Prediction of settlement of existing tunnels to a new tunnel excavation underneath based on nonlinear subgrade reaction

With the rapid development of urban tunnel construction, the number of tunnel undercrossing projects beneath existing tunnels is increasing, making the accurate prediction and control of tunnel longitudinal settlement crucial for ensuring structural safety. Traditional beam-spring models assume that the subgrade reaction modulus k is constant, but this assumption is less applicable in scenarios involving large deformations in weak clay. Based on the Mobilized Strength Design (MSD) theory, this paper proposes a new method for predicting tunnel longitudinal settlement, focusing on the nonlinear relationship between the subgrade reaction and longitudinal settlement. Using the principle of energy conservation, a nonlinear subgrade reaction model based on soil stress-strain relationships is developed, and the subgrade reaction is fitted using a hyperbolic function. This model is applied to a case of three tunnels undercrossing an existing tunnel in Shanghai's soft soil region, with results showing that the MSD-based calculation closely matches actual monitoring data, validating the effectiveness and applicability of the model. This paper provides a more accurate calculation method for settlement prediction and structural design in tunnel undercrossing projects, with significant theoretical and practical value.