锚杆（索）挡土墙系统可靠性分析计算方法
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摘要
锚固边坡中存在的不确定性因素多且复杂，故利用中值安全系数的传统方法来设计或分析锚固边坡，既不能较好地体现问题的复杂性与不确定性，也不能准确地评价工程的长期稳定性，应引入考虑荷载及抗力时变性且以概率统计理论为基础的分析设计方法。为此，本文结合国家自然科学基金(50878082)、交通部西部项目(200631880237)，考虑锚固计算参数和岩土体参数的统计特性，以锚杆挡土墙为主要研究对象，建立其系统时变可靠性分析模型与计算方法。主要研究内容和成果如下：
(1)假定墙后填土的滑裂面曲线为通过墙踵的对数螺线函数，根据能量原理，推导出了墙面及填土面倾斜、墙面粗糙，既适用于砂性土又适用于粘性土的主动土压力上限解，并引入采用基于自然选择的改进粒子群算法对最危险滑裂面进行全局搜索。将本文解与砂性土土压力系数的经典上限解进行详细对比，发现当墙面倾角较小时两者差别甚微，但当墙面倾角大于30°时，经典上限解则明显偏小，而本文解与基于最优性原理的极限平衡解较接近。
(2)分别从是否考虑锚杆失效顺序的影响两个方面对板肋式锚杆挡墙的系统可靠性进行了分析。不考虑锚杆失效顺序时，以肋柱上的所有锚杆抗力之和作为系统锚杆的总抗力来建立极限状态方程。考虑锚杆失效顺序的影响时，将肋柱视为连续梁，锚杆视为弹性支座，引人锚杆与锚固段周围岩土体的复合刚度系数，用位移法导出各根锚杆所受荷载的统一计算公式。同时也考虑了锚杆的多种失效模式以及各种失效模式之间的相关性，提出了单根锚杆三种破坏模式串联系统与多根锚杆并联系统的系统可靠性分析方法和步骤，并编制了计算程序。
(3)将框架梁张拉阶段破坏和工作阶段纵梁与横梁的破坏，梁的正截面与斜截面的破坏以及锚杆的破坏等主要失效模式视为串联系统，提出了双梁双柱型框架预应力锚索的系统可靠性分析模型。然后基于各失效模式功能函数之间的相关系数矩阵，导出了其系统可靠性计算方法并编制了计算程序。
(4)基于矩阵位移法建立了框架预应力锚索挡墙在土压力荷载下的内力计算模型并编制了计算程序。视锚杆的失效为脆性破坏与延性破坏的中间状态，分别按脆性破坏与延性破坏计算锚杆体系失效概率的上下限。对工程实例的计算结果表明，若将锚杆视为脆性结构，当其中一根锚杆破坏后其邻近锚杆失效概率迅速增加，验证了脆性构件组成的超静定结构可视为串联系统；然后基于各根锚杆功能函数之间的相关系数矩阵，得到了脆性破坏时锚杆体系失效概率的上限；最后以立柱上所有锚杆同时达到极限状态的理想状态构建锚杆体系延性破坏时的功能函数，得到了其失效概率的下限。
(5)提出了按全概率法对边坡锚杆进行设计的思路。考虑到验算点法求可靠指标需要迭代计算，不能根据目标可靠指标直接求得设计参数，提出了基于二分法全概率设计的计算流程，一般只需几次迭代就能寻找到目标可靠指标下的设计参数。构建了基于可靠性锚杆挡墙优化设计模型，并运用粒子群智能优化算法对该模型进行优化计算。
(6)根据已有研究成果和工程经验假定土体抗剪强度参数及锚杆抗力随时间的衰减函数形式，同时引入统一强度理论，得到了考虑中主应力系数的锚杆挡墙时变可靠性分析模型。据此模型编制程序对一土质边坡锚杆挡墙进行分析，发现时变性比统一强度理论对计算结果的影响更大。
Anchored slopes have a number of complicate uncertain factors and cannot bedesigned or analyzed by using traditional methods of medium value of factor of safety,since this method is not only able to demonstrate the complexity and uncertainty ofthis issue, but also is incapable of evaluating the long-term stability accurately.Herein a novel design approach was developed by taking the time-varying of loadsand resistance into account based on the probability statistics theory. This workcombining with National Natural Science Funds (50878082) and Western Project ofMinistry of Communication (200631880237) devoted into the establishment ofanalytical model of system time-varying reliability and corresponding calculationmethod for anchored retaining wall considering the statistical characteristic ofcomputational parameters of both anchorage and soils. The content and achievementswere listed as follows:
(1)Assuming a log-spiral sliding surface passing through the toe of retaining wall,based on energy method, the upper bound of active earth pressure for rough walls withinclined backfill was formulated. The formula can be applied to sandy soil and clayedsoil. Extracting the screw-in angle θ0and screw-out angle θhthrough the slope asvariable, hybrid particle swarm optimization was used to search the most dangeroussliding surface globally. For sandy soil, the earth pressure coefficients in this workagree with the classical upper bound solutions of limit analysis when the inclinationof wall is small, but obviously bigger than the classical solutions while the wall angleis larger than30°. Compared to other well-known solutions obtained by limitequilibrium based on optimum principle, the solution herein is more approximate thanthe classical upper bound solution.
(2)System reliability of anchored retaining wall of rib-reinforced plate wasanalyzed by considering and ignoring the failure sequence of anchor. When thesequence is ignored, the limit state equation was established by summing resistance ofall the anchors as the total resistance of system anchor. When the sequence isconsidered, the rib column is idealized to a continuous beam and anchor to be elasticsupport, the general computational formula of load acting on each anchor was derivedby using displacement method and introducing a compound stiffness coefficientdefining anchor and the surrounding soil of anchorage. Furthermore, considering multiple failure modes of anchor and relativity of each failure mode, the analyticalmethods of system reliability and corresponding computational programs weredeveloped, for both serial system of three failure modes of single anchor and parallelsystem of multiple anchors.
(3)Some main failure modes, such as failures of horizontal beams and verticalbeams on the stretching and working period of framework beam, failures of normaland diagonal sections of beam and anchor failure, were molded to be a serial systemand the analytical model of system reliability for retaining wall of pre-stressed anchorcable with double beams and double columns. Based on the correlation coefficientmatrix of performance functions of every failure mode, the calculation method andprogram of its system reliability was developed.
(4)Calculation model and program of internal forces for retaining wall withframework and prestressed anchor cable was developed based on matrix displacementmethod. Anchor failure was defined to be a medium state of brittle failure and ductilefailure, and the upper and lower limits of system failure probability were computedaccording to brittle and ductile failures respectively. Computed results of practicalcase indicate that when anchor is a brittle structure, the failure of one anchor willincrease marvelously the failure probability of its neighboring anchors, which verifiedthe assumption of idealizing the indeterminate structure composed of brittle elementsto a serial system; then the upper and lower limits of system failure probability foranchor under brittle failure was obtained based on correlation coefficient matrix ofperformance function of each anchor; finally performance function of anchor systemunder ductile failure was derived and its lower limit of failure probability wasobtained on the ideal state while all the anchors on the column come into the limitstate simultaneously.
(5)A design technique of slope anchor by total probability method was proposed.Design point method is incapable of solving for designing parameters directlyaccording to the object of reliability index obtained by iterative computation.Computing procedure of total probability based on method of bisection is able tosearch for designing parameters on the object of reliability index in several iterations.An optima design model of anchored retaining wall based on reliability wasestablished and computed by using particle swarm algorithm.
(6)Decaying functions of shearing strength parameters and anchor resistance overtime were assumed referring to the published research works and engineeringexperience, thus an analytical model of time-varying reliability for anchored retaining wall considering middle principle stress coefficient was obtained by introducingunified strength theory. The corresponding computer program was used to analyze ananchored retaining wall of soil slope. Results comparison reveals that the influence oftime-varying on computed results is larger than that rendered by middle principlestress.
(1)假定墙后填土的滑裂面曲线为通过墙踵的对数螺线函数，根据能量原理，推导出了墙面及填土面倾斜、墙面粗糙，既适用于砂性土又适用于粘性土的主动土压力上限解，并引入采用基于自然选择的改进粒子群算法对最危险滑裂面进行全局搜索。将本文解与砂性土土压力系数的经典上限解进行详细对比，发现当墙面倾角较小时两者差别甚微，但当墙面倾角大于30°时，经典上限解则明显偏小，而本文解与基于最优性原理的极限平衡解较接近。
(2)分别从是否考虑锚杆失效顺序的影响两个方面对板肋式锚杆挡墙的系统可靠性进行了分析。不考虑锚杆失效顺序时，以肋柱上的所有锚杆抗力之和作为系统锚杆的总抗力来建立极限状态方程。考虑锚杆失效顺序的影响时，将肋柱视为连续梁，锚杆视为弹性支座，引人锚杆与锚固段周围岩土体的复合刚度系数，用位移法导出各根锚杆所受荷载的统一计算公式。同时也考虑了锚杆的多种失效模式以及各种失效模式之间的相关性，提出了单根锚杆三种破坏模式串联系统与多根锚杆并联系统的系统可靠性分析方法和步骤，并编制了计算程序。
(3)将框架梁张拉阶段破坏和工作阶段纵梁与横梁的破坏，梁的正截面与斜截面的破坏以及锚杆的破坏等主要失效模式视为串联系统，提出了双梁双柱型框架预应力锚索的系统可靠性分析模型。然后基于各失效模式功能函数之间的相关系数矩阵，导出了其系统可靠性计算方法并编制了计算程序。
(4)基于矩阵位移法建立了框架预应力锚索挡墙在土压力荷载下的内力计算模型并编制了计算程序。视锚杆的失效为脆性破坏与延性破坏的中间状态，分别按脆性破坏与延性破坏计算锚杆体系失效概率的上下限。对工程实例的计算结果表明，若将锚杆视为脆性结构，当其中一根锚杆破坏后其邻近锚杆失效概率迅速增加，验证了脆性构件组成的超静定结构可视为串联系统；然后基于各根锚杆功能函数之间的相关系数矩阵，得到了脆性破坏时锚杆体系失效概率的上限；最后以立柱上所有锚杆同时达到极限状态的理想状态构建锚杆体系延性破坏时的功能函数，得到了其失效概率的下限。
(5)提出了按全概率法对边坡锚杆进行设计的思路。考虑到验算点法求可靠指标需要迭代计算，不能根据目标可靠指标直接求得设计参数，提出了基于二分法全概率设计的计算流程，一般只需几次迭代就能寻找到目标可靠指标下的设计参数。构建了基于可靠性锚杆挡墙优化设计模型，并运用粒子群智能优化算法对该模型进行优化计算。
(6)根据已有研究成果和工程经验假定土体抗剪强度参数及锚杆抗力随时间的衰减函数形式，同时引入统一强度理论，得到了考虑中主应力系数的锚杆挡墙时变可靠性分析模型。据此模型编制程序对一土质边坡锚杆挡墙进行分析，发现时变性比统一强度理论对计算结果的影响更大。
Anchored slopes have a number of complicate uncertain factors and cannot bedesigned or analyzed by using traditional methods of medium value of factor of safety,since this method is not only able to demonstrate the complexity and uncertainty ofthis issue, but also is incapable of evaluating the long-term stability accurately.Herein a novel design approach was developed by taking the time-varying of loadsand resistance into account based on the probability statistics theory. This workcombining with National Natural Science Funds (50878082) and Western Project ofMinistry of Communication (200631880237) devoted into the establishment ofanalytical model of system time-varying reliability and corresponding calculationmethod for anchored retaining wall considering the statistical characteristic ofcomputational parameters of both anchorage and soils. The content and achievementswere listed as follows:
(1)Assuming a log-spiral sliding surface passing through the toe of retaining wall,based on energy method, the upper bound of active earth pressure for rough walls withinclined backfill was formulated. The formula can be applied to sandy soil and clayedsoil. Extracting the screw-in angle θ0and screw-out angle θhthrough the slope asvariable, hybrid particle swarm optimization was used to search the most dangeroussliding surface globally. For sandy soil, the earth pressure coefficients in this workagree with the classical upper bound solutions of limit analysis when the inclinationof wall is small, but obviously bigger than the classical solutions while the wall angleis larger than30°. Compared to other well-known solutions obtained by limitequilibrium based on optimum principle, the solution herein is more approximate thanthe classical upper bound solution.
(2)System reliability of anchored retaining wall of rib-reinforced plate wasanalyzed by considering and ignoring the failure sequence of anchor. When thesequence is ignored, the limit state equation was established by summing resistance ofall the anchors as the total resistance of system anchor. When the sequence isconsidered, the rib column is idealized to a continuous beam and anchor to be elasticsupport, the general computational formula of load acting on each anchor was derivedby using displacement method and introducing a compound stiffness coefficientdefining anchor and the surrounding soil of anchorage. Furthermore, considering multiple failure modes of anchor and relativity of each failure mode, the analyticalmethods of system reliability and corresponding computational programs weredeveloped, for both serial system of three failure modes of single anchor and parallelsystem of multiple anchors.
(3)Some main failure modes, such as failures of horizontal beams and verticalbeams on the stretching and working period of framework beam, failures of normaland diagonal sections of beam and anchor failure, were molded to be a serial systemand the analytical model of system reliability for retaining wall of pre-stressed anchorcable with double beams and double columns. Based on the correlation coefficientmatrix of performance functions of every failure mode, the calculation method andprogram of its system reliability was developed.
(4)Calculation model and program of internal forces for retaining wall withframework and prestressed anchor cable was developed based on matrix displacementmethod. Anchor failure was defined to be a medium state of brittle failure and ductilefailure, and the upper and lower limits of system failure probability were computedaccording to brittle and ductile failures respectively. Computed results of practicalcase indicate that when anchor is a brittle structure, the failure of one anchor willincrease marvelously the failure probability of its neighboring anchors, which verifiedthe assumption of idealizing the indeterminate structure composed of brittle elementsto a serial system; then the upper and lower limits of system failure probability foranchor under brittle failure was obtained based on correlation coefficient matrix ofperformance function of each anchor; finally performance function of anchor systemunder ductile failure was derived and its lower limit of failure probability wasobtained on the ideal state while all the anchors on the column come into the limitstate simultaneously.
(5)A design technique of slope anchor by total probability method was proposed.Design point method is incapable of solving for designing parameters directlyaccording to the object of reliability index obtained by iterative computation.Computing procedure of total probability based on method of bisection is able tosearch for designing parameters on the object of reliability index in several iterations.An optima design model of anchored retaining wall based on reliability wasestablished and computed by using particle swarm algorithm.
(6)Decaying functions of shearing strength parameters and anchor resistance overtime were assumed referring to the published research works and engineeringexperience, thus an analytical model of time-varying reliability for anchored retaining wall considering middle principle stress coefficient was obtained by introducingunified strength theory. The corresponding computer program was used to analyze ananchored retaining wall of soil slope. Results comparison reveals that the influence oftime-varying on computed results is larger than that rendered by middle principlestress.
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