  When considering initial stress field in geomaterial, nonzero resultant of
shallow tunnel excavation exists, which produces logarithmic items in complex
potentials, and would further lead to a unique displacement singularity at
infinity to violate geo-engineering fact in real world. The mechanical and
mathematical reasons of such a unique displacement singularity in the existing
mechanical models are elaborated, and a new mechanical model is subsequently
proposed to eliminate this singularity by constraining far-field ground surface
displacement, and the original unbalanced resultant problem is converted into
an equilibrium one with mixed boundary conditions. To solve stress and
displacement in the new model, the analytic continuation is applied to
transform the mixed boundary conditions into a homogenerous Riemann-Hilbert
problem with extra constraints, which is then solved using an approximate and
iterative method with good numerical stability. The Lanczos filtering is
applied to the stress and displacement solution to reduce the Gibbs phenomena
caused by abrupt change of the boundary conditions along ground surface.
Several numerical cases are conducted to verify the proposed mechanical model
and the results strongly validate that the proposed mechanical model
successfully eliminates the displacement singularity caused by unbalanced
resultant with good convergence and accuracy to obtain stress and displacement
for shallow tunnel excavation. A parametric investigation is subsequently
conducted to study the influence of tunnel depth, lateral coefficient, and free
surface range on stress and displacement distribution in geomaterial.
