中文摘要：

在解答圆形孔口弹塑性问题基础上，采用复变函数方法推导椭圆孔口塑性区半径计算公式。对比分析表明：该公式计算结果与基于摄动法计算结果相近，但参数较少，且能反应轴对称荷载下状态。针对常见中、小尺度隐伏干溶洞，以隧道周围塑性区和溶洞周围塑性区贯通与否作为中间岩柱稳定性判断标准，基于本文计算椭圆孔口塑性区理论建立隧道与不同方位、形态溶洞间岩柱最小安全厚度力学模型；采用FLAC^3D进行数值正交试验，通过对计算结果多元回归分析，建立基于数值计算的安全厚度预测公式，为验证力学模型提供参考。以宜万线鲁竹坝隧道和五爪观岩溶隧道为例验证2种方法的可靠性和合理性，为类似工程提供参考。

英文摘要：

On the basis of elastic-plastic resolution of the zone around the elliptical hole portal was deduced with circular hole portal, the formula of the radius of plastic the complex variable function method. Comparison of results calculated by the above deduced formula and results based on perturbation method shows that they are close and the above deduced formula needs less parameters and reflects conditions of axisymmetrical loading. Aiming at small and medium sized cconcealed dry caves, whether the plastic zone around tunnel connects that of karst cave is taken as a criterion for judging stability of rock pillar, subsequently, the mechanical model of rock pillar stability between tunnel and karst caves of different locations and forms was established based on the deduced formula of the radius of the plastic zone. Through multiple regressive analysis on the numerical orthogonal results by FLAC3D, the predicting model of safety thickness was obtained, thus providing reference to verify the mechanical model. Taking for examples the Luzhuba Tunnel and Wuzhaoguan Tunnel of Yiwan Railway Line, the reliability and rationality of the proposed methods were proved, so providing reference for similar engineering projects.