Fuquan Chen's scientific contributions

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.

Three-dimensional effect of tunnel face and gravitational excavation generally occur in shallow tunnelling, which are nevertheless not adequately considered in present complex variable solutions. In this paper, a new time-dependent complex variable solution on quasi three-dimensional shallow tunnelling in gravitational geomaterial is derived, and the far-field displacement singularity is eliminated by fixed far-field ground surface in the whole excavation time span. With an equivalent coefficient of three-dimensional effect, the quasi three-dimensional shallow tunnelling is transformed into a plane strain problem with time-dependent virtual traction along tunnel periphery. The mixed boundaries of fixed far-field ground surface and nearby free segment form a homogenerous Riemann-Hilbert problem with extra constraints of the virtual traction along tunnel periphery, which is simultaneously solved using an iterative linear system with good numerical stability. The mixed boundary conditions along the ground surface in the whole excavation time span are well satisified in a numerical case, which is further examined by comparing with corresponding finite element solution. The results are in good agreements, and the proposed solution illustrates high efficiency. More discussions are made on excavation rate, viscosity, and solution convergence. A latent paradox is disclosed for objectivity.