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When considering initial stress field in geomaterial, nonzero resultant ofshallow tunnel excavation exists, which produces logarithmic items in complexpotentials, and would further lead to a unique displacement singularity atinfinity to violate geo-engineering fact in real world. The mechanical andmathematical reasons of such a unique displacement singularity in the existingmechanical models are elaborated, and a new mechanical model is subsequentlyproposed to eliminate this singularity by constraining far-field ground surfacedisplacement, and the original unbalanced resultant problem is converted intoan equilibrium one with mixed boundary conditions. To solve stress anddisplacement in the new model, the analytic continuation is applied totransform the mixed boundary conditions into a homogenerous Riemann-Hilbertproblem with extra constraints, which is then solved using an approximate anditerative method with good numerical stability. The Lanczos filtering isapplied to the stress and displacement solution to reduce the Gibbs phenomenacaused by abrupt change of the boundary conditions along ground surface.Several numerical cases are conducted to verify the proposed mechanical modeland the results strongly validate that the proposed mechanical modelsuccessfully eliminates the displacement singularity caused by unbalancedresultant with good convergence and accuracy to obtain stress and displacementfor shallow tunnel excavation. A parametric investigation is subsequentlyconducted to study the influence of tunnel depth, lateral coefficient, and freesurface range on stress and displacement distribution in geomaterial.

Reasonable mechanical model on shallow tunnel excavation to eliminate displacement singularity caused by unbalanced resultant