基于非连续面拓扑优化技术的隧道开挖面稳定分析方法

Due to the variety of failure modes on the tunnel face stability, including non-convexity of the critical slip surface, and /or location the slip surface in global optimization, the novel implementation of limit analysis with discontinuity topology optimization is presented. By exploring the nature of the analogy between optimum trusses and optimum layouts of discontinuities on the kinematically admissible velocity field or the statically admissible stress field, the procedure is used to determine the critical layout of discontinuities (energy dissipation) and associated upper bound limit analysis for tunnel face stability problems. The alternative approximation procedure to the traditional finite element method might involve discretization of a given body using a suitably large number of nodes laid out on a grid, with the failure mechanism comprising the most critical subset of potential discontinuities interconnecting these nodes. Potential discontinuities which interlink nodes laid out across the problem domain are permitted to crossover one another, giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology. Highly efficient SOCP (second-order cone programming) solvers developed by the primal-dual interior-point method can be employed when certain popular failure criteria are specified (e.g. Hoek-Brown and Mohr-Coulomb). Furthermore, in the analysis, the effect of ground water on the tunnel face stability expressed by applying pore pressure ratio (ru) is discussed. Subsequently, experiments have been carried out at 1g using dry sand and transparent soil surrogate with different cover-to-diameter ratio. The complete soil displacement/velocity until failure is investigated by means of Particle Image Velocimetry (PIV). The acquired data from the model test with the developed optical system could be used to trace the soil movement and the failure mode throughout face collapse and demonstrate the effectiveness and efficiency of the proposed method. In short, the combination of the kinematical limit analysis, discontinuity topology optimization and SOCP results in an innovative, efficient and robust numerical analysis tool for tunnel face stability problem.

本研究针对当前隧道开挖面稳定性分析中所存在的一些问题（破坏形式多样、滑移面函数非凸或滑移体区域闭合等），通过将机动许可的速度场和静力许可的应力场的构造转变为桁架结构拓扑优化布局的形式，采用点阵格栅离散方式，建立以非连续面（能量耗散）的布局为手段的优化问题，最终借助二阶锥形规划的原-对偶变步长内点法进行求解；并进一步引入孔隙水压力比系数，探讨地下水位对隧道开挖面稳定性的影响。在此基础上，通过模型试验和非接触粒子图像测速技术完整描述隧道开挖面的位移场或速度场，以便验证分析方法的准确性和有效性。本研究成果将进一步拓展极限定理的应用范畴，为隧道开挖面稳定问题提供一种新颖、快捷、有效的分析方法。

本研究针对当前隧道开挖面稳定性分析中所存在的一些问题（破坏形式多样、滑移面函数非凸或滑移体区域闭合等），通过将机动许可的速度场和静力许可的应力场的构造转变为桁架结构拓扑优化布局的形式，采用点阵格栅离散方式，建立以非连续面（能量耗散）的布局为手段的优化问题，最终借助二阶锥形规划的原-对偶变步长内点法进行求解；并进一步引入孔隙水压力比系数，探讨地下水位对隧道开挖面稳定性的影响。为获得量化数据，在常规重力场条件下，开展不同相对深度（覆土厚度与隧道直径比C/D=0.5、1.0、3.0、4.0、5.0）的系列模型试验，以模拟隧道开挖面失稳破坏。对破坏区域和土拱效应等因素进行了探讨和比较，极限支护力随着相对深度增加而增加，并最终趋于定值。隧道作业面失稳破坏的过程是破坏区域尺寸逐渐扩大并延伸至地表。数值模拟证实土拱效应在破坏区域的上部，在破坏区域内土体逐步松散。从试验破坏类型可知，覆土深度和破坏扩展区域对其有一定的影响。尤其是扩展区域影响与试验砂土初始密度关系密切，在密砂中烟囱-楔体破坏类型延伸至试验地表。与理论模型和典型模型试验的比对，烟囱-楔体模型的准确性得以验证，并提出了一种涵盖相关影响因素的解析公式。研究分析表明，Vermeer和Ruse以及Leca和Dormieux的计算结果与实测值达到较高的置信程度。通过课题研究最终发现，破坏模型和土拱效应对准确预测砂土作业面支护力影响甚大。在此基础上，通过模型试验和非接触粒子图像测速技术完整描述隧道开挖面的位移场或速度场，以验证分析方法的准确性和有效性。本研究成果将进一步拓展极限定理的应用范畴，为隧道开挖面稳定问题提供一种新颖、快捷、有效的分析方法。