Predicting Metro Tunnel Deformation from Adjacent Excavation Using a Nonlinear Shear-Considered Model

To more accurately predict existing shield tunnel deformation induced by adjacent excavation, this study developed a nonlinear Pasternak–Timoshenko model (NPTM). The model innovatively integrates nonlinear soil response with the tunnel’s structural shear deformation. Validation against a finite element model and two engineering cases confirmed the NPTM’s reliability. A key finding was that for wide excavations, soil nonlinearity dominated, and the deformation peak occurred at the excavation edge. Conversely, for narrow excavations, the tunnel’s structural shear behavior was more critical. Parametric analysis revealed deformation was highly sensitive to the pit–tunnel distance, d , and soil undrained shear strength, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>u</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . Quantitatively, the benefit of increasing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>u</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> diminished significantly when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>u</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> exceeded 80 kPa. This suggests an economic threshold for ground improvement. Furthermore, deformation attenuated sharply when the pit–tunnel distance, d , exceeded 15 m. The model provides a practical, preliminary design tool for helping engineers to identify critical deformation zones and optimize protective measures.