路基下伏矩形溶洞的稳定性解析法

为评价荷载作用下的路基下伏矩形溶洞的稳定性，首先根据岩溶区路基承载特性建立简化的力学分析模型，并进一步得到等效计算模型。其次，基于复变函数理论，提出矩形溶洞任意截面映射函数的确定方法，并给出常用矩形截面映射函数的具体表达式。然后，求得矩形溶洞在自重与路基荷载联合作用下的地层应力；在此基础上，进一步求得任意截面的最大、最小主应力，同时引入Griffith强度准则，对溶洞的稳定性进行评价。最后，通过数值方法及工程实例对本文计算方法进行验算。研究结果表明：该方法所得水平应力和切应力与数值结果误差在5%以内，竖直应力误差在8%以内，工程实际情况与理论计算结果吻合良好，对岩溶区路基设计计算有一定的参考价值；值得注意的是，矩形溶洞4个顶点处的水平应力及竖向应力值都比较大，应力变化幅度较为明显，存在严重的应力集中现象，说明矩形溶洞的4个顶点比较容易破坏，在工程实践中应特别注意该处的验算。

Stability Assessment Method for Subgrade with Underlying Rectangular Cavity

In order to present a stability assessment method for subgrade with underlying cavity, a simplified mechanical analysis model was established based on the bearing capacity of subgrade in Karst areas, and equivalent calculation model was further obtained. By dint of the complex variable function, the mapping function identification of arbitrary cross sections of the rectangular cavity was proposed. Meanwhile, the specific expressions of mapping functions for common rectangular sections were also presented. The geostatic stress field influenced by a combination factors between the gravity and subgrade loads was obtained in semi-finite space. On this basis, the major and minor principal stresses were obtained, and the stability of the cavity was evaluated based on Griffith failure criterion. In addition, the theoretical result was validated by case records and the numerical method. The results show that the errors between the predictions and the numerical results are less than 5% for the horizontal stress as well as the shear stress, and 8% for the vertical stress.Besides, the proposed results are in good agreement with the observations in engineering practices, and the proposed method has a reference for the preliminary design. It is worth noting that the lager horizontal and vertical stresses appear at the four corners. The stress variation ranges are significant due to stress concentrations. In particular, the four corners are easy to be failed in the actual engineering, and the checking computations should be paid special attention.