竖井圆形冻结壁弹性设计理论的对比研究

对井筒冻结壁弹性设计理论的3个解析公式进行对比分析，用图解的方式展示出用叠加原理求解基于冻结壁和围岩相互作用的力学模型两种方法，揭示冻结壁外缘载荷随冻结壁厚度和刚度变化的规律。通过对用3种冻结壁厚度公式设计的差异性分析，说明采用重液公式确定拉梅公式中载荷的不合理性，提出基于太沙基有效应力原理的自重初始应力场计算方法。结合案例，比较3种解析公式得到的地层原岩水平载荷和冻结壁厚度的函数关系，用定义域和值域的数学原理研究各个冻结壁弹性设计公式的适用范围，阐释其工程实际意义，并就弹性设计的实用意义进行审慎性评述。

Comparative study of elastic design theories of circular frozen wall of shaft

This paper gives the contrast studies on the mechanical models of the 3 piece of analytic formulae for elastic frozen wall of shaft sinking, and illustrate the two methods to solve mechanical interaction problem between frozen wall and surrounding rock with diagraph based on superposition principles. The basic law are revealed, that the load on frozen wall varies with their own thickness and rigidity. Upon the analysis of thickness difference calculated by the three formulas, the way of “heavy liquid formula” to evaluate the load on frozen wall of Lame formula is proved unreasonable. One proposal is put forward to evaluate initial stress field based on the principle of gravity fields and Terzaghi effective stress. The relationship between the original horizontal ground load and thickness of frozen wall illustrated by three formulas are shown with a practical example. The limitation of elastic design are studied with the mathematical principles of value region and domain，which are endowed with engineering meaning. The practical usage for the application condition of elastic design are further discussed deliberately.