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.

Residual fatigue strength of 48MnV crankshaft based on safety factor

Residual fatigue strength of 48MnV crankshaft was studied and analyzed based on safety factor. Three different status crankshafts were used to the hop-up tests, which maintain new after 500h hop-up tests and after 1000h hop-up tests. Then, crankshafts were cut into unit cranks. The unit cranks were used to do endurance bending tests to get the residual fatigue strength. Finally, the results were analyzed based on safety factor. The results show that safety factor of crankshaft descends a little with the increase of the running time, and the residual safety factor is still much bigger than the endurable safety factor. Furthermore, after the crankshaft accomplishes a full life cycle, the residual fatigue strength of the crankshaft is enough to remanufacture and fulfill the next life cycle.

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.

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.

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.

土体抗剪强度各向异性对边坡滑动模式与稳定性的影响

基于极限分析法中的上限定理,开展了考虑土体抗剪强度各向异性的边坡稳定性研究,通过参数分析研究了土体抗剪强度各向异性对边坡失稳滑动方式与边坡稳定性安全系数的影响规律.结果表明:边坡稳定性安全系数随着抗剪强度各向异性系数减小而减小,其影响程度随着土体内摩擦角和坡度的减小而增大;对于土体黏聚力较大、内摩擦角较小的缓坡,随着抗剪强度各向异性系数减小,边坡的最危险滑动面会由坡脚深层破坏转变为坡底深层破坏,滑动范围显著增大;基于计算结果绘制了稳定图(stability chart),实现了考虑土体抗剪强度各向异性影响的边坡稳定性安全系数的快速计算与最危险滑动方式的判别.

考虑安全系数的汽车传动轴结构可靠性分析

合理地设计和选用汽车传动轴对保证整车动力系统可靠性非常重要。考虑安全系数的影响,建立传动轴应力极限状态的可靠性数模,将可靠性设计理论、一次二阶矩方法(FSOM)和Monte-Carlo仿真(MCS)数值模拟法相结合,计算了结构可靠度和可靠性灵敏度。以某型汽车传动轴为算例,讨论汽车传动轴在安全系数影响下选用的可靠性,得到了汽车传动轴结构可靠性最大的影响因素,为汽车传动轴后续的结构选型及稳健优化设计提供了重要的参考价值。

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 analysis for rock slope stability using basic Hoek–Brown strength criterion

Hoek–Brown(HB)strength criterion can reflect rock’s inherent failure nature,so it is more suitable for analyzing the stability of rock slopes.However,the traditional limit equilibrium methods are at present only suitable for analyzing the rock slope stability using the linear equivalent Mohr–Coulomb(EMC)strength parameters instead of the nonlinear HB strength criterion.Therefore,a new method derived to analyze directly the rock slope stability using the nonlinear HB strength criterion for arbitrary curve slip surface was described in the limit equilibrium framework.The current method was established based on certain assumptions concerning the stresses on the slip surface through amending the initial normal stressσ0 obtained without considering the effect of inter-slice forces,and it can satisfy all static equilibrium conditions of the sliding body,so the current method can obtain the reasonable and strict factor of safety(FOS)solutions.Compared with the results of other methods in some examples,the feasibility of the current method was verified.Meanwhile,the parametric analysis shows that the slope angleβhas an important influence on the difference of the results obtained using the nonlinear HB strength criterion and its linear EMC strength parameters.Forβ≤45°,both of the results are similar,showing the traditional limit equilibrium methods using the linear EMC strength parameters and the current method are all suitable to analyze rock slope stability,but forβ>60°,the differences of both the results are obvious,showing the actual slope stability state can not be reflected in the traditional limit equilibrium methods,and then the current method should be used.

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.

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。

基于允许可靠度的薄壁圆筒静强度安全系数

为建立钢制单层承压薄壁圆筒静强度的可靠性设计技术,当圆筒静强度与载荷分别符合正态分布且静强度分布参数为区间值时,应用概率论知识,构建了圆筒静强度在不同工况的可靠度系数、安全系数和工况系数三者之间的关系。研究表明:1)在一般气压试验或气液组合试验时,圆筒屈服强度的允许可靠度系数应不小于1.549且不超过2.115,爆破强度的允许可靠度系数应不小于4.081且不超过5.414。2)在一般液压试验时,圆筒屈服强度的允许可靠度系数应不小于0.605且不超过1.005,爆破强度的允许可靠度系数应不小于3.304且不超过4.430。3)在正常操作时,圆筒屈服强度的允许可靠度系数应不小于1.961且不超过2.484,爆破强度的允许可靠度系数应不小于4.280且不超过5.456。4)在允许可靠度系数满足上述取值范围,且工况系数符合中国标准时,圆筒屈服安全系数可取1.40,爆破安全系数可取2.00。

隧道临界稳定断面确定方法及应用

文中提出一种基于参数化建模和强度折减法的隧道临界稳定断面确定方法.通过定义数值模型的关键点坐标,实现了基于FLAC3D的多心圆断面隧道参数化建模.定义一个尺寸调整系数,为强度折减计算得到的安全系数和安全系数目标值的比值.当尺寸调整系数大于1时,说明计算安全系数大于目标安全系数,隧道开挖断面小于临界稳定断面,可将隧道几何尺寸乘以尺寸调整系数,使得隧道开挖断面等比例扩大;反之,则说明隧道开挖断面大于临界稳定断面,将隧道几何尺寸乘以尺寸调整系数,使得隧道开挖断面等比例缩小.通过FLAC3D内置的FISH语言编程,根据尺寸调整系数,对隧道开挖断面进行等比例调整,直至尺寸调整系数等于1,迭代终止,得到最终临界稳定断面.

循环进尺对隧道洞口段施工动态稳定性影响研究

研究施工过程中隧道-围岩相互作用和破坏机理对维持结构稳定至关重要,采用有限元软件建立了福建省福州市罗汉山隧道计算模型,讨论了施工过程中围岩和结构位移及塑性区发展,基于强度折减法分析了考虑前切面和不同循环进尺下隧道模型的安全系数变化规律。通过分析可知,隧道洞口段围岩和边坡中塑性区贯通发育是其破坏的主要原因,塑性区贯通后边坡进入失稳状态,进而将荷载和变形传递给隧道结构;通过强度折减法获得了不同循环进尺下的安全系数,循环进尺越小隧道洞口段的边坡稳定性越高。研究成果可为隧道洞口段施工稳定性的估计和失稳预测提供理论依据。

基于不同失稳判据的黄土边坡稳定性数值计算分析

安全系数是边坡稳定性评价的一项重要指标,依据不同失稳判据计算得到的安全系数存在差异,会直接影响边坡稳定性状态的评价。以万花山治沟造地工程台阶型开挖边坡为对象,运用FLAC3D有限差分软件,采用强度折减法,选择计算不收敛判据、塑性区贯通判据、位移突变判据3种失稳判据,对黄土边坡安全系数进行数值计算。对比分析3种判据所得的分析结果及优缺点表明:3种失稳判据得出的安全系数大小排序为位移突变判据>计算不收敛判据>塑性区贯通判据。计算不收敛判据使用简便,求解快速,但不能展示折减过程坡体塑性区的变化情况;塑性区贯通判据不宜单独作为边坡失稳判据,需要结合不平衡力综合评估,但可以展示坡体剪切和拉伸塑性区;位移突变判据求解过程复杂,但能真实地反映坡体位移变化导致的临界破坏状态。建议类似工程优先选用求解过程快速的计算不收敛判据,然后结合塑性区贯通情况与坡体位移变化状态对边坡稳定性进行综合评价。

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。