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.

Attribute Reduction for Information Systems via Strength of Rules and Similarity Matrix

An information system is a type of knowledge representation,and attribute reduction is crucial in big data,machine learning,data mining,and intelligent systems.There are several ways for solving attribute reduction problems,but they all require a common categorization.The selection of features in most scientific studies is a challenge for the researcher.When working with huge datasets,selecting all available attributes is not an option because it frequently complicates the study and decreases performance.On the other side,neglecting some attributes might jeopardize data accuracy.In this case,rough set theory provides a useful approach for identifying superfluous attributes that may be ignored without sacrificing any significant information;nonetheless,investigating all available combinations of attributes will result in some problems.Furthermore,because attribute reduction is primarily a mathematical issue,technical progress in reduction is dependent on the advancement of mathematical models.Because the focus of this study is on the mathematical side of attribute reduction,we propose some methods to make a reduction for information systems according to classical rough set theory,the strength of rules and similarity matrix,we applied our proposed methods to several examples and calculate the reduction for each case.These methods expand the options of attribute reductions for researchers.

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.

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.

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.

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 asη.With the increase in the slope angle,ηincreases;in particular,when the slope angle is 45°,ηis 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 and stiffness reduction factors for infilled frames with openings

Framed structures are usually infilled with masonry walls. They may cause a significant increase in both stiffness and strength, reducing the deformation demand and increasing the energy dissipation capacity of the system. On the other hand, irregular arrangements of the masonry panels may lead to the concentration of damage in some regions, with negative effects; for example soft story mechanisms and shear failures in short columns. Therefore, the presence ofinfill walls should not be neglected, especially in regions of moderate and high seismicity. To this aim, simple models are available for solid infills walls, such as the diagonal no-tension strut model, while infilled frames with openings have not been adequately investigated. In this study, the effect of openings on the strength and stiffness of infilled frames is investigated by means of about 150 experimental and numerical tests. The main parameters involved are identified and a simple model to take into account the openings in the infills is developed and compared with other models proposed by different researchers. The model, which is based on the use of strength and stiffness reduction factors, takes into account the opening dimensions and presence of reinforcing elements around the opening. An example of an application of the proposed reduction factors is also presented.

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.

Stability analysis of shallow tunnels subjected to seepage with strength reduction theory

Based on strength reduction theory,the stability numbers of shallow tunnels were investigated within the framework of upper and lower bound theorems of limit analysis. Stability solutions taking into account of water seepage were presented and compared with those without considering seepage. The comparisons indicate that the maximum difference does not exceed 3.7%,which proves the present method credible. The results show that stability numbers of shallow tunnels considering seepage are much less than those without considering seepage,and that the difference of stability numbers between considering seepage and without considering seepage increase with increasing the depth ratio. The stability numbers decrease with increasing permeability coefficient and groundwater depth. Seepage has significant effects on the stability numbers of shallow tunnels.

Mesomechanics Finite-element Method for Determining the Shear Strength of Mudded Intercalation Materials

A new method regarding mesomechanics finite-element research is proposed to predict the peak shear strength of mudded intercalation materials on a mesoscopic scale. Based on geometric and mechanical parameters, along with the strain failure criteria obtained by sample＇s deformation characteristics, uniaxial compression tests on the sample were simulated through a finite-element model, which yielded values consistent with the data from the laboratory uniaxial compression tests, implying that the method is reasonable. Based on this model, a shear test was performed to calculate the peak shear strength of the mudded intercalation, consistent with values reported in the literature, thereby providing a new approach for investigating the mechanical properties of mudded intercalation materials.

Limit analysis of vertical anti-pulling screw pile group under inclined loading on 3D elastic-plastic finite element strength reduction method

Based on the functional theory, catastrophe theory, simultaneity principle and the idea of strength reduction method(SRM), the bearing capacity functional and SRM of pile group foundation were established, and the criteria of ultimate load and the concept of safety storage coefficient(CSS) were advanced. The inclined ultimate loads by the static loading test, load increment method(LIM) and SRM are compared. Theoretically, the ultimate load of piles does not change with the loading levels when it is calculated by SRM. When the one strength reduction parameter is applied in the calculation boundary, there are calculating errors because the bearing capacity action of soils happened in the finite zone. The inclined loadings are 108, 132 and 144 kN, and SSC are 1.07, 0.94 and 0.79, respectively, so the calculation values of ultimate loads are about 115.56, 124.08 and 113.76 kN, respectively. The error between calculations and observation values is less than 6%. But the error between calculations of LIM and observations is 20%. Because of the effect of inclined loading, the push-rotation phenomenon of screw pile group appears. Under this testing, the ultimate bearing capacity of piles is mostly determined by the horizontal ultimate bearing capacity, and the effect of the vertical component of inclined load should also be considered.

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 bedding rock slope can be divided into two types by the angle between the bedding plane inclination and slope surface inclination α;when α≤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 α;for inverse bedding slopes,when the bedding plane inclination angle β is small,the safety factor F of the slope increases at first,then decreases with an increase in α;when β is large,the safety factor F increases with an increase in α.

Progressive Modelling of the Gravity-induced Landslide Using the Local Dynamic Strength Reduction Method

The failure of slope is a progressive process, and the whole sliding surface is caused by the gradual softening of soil strength of the potential sliding surface. From this viewpoint, a local dynamic strength reduction method is proposed to capture the progressive failure of slope. This method can calculate the warning deformation of landslide in this study. Only strength parameters of the yielded zone of landslide will be reduced by using the method. Through continuous local reduction of the strength parameters of the yielded zone, the potential sliding surface developed gradually and evolved to breakthrough finally. The result shows that the proposed method can simulate the progressive failure of slope truly. The yielded zone and deformation of landslide obtained by the method are smaller than those of overall strength reduction method. The warning deformation of landslide can be obtained by using the local dynamic strength reduction method which is based on the softening characteristics of the sliding surface.

Upper bound solutions of stability factor of shallow tunnels in saturated soil based on strength reduction technique

Based on the upper bound theorem of limit analysis,the factor of safety for shallow tunnel in saturated soil is calculated in conjunction with the strength reduction technique.To analyze the influence of the pore pressure on the factor of safety for shallow tunnel,the power of pore pressure is regarded as a power of external force in the energy calculation.Using the rigid multiple-block failure mechanism,the objective function for the factor of safety is constructed and the optimal solutions are derived by employing the sequential quadratic programming.According to the results of optimization calculation,the factor of safety of shallow tunnel for different pore pressure coefficients and variational groundwater tables are obtained.The parameter analysis shows that the pore pressure coefficient and the location of the groundwater table have significant influence on the factor of safety for shallow tunnel.

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 m,slope foot gradient β,height of slope H,slope top gradient α and soil bulk density γ have significant effects on the safety factor of the slope.

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.

A case study of multi-seam coal mine entry stability analysis with strength reduction method

In this paper,the advantage of using numerical models with the strength reduction method(SRM) to evaluate entry stability in complex multiple-seam conditions is demonstrated.A coal mine under variable topography from the Central Appalachian region is used as a case study.At this mine,unexpected roof conditions were encountered during development below previously mined panels.Stress mapping and observation of ground conditions were used to quantify the success of entry support systems in three room-and-pillar panels.Numerical model analyses were initially conducted to estimate the stresses induced by the multiple-seam mining at the locations of the affected entries.The SRM was used to quantify the stability factor of the supported roof of the entries at selected locations.The SRM-calculated stability factors were compared with observations made during the site visits,and the results demonstrate that the SRM adequately identifies the unexpected roof conditions in this complex case.It is concluded that the SRM can be used to effectively evaluate the likely success of roof supports and the stability condition of entries in coal mines.

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.