地下洞室预应力锚索合理张拉吨位快速反分析

 预应力锚索在安装后，即有一个初始应力，并且应力随地下洞室后期开挖而变化。如何选择一个合理的初始张拉吨位，使锚索在洞室开挖完毕后达到指定的应力，既保证发挥锚索的作用，也留有一定的安全余地，是一个关键的问题。将该问题转化为求解锚索初始张拉系数的最优化问题。介绍预应力锚索的应力计算理论后，对常规的变尺度法进行改进，利用基于Broyden族的最优自调节变尺度法对尺度矩阵进行修正，使用向前差商来逼近梯度，采用Wolfe准则进行不精确线性搜索来确定最优步长，从而得到带一维不精确搜索的最优自调节差商变尺度法，用来反演预应力锚索的合理的初始张拉系数。同时针对反分析计算量大的特点，采用增量变塑性刚度迭代法，避免因预应力改变而需要重新组成刚度矩阵的问题，从而大大提高反分析的计算速度。最后将其应用于锦屏二级水电站地下厂房的预应力锚索初始合理张位吨位的快速反分析。实例表明，该方法具有收敛速度快，计算量小，数值稳定性好的特点。

FAST BACK ANALYSIS OF REASONABLE TENSILE TONNAGE OF PRESTRESSED ANCHOR CABLE IN UNDERGROUND ENGINEERING

Recognized as an important way to ensure the stability of underground chambers，prestressed anchor cables are widely used in underground engineering. There is an initial stress after the prestressed anchor cable is installed，and the stress varies with the consequence of excavation. How to select an appropriately initial tensile tonnage to make the stress of prestressed anchor cable reach the designed stress so as not only to exert the effect of prestressed cable but also to preserve a certain of safety margin is an important issue. The issue is converted to an optimization problem on reasonable tensile coefficient of prestressed anchor cable. Firstly，stress calculation theory of prestressed anchor cable is introduced. Then，the optimal self-adjusting variable-metric algorithm using difference coefficients and imprecise linear search is proposed and applied to inversion of reasonable tensile coefficient of prestressed anchor cable. The algorithm improves the conventional variable-metric method by using self-adjusting variable-metric method based on Broyden¢s family to update metric matrix，makes different coefficients approach gradient and imprecise linear search method find optimal step length. At the same time，by using incremental variable plastic stiffness matrix method，reassembling stiffness matrix is avoided when prestress is modified，consequently computing speed is improved. A case study is given at last，which proves that the algorithm¢s superiorities of super-linear convergence，less computation，and better numerical stability.