positives.The findings emphasise the importance of using a variety of terrain characteristics and different approaches to characterise the rock slope.展开更多
Accurate identification and effective support of key blocks are crucial for ensuring the stability and safety of rock slopes.The number of structural planes and rock blocks were reduced in previous studies.This impair...Accurate identification and effective support of key blocks are crucial for ensuring the stability and safety of rock slopes.The number of structural planes and rock blocks were reduced in previous studies.This impairs the ability to characterize complex rock slopes accurately and inhibits the identification of key blocks.In this paper,a knowledge-data dually driven paradigm for accurate identification of key blocks in complex rock slopes is proposed.Our basic idea is to integrate key block theory into data-driven models based on finely characterizing structural features to identify key blocks in complex rock slopes accurately.The proposed novel paradigm consists of(1)representing rock slopes as graph-structured data based on complex systems theory,(2)identifying key nodes in the graph-structured data using graph deep learning,and(3)mapping the key nodes of graph-structured data to corresponding key blocks in the rock slope.Verification experiments and real-case applications are conducted by the proposed method.The verification results demonstrate excellent model performance,strong generalization capability,and effective classification results.Moreover,the real case application is conducted on the northern slope of the Yanqianshan Iron Mine.The results show that the proposed method can accurately identify key blocks in complex rock slopes,which can provide a decision-making basis and rational recommendations for effective support and instability prevention of rock slopes,thereby ensuring the stability of rock engineering and the safety of life and property.展开更多
Sudden and unforeseen seismic failures of coal mine overburden(OB)dump slopes interrupt mining operations,cause loss of lives and delay the production of coal.Consideration of the spatial heterogeneity of OB dump mate...Sudden and unforeseen seismic failures of coal mine overburden(OB)dump slopes interrupt mining operations,cause loss of lives and delay the production of coal.Consideration of the spatial heterogeneity of OB dump materials is imperative for an adequate evaluation of the seismic stability of OB dump slopes.In this study,pseudo-static seismic stability analyses are carried out for an OB dump slope by considering the material parameters obtained from an insitu field investigation.Spatial heterogeneity is simulated through use of the random finite element method(RFEM)and the random limit equilibrium method(RLEM)and a comparative study is presented.Combinations of horizontal and vertical spatial correlation lengths were considered for simulating isotropic and anisotropic random fields within the OB dump slope.Seismic performances of the slope have been reported through the probability of failure and reliability index.It was observed that the RLEM approach overestimates failure probability(P_(f))by considering seismic stability with spatial heterogeneity.The P_(f)was observed to increase with an increase in the coefficient of variation of friction angle of the dump materials.Further,it was inferred that the RLEM approach may not be adequately applicable for assessing the seismic stability of an OB dump slope for a horizontal seismic coefficient that is more than or equal to 0.1.展开更多
A DFN-DEC(discrete fracture network-distinct element code)method based on the MATLAB platform is developed to generate heterogeneous DFN.Subsequently,the effects of the spatial variability(the meanμand the standard d...A DFN-DEC(discrete fracture network-distinct element code)method based on the MATLAB platform is developed to generate heterogeneous DFN.Subsequently,the effects of the spatial variability(the meanμand the standard deviationσ)of the geometric properties(i.e.,the fracture dip D,the trace length T and the spacing S)of both the gently-dipping(denoted with 1)and the steeply-dipping(denoted with 2)fractures on the stability of granite slope are investigated.Results indicate that the proposed DFN-DEC method is robust,generating fracture networks that resemble reality.In addition,the spatial variability of fracture geometry,influencing the structure of granite slope,plays a significant role in slope stability.The mean stability of the slope decreases with the increase ofμ_(D_(1))(the mean of gently-dipping fracture dip),σ_(D_(2))(the mean of steeply-dipping fracture dip),μ_(T_(1))(the mean of gently-dipping fracture trace length),μ_(T_(2))(the mean of steeply-dipping fracture trace length),σ_(T_(1))(the standard deviation of gently-dipping fracture trace length),σ_(T_(2))(the standard deviation of steeply-dipping fracture trace length),and the decrease ofσ_(D_(1))(the standard deviation of gently-dipping fracture dip),μ_(D_(2))(the standard deviation of steeply-dipping fracture dip),μ_(S_(1))(the mean of gently-dipping fracture spacing)andμ_(S_(2))(the mean of steeply-dipping fracture spacing).Among them,μ_(T_(1)),μ_(D_(1))andμ_(S_(1))have the major impact.When the fracture spacing is large,the variability in the fracture geometry becomes less relevant to slope stability.When within some ranges of the fracture spacing,the spatial varying of dips can increase the slope stability by forming an interlaced structure.The results also show that the effects of the variability of trace length on slope stability depend on the variability of dip.These findings highlight the importance of spatial variability in the geometry of fractures to rock slope stability analysis.展开更多
This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor ...This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor series.This expansion enables the reasonable construction of a function describing the NS on the SS.Additionally,by directly incorporating the nonlinear Generalized Hoke-Brown(GHB)strength criterion and utilizing the slope factor of safety(FOS)definition,a function of the shear stress on the SS is derived.This function considers the mutual feedback mechanism between the NS and strength parameters of the SS.The stress constraints conditions are then introduced at both ends of the SS based on the spatial stress relation of one point.Determining the slope FOS and stress solution for the SS involves considering the mechanical equilibrium conditions and the stress constraint conditions satisfied by the sliding body.The proposed approach successfully simulates the tension-shear stress zone near the slope top and provides an intuitive description of the concentration effect of compression-shear stress of the SS near the slope toe.Furthermore,compared to other methods,the present method demonstrates superior processing capabilities for the embedded nonlinear GHB strength criterion.展开更多
Probabilistic analysis is a rational approach for engineering design because it provides more insight than traditional deterministic analysis. Probabilistic evaluation on seismic stability of three dimensional (3D) sl...Probabilistic analysis is a rational approach for engineering design because it provides more insight than traditional deterministic analysis. Probabilistic evaluation on seismic stability of three dimensional (3D) slopes is studied in this paper. The slope safety factor is computed by combining the kinematic approach of limit analysis using a three-dimensional rotational failure mechanism with the pseudo-dynamic approach. The variability of input parameters, including six pseudo-dynamic parameters and two soil shear strength parameters, are taken into account by means of Monte-Carlo Simulations (MCS) method. The influences of pseudo-dynamic input variables on the computed failure probabilities are investigated and discussed. It is shown that the obtained failure probabilities increase with the pseudo-dynamic input variables and the pseudo-dynamic approach gives more conservative failure probability estimates compared with the pseudo-static approach.展开更多
Slope toe excavation strongly influences the stress balance of natural slopes and redistributes the stress of the slope body. Consequently, the sliding failure of toe-cut slopes is increasingly becoming more frequent,...Slope toe excavation strongly influences the stress balance of natural slopes and redistributes the stress of the slope body. Consequently, the sliding failure of toe-cut slopes is increasingly becoming more frequent, particularly in regions with persistent rainfall. The effects of external factors, namely, toe excavation and persistent rainfall, which lead to toe-cut slope failure were investigated through the numerical analysis of typical toe-cut slopes in the southeastern coastal region of China. Based on the grey relational theory, sensitivity analysis was carried out on the controlling factors to determine the degree of influence exerted by the external factors on the stability of toe-cut slopes. The stability analysis of toe-cut slopes reinforced by pileanchor structures under earthquake conditions was carried out using pseudo-static analysis. The safety factor of toe-cut slopes significantly decreases as the excavation height, rainfall duration, and rainfall intensity increase. The slope stability is more sensitive to the excavation height of a toe-cut slope than it is to rainfall. The stability of a toe-cut slope reinforced by a pile-anchor structure was also analyzed under rainfall and earthquake conditions using the limit equilibrium method and pseudo-static analysis, respectively. The slope stability significantly improved when the slope was reinforced by a pile-anchor structure, even when the slope was subjected to persistent rainfall and earthquakes. The findings of this study can provide important guidance for the prevention of geological disasters in mountainous areas.展开更多
Rock slope stability is of great concern along highway routes as stability problems on cut slopes may cause fatal events as well as loss of property.In rock slope engineering,stability evaluations are commonly perform...Rock slope stability is of great concern along highway routes as stability problems on cut slopes may cause fatal events as well as loss of property.In rock slope engineering,stability evaluations are commonly performed by means of analytical or numerical analyses,principally considering the factor of safety concept.As a matter of fact,the probabilistic assessment of slope stability is progressively getting popularity due to difficulties in assigning the most appropriate values to design parameters in analytical or numerical methods.Additionally,the effect of heterogeneities in rock masses and discontinuities on the analysis results is minimized through the probabilistic concept.In this study,slope stability of high and steep sedimentary rock cut slopes along a state highway in AdilcevazBitlis(Turkey) was evaluated on the basis of probabilistic approach using the Slope Stability Probability Classification(SSPC) system.The probabilistic assessment indicates major slope stability problems because of discontinuity controlled and discontinuity orientation independent mass movements.Almost all studied cut slopes suffer from orientation-independent stability problems with very low stability probabilities.Additionally,the probability of planar and toppling failures issignificantly high with respect to the SSPC system.The stability problems along the investigated rock slopes were also verified by field reconnaissance.Remedial measures such as slope re-design and reinforcement at the studied locations should be taken to prevent hazardous events along the highway.On the other hand,the probabilistic approach may be a useful tool during rock slope engineering to overcome numerous uncertainties when probabilistic and analytic results are compared.展开更多
New plasticity solutions to the drained stability of conical slopes in homogeneous cohesive-frictional soils were investigated by axisymmetric finite element limit analysis. Three parameters were studied,i.e. excavate...New plasticity solutions to the drained stability of conical slopes in homogeneous cohesive-frictional soils were investigated by axisymmetric finite element limit analysis. Three parameters were studied,i.e. excavated height ratios, slope inclination angles, and soil friction angles. The influences of these parameters on the stability factor and predicted failure mechanism of conical slopes were discussed. A new design equation developed from a nonlinear regression of the lower bound solution was proposed for drained stability analyses of a conical slope in practice. Numerical examples were given to demonstrate a practical application of the proposed equation to stability evaluations of conical slopes with both associated and non-associated flow rules.展开更多
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 consid...One of the critical aspects in mine design is slope stability analysis and the determination of stable slopes. In the Chador- Malu iron ore mine, one of the most important iron ore mines in central Iran, it was considered vital to perform a comprehensive slope stability analysis. At first, we divided the existing rock hosting pit into six zones and a geotechnical map was prepared. Then, the value of MRMR （Mining Rock Mass Rating） was determined for each zone. Owing to the fact that the Chador-Malu iron ore mine is located in a highly tectonic area and the rock mass completely crushed, the Hoek-Brown failure criterion was found suitable to estimate geo-mechanical parameters. After that, the value of cohesion （c） and friction angle （tp） were calculated for different geotechnical zones and relative graphs and equations were derived as a function of slope height. The stability analyses using numerical and limit equilibrium methods showed that some instability problems might occur by increasing the slope height. Therefore, stable slopes for each geotechnical zone and prepared sections were calculated and presented as a function of slope height.展开更多
Two calculation modes for the effect of external load on slope stability, i.e., mode I in which the external load is thought to act on slope surface, and mode II in which the external load is thought to act on slip su...Two calculation modes for the effect of external load on slope stability, i.e., mode I in which the external load is thought to act on slope surface, and mode II in which the external load is thought to act on slip surface along the force action line, were considered. Meanwhile, four basic distribution patterns of external load were used, of which complex external loads could be composed. In analysis process, several limit equilibrium methods, such as Swedish method, simplified Bishop method, simplified Janbu method, Spencer method, Morgenstern-Price(M-P) method, Sarma method, and unbalanced thrust method, were also adopted to contrast their differences in slope stability under the external load. According to parametric analysis, some conclusions can be obtained as follows:(1) The external load, with the large magnitude, small inclination angle, and acting position close to the slope toe,has more positive effect on slope stability;(2) The results calculated using modes I and II of external load are similar, indicating that the calculation mode of external load has little influence on slope stability;(3) If different patterns of external loads are equivalent to each other, their slope stability under these external loads are the same, and if not, the external load leads to the better slope stability,as action position of the resultant force for external load is closer to the lower sliding point of slip surface.展开更多
The geological structure of the Changshanhao open-pit mine in Urad Middle Banner,Inner Mongolia,China is extremely complicated,and slope instability has frequently occurred in various forms,such as wedge sliding,beddi...The geological structure of the Changshanhao open-pit mine in Urad Middle Banner,Inner Mongolia,China is extremely complicated,and slope instability has frequently occurred in various forms,such as wedge sliding,bedding sliding,and toppling failure.In order to study the failure mechanisms of these slopes,the geological structure and mechanical rock properties were investigated based on field investigations and laboratory tests.Numerical models for the present mining area and final mining area of the original scheme were established to analyze slope stability.The results showed that the unique geomorphological characteristics of the mining area were generated by geological tectonism,and the north side of the stope is an anti-dip layered rock slope and the south side is a dip layered rock slope.Slope failure is the consequence of endogenic and exogenic integration,including physical and mechanical properties of the rock mass,geological structures such as faults and joints,and human-caused factors such as blasting and excavation disturbances.Then the original excavation scheme was redesigned mainly by optimizing the slope angle and decreasing the final mining depth to maintain slope stability.Finally,the Monte Carlo method was used to analyze the reliability of the slope angle optimization scheme.The open-pit mine excavation plan that meets the stability requirements was obtained eventually.展开更多
According to theory of unsaturated soil strength and Green-Ampt model, an analysis method based on limit equilibrium theory is introduced to consider rainfall infiltration effects in loess slope stability analysis. Th...According to theory of unsaturated soil strength and Green-Ampt model, an analysis method based on limit equilibrium theory is introduced to consider rainfall infiltration effects in loess slope stability analysis. The relationships between wetting band depth and surficial stability of slopes are analyzed. It is found that the infiltration adds to the weight of the soil and at the same time reduces the shear strength provided by matric suction of the soil. The wetting band depth plays a key role in the stability of slopes. The minimum rainfall intensity and the minimum rainfall duration needed to infiltrate to the wetting front depth are calculated based on the Green-Ampt model. The method in this paper will contribute to the predication of slope stability considering rainfall characteristics.展开更多
基金Projects(51034005,41002090) supported by National Natural Science Foundation of ChinaProject(2011QZ05) supported by the Fundamental Research Funds for the Central Universities,China
文摘A methodology was proposed for the design of micropiles to increase earth slopes stability. An analytic model based on bearn-colurnn equation and an existing P-y curve method was set up and used to find the shear capacity of the micropile. Then, a step-by-step design procedure for stabilization of earth slope with rnicropiles was introduced, involving six main steps： 1） Choosing a location for the rnicropiles within the existing slope; 2） Selecting micropile cross section; 3） Estimating length of rnicropile; 4） Evaluating shear capacity of mieropiles; 5） Calculating spacing required to provide force to stabilize the slope; 6） Designing the concrete cap beam. The application of the method to an embankment landslide in Qinghai Province was described in detail. In the final design, three rows of rnicropiles were adopted as a group and a total of 126 rnicropiles with 0.23 m in diameter were used. The micropile length ranged between 15 and 18 m, with the spacing 1.5 m at in-row direction. The monitoring data indicate that slope movement has been effectively controlled as a result of the slope stabilization measure, which verifies the reasonability of the design method.
基金We acknowledge the funding support from the National Key R&D Program of China(Grant No.2022YFC3080100)the National Natural Science Foundation of China(Grant No.42102316)the opening fund of State Key Laboratory of Hydraulics and Mountain River Engineering,Sichuan University(Grant No.SKHL2306).
文摘The discrete fracture system of a rock mass plays a crucial role in controlling the stability of rock slopes.To fully account for the geometric shape and distribution characteristics of jointed rock masses,terrestrial laser scanning(TLS)was employed to acquire high-resolution point-cloud data,and a developed automatic discontinuity-identification technology was coupled to automatically interpret and characterize geometric information such as orientation,trace length,spacing,and set number of the discontinuities.The discrete element method(DEM)was applied to study the influence of the geometric morphology and distribution characteristics of discontinuities on slope stability by generating a discrete fracture network(DFN)with the same statistical characteristics as the actual discontinuities.Based on slope data from the Yebatan Hydropower Station,a simulation was conducted to verify the applicability of the automatic discontinuity identification technology and the discrete fracture network-discrete element method(DFN-DEM).Various geological parameters,including trace length,persistence,and density,were examined to investigate the morphological evolution and response characteristics of rock slope excavation under different joint combination conditions through simulation.The simulation results indicate that joint parameters affect slope stability,with density having the most significant impact.The impact of joint parameters on stability is relatively small within a reasonable range but becomes significant beyond a certain threshold,further validating that the accuracy of field geological surveys is critical for simulation.This study provides a scientific basis for the construction of complex rock slope models,engineering assessments,and disaster prevention and mitigation,which is of great value in both theory and engineering applications.
基金supported by the Postdoctoral Science Foundation of the Power China Chengdu Engineering Corporation Limited(No.P66725)Science and Technology Fund Support Project of Power China Chengdu Engineering Corporation.(No.PA1717)。
文摘Landslides triggered by high gas pressure represent a distinct geotechnical hazard,especially in scenarios without significant rainfall.Recent studies have revealed that high-pressure gas accumulation within slopes can be a dominant trigger for large-scale failures although the processes behind this remain not well understood.This study examines how unsaturated soil slopes fail under high gas pressure using a combination of laboratory experiments and numerical simulations.A key discovery is that gas pressure changes slope stability by redistributing pore fluids and altering effective stress,with distinct depthdependent effects.Moreover,a novel concept of critical stable gas pressure(P_(ac))is proposed as a practical threshold for stability assessment,which is depthdependent,with extreme values at shallow and intermediate depths,reflecting the interplay between gas diffusion and overburden resistance.This study advances the mechanistic understanding of gasinduced slope instability and offers actionable benchmarks for managing related risks in engineering projects including waste landfill management and shale gas operations.
文摘The network of Himalayan roadways and highways connects some remote regions of valleys or hill slopes,which is vital for India’s socio-economic growth.Due to natural and artificial factors,frequency of slope instabilities along the networks has been increasing over last few decades.Assessment of stability of natural and artificial slopes due to construction of these connecting road networks is significant in safely executing these roads throughout the year.Several rock mass classification methods are generally used to assess the strength and deformability of rock mass.This study assesses slope stability along the NH-1A of Ramban district of North Western Himalayas.Various structurally and non-structurally controlled rock mass classification systems have been applied to assess the stability conditions of 14 slopes.For evaluating the stability of these slopes,kinematic analysis was performed along with geological strength index(GSI),rock mass rating(RMR),continuous slope mass rating(CoSMR),slope mass rating(SMR),and Q-slope in the present study.The SMR gives three slopes as completely unstable while CoSMR suggests four slopes as completely unstable.The stability of all slopes was also analyzed using a design chart under dynamic and static conditions by slope stability rating(SSR)for the factor of safety(FoS)of 1.2 and 1 respectively.Q-slope with probability of failure(PoF)1%gives two slopes as stable slopes.Stable slope angle has been determined based on the Q-slope safe angle equation and SSR design chart based on the FoS.The value ranges given by different empirical classifications were RMR(37-74),GSI(27.3-58.5),SMR(11-59),and CoSMR(3.39-74.56).Good relationship was found among RMR&SSR and RMR&GSI with correlation coefficient(R 2)value of 0.815 and 0.6866,respectively.Lastly,a comparative stability of all these slopes based on the above classification has been performed to identify the most critical slope along this road.
基金supported by the National Natural Science Foundation of China (No.51978588).
文摘The high and steep slopes along a high-speed railway in the mountainous area of Southwest China are mostly composed of loose accumulations of debris with large internal pores and poor stability,which can easily induce adverse geological disasters under rainfall conditions.To ensure the smooth construction of the high-speed railway and the subsequent safe operation,it is necessary to master the stability evolution process of the loose accumulation slope under rainfall.This article simulates rainfall using the finite element analysis software’s hydromechanical coupling module.The slope stability under various rainfall situations is calculated and analysed based on the strength reduction method.To validate the simulation results,a field monitoring system is established to study the deformation characteristics of the slope under rainfall.The results show that rainfall duration is the key factor affecting slope stability.Given a constant amount of rainfall,the stability of the slope decreases with increasing duration of rainfall.Moreover,when the amount and duration of rainfall are constant,continuous rainfall has a greater impact on slope stability than intermittent rainfall.The setting of the field retaining structures has a significant role in improving slope stability.The field monitoring data show that the slope is in the initial deformation stage and has good stability,which verifies the rationality of the numerical simulation method.The research results can provide some references for understanding the influence of rainfall on the stability of loose accumulation slopes along high-speed railways and establishing a monitoring system.
文摘Assessing the stability of slopes is one of the crucial tasks of geotechnical engineering for assessing and managing risks related to natural hazards,directly affecting safety and sustainable development.This study primarily focuses on developing robust and practical hybrid models to predict the slope stability status of circular failure mode.For this purpose,three robust models were developed using a database including 627 case histories of slope stability status.The models were developed using the random forest(RF),support vector machine(SVM),and extreme gradient boosting(XGB)techniques,employing 5-fold cross validation approach.To enhance the performance of models,this study employs Bayesian optimizer(BO)to fine-tuning their hyperparameters.The results indicate that the performance order of the three developed models is RF-BO>SVM-BO>XGB-BO.Furthermore,comparing the developed models with previous models,it was found that the RF-BO model can effectively determine the slope stability status with outstanding performance.This implies that the RF-BO model could serve as a dependable tool for project managers,assisting in the evaluation of slope stability during both the design and operational phases of projects,despite the inherent challenges in this domain.The results regarding the importance of influencing parameters indicate that cohesion,friction angle,and slope height exert the most significant impact on slope stability status.This suggests that concentrating on these parameters and employing the RF-BO model can effectively mitigate the severity of geohazards in the short-term and contribute to the attainment of long-term sustainable development objectives.
基金supported by National Natural Science Foundation of China(Grant No.42372330)Science and Technology Research Program of Institute of Mountain Hazards and Environment,Chinese Academy of Sciences(Grant No.IMHE-CXTD-01-IMHE-ZYTS-12)Sichuan Science and Technology Program(Grant No.2024NSFSC0102).
文摘The hydro-mechanical responses of vegetated deposited slopes are complex and far from clear.On one hand,the soils in deposited slopes are typically poorly consolidated and widely graded,making them vulnerable to internal erosion during rainfall infiltration.On the other hand,vegetation plays a significant role in influencing the hydro-mechanical properties of the soil at the slope surface.This paper presents a coupled seepage-erosion model to investigate the rainfall-induced internal erosion process within vegetated deposited slopes and its impact on slope stability.The detailed seepage-erosion coupling processes were simulated for a series of 1D rooted soil columns with varying root distributions,as well as 2D vegetated layered slopes under both light and heavy rainfall conditions.The numerical results reveal that roots can significantly mitigate rainfall-induced internal erosion,even with shallow root lengths.However,their protective effect on the slope increases as the root density in the superficial soil layer increases.Transpiration can rapidly restore matric suction in the shallow soil during rain intervals,slowing the rainfall-induced seepage-erosion process and thereby increasing slope stability.However,in the absence of transpiration,roots may either accelerate or inhibit the seepage-erosion process,depending on the specific rainfall conditions.
基金support in providing the data and the Universiti Teknologi Malaysia supported this work under UTM Flagship CoE/RG-Coe/RG 5.2:Evaluating Surface PGA with Global Ground Motion Site Response Analyses for the highest seismic activity location in Peninsular Malaysia(Q.J130000.5022.10G47)Universiti Teknologi Malaysia-Earthquake Hazard Assessment in Peninsular Malaysia Using Probabilistic Seismic Hazard Analysis(PSHA)Method(Q.J130000.21A2.06E9).
文摘The prediction of slope stability is a complex nonlinear problem.This paper proposes a new method based on the random forest(RF)algorithm to study the rocky slopes stability.Taking the Bukit Merah,Perak and Twin Peak(Kuala Lumpur)as the study area,the slope characteristics of geometrical parameters are obtained from a multidisciplinary approach(consisting of geological,geotechnical,and remote sensing analyses).18 factors,including rock strength,rock quality designation(RQD),joint spacing,continuity,openness,roughness,filling,weathering,water seepage,temperature,vegetation index,water index,and orientation,are selected to construct model input variables while the factor of safety(FOS)functions as an output.The area under the curve(AUC)value of the receiver operating characteristic(ROC)curve is obtained with precision and accuracy and used to analyse the predictive model ability.With a large training set and predicted parameters,an area under the ROC curve(the AUC)of 0.95 is achieved.A precision score of 0.88 is obtained,indicating that the model has a low false positive rate and correctly identifies a substantial number of true positives.The findings emphasise the importance of using a variety of terrain characteristics and different approaches to characterise the rock slope.
基金supported by the National Natural Science Foundation of China(Grant Nos.42277161,42230709).
文摘Accurate identification and effective support of key blocks are crucial for ensuring the stability and safety of rock slopes.The number of structural planes and rock blocks were reduced in previous studies.This impairs the ability to characterize complex rock slopes accurately and inhibits the identification of key blocks.In this paper,a knowledge-data dually driven paradigm for accurate identification of key blocks in complex rock slopes is proposed.Our basic idea is to integrate key block theory into data-driven models based on finely characterizing structural features to identify key blocks in complex rock slopes accurately.The proposed novel paradigm consists of(1)representing rock slopes as graph-structured data based on complex systems theory,(2)identifying key nodes in the graph-structured data using graph deep learning,and(3)mapping the key nodes of graph-structured data to corresponding key blocks in the rock slope.Verification experiments and real-case applications are conducted by the proposed method.The verification results demonstrate excellent model performance,strong generalization capability,and effective classification results.Moreover,the real case application is conducted on the northern slope of the Yanqianshan Iron Mine.The results show that the proposed method can accurately identify key blocks in complex rock slopes,which can provide a decision-making basis and rational recommendations for effective support and instability prevention of rock slopes,thereby ensuring the stability of rock engineering and the safety of life and property.
基金the financial support provided by MHRD,Govt.of IndiaCoal India Limited for providing financial assistance for the research(Project No.CIL/R&D/01/73/2021)the partial financial support provided by the Ministry of Education,Government of India,under SPARC project(Project No.P1207)。
文摘Sudden and unforeseen seismic failures of coal mine overburden(OB)dump slopes interrupt mining operations,cause loss of lives and delay the production of coal.Consideration of the spatial heterogeneity of OB dump materials is imperative for an adequate evaluation of the seismic stability of OB dump slopes.In this study,pseudo-static seismic stability analyses are carried out for an OB dump slope by considering the material parameters obtained from an insitu field investigation.Spatial heterogeneity is simulated through use of the random finite element method(RFEM)and the random limit equilibrium method(RLEM)and a comparative study is presented.Combinations of horizontal and vertical spatial correlation lengths were considered for simulating isotropic and anisotropic random fields within the OB dump slope.Seismic performances of the slope have been reported through the probability of failure and reliability index.It was observed that the RLEM approach overestimates failure probability(P_(f))by considering seismic stability with spatial heterogeneity.The P_(f)was observed to increase with an increase in the coefficient of variation of friction angle of the dump materials.Further,it was inferred that the RLEM approach may not be adequately applicable for assessing the seismic stability of an OB dump slope for a horizontal seismic coefficient that is more than or equal to 0.1.
基金supported by the National Natural Science Foundation of China(Nos.41807264,41972289)the Engineering Research Center of Rock-Soil Drilling&Excavation and Protection,Ministry of Education(No.202102)+3 种基金the Key Laboratory of Geological Hazards on Three Gorges Reservoir Area(China Three Gorges University),Ministry of Education(No.2020KDZ01)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(Nos.CUG170686,CUGQY1932)the China Scholarship Council(No.201406410032)the Science and Technology Research Project of Education Department of Hubei Province(Nos.B2019452,B2024509)。
文摘A DFN-DEC(discrete fracture network-distinct element code)method based on the MATLAB platform is developed to generate heterogeneous DFN.Subsequently,the effects of the spatial variability(the meanμand the standard deviationσ)of the geometric properties(i.e.,the fracture dip D,the trace length T and the spacing S)of both the gently-dipping(denoted with 1)and the steeply-dipping(denoted with 2)fractures on the stability of granite slope are investigated.Results indicate that the proposed DFN-DEC method is robust,generating fracture networks that resemble reality.In addition,the spatial variability of fracture geometry,influencing the structure of granite slope,plays a significant role in slope stability.The mean stability of the slope decreases with the increase ofμ_(D_(1))(the mean of gently-dipping fracture dip),σ_(D_(2))(the mean of steeply-dipping fracture dip),μ_(T_(1))(the mean of gently-dipping fracture trace length),μ_(T_(2))(the mean of steeply-dipping fracture trace length),σ_(T_(1))(the standard deviation of gently-dipping fracture trace length),σ_(T_(2))(the standard deviation of steeply-dipping fracture trace length),and the decrease ofσ_(D_(1))(the standard deviation of gently-dipping fracture dip),μ_(D_(2))(the standard deviation of steeply-dipping fracture dip),μ_(S_(1))(the mean of gently-dipping fracture spacing)andμ_(S_(2))(the mean of steeply-dipping fracture spacing).Among them,μ_(T_(1)),μ_(D_(1))andμ_(S_(1))have the major impact.When the fracture spacing is large,the variability in the fracture geometry becomes less relevant to slope stability.When within some ranges of the fracture spacing,the spatial varying of dips can increase the slope stability by forming an interlaced structure.The results also show that the effects of the variability of trace length on slope stability depend on the variability of dip.These findings highlight the importance of spatial variability in the geometry of fractures to rock slope stability analysis.
基金Project(52278380)supported by the National Natural Science Foundation of ChinaProject(2023JJ30670)supported by the National Science Foundation of and Technology Major Project of Hunan Province,China。
文摘This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor series.This expansion enables the reasonable construction of a function describing the NS on the SS.Additionally,by directly incorporating the nonlinear Generalized Hoke-Brown(GHB)strength criterion and utilizing the slope factor of safety(FOS)definition,a function of the shear stress on the SS is derived.This function considers the mutual feedback mechanism between the NS and strength parameters of the SS.The stress constraints conditions are then introduced at both ends of the SS based on the spatial stress relation of one point.Determining the slope FOS and stress solution for the SS involves considering the mechanical equilibrium conditions and the stress constraint conditions satisfied by the sliding body.The proposed approach successfully simulates the tension-shear stress zone near the slope top and provides an intuitive description of the concentration effect of compression-shear stress of the SS near the slope toe.Furthermore,compared to other methods,the present method demonstrates superior processing capabilities for the embedded nonlinear GHB strength criterion.
文摘Probabilistic analysis is a rational approach for engineering design because it provides more insight than traditional deterministic analysis. Probabilistic evaluation on seismic stability of three dimensional (3D) slopes is studied in this paper. The slope safety factor is computed by combining the kinematic approach of limit analysis using a three-dimensional rotational failure mechanism with the pseudo-dynamic approach. The variability of input parameters, including six pseudo-dynamic parameters and two soil shear strength parameters, are taken into account by means of Monte-Carlo Simulations (MCS) method. The influences of pseudo-dynamic input variables on the computed failure probabilities are investigated and discussed. It is shown that the obtained failure probabilities increase with the pseudo-dynamic input variables and the pseudo-dynamic approach gives more conservative failure probability estimates compared with the pseudo-static approach.
基金The authors sincerely appreciate the financial support provided to this study by the National Key R&D Program of China(No.2017YFC1501304)。
文摘Slope toe excavation strongly influences the stress balance of natural slopes and redistributes the stress of the slope body. Consequently, the sliding failure of toe-cut slopes is increasingly becoming more frequent, particularly in regions with persistent rainfall. The effects of external factors, namely, toe excavation and persistent rainfall, which lead to toe-cut slope failure were investigated through the numerical analysis of typical toe-cut slopes in the southeastern coastal region of China. Based on the grey relational theory, sensitivity analysis was carried out on the controlling factors to determine the degree of influence exerted by the external factors on the stability of toe-cut slopes. The stability analysis of toe-cut slopes reinforced by pileanchor structures under earthquake conditions was carried out using pseudo-static analysis. The safety factor of toe-cut slopes significantly decreases as the excavation height, rainfall duration, and rainfall intensity increase. The slope stability is more sensitive to the excavation height of a toe-cut slope than it is to rainfall. The stability of a toe-cut slope reinforced by a pile-anchor structure was also analyzed under rainfall and earthquake conditions using the limit equilibrium method and pseudo-static analysis, respectively. The slope stability significantly improved when the slope was reinforced by a pile-anchor structure, even when the slope was subjected to persistent rainfall and earthquakes. The findings of this study can provide important guidance for the prevention of geological disasters in mountainous areas.
基金financially supported by the Scientific Research Projects Office of YüzüncüYil University(YYU-BAP,Project Number 2012-FBEYL48)
文摘Rock slope stability is of great concern along highway routes as stability problems on cut slopes may cause fatal events as well as loss of property.In rock slope engineering,stability evaluations are commonly performed by means of analytical or numerical analyses,principally considering the factor of safety concept.As a matter of fact,the probabilistic assessment of slope stability is progressively getting popularity due to difficulties in assigning the most appropriate values to design parameters in analytical or numerical methods.Additionally,the effect of heterogeneities in rock masses and discontinuities on the analysis results is minimized through the probabilistic concept.In this study,slope stability of high and steep sedimentary rock cut slopes along a state highway in AdilcevazBitlis(Turkey) was evaluated on the basis of probabilistic approach using the Slope Stability Probability Classification(SSPC) system.The probabilistic assessment indicates major slope stability problems because of discontinuity controlled and discontinuity orientation independent mass movements.Almost all studied cut slopes suffer from orientation-independent stability problems with very low stability probabilities.Additionally,the probability of planar and toppling failures issignificantly high with respect to the SSPC system.The stability problems along the investigated rock slopes were also verified by field reconnaissance.Remedial measures such as slope re-design and reinforcement at the studied locations should be taken to prevent hazardous events along the highway.On the other hand,the probabilistic approach may be a useful tool during rock slope engineering to overcome numerous uncertainties when probabilistic and analytic results are compared.
文摘New plasticity solutions to the drained stability of conical slopes in homogeneous cohesive-frictional soils were investigated by axisymmetric finite element limit analysis. Three parameters were studied,i.e. excavated height ratios, slope inclination angles, and soil friction angles. The influences of these parameters on the stability factor and predicted failure mechanism of conical slopes were discussed. A new design equation developed from a nonlinear regression of the lower bound solution was proposed for drained stability analyses of a conical slope in practice. Numerical examples were given to demonstrate a practical application of the proposed equation to stability evaluations of conical slopes with both associated and non-associated flow rules.
文摘One of the critical aspects in mine design is slope stability analysis and the determination of stable slopes. In the Chador- Malu iron ore mine, one of the most important iron ore mines in central Iran, it was considered vital to perform a comprehensive slope stability analysis. At first, we divided the existing rock hosting pit into six zones and a geotechnical map was prepared. Then, the value of MRMR （Mining Rock Mass Rating） was determined for each zone. Owing to the fact that the Chador-Malu iron ore mine is located in a highly tectonic area and the rock mass completely crushed, the Hoek-Brown failure criterion was found suitable to estimate geo-mechanical parameters. After that, the value of cohesion （c） and friction angle （tp） were calculated for different geotechnical zones and relative graphs and equations were derived as a function of slope height. The stability analyses using numerical and limit equilibrium methods showed that some instability problems might occur by increasing the slope height. Therefore, stable slopes for each geotechnical zone and prepared sections were calculated and presented as a function of slope height.
基金Project(2015M580702)supported by the China Postdoctoral Science FoundationProject(51608541)supported by the National Natural Science Foundation of ChinaProject(2014122006)supported by the Guizhou Provincial Department of Transportation Foundation,China
文摘Two calculation modes for the effect of external load on slope stability, i.e., mode I in which the external load is thought to act on slope surface, and mode II in which the external load is thought to act on slip surface along the force action line, were considered. Meanwhile, four basic distribution patterns of external load were used, of which complex external loads could be composed. In analysis process, several limit equilibrium methods, such as Swedish method, simplified Bishop method, simplified Janbu method, Spencer method, Morgenstern-Price(M-P) method, Sarma method, and unbalanced thrust method, were also adopted to contrast their differences in slope stability under the external load. According to parametric analysis, some conclusions can be obtained as follows:(1) The external load, with the large magnitude, small inclination angle, and acting position close to the slope toe,has more positive effect on slope stability;(2) The results calculated using modes I and II of external load are similar, indicating that the calculation mode of external load has little influence on slope stability;(3) If different patterns of external loads are equivalent to each other, their slope stability under these external loads are the same, and if not, the external load leads to the better slope stability,as action position of the resultant force for external load is closer to the lower sliding point of slip surface.
基金supported by the National Key Research and Development Program of China Grant NO. 2016YFC0600901the Fundamental Research Funds for the Central Universities Grant NO. 2015QB02。
文摘The geological structure of the Changshanhao open-pit mine in Urad Middle Banner,Inner Mongolia,China is extremely complicated,and slope instability has frequently occurred in various forms,such as wedge sliding,bedding sliding,and toppling failure.In order to study the failure mechanisms of these slopes,the geological structure and mechanical rock properties were investigated based on field investigations and laboratory tests.Numerical models for the present mining area and final mining area of the original scheme were established to analyze slope stability.The results showed that the unique geomorphological characteristics of the mining area were generated by geological tectonism,and the north side of the stope is an anti-dip layered rock slope and the south side is a dip layered rock slope.Slope failure is the consequence of endogenic and exogenic integration,including physical and mechanical properties of the rock mass,geological structures such as faults and joints,and human-caused factors such as blasting and excavation disturbances.Then the original excavation scheme was redesigned mainly by optimizing the slope angle and decreasing the final mining depth to maintain slope stability.Finally,the Monte Carlo method was used to analyze the reliability of the slope angle optimization scheme.The open-pit mine excavation plan that meets the stability requirements was obtained eventually.
文摘According to theory of unsaturated soil strength and Green-Ampt model, an analysis method based on limit equilibrium theory is introduced to consider rainfall infiltration effects in loess slope stability analysis. The relationships between wetting band depth and surficial stability of slopes are analyzed. It is found that the infiltration adds to the weight of the soil and at the same time reduces the shear strength provided by matric suction of the soil. The wetting band depth plays a key role in the stability of slopes. The minimum rainfall intensity and the minimum rainfall duration needed to infiltrate to the wetting front depth are calculated based on the Green-Ampt model. The method in this paper will contribute to the predication of slope stability considering rainfall characteristics.
