Variation analysis of ultimate pullout capacity of shallow horizontal strip anchor plate with 2-layer overlying soil based on nonlinear M-C failure criterion

Based on the nonlinear Mohr-Coulomb failure criterion and an associated flow rule,a kinematic admissible velocity field of failure mechanism of the 2-layer soil above a shallow horizontal strip anchor plate is constructed.The ultimate pull-out force and its corresponding failure mechanism through the upper bound limit analysis according to a variation principle are deduced.When the 2-layer overlying soil is degraded into single-layer soil,the model of ultimate pullout force could also be degraded into the model of single-layer soil.And the comparison between results of single-layer soil variation method and those calculated by rigid limit analysis method proves the correctness of our method.Based on that,the influence of changes of geotechnical parameters on ultimate pullout forces and failure mechanism of a shallow horizontal strip anchor with the 2-layer soil above are analyzed.The results show that the ultimate pull-out force and failure mechanism of a shallow horizontal strip anchor with the 2-layer soil above are affected by the nonlinear geotechnical parameters greatly.Thus,it is very important to obtain the accurate geotechnical parameters of 2-layer soil for the evaluation of the ultimate pullout capacity of the anchor plate.

Upper bound solutions for supporting pressures of shallow tunnels with nonlinear failure criterion

Linear failure criterion is widely used in calculation of earth pressure acting on shallow tunnels. However, experimental evidence shows that nonlinear failure criterion is able to represent fairly well the failure of almost all types of rocks, A nonlinear Hock-Brown failure criterion is employed to estimate the supporting pressures of shallow tunnels in limit analysis framework. Two failure mechanisms are proposed for calculating the work rate of extemal force and the internal energy dissipation. A tangential line to the nonlinear failure criterion is used to formulate the supporting pressure problem as a nonlinear programming problem. The objective function formulated in this way is minimized with respect to the failure mechanism and the location of tangency point. In order to assess the validity, the supporting pressures for the proposed failure mechanisms are calculated and compared with each other, and the present results are compared with previously published solutions when the nonlinear criterion is reduced to linear criterion. The agreement supports the validity of the proposed failure mechanisms. An experiment is conducted to investigate the influences of the nonlinear criterion on collapse shape and supporting pressures of shallow tunnels.

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.

Energy analysis of rock plug thickness in karst tunnels based on non-associated flow rule and nonlinear failure criterion

The geological hazards, such as water inrush and mud outburst, are easily induced by the high water pressure caverns ahead of a karst tunnel face. Therefore, it is a pivotal issue to determine the reserved thickness of rock plug during the construction of tunnels. The limit analysis principle is employed to analyze the safe thickness from the point of energy dissipation, and the nonlinear and non-associated characteristics of geotechnical materials are both considered. On the basis of a plane failure pattern of rock plug, the expressions of detaching curve and rock plug thickness are derived. The effect of each parameter on the safe thickness of rock plug is discussed in detail, which interprets the corresponding failure scope of rock plug. The obtained results indicate that the thickness of rock plug is highly influenced by the nonlinear dilatancy coefficient and the nonlinear coefficient. The proposed method is validated by a comparison of the calculated results with those of the engineering project of the "526 karst cavern" of Yunwushan tunnel. This proposed method can provide reference basis for the design and excavation of karst tunnels in the future.

Kinematical analysis of highway tunnel collapse using nonlinear failure criterion

For different kinds of rocks,the collapse range of tunnel was studied in the previously published literature.However,some tunnels were buried in soils,and test data showed that the strength envelopes of the soils followed power-law failure criterion.In this work,deep buried highway tunnel with large section was taken as objective,and the basic expressions of collapse shape and region were deduced for the highway tunnels in soils,based on kinematical approach and power-law failure criterion.In order to see the effectiveness of the proposed expressions,the solutions presented in this work agree well with previous results if the nonlinear failure criterion is reduced to a linear Mohr-Coulomb failure criterion.The present results are compared with practical projects and tunnel design code.The numerical results show that the height and width of tunnel collapse are greatly affected by the nonlinear criterion for the tunnel in soil.

Safe retaining pressures for pressurized tunnel face using nonlinear failure criterion and reliability theory

Based on the active failure mechanism and passive failure mechanism for a pressurized tunnel face, the analytical solutions of the minimum collapse pressure and maximum blowout pressure that could maintain the stability of pressurized tunnel faces were deduced using limit analysis in conjunction with nonlinear failure criterion under the condition of pore water pressure. Due to the objective existence of the parameter randomness of soil, the statistical properties of random variables were determined by the maximum entropy principle, and the Monte Carlo method was employed to calculate the failure probability of a pressurized tunnel. The results show that the randomness of soil parameters exerts great influence on the stability of a pressurized tunnel, which indicates that the research should be done on the topic of determination of statistical distribution for geotechnical parameters and the level of variability. For the failure probability of a pressurized tunnel under multiple failure modes, the corresponding safe retaining pressures and optimal range of safe retaining pressures are calculated by introducing allowable failure probability and minimum allowable failure probability. The results can provide practical use in the pressurized tunnel engineering.

Upper bound solution of surrounding rock pressure of shallow tunnel under nonlinear failure criterion

The nonlinear Baker failure criterion is introduced into the upper-bound limit analysis to examine the face stability of a shallow tunnel. The tunnel face under the ultimate limit state is analyzed from the perspective of energy balance. The work rates of external forces and internal energy dissipation are calculated. An analytical solution of necessary face pressures is derived. The optimal upper-bound solution of the face pressures is obtained by optimization. The results show that the three dimensionless parameters A, T, n of nonlinear Baker failure criterion have different effects on the necessary face pressures and the pattern failure mechanisms ahead of tunnel face. A is the most important one;n takes the second place, and T is the least one. The computed necessary face pressures are nonlinearly increasing when A is reduced. Combined with the actual monitoring data of Taxia tunnel, the calculation results in this paper is verified. It is suggested that the tunnel face supports should be strengthened timely in soft rocks to prevent the occurrence of face collapse.

Upper bound analysis of ultimate pullout capacity of shallow 3-D circular plate anchors based on nonlinear Mohr-Coulomb failure criterion

Based on the nonlinear Mohr-Coulomb failure criterion and the associated flow rules,the three-dimensional(3-D)axisymmetric failure mechanism of shallow horizontal circular plate anchors that are subjected to the ultimate pullout capacity(UPC)is determined.A derivative function of the projection function for projecting the 3-D axisymmetric failure surface on plane is deduced using the variation theory.By using difference principle,the primitive function of failure surface satisfying boundary condition and numerical solution to its corresponding ultimate pullout capacity function are obtained.The influences of nonlinear Mohr-Coulomb parameters on UPC and failure mechanism are studied.The result shows that UPC decreases with dimensionless parameter m and uniaxial tensile strength increases but increases when depth and radius of plate anchor,surface overload,initial cohesion,geomaterial density and friction angle increase.The failure surface is similar to a symmetrical spatial funnel,and its shape is mainly determined by dimensionless parameter m;the surface damage range expands with the increase of radius and depth of the plate anchor as well as initial cohesion but decreases with the increase of dimensionless parameter m and uniaxial tensile strength as well as geomaterial density.As the dimensionless parameter m=2.0,the numerical solution of UPC based on the difference principle is proved to be feasible and effective through the comparison with the exact solution.In addition,the comparison between solutions of UPC computed by variation method and those computed by upper bound method indicate that variation method outperforms upper bound method.

Energy analysis of stability of twin shallow tunnels based on nonlinear failure criterion

Based on nonlinear Mohr-Coulomb failure criterion, the analytical solutions of stability number and supporting force on twin shallow tunnels were derived using upper bound theorem of limit analysis. The optimized solutions were obtained by the technique of sequential quadratic programming. When nonlinear coefficient equals 1 and internal friction angle equals 0, the nonlinear Mohr-Coulomb failure criterion degenerates into linear failure criterion. The calculated results of stability number in this work were compared with previous results, and the agreement verifies the effectiveness of the present method. Under the condition of nonlinear Mohr-Coulomb failure criterion, the results show that the supporting force on twin shallow tunnels obviously increases when the nonlinear coefficient, burial depth, ground load or pore water pressure coefficients increase. When the clear distance is 0.5to 1.0 times the diameter of tunnel, the supporting force of twin shallow tunnels reaches its maximum value, which means that the tunnels are the easiest to collapse. While the clear distance increases to 3.5 times the diameter of tunnel, the calculation for twin shallow tunnels can be carried out by the method for independent single shallow tunnel. Therefore, 3.5 times the diameter of tunnel serves as a critical value to determine whether twin shallow tunnels influence each other. In designing twin shallow tunnels,appropriate clear distance value must be selected according to its change rules and actual topographic conditions, meanwhile, the influences of nonlinear failure criterion of soil materials and pore water must be completely considered. During the excavation process, supporting system should be intensified at the positions of larger burial depth or ground load to avoid collapses.

THREE-DIMENSIONAL SLOPE STABILITY ANALYSIS BASED ON NONLINEAR FAILURE ENVELOPE

The effects of nonlinearity of strength envelopes on 3D slope stability analysis are investigated.A power relation for the nonlinear envelope is employed to derive the 3D factor of safety equations of an extended Spencer method hich satisfies boty force equilibrium and moment equilibrium.Then,a search procedure is presented based on dynamic programming to determine the 3D critical slip surface for a general slope,Linear and nonlinear strength envelopes used for slope stability computations are obtained by fitting curves to the 103 strength data of consolidated-undrained(CU)triaxial compression tests for compacted Israeli clay.Results of a typical 3D problem show that a linear approximation of the nonlinear strength envelope may lead to a significant overestimation of calculated safety factors.

System reliability analysis of seismic pseudo-static stability of rock wedge based on nonlinear Barton–Bandis criterion

Based on the nonlinear Barton–Bandis(B–B)failure criterion,this study considers the system reliability of rock wedge stability under the pseudo-static seismic load.The failure probability(Pf)of the system is calculated based on the Monte−Carlo method when considering parameter correlation and variability.Parameter analysis and sensitivity analysis are carried out to explore the influence of parameters on reliability.The relationships among the failure probability,safety factor(Fs),and variation coefficient are explored,and then stability probability curves of the rock wedge under the pseudo-static seismic load are drawn.The results show that the parameter correlation of the B–B failure criterion has a significant influence on the failure probability,but correlation increases system reliability or decreases system reliability affected by other parameters.Under the pseudo-static seismic action,sliding on both planes is the main failure mode of wedge system.In addition,the parameters with relatively high sensitivity are two angles related to the joint dip.When the coefficient of variation is consistent,the probability of system failure is a function of the safety factor.

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。

非线性破坏准则下浅埋隧道的稳定性分析

隧道围岩压力值是浅埋隧道设计计算的重要参数。为进一步提高围岩压力计算结果的可靠性,以传统浅埋隧道坍塌模型为基础,提出了圆弧滑移面破坏模式,同时基于非线性Mohr-Coulomb破坏准则,运用极限分析上限法推导了地震力作用下浅埋隧道围岩压力的计算公式,验证了计算结果的可靠性,并对影响因素进行了探讨。与实际工程和已有成果的对比分析证明了理论公式具有较高的可靠性和准确度。研究还发现:围岩压力受非线性系数和初始粘聚力的影响较为显著,非线性系数越大、初始粘聚力越小,围岩压力越大;随着待定参数K(水平围岩压力与竖向围岩压力的比值)的减小,水平围岩压力减小,竖向围岩压力增大;地震力对围岩压力的影响不容忽视,竖向地震力单独作用对围岩压力的影响最大,水平和竖向地震力共同作用的影响次之,而仅有水平地震力作用的影响最小。随着水平与竖向地震力系数的增大,围岩压力也在增大。分析结果对于大部分的隧道,尤其是易受地震影响的浅埋隧道研究具有较高的参考价值。

输电直线杆塔风灾易损性的准静态分析方法

如何合理并高效地评估既有输电杆塔的抗风承载性能及安全裕度,对电网的风灾预测及运维管理具有重要的意义。该文提出一种考虑风向效应杆塔结构易损性评估的高效实用方法。首先基于风工程原理,采用准静态分析框架推导给出不同设计风速下的杆塔整体风荷载的极值概率分布;随后综合考虑输电塔结构参数的不确定性及初始缺陷,通过非线性静力推覆分析(nonlinear static pushover analysis,NSPA)考察杆塔结构的抗风承载能力性能及对应的破坏准则;进而依据随机抽样分析得到杆塔结构的抗风承载力的概率模型;最后采用极限状态函数计算不同风向角下的杆塔风灾易损性概率曲线。研究表明,基于首次超越概率理论可以方便得到准静态分析框架下的整体风效应概率分布;准静态的基底剪力响应不受结构非线性状态影响,可作为整体风荷载作用的评价指标;基于构件屈服破坏与整体破坏内在联系,可建立合理的轻微、严重和倒塌的破坏准则;风向角对杆塔的抗风承载性能和易损性均有着显著影响,杆塔在60°风向角下的易损概率最高。

用非线性M-C破坏准则计算深埋硐室围岩压力上限解

在构建深埋硐室破坏机制的基础上,采用切线法将非线性Mohr-Coulomb破坏准则运用到极限分析上限法中,推导非线性Mohr-Coulomb破坏准则下深埋硐室围岩压力的上限解析解.结果表明:非线性系数、初始粘聚力是影响围岩压力的主要因素,效果非常显著,而侧压力比例系数、硐室断面尺寸以及轴向拉应力影响效果相对较小.针对深埋硐室的支护设计,采用非线性Mohr-Coulomb破坏准则进行计算更加科学.

基于非线性M-C准则的圆形基础下伏土洞抗冲切破坏研究

针对土体材料特点,引入非线性Mohr-Coulomb准则及相关流动法则,构建圆形刚性基础下伏土洞冲切破坏模式。采用极限分析上限法推导出其极限承载力的计算公式,得出参数任意组合条件下圆形刚性基础下伏土洞冲切极限承载力。利用Plaxis 3D软件建模分析,并与理论解进行对比,验证本文方法的有效性。研究结果表明:非线性系数m对极限承载力的影响较大,在其他参数条件一定的情况下,极限承载力与m呈非线性负相关,且趋于稳定。极限承载力随土体初始黏聚力C_0,顶板厚度以及刚性基础宽度的增大而增大,随土体重度、土体抗拉强度的增大而减小。

Combined influence of nonlinearity and dilation on slope stability evaluated by upper-bound limit analysis

The combined influence of nonlinearity and dilation on slope stability was evaluated using the upper-bound limit analysis theorem.The mechanism of slope collapse was analyzed by dividing it into arbitrary discrete soil blocks with the nonlinear Mohr–Coulomb failure criterion and nonassociated flow rule.The multipoint tangent(multi-tangent) technique was used to analyze the slope stability by linearizing the nonlinear failure criterion.A general expression for the slope safety factor was derived based on the virtual work principle and the strength reduction technique,and the global slope safety factor can be obtained by the optimization method of nonlinear sequential quadratic programming.The results show better agreement with previous research result when the nonlinear failure criterion reduces to a linear failure criterion or the non-associated flow rule reduces to an associated flow rule,which demonstrates the rationality of the presented method.Slope safety factors calculated by the multi-tangent inclined-slices technique were smaller than those obtained by the traditional single-tangent inclined-slices technique.The results show that the multi-tangent inclined-slices technique is a safe and effective method of slope stability limit analysis.The combined effect of nonlinearity and dilation on slope stability was analyzed,and the parameter analysis indicates that nonlinearity and dilation have significant influence on the result of slope stability analysis.

Slope stability analysis considering joined influences of nonlinearity and dilation

The soil masses of slopes were assumed to follow a nonlinear failure criterion and a nonassociated flow rule.The stability factors of slopes were calculated using vertical slice method based on limit analysis.The potential sliding mass was divided into a series of vertical slices as well as the traditional slice technique.Equating the external work rate to the internal energy dissipation,the optimum solutions to stability factors were determined by the nonlinear programming algorithm.From the numerical results,it is found that the present solutions agree well with previous results when the nonlinear criterion reduces to the linear criterion,and the nonassociated flow rule reduces to the associated flow rule.The stability factors decrease by 39.7%with nonlinear parameter varying from 1.0 to 3.0.Dilation and nonlinearity have significant effects on the slope stability factors.

Effects of nonlinear strength parameters on stability of 3D soil slopes

Actual slope stability problems have three-dimensional(3D) characteristics and the soils of slopes have curved failure envelopes. This incorporates a power-law nonlinear failure criterion into the kinematic approach of limit analysis to conduct the evaluation of the stability of 3D slopes. A tangential technique is adopted to simplify the nonlinear failure criterion in the form of equivalent Mohr-Coulomb strength parameters. A class of 3D admissible rotational failure mechanisms is selected for soil slopes including three types of failure mechanisms: face failure, base failure, and toe failure. The upper-bound solutions and corresponding critical slip surfaces can be obtained by an efficient optimization method. The results indicate that the nonlinear parameters have significant influences on the assessment of slope stability, especially on the type of failure mechanism. The effects of nonlinear parameters appear to be pronounced for gentle slopes constrained to a narrow width. Compared with the solutions derived from plane-strain analysis, the 3D solutions are more sensitive to the values of nonlinear parameters.

基于三参数破坏准则的均质边坡稳定性上限分析

非线性特征是岩土体材料的固有特性.研究表明,在此特征条件下,基于旋转失稳机制的均质边坡潜在滑动面并非单一对数螺旋线.本文假定岩土体材料服从三参数非线性强度准则,在极限分析上限定理的基础上,构建了均质边坡旋转失稳机制;通过拟静力方法考虑地震荷载,基于力学平衡方程结合变分原理获得边坡临界滑动面及其应力分布的微分方程组,采用Runge-Kutta方法进行求解,并基于虚功率原理结合免疫算法获得边坡最小临界高度.通过与有限元极限分析法(FELA)的结果进行对比验证了非线性上限变分分析方法的准确性和有效性.在此基础上,分析了无量纲强度参数(T、A、n)、水平地震加速度系数(kx)、边坡倾角(β)等因素对边坡稳定系数(Fn)、潜在滑动面及其应力分布的影响规律.本方法无需假定边坡潜在滑动面,丰富了边坡稳定性非线性分析理论,可为边坡的加固设计提供理论支持和有益参考.