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.

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.

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.

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.

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.

Effect of structural characteristics distribution on strength demand and ductility reduction factor of MDOF systems considering soil-structure interaction

It is known that structural stiffness and strength distributions have an important role in the seismic response of buildings. The effect of using different code-specified lateral load patterns on the seismic performance of fixed-base buildings has been investigated by researchers during the past two decades. However, no investigation has yet been carried out for the case of soil-structure systems. In the present study, through intensive parametric analyses of 21,600 linear and nonlinear MDOF systems and considering five different shear strength and stiffness distribution patterns, including three code-specified patterns as well as uniform and concentric patterns subjected to a group of earthquakes recorded on alluvium and soft soils, the effect of structural characteristics distribution on the strength demand and ductility reduction factor of MDOF fixed-base and soil-structure systems are parametrically investigated. The results of this study show that depending on the level of inelasticity, soil flexibility and number of degrees-of-freedoms (DOFs), structural characteristics distribution can significantly affect the strength demand and ductility reduction factor of MDOF systems. It is also found that at high levels of inelasticity, the ductility reduction factor of low-rise MDOF soil-structure systems could be significantly less than that of fixed-base structures and the reduction is less pronounced as the number of stories increases.

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.

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.

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.

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.

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.

Reinforcement strength reduction in FEM for mechanically stabilized earth structures

The factor of safety of mechanically stabilized earth(MSE) structures can be analyzed either using limit equilibrium method(LEM) or strength reduction method(SRM) in finite element/difference method. In LEM, the strengths of the reinforcement members and soils are reduced with the same factor. While using the SRM, only soil strength is reduced during the calculation of the factor of safety. This causes inconsistence in calculating the factor of safety of the MSE structures. To overcome this, an iteration method is proposed to consider the strength reduction of the reinforcements in SRM. The method is demonstrated by using PLAXIS, a finite element software. The results show that the factor of safety converges after a few iterations. The reduction of strength has different effects on the factor of safety depending on the properties of the reinforcements and the soil, and failure modes.

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.

考虑水力效应的裂缝边坡稳定性非线性能耗分析

现有考虑水力效应的裂缝边坡稳定性分析大多基于线性破坏准则,而岩土体破坏往往呈现非线性特征,因此开展水力效应影响下的裂缝边坡稳定性非线性极限上限分析具有重要意义。基于极限分析上限定理及强度折减技术,结合“外切线法”非线性破坏准则,构建坡顶含竖直裂缝的边坡对数螺旋线破坏模式,根据虚功原理推导出裂缝边坡安全系数解析式,通过MATLAB优化计算,结合边坡工程实例探讨了典型因素对裂缝边坡稳定性、临界裂缝及滑动面位置的影响规律。研究结果表明:随着地下水位h的持续上升,边坡安全系数不断降低,临界裂缝深度逐渐增大且临界裂缝位置逐渐向坡顶缘偏移;非线性系数m明显影响边坡的稳定性,边坡安全系数随着非线性系数的增大显著减小,采用线性破坏准则会高估地下水位变化对边坡稳定性的影响;随着非线性系数的增大,临界裂缝深度随之增大,临界裂缝位置距离坡顶缘越来越远,滑坡体体积逐渐增大;裂缝与坡顶缘距离l m随着非线性系数m的增大而增大(当m增大0.2时,l m增大约1 m),且随着裂缝与坡顶缘距离的增大,边坡安全系数无明显变化,临界裂缝深度先逐渐减小后趋于稳定。

基于PFC模拟的饱和粉砂强度折减范围研究

为验证基于颗粒流程序(particle flow code,PFC)模拟的饱和粉砂土体变形和破坏状态下土力学参数与孔隙度的关系,以呼和浩特市地铁2号线公主府站至呼和浩特站盾构区间前期钻探土样为研究基础,对饱和粉砂进行一系列密度梯度的三轴不固结不排水室内试验,根据换算公式将密度指标转化为孔隙度指标,对孔隙度与内摩擦角之间的关系式以及孔隙度、围压与变形模量之间的定量关系式进行拟合。通过离散元法进行三轴数值模拟试验,监测试件在压剪过程中孔隙度随试件变形的变化规律,从而确定饱和粉砂在弹塑性变形阶段和破坏阶段土体孔隙度与变形模量及内摩擦角之间的关系。结果表明,土体强度随密度的增加而增加,基本呈现线性增加的规律。将孔隙度随土体应变变化的曲线对应到内摩擦角随孔隙度变化的拟合曲线中,可以得到饱和粉砂不同阶段土力学参数的取值范围,明确土体强度折减范围。通过PFC模拟曲线确定不同阶段对应的区段,为完善饱和粉砂强度折减规律分析提供了新的方法。

高寒地区某高陡露天矿山边坡冻融循环条件下稳定性分析

为分析西部高寒高海拔地区某露天矿山设计边坡在冻融影响下的稳定性及变形破坏特征,本文参考设计情况选定了典型计算剖面,并基于岩石的冻融强度试验结果及常规力学计算结果,确定了岩体的计算力学参数;针对冻融对岩体边坡的影响,推断冻融层的分布规律,在此基础上结合地层信息确定数值计算的力学参数赋值;此后采用有限差分程序,定量分析了在自重、岩体开挖、爆破及地震荷载作用下边坡的力学响应特性,并结合强度折减算法,求解得到了对应的潜在滑动面形态及安全系数,结果显示研究边坡安全系数分别为:自重+地下水—1.465,自重+地下水+爆破振动—1.402,自重+地下水+地震—1.363,均满足现行规范要求。本研究成果为高寒地区冻融岩层的力学特性以及受冻融影响露天煤矿的边坡稳定性研究提供了参考。

基于位移变形监测和FLAC^(2D)南大沟排土场边坡稳定性分析

露天矿排土场作为矿山废土石的收容所,其稳定性直接关系着矿山生产安全和人员生命财产安全,是矿山安全管理的重点。为了研究南大沟排土场高边坡的稳定性和确保排土场后期安全运营,本文深入分析了该排土场工程地质资料,结合现场调查和堆排现状图,建立了典型边坡剖面的数值计算模型,创新性采用FLAC^(2D)数值分析软件定量评价和位移变形监测相结合的手段对南大沟排土场边坡稳定性进行了综合分析,再现了边坡潜在破坏的演化过程。通过分析稳定性计算结果和位移监测数据可以得到:其边坡破坏模式为顶部平台拉裂,下部以圆弧形剪出;经定性评价、定量计算后,三种工况下的边坡稳定性系数高于规范规定的安全系数,达到了安全等级一级的要求,排土场边坡整体处于稳定状态,证明了现有排土场的安全性和稳定性;通过位移监测数据结果表明排土场一年多内累计变形都维持在预警值范围以内,有较强的自稳能力。数值模拟与变形监测手段相结合的综合分析评价方法准确且合理,为矿山开采和废石堆排提供了安全保障,同时也为排土场稳定性分析提供了技术指导。该综合分析方法为其他矿山排土场边坡稳定性分析提供了借鉴。

基于响应面法的砂质黄土路堑高边坡稳定性研究

为给砂质黄土路堑高边坡设计提供参考,以甘肃某山区砂质黄土路堑高边坡为工程依托,采用强度折减法研究坡高、坡率和台阶高度对边坡安全系数的影响规律,在此基础上采用响应面法,以边坡安全系数为基准对黄土路堑高边坡坡形进行优化设计。研究结果表明:边坡稳定安全系数(F S)与单级坡高呈负相关关系,与单级坡率、台阶宽度呈正相关关系;坡形参数对边坡F S影响程度为:台阶宽度>单级坡高>单级坡率;基于回归模型方程给出的数值解得到不同坡高(H)条件下的最优坡形设计方案。研究结果可为西北砂质黄土高边坡稳定性设计和针对性治理提供理论基础。

深海能源土含气储层边坡稳定性研究

深海能源土开采不当往往会造成含水合物储层的强度劣化,诱发海床失稳问题。为探究深海能源土开采对含气储层边坡稳定性的影响,以深海能源土采挖回填装置的开采工况为实际工程背景,针对3种工况下能源土采挖回填诱发的海底滑坡现象,基于有限元强度折减法建立数值模型,分析不同黏土含量、含气量及回填加固等因素引起的水合物含气储层稳定性问题,得到相应安全系数。研究结果表明:黏土含量越高,海底沉积物边坡的安全系数越低,边坡稳定性越差;含气量对深海能源土含气储层的边坡稳定性呈非线性影响,安全系数随含气量的增加呈先上升后下降的趋势;采用胶结性材料进行回填加固处理可提高海底边坡安全系数,边坡稳定性增强。