arXiv subjects

Luo-bin Lin

Publications and source records attributed to Luo-bin Lin.

4 recordsLinked to original sources

arXiv2024

Complex variable solution on asymmetrical sequential shallow tunnelling in gravitational geomaterial considering static equilibrium

Asymmetrical sequential excavation is common in shallow tunnel engineering, especially for large-span tunnels. Owing to the lack of necessary conformal mappings, existing complex variable solutions on shallow tunnelling are only suitable for symmetrical cavities, and can not deal with asymmetrical sequential tunnelling effectively. This paper proposes a new complex variable solution on asymmetrical sequential shallow tunnelling by incorporating a bidirectional conformal mapping scheme consisting of Charge Simulation Method and Complex Dipole Simulation Method. Moreover, to eliminate the far-field displacement singularity of present complex variable method, a rigid static equilibrium mechanical model is established by fixing the far-field ground surface to equilibriate the nonzero resultant along cavity boundary due to gravitational shallow tunnelling. The corresponding mixed boundary conditions along ground surface are transformed into homogenerous Riemann-Hilbert problems with extra constraints of traction along cavity boundaries, which are solved in an iterative manner to obtain reasonable stress and displacement fields of asymmetrical sequential shallow tunnelling. The proposed solution is validated by sufficient comparisons with equivalent finite element solution with good agreements. The comparisons also suggest that the proposed solution should be more accurate than the finite element one. A parametric investigation is finally conducted to illustrate possible practical applications of the proposed solution with several engineering recommendations. Additionally, the theoretical improvements and defects of the proposed solution are discussed for objectivity.

math.NA↗

arXiv2024

Far-field displacement singularity elimination for time-dependent complex variable method on quasi-three dimensional gravitational shallow tunnelling

This paper identifies the nonzero resultant and consequent unique displacement singularity of time-dependent complex variable method on quasi-three dimensional shallow tunnelling in visco-elastic and gravitational geomaterial. The quasi-three dimensional problem is equivalently simplified into a plane-strain one using a time-dependent coefficient of convergence confinement method to simulate the progressive release of initial stress field. The unique displacement singularity is thereby eliminated by fixing the far-field ground surface to produce corresponding counter-acting force to equilibriate the nonzero resultant to formalize a strict equilibrium mechanical model. 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 satisfied, and detailed comparisons with corresponding finite element solution are conducted. The comparison 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 additionally disclosed for objectivity.

math.NA↗

arXiv2024

Complex variable solution on over-/under-break shallow tunnelling in gravitational geomaterial with reasonable far-field displacement

Over-/under-break excavation is a common phenomenon in shallow tunnelling, which is nonetheless not generally considered in existing complex variable solutions. In this paper, a new equilibrium mechanical model on over-/under-break shallow tunnelling in gravitational geomaterial is established by fixing far-field ground surface to form a corresponding mixed boundary problem. With integration of a newly proposed bidirectional composite conformal mapping using Charge Simulation Method, a complex variable solution of infinite complex potential series is subsequently derived using analytic continuation to tranform the mixed boundaries into a homogenerous Riemann-Hilbert problem, which is iteratively solved to obtain the stress and displacement in geomaterial. The infinite complex potential series of the complex variable solution are truncated to obtain numerical results, which is rectified by Lanczos filtering to reduce the oscillation of Gibbs phenomena. The bidirectional conformal mapping is discussed and validated via several numerical cases, and the subsequent complex variable solution is verified by examining the Lanczos filtering and solution convergence, and comparing with corresponding finite element solution and existing analytical solution. Further discussions are made to disclose possible defects of the proposed solution for objectivity.

math.NA↗

arXiv2023

A new complex variable solution on noncircular shallow tunnelling with reasonable far-field displacement

A new mechanical model on noncircular shallow tunnelling considering initial stress field is proposed in this paper by constraining far-field ground surface to eliminate displacement singularity at infinity, and the originally unbalanced tunnel excavation problem in existing solutions is turned to an equilibrium one of mixed boundaries. By applying analytic continuation, the mixed boundaries are transformed to a homogenerous Riemann-Hilbert problem, which is subsequently solved via an efficient and accurate iterative method with boundary conditions of static equilibrium, displacement single-valuedness, and traction along tunnel periphery. The Lanczos filtering technique is used in the final stress and displacement solution to reduce the Gibbs phenomena caused by the constrained far-field ground surface for more accurte results. Several numerical cases are conducted to intensively verify the proposed solution by examining boundary conditions and comparing with existing solutions, and all the results are in good agreements. Then more numerical cases are conducted to investigate the stress and deformation distribution along ground surface and tunnel periphery, and several engineering advices are given. Further discussions on the defects of the proposed solution are also conducted for objectivity.

math.NA↗