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.

Application of dynamic analysis of strength reduction in the slope engineering under earthquake

At present,the methods of analyzing the stability of slope under earthquake are not accurate and reasonable because of some limitations. Based on the real dynamic tensile-shear failure mechanism of slope,the paper proposes dynamic analysis of strength reduction FEM (finite element method) and takes the reduction of shear strength parameters and tensile strength parameters into consideration. And it comprehensively takes the transfixion of the failure surface,the non-convergence of calculation and mutation of displacement as the criterion of dynamic instability and failure of the slope. The strength reduction factor under limit state is regarded as the dynamic safety factor of the slope under earthquake effect and its advantages are introduced. Finally,the method is applied in the seismic design of anchors supporting and anti-slide pile supporting of the slope. Calculation examples show that the application of dynamic analysis of strength reduction is feasible in the seismic design of slope engineering,which can consider dynamic interaction of supporting structure and rock-soil mass. Owing to its preciseness and great advantages,it is a new method in the seismic design of slope supporting.

Application of the strength reduction FEM to diversion tunnel plug stability

Firstly,the common design principles for diversion tunnel plug are generalized,and two kinds of numerical analysis methods are discussed.Then the strength reduction FEM is introduced in numerical model analysis and the design steps of the plug's length are illustrated.During the progress to determine the plug's length,the equivalent plastic strain on the potential slip surface is assumed as the flag to tell the failure against sliding,and the plug stability is overall estimated from the plastic zone range and connectivity.

Upper bound analysis of slope stability with nonlinear failure criterion based on strength reduction technique

Based on the upper bound limit analysis theorem and the shear strength reduction technique, the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its corresponding critical failure mechanism by means of the kinematical approach of limit analysis theory. The nonlinear shear strength parameters were treated as variable parameters and a kinematically admissible failure mechanism was considered for calculation schemes. The iterative optimization method was adopted to obtain the safety factors. Case study and comparative analysis show that solutions presented here agree with available predictions when nonlinear criterion reduces to linear criterion, and the validity of present method could be illuminated. From the numerical results, it can also be seen that nonlinear parameter rn, slope foot gradient ,β, height of slope H, slope top gradient a and soil bulk density γ have significant effects on the safety factor of the slope.

Couple analysis on strength reduction theory and rheological mechanism for slope stability

Considering the rheological properties of rock and soil body,and exploiting the merit of strength reduction technique,a theory of couple analysis is brought forward on the basis of strength reduction theory and rheological properties.Then,the concept and the calculation procedure of the safety factor are established at different time.Making use of finite element software ANSYS,the most dangerous sliding surface of the slope can be obtained through the strength reduction technique.According to the dynamic safety factor based on rheological mechanism,a good forecasting could be presented to prevent and cure the landslide.The result shows that the couple analysis reveals the process of the slope failure with the time and the important influence on the long-term stability due to the rheological parameters.

Limit equilibrium method(LEM) of slope stability and calculation of comprehensive factor of safety with double strength-reduction technique

When the slope is in critical limit equilibrium(LE) state, the strength parameters have different contribution to each other on maintaining slope stability. That is to say that the strength parameters are not simultaneously reduced. Hence, the LE stress method is established to analyze the slope stability by employing the double strengthreduction(DSR) technique in this work. For calculation model of slope stability under the DSR technique, the general nonlinear Mohr–Coulomb(M–C) criterion is used to describe the shear failure of slope. Meanwhile, the average and polar diameter methods via the DSR technique are both adopted to calculate the comprehensive factor of safety(FOS) of slope. To extend the application of the polar diameter method, the original method is improved in the proposed method. After comparison and analysis on some slope examples, the proposed method's feasibility is verified. Thereafter, the stability charts of slope suitable for engineering application are drawn. Moreover, the studies show that:(1) the average method yields similar results as that of the polardiameter method;(2) compared with the traditional uniform strength-reduction(USR) technique, the slope stability obtained using the DSR techniquetends to be more unsafe; and(3) for a slope in the critical LE state, the strength parameter φ, i.e., internal friction angle, has greater contribution on the slope stability than the strength parameters c, i.e., cohesion.

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.

Strength reduction method for slope based on a ubiquitous-joint criterion and its application

In order to expand the application of strength reduction methods with the ubiquitous-joint criterion, the corresponding program is compiled using FLAC3D software. A procedure for strength reduction in the ubiquitous-joint criterion is proposed to study the safety factor of slopes as well as the relationships of the bedding plane inclination angle β and the safety factor F. The results show that： 1） for the bedding rock slope, the various failure modes cause different variations of the safety factor F; 2） a bed- ding rock slope can be divided into two types by the angle between the bedding plane inclination and slope surface inclination a; when a_〈45~, the bedding slope can be strictly defined as the subsequent bedding rock slope; when 45°〈α〈90°, the bedding slope is defined as an oblique bedding slope; 3） for bedding rock slopes, the safety factor increases with an increase in a; for inverse bed- ding slopes, when the bedding plane inclination angle fl is small, the safety factor F of the slope increases at first, then decreases with an increase in a; when β is large, the safety factor F increases with an increase in α.

Multi-factor sensitivity analysis on the stability of submarine hydrate-bearing slope

There are many factors affecting the instability of the submarine hydrate-bearing slope (SHBS),and the interaction with hydrate is very complicated.In this paper,the mechanical mechanism of the static liquefaction and instability of submarine slope caused by the dissociation of natural gas hydrate (NGH) resulting in the rapid increase of pore pressure of gas hydrate-bearing sediments (GHBS) and the decrease of effective stress are analyzed based on the time series and type of SHBS.Then,taking the typical submarine slope in the northern South China Sea as an example,four important factors affecting the stability of SHBS are selected,such as the degree of hydrate dissociation,the depth of hydrate burial,the thickness of hydrate,and the depth of seawater.According to the principle of orthogonal method,25 orthogonal test schemes with 4 factors and 5 levels are designed and the safety factors of submarine slope stability of each scheme are calculated by using the strength reduction finite element method.By means of the orthogonal design range analysis and the variance analysis,sensitivity of influential factors on stability of SHBS are obtained.The results show that the degree of hydrate dissociation is the most sensitive,followed by hydrate burial depth,the thickness of hydrate and the depth of seawater.Finally,the concept of gas hydrate critical burial depth is put forward according to the influence law of gas hydrate burial depth,and the numerical simulation for specific submarine slope is carried out,which indicates the existence of critical burial depth.

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

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

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.

Stability analysis of submarine slopes in the area of the test production of gas hydrate in the South China Sea

In this paper, the mechanical properties of gas hydrate-bearing sediments (GHBS) were summarized and the instability mechanism of submarine hydrate-bearing slope (SHBS) was analyzed under the background of the test production of gas hydrate in the northern part of the South China Sea. The strength reduction finite element method (SRFEM) was introduced to the stability analysis of submarine slopes for the safety of the test production. Two schemes were designed to determine the physical and mechanical parameters of four target wells. Through the division of the hydrate dissociation region and the design of four working conditions, the range and degree of hydrate dissociation at different stages during the test production were simulated. Based on the software ABAQUS, 37 FEM models of SHBS were set up to analyze and assess the stability of the submarine slopes in the area of the test production. Necessary information such as safety factors, deformation, and displacement were obtained at different stages and under different working conditions. According to the calculation results, the submarine slope area is stable before the test production, and the safety factors almost remains the same during and after the test production. All these indicate that the test production has no obvious influence on the area of the test production and the submarine slopes in the area are stable during and after the test production.

Study on the FEM design of reinforced earth retaining wall with geogrid

At present,limit equilibrium method is often adopted in the design of reinforced earth retaining wall. Geotechnical engineers home and abroad have done a lot of work to improve the traditional calculation methods in recent years,while there are lots of defects. This paper first identifies the location of failure surface and safety factor through the finite element program of PLAXIS and then analyses the influencing factors of the stability of reinforced earth retaining wall with geogrid. The authors adopt strength reduction FEM (finite element method)in the design and stability analysis of reinforced earth retaining wall and have achieved some satisfying results. Without any assumptions,the new design method can automatically judge the failure mode of reinforced earth retaining wall,consider the influence of axial tensile stiffness of the reinforcement stripe on the stability of retaining wall,identify reasonable distance and length of the reinforcement stripe,and choose suitable parameters of reinforcement stripe,including strength,stiffness and pseudo-friction coefficient which makes the design optimal. It is proved through the calculation examples that this method is more reasonable,reliable and economical in the design of reinforced earth retaining wall.

Numerical Analysis of the Stability of Embankment Slope Reinforced with Piles

The effects of stabilizing piles on the stability of an embankment slope are analyzed by numerical simulation. The shear strength reduction method is used for the analysis, and the soil - pile interaction is simulated with zero-thickness elasto-plastic interface elements. Effects of pile spacing and pile position on the safety factor of slope and the behavior of piles under these conditions are given. The numerical analysis indicates that the positions of the pile have significant influence on the stability of the slope, and the pile needs to be installed in the middle of the slope for maximum safety factors. In the end, the soil arching effect closely associated with the space between stabilizing piles is analyzed. The results are helpful for design and construction of stabilizing piles.

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.

A strength reduction method based on double reduction parameters and its application

In the traditional strength reduction method,the cohesion and the friction angle adopt the same reduction parameter,resulting in equivalent proportional reduction.This method does not consider the different effects of the cohesion and friction angle on the stability of the same slope and is defective to some extent.Regarding this defect,a strength reduction method based on double reduction parameters,which adopts different reduction parameters,is proposed.The core of the double-parameter reduction method is the matching reduction principle of the slope with different angles.This principle is represented by the ratio of the reduction parameter of the cohesion to that of the friction angle,described as η.With the increase in the slopeangle,ηincreases; in particular,when the slope angle is 45°,tηis 1.0.Through the matching reduction principle,different safety margin factors can be calculated for the cohesion and friction angle.In combination with these two safety margin factors,a formula for calculating the overall safety factor of the slope is proposed,reflecting the different contributions of the cohesion and friction angle to the slope stability.Finally,it is shown that the strength reduction method based on double reduction parameters acquires a larger safety factor than the classic limit equilibrium method,but the calculation results are very close to those obtained by the limit equilibrium method.

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.

Directly searching method for slip plane and its influential factors based on critical state of slope

In order to determine the slip plane of slope directly by the calculation results of strength reduction method, and analyze the influential factors of slope stability, a numerical model was established in plane strain mode by FLAC3D for homogeneous soil slope, whose parameters were reduced until the slope reached the critical state. Then FISH program was used to get the location data of slip plane from displacement contour lines. Furthermore, the method to determine multiple slip planes was also proposed by setting different heights of elastic areas. The influential factors for the stability were analyzed, including cohesion, internal friction angle, and tensile strength. The calculation results show that with the increase of cohesion, failure mode of slope changes from shallow slipping to the deep slipping, while inclination of slip plane becomes slower and slipping volume becomes larger; with the increase of friction angle, failure mode of slope changes from deep slipping to shallow slipping, while slip plane becomes steeper and upper border of slip plane comes closer to the vertex of slope; the safety factor increases little and slip plane goes far away from vertex of slope with the increase of tensile strength.

A new double reduction method for slope stability analysis

The core of strength reduction method(SRM) involves finding a critical strength curve that happens to make the slope globally fail and a definition of factor of safety(FOS). A new double reduction method, including a detailed calculation procedure and a definition of FOS for slope stability was developed based on the understanding of SRM. When constructing the new definition of FOS, efforts were made to make sure that it has concise physical meanings and fully reflects the shear strength of the slope. Two examples, slopes A and B with the slope angles of 63° and 34° respectively, were given to verify the method presented. It is found that, for these two slopes, the FOSs from original strength reduction method are respectively 1.5% and 38% higher than those from double reduction method. It is also found that the double reduction method predicts a deeper potential slide line and a larger slide mass. These results show that on one hand, the double reduction method is comparative to the traditional methods and is reasonable, and on the other hand, the original strength reduction method may overestimate the safety of a slope. The method presented is advised to be considered as an additional option in the practical slope stability evaluations although more useful experience is required.

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.