基于广义可靠指标相对安全率的岩土工程设计安全判据

Safety criteria for geotechnical design based on generalized reliability ratio of safety margin

相对安全率为建立确定性设计和可靠度设计安全判据的定量关系以及验证安全判据的普适性提供了有效工具。然而,目前相对安全率准则仅适用于岩土工程结构响应(如挡土墙抗滑稳定安全系数F_S)服从正态或对数正态分布的工况。基于F_S的累计概率分布函数提出了广义可靠指标相对安全率,适用于F_S服从任意概率分布的设计工况,克服了现有可靠指标相对安全率仅适用于正态和对数正态分布的局限,拓宽了相对安全率准则的应用范围。基于所提广义可靠指标相对安全率,证明了F_S服从正态或对数正态分布条件下安全系数相对安全率和可靠指标相对安全率相等是确定性设计和可靠度设计安全判据等价(两种方法对应的设计可行域相同)的充分条件,F_S服从任意概率分布条件下安全系数相对安全率和广义可靠指标相对安全率相等是确定性设计和可靠度设计安全判据等价的充分条件。通过重力式挡土墙抗滑稳定算例,说明了基于广义可靠指标相对安全率标定抗滑稳定允许安全系数的过程,比较了广义可靠指标相对安全率与可靠指标相对安全率的标定结果,验证了基于广义可靠指标相对安全率标定安全判据的合理性。

Ratio of safety margin(RSM)provides a rational tool for establishing the quantitative relationship between the safety criteria of deterministic design and reliability-based design and for verifying the universality of safety criteria.However,the existing definition of RSM is only applicable to design situations,where the response(e.g.,safety factor F_S of stability against sliding of retaining wall)follows normal and/or lognormal distributions.This paper proposed a generalized reliability RSM(RRSM)based on the cumulative probability distribution function of F_S.The generalized RRSM is applicable to design situations with F_S following arbitrary probability distributions and overcomes the limitation resulted from the normal and/or lognormal assumption.This makes the RSM principle feasible in general design situations.Based on the generalized RRSM,it is proved that equality between RSM of F_S and RRSM guarantees the equivalence between safety criteria of deterministic design and reliability-based design(i.e.,identical feasible design domains)when F_S follows normal and/or lognormal distributions.Similarly,it is also proved that equality between RSM of F_S and generalized RRSM guarantees the equivalence between safety criteria of deterministic design and reliability-based design when F_S follows arbitrary probability distributions.Calibration of allowable F_S based on generalized RRSM is illustrated through a gravity earth retaining wall example.Results obtained from RRSM and generalized RRSM are compared for validating the calibration results based on generalized RRSM.