基于椭球体失稳坍落理论的隧道掌子面失稳计算研究

为研究维持软弱围岩隧道掌子面稳定所需的掌子面支护力，以筒仓理论和太沙基压力理论为基础，借鉴运用椭球体失稳坍落理论，建立隧道掌子面失稳理论计算模型，推导隧道掌子面失稳计算公式，求出维持掌子面稳定的最小支护力和完整失稳坍落椭球体的临界埋深值。通过分析隧道埋深与坍落椭球体高度的4种位置关系对计算参数的影响，给出不同位置关系情况下竖向深度z和作用于椭圆台台面的土压力q0的求解方法，并将推导公式与经典公式进行对比，验证推导公式的合理性。最后，运用推导出的隧道掌子面失稳计算公式对实例进行分析，求得维持掌子面稳定的掌子面最小支护比，并用数值模拟方法进行验证。验证结果表明： 推导公式与数值模拟结果具有较好的一致性。

Study of Failure Calculation of Tunnel Face Based on Drawing Ellipsoid Theory

The instability model of tunnel face is established based on silo theory, Terzaghi′s theory and collapse theory of ellipsoid, so as to study the supporting force for maintaining the stability of tunnel face in soft surrounding rock. The formula for calculating the instability of tunnel face is derived and the minimum supporting force of tunnel face and the critical height of complete slump ellipsoid are obtained. And then the values of vertical depth z at different position relationships and soil pressure q0 on ellipsoid surface are given by analyzing four positional relationships between tunnel depth and height of slump ellipsoid. The rationality of the derivation formula and classic formula is verified by comparing. Finally, the ratio of minimum supporting force for maintaining the stability of tunnel face is obtained by a case study. The results indicate that the derivation formula is consistent with numerical simulation.