Mechanical issues of noncircular and asymmetrical tunnelling can be estimated using complex variable method with suitable conformal mapping. Exsiting solution schemes of conformal mapping for noncircular tunnel generally need iteration or optimization strategy, and are thereby mathematically complicated. This paper proposes a new bidirectional conformal mapping for deep and shallow tunnels of noncircular and asymmetrical shapes by incorporating Charge Simulation Method. The solution scheme of this new bidirectional conformal mapping only involves a pair of linear systems, and is therefore logically straight-forward, computationally efficient, and practically easy in coding. New numerical strategies are developed to deal with possible sharp corners of cavity by small arc simulation and densified collocation points. Several numerical examples are presented to illustrate the geometrical usage of the new bidirectional conformal mapping. Furthermore, the new bidirectional conformal mapping is embedded into two complex variable solutions of noncircular and asymmetrical shallow tunnelling in gravitational geomaterial with reasonable far-field displacement. The respective result comparisons with finite element solution and exsiting analytical solution show good agreements, indicating the feasible mechanical usage of the new bidirectional conformal mapping.

翻译：非圆形非对称隧道的力学问题可采用复变函数法配合适当的保角映射进行估算。现有针对非圆形隧道的保角映射求解方案通常需要迭代或优化策略，因而数学处理较为复杂。本文通过结合电荷模拟法，提出了一种适用于深埋与浅埋非圆形非对称隧道的新型双向保角映射。该双向保角映射的求解方案仅涉及一对线性方程组，因此逻辑清晰、计算高效且易于编程实现。研究提出了新的数值策略，通过小圆弧模拟和加密配置点来处理孔洞可能存在的尖锐角点。文中给出了若干数值算例以说明新型双向保角映射的几何应用。此外，将该双向保角映射嵌入到两种考虑合理远场位移的重力地质材料中非圆形非对称浅埋隧道复变函数解中。通过与有限元解及现有解析解的对比，结果吻合良好，验证了该新型双向保角映射在力学分析中的可行性。