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

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

Study on Strength Reduction Law and Meso-Crack Evolution of Lower Layered Cemented Tailings Backfill

The green disposal of tailings solid waste is a problem to be solved in mine production.Cemented tailings filling stoping method can realize the dual goals of solid waste resource utilization and mined-out area reduction.However,the volume of the mined-out area of the open-pit method is larger than the filling capacity,resulting in the complex stratification of the underground backfill,and the strength of the backfill cannot meet the requirements.In this paper,according to the delamination situation,the specimens of horizontal and inclination angle layered cemented tailings backfill(LCTB)is made for a uniaxial compression test,and the failure process of delamination backfill is reduced by PFC.The results show that the corresponding reduction factorφof horizontal LCTB is 0.560–0.932,and the correspondingφvalue of inclination angle LCTB is 0.338–0.772.The failure mode of backfill in different layers is mainly manifested as a tensile failure.The PFC numerical simulation results are consistent with laboratory test results,which verifies the correctness of backfill failure.The research results provide a reliable theoretical basis for the strength design of backfill in goaf,which is of great significance for solid waste utilization and environmental protection.

Strength reduction and step-loading finite element approaches in geotechnical engineering

The finite element limit analysis method has the advantages of both numerical and traditional limit equilibrium techniques and it is particularly useful to geotechnical engineering.This method has been developed in China,following well-accepted international procedures,to enhance understanding of stability issues in a number of geotechnical settings.Great advancements have been made in basic theory,the improvement of computational precision,and the broadening of practical applications.This paper presents the results of research on（1） the efficient design of embedded anti-slide piles,（2） the stability analysis of reservoir slopes with strength reduction theory,and（3） the determination of the ultimate bearing capacity of foundations using step-loading FEM（overloading）.These three applications are evidence of the design improvements and benefits made possible in geotechnical engineering by finite element modeling.

Application of strength reduction method to dynamic anti-sliding stability analysis of high gravity dam with complex dam foundation

Considering that there are some limitations in analyzing the anti-sliding seismic stability of dam-foundation systems with the traditional pseudo-static method and response spectrum method, the dynamic strength reduction method was used to study the deep anti-sliding stability of a high gravity dam with a complex dam foundation in response to strong earthquake-induced ground action. Based on static anti-sliding stability analysis of the dam foundation undertaken by decreasing the shear strength parameters of the rock mass in equal proportion, the seismic time history analysis was carried out. The proposed instability criterion for the dynamic strength reduction method was that the peak values of dynamic displacements and plastic strain energy change suddenly with the increase of the strength reduction factor. The elasto-plastic behavior of the dam foundation was idealized using the Drucker-Prager yield criterion based on the associated flow rule assumption. The result of elasto-plastic time history analysis of an overflow dam monolith based on the dynamic strength reduction method was compared with that of the dynamic linear elastic analysis, and the reliability of elasto-plastic time history analysis was confirmed. The results also show that the safety factors of the dam-foundation system in the static and dynamic cases are 3.25 and 3.0, respectively, and that the F2 fault has a significant influence on the anti-sliding stability of the high gravity dam. It is also concluded that the proposed instability criterion for the dynamic strength reduction method is feasible.

Strength reduction factors for seismic analyses of buildings exposed to near-fault ground motions

To estimate the near-fault inelastic response spectra, the accuracy of six existing strength reduction factors （R） proposed by different investigators were evaluated by using a suite of near-fault earthquake records with directivity-induced pulses. In the evaluation, the force-deformation relationship is modelled by elastic-perfectly plastic, bilinear and stiffness degrading models, and two site conditions, rock and soil, are considered. The R-value ratio （ratio of the R value obtained from the existing R-expressions （or the R-p-T relationships） to that from inelastic analyses） is used as a measurement parameter. Results show that the R-expressions proposed by Ordaz ＆ Perez-Rocha are the most suitable for near-fault ground motions, followed by the Newmark ＆ Hall and the Berrill et al. relationships. Based on an analysis using the near-fault ground motion dataset, new expressions of R that consider the effects of site conditions are presented and verified.

Seismic stability safety evaluation of gravity dam with shear strength reduction method

A new method of numerical seismic stability safety evaluation for a rock slope is proposed based on the analysis of a gravity dam foundation subjected to earthquake loading. The shear strengths of the weak discontinuities are divided by different shear strength reduction ratios （K） and numerical seismic analysis is carried out after the static analysis is completed. With different K values, the curves of the permanent horizontal displacement of key points of the dam foundation （K-displacement curves） are studied. According to the curve change, the distribution of plastic zones in the foundation, and the slow convergence of the finite element method （FEM）, the seismic stability safety factor is defined as Kwhen the gravity dam is in the limit equilibrium state subjected to earthquake loading. These concepts were applied to the evaluation of seismic stability safety of a gravity dam for a hydropower project. The analysis of the example shows that the proposed method is feasible and is an effective method of seismic stability safety evaluation.

Study on strength reduction factors consid-ering the effect of classification of design earthquake

The strength reduction factors are not only the key factors in determining seismic action for force-based seismic design, but also the key parameters to derive the inelastic response spectra for performance-based seismic design. In this paper, with a high quality ground motion database that includes a reasonable-sized set of records from China, a statistical study on the strength reduction factors is conducted and a new expression of strength reduction factors involving classification of design earthquake, which is an important concept to determine design spectra in Chinese seismic design code, is proposed. The expression of strength reduction factors can reflect the ground motion characteristics of China to a certain extent and is particularly suitable for Chinese seismic design. Then, the influence effects of site condition, classification of design earthquake, period of vibration, ductility level, earthquake magnitude and distance to fault on strength reduction factors are investigated. It is concluded that the effect of site condition on the strength reduction factors cannot be neglected, especially for the short-period structures of higher ductility. The classification of design earthquake also has an important effect on strength reduction factors and it may be unsuitable to use the existing expressions of strength reduction factors to the design spectra of current Chinese seismic code. The earthquake magnitude has no practical effect on strength reduction factors and if the near-fault records with forward directivity effect are not taken into consideration, the effect of distance to fault on strength reduction factors can also be neglected.

A New Criterion for Defining Inhomogeneous Slope Failure Using the Strength Reduction Method

A new variational method treating the system as a whole with rigorous mathematical and physical derivation was presented in this paper.Combined with classical and engineering examples,variational energy expressions of slopes were derived.In addition,the calculation programs were written in the FISH language set in FLAC3D(fast Lagrangian analysis of continua in three dimensions)software.Factors of safety(FOSs)of the models were determined by the variational method based on the strength reduction method(SRM)and then compared with other criteria or methods.The result showed that the variational method reflected the process of slope plasticity and failure uniformly and was feasible to analyze the stability of inhomogeneous slopes.The method was applicable to both two-dimensional and three-dimensional heterogeneous slopes.The small error with other criteria or methods also showed the accuracy of this method.This method unified other criteria,avoided the artificial error of other criteria,and provided a logical derivation for the instability of heterogeneous slope.This method considered the system as a whole and avoided the shortcomings of the general method of one-sided instability analysis.The proposed method is of great significance as it considers the coupling effect of stress and strain of materials and gives the mechanical basis for the instability of complex slopes.

Stability analysis of loose accumulation slopes under rainfall:case study of a high‑speed railway in Southwest China

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.

Safety Length Simulation of Natural Gas Pipeline Subjected to Transverse Landslide

The safety of natural gas pipeline is often severely threatened by the transverse landslide. At home and abroad, it is the first time to study the safe length of the pipeline when affected by landslide, and take the safe length of the pipeline as an engineering practical index. Therefore, it is of great significance to study the influence of transverse landslide affecting the safety of natural gas pipeline when a certain length of pipeline is thrusted, and to establish practical index and simulation method for prediction and prevention of the landslide hazards to gas pipeline. Based on the current research results, this study could be divided into three steps: First of all, with the help of ANSYS finite element software, the model of transverse landslide acting on the gas pipeline can be set up, then the length value of gas pipeline safely withstanding transverse landslide can be calculated;Secondly, using the strength reduction method, which is commonly used in the research of landslide stability, can establish three-dimensional model of the landslide and pipes in the ABAQUS finite element software, next, under the same landslide pushed length, the calculation results will be obtained;Finally, to draw reliable conclusions, all calculated results of the former two methods will be linked to synthetically and comparatively analyze, then the length value of common X80 gas pipeline safely bearing transverse landslide can be got. All results can provide some references for engineering and design.

Effect of Inclined Tension Crack on Rock Slope Stability by SSR Technique

The tension cracks and joints in rock or soil slopes affect their failure stability.Prediction of rock or soil slope failure is one of the most challenging tasks in the earth sciences.The actual slopes consist of inhomogeneous materials,complex morphology,and erratic joints.Most studies concerning the failure of rock slopes primarily focused on determining Factor of Safety(FoS)and Critical Slip Surface(CSS).In this article,the effect of inclined tension crack on a rock slope failure is studied numerically with Shear Strength Reduction Factor(SRF)method.An inclined Tension Crack(TC)influences the magnitude and location of the rock slope’s Critical Shear Strength Reduction Factor(CSRF).Certainly,inclined cracks are more prone to cause the failure of the slope than the vertical TC.Yet,all tension cracks do not lead to failure of the slope mass.The effect of the crest distance of the tension crack is also investigated.The numerical results do not show any significant change in the magnitude of CSRF unless the tip of the TC is very near to the crest of the slope.ATC is also replaced with a joint,and the results differ from the corresponding TC.These results are discussed regarding shear stress and Critical Slip Surface(CSS).

Finite element analyses of slope stability problems using non-associated plasticity

In recent years, finite element analyses have increasingly been utilized for slope stability problems. In comparison to limit equilibrium methods, numerical analyses do not require any definition of the failure mechanism a priori and enable the determination of the safety level more accurately. The paper compares the performances of strength reduction finite element analysis(SRFEA) with finite element limit analysis(FELA), whereby the focus is related to non-associated plasticity. Displacement-based finite element analyses using a strength reduction technique suffer from numerical instabilities when using non-associated plasticity, especially when dealing with high friction angles but moderate dilatancy angles. The FELA on the other hand provides rigorous upper and lower bounds of the factor of safety(FoS) but is restricted to associated flow rules. Suggestions to overcome this problem, proposed by Davis(1968), lead to conservative FoSs; therefore, an enhanced procedure has been investigated. When using the modified approach, both the SRFEA and the FELA provide very similar results. Further studies highlight the advantages of using an adaptive mesh refinement to determine FoSs. Additionally, it is shown that the initial stress field does not affect the FoS when using a Mohr-Coulomb failure criterion.

Stability analysis of bank slope under conditions of reservoir impounding and rapid drawdown

Stability of an ancient landslide in a reservoir area is analyzed by using centrifugal model tests, soil laboratory tests and numerical analysis. Special attention is paid to variation in water level, simulation of large-scale heterogeneous prototype slope, and strength reduction of sliding zone soils after slope sliding. The results of centrifugal model test show that reservoir impounding can reduce sliding resistance at the slope toe, followed by toe collapsing and front cracking of slope. Rapid drawdown can produce hydrodynamic pressure towards reservoir at the front of slope. Deformation is observed in the middle and upper slope, which reduces the slope stability further and forms the pull-typed landslide trend. Reinforcement of slope toe is effective for preventing the progressive failure. The results of laboratory test show that slope toe sliding will lead to the redistribution of soil density and moisture content, which will reduce the shear strength of soil in sliding zone, and the cohesion of immersed soil is reduced gradually and finally vanishes with time. The numerical results show that the strength reduction method used in finite element method (FEM) is very effective in capturing the progressive failure induced by reservoir water level fluctuations, and the evolution of failure surface derived from numerical simulation is very similar to that observed in centrifugal model test.

Study on embedded length of piles for slope reinforced with one row of piles

The embedded length of anti-slide piles for slope is analyzed by three-dimensional elastoplastic shear strength reduction method. The effect of embedded pile length on the factor of safety and pile behavior is analyzed. Furthermore, the effects of pile spacing, pile head conditions, pile bending stiffness and soil properties on length and behavior of pile are also analyzed. The results show that the pile spacing and the pile head conditions have significant influences on the critical embedded length of pile. It is found that the critical embedded length of pile, beyond which the factor of safety does not increase, increases with the decrease in pile spacing. The smaller the pile spacing is, the larger the integrity of the reinforced slope will be. A theoretical analysis of the slip surface is also conducted, and the slip surface determined by the pressure on piles, considering the influences of both soil and piles for slope, is in agreement with the ones in previous studies.

Factor of safety of strain-softening slopes

Stability analysis of strain-softening slopes is carried out using the shear strength reduction method and Mohr-Coulomb model with degrading cohesion and friction angle.The e ffect of strain-softening behavior on the slope factor of safety is investigated by performing a series of analyses for various slope geometries and strength properties.Stability charts and equations are developed to estimate the factor of safety of strain-softe ning slopes from the results of traditional stability analysis based on perfectly-plastic behavior.Two example applications including an open pit mine in weak rock and clay shale slope with daylighting bedding planes are presented.The results of limit equilibrium analysis and shear strength reduction method with perfectly-plastic models were in close agreement.Using perfectly-plastic models with peak strength properties led to overly optimistic results while adopting residual strength properties gave excessively conservative outcomes.The shear strength reduction method with a strain-softening model gave realistic factors of safety while accounting for the process of strength degradation.

Numerical analysis of rainfall effects in external overburden dump

The effect of slope angle for external overburden dump in response to average and heavy rainfall has been analyzed using a two dimensional finite difference method of transient water flow through unsaturated–saturated soil. The external dump stability is evaluated for five geomaterial types on the basis of globally accepted safety factor analysis technique, based on shear strength reduction approach using finite difference method. The results obtained from the finite difference method of analysis indicate that the external dump with more than 30° slope angle is greatly influenced by the rainfall under the studied conditions for geomaterial 3, 4 and 5, whereas dumps with geomaterial 1 and 2 remain safe. The analysis shows that major slope failure is out of preview for the studied rainfall conditions.

Fatigue Characterization on a Cast Aluminum Beam of a High-Speed Train Through Numerical Simulation and Experiments

The cast aluminum beam is a key structure for carrying the body-hung traction motor of a high-speed train;its fatigue property is fundamental for predicting the residual life and service mileage of the structure.To characterize the structural fatigue property,a finite element-based method is developed to compute the stress concentration factor,which is used to obtain the structural fatigue strength reduction factors.A full-scale fatigue test on the cast aluminum beam is designed and implemented for up to ten million cycles,and the corresponding finite element model of the beam is validated using the measured data of the gauges.The results show that the maximum stress concentration occurs at the fillet of the supporting seat,where the structural fatigue strength reduction factor is 2.45 and the calculated fatigue limit is 35.4 MPa.Moreover,no surface cracks are detected using the liquid penetrant test.Both the experimental and simulation results indicate that the cast aluminum beam can satisfy the service life requirements under the designed loading conditions.

Finite element analysis of slope stability by expanding the mobilized principal stress Mohr's circles-Development, encoding and validation

In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies.However,the application of finite element method(FEM)to slope stability as a strength reduction method(SRM)or as finite element limit analysis(FELA)is not always a success for the drawbacks that characterize both methods.To increase the performance of finite element analysis in this problem,a new approach is proposed in this paper.It consists in gradually expanding the mobilized stress Mohr’s circles until the soil failure occurs according to a prescribed non-convergence criterion.The present approach called stress deviator increasing method(SDIM)is considered rigorous for three main reasons.Firstly,it preserves the definition of the factor of safety(FOS)as the ratio of soil shear strength to the mobilized shear stress.Secondly,it maintains the progressive development of shear stress resulting from the increase in the principal stress deviator on the same plane,on which the shear strength takes place.Thirdly,by introducing the concept of equivalent stress loading,the resulting trial stresses are checked against the violation of the actual yield criterion formed with the real strength parameters rather than those reduced by a trial factor.The new numerical procedure was encoded in a Fortran computer code called S^(4)DINA and verified by several examples.Comparisons with other numerical methods such as the SRM,gravity increasing method(GIM)or even FELA by assessing both the FOS and contours of equivalent plastic strains showed promising results.

Quasi-Monte Carlo Simulation-Based SFEM for Slope Reliability Analysis

Considering the stochastic spatial variation of geotechnical parameters over the slope, a Stochastic Finite Element Method (SFEM) is established based on the combination of the Shear Strength Reduction (SSR) concept and quasi-Monte Carlo simulation. The shear strength reduction FEM is superior to the slice method based on the limit equilibrium theory in many ways, so it will be more powerful to assess the reliability of global slope stability when combined with probability theory. To illustrate the performance of the proposed method, it is applied to an example of simple slope. The results of simulation show that the proposed method is effective to perform the reliability analysis of global slope stability without presupposing a potential slip surface.

Reliability Assessment of an Open Pit Slope on Bong Iron Ore Mine

Slope stability on Bong mine is crucial for securing a balance in the gross national product of Liberia. The mine is being operated using conventional open pit methods with slope angles optimally designed to maximize ore stripping quantity. However, a working slope has displayed signs of uncertainty. The overall inclination of the slope is 56°, and the proposed maximal excavation is 315.42 m, but current depth in ore is approximately 50%. Based on the study of slope geological characteristics, the physical and mechanical parameters of rock mass and the geometrical calculation of stoping, the study is tailored on the mechanism of inspecting stress-strain behavior in response to seasonal variation of rock moisturization as a more suitable means of stope slope stability analysis in this case. This study took full account of local rainfall and other meteorological conditions. Slope stability is investigated via stereographic projections and stability assessment using the Shear Strength Reduction (SSR) method based on FLAC (Fast Lagrangian Analysis of Continua) numerical modeling technique in three dimensions to predict the stress-strain behavior of the open-pit slope and evaluate its stability state. Global stability has been analyzed under natural and saturated conditions and it is found that the slope is critically stable and needs proper attention.