含空洞地层初始破坏的复变函数解析研究
Analytic solution to initial damage of cavern strata by complex function method
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摘要: 为分析城市浅部地层中椭圆形空洞的稳定性,采用复变函数理论求得了自重应力及竖向均布荷载作用下含隐伏椭圆形空洞地层应力场的精确解答。以莫尔-库仑剪切屈服准则及土体抗拉强度等于零为判别依据,求得洞周初始塑性区范围,分析了空洞形状及外部荷载对塑性区位态的影响。结果表明:①在自重应力场下,地层中近圆形或瘦长状椭圆空洞自身稳定性相对扁平状空洞较好;扁平状空洞以受拉破坏为主。②外部荷载作用下地层空洞破坏模式为拉-剪综合破坏,随着外部荷载的增大,剪切塑性区与受拉区贯通,并向地层深部转移,加速地层空洞的失稳破坏。③在大量分析计算的基础上给出了空洞地层的5种分区模式。空洞地层灾变事故控制的核心是空洞结构自身的稳定性,空洞地层初始破坏的分析是确定其破坏模式以及破坏区域的关键。研究结果对城市空洞地层灾变事故的预测、评估及其处理具有重要意义。Abstract: To analyze the stability of oval cavities in shallow strata in urban areas, taking both gravity stress and vertical uniformly distributed load into consideration, the accurate solution to the stress field of concealed oval cavity is got by means of the complex function method. Assuming that the Mohr-Coulomb yield criterion and the tensile stress of soil equal zero as the discriminate rule, the scope of plastic zone is obtained. The results reveal that: (1) Under the gravity stress field, the stability of round-shaped and slender-shaped cavities is better than that of the flat-shaped ones. The failure of the flat-shaped caverns is mainly caused by tensile stress. (2) Under the action of external load, the failure mode of cavern strata is a comprehensive tensile-shear failure. With the increment of external load, the plastic zone caused by shear stress will connect with the tensile zone, which will accelerate the failure caused by cavity destabilization. (3) Five kinds of partition patterns of cavern strata are put forward based on a great number of analyses and calculations. Therefore, the stability of cavern strata becomes the core of preventing catastrophic accidents. The results are of great significance in the prediction, evaluation and handling of catastrophic accidents caused by cavity strata.