Purpose This study aims to develop an analytical framework for evaluating longitudinal deformation of shield tunnels subjected to discrete surface loads, explicitly incorporating the stiffness effect of pavement-hardened layers. The model introduces a synergistic deformation mechanism that couples segmental rotation and misalignment, enabling more accurate prediction compared to traditional continuous-load assumptions. Validation through PLAXIS 3D simulations and field monitoring demonstrates its reliability. The framework provides practical guidance for optimizing temporary support layouts and controlling tunnel deformation during surface construction, ensuring the structural safety and serviceability of shield tunnels in complex urban environments. Design/methodology/approach An analytical model was developed to evaluate shield tunnel deformation under discrete surface loads, incorporating the stiffness equivalence of pavement-hardened layers. The model integrates a synergistic mechanism coupling segmental rotation and misalignment, formulated using enhanced elasticity theory for granular soils and solved via a Fourier-series-based variational method. PLAXIS 3D finite element simulations were conducted to replicate staged construction loading and validate model predictions. Field monitoring data from a metro tunnel in Ningbo, China, were used for comparison, confirming the model's accuracy and practical applicability in optimizing temporary support layouts for tunnel deformation control. Findings The proposed model accurately predicts shield tunnel deformation under discrete surface loads, with displacement errors within 7% compared to field measurements. Considering the pavement-hardened layer reduces predicted tunnel displacement by up to 52% and decreases misalignment, rotation, and shear forces by about 30%. Temporary support layout significantly influences deformation patterns; optimized arrangements yield more uniform and reduced displacements. The relationship between surface surcharge and tunnel deformation is nearly linear within typical load ranges, with excessive concentrated loads quickly exceeding settlement warning thresholds. The model offers a practical basis for safe construction planning above operational shield tunnels. Research limitations/implications The proposed model assumes linear elastic soil behavior and does not account for complex nonlinear, dynamic, or time-dependent effects such as creep and long-term consolidation. The hardened layer is represented through stiffness equivalence, neglecting potential cracking or degradation under repeated loading. Validation is based on one metro tunnel case, which may limit direct applicability to other geologies or structural configurations. Future research should extend the framework to incorporate nonlinear soil constitutive models, dynamic load scenarios, and broader field datasets to enhance predictive capability and applicability in more diverse urban tunneling environments. Practical implications The developed analytical framework provides a practical tool for assessing shield tunnel performance under discrete surface loads in urban construction. Incorporating the stiffness effect of pavement-hardened layers, it enables more accurate deformation prediction, avoiding overly conservative designs. Engineers can use the model to determine allowable surface surcharge limits, optimize temporary support layouts, and minimize adverse impacts on operational tunnels. This approach supports safer construction planning, reduces maintenance risks, and ensures serviceability of existing tunnel infrastructure, offering a reliable basis for decision-making in projects involving heavy surface equipment or temporary structural supports. Social implications Accurate prediction and control of tunnel deformation under surface construction loads enhance the safety and reliability of urban transportation networks. By preventing excessive settlement and structural damage, the proposed approach helps avoid service interruptions, costly repairs, and potential safety hazards to the public. Optimizing temporary support layouts reduces environmental disturbance and minimizes disruption to surface traffic during construction. The method supports sustainable urban development by enabling efficient use of existing underground infrastructure while accommodating aboveground construction demands, contributing to safer cities and improved public confidence in large-scale infrastructure projects. Originality/value This study introduces an analytical framework that, for the first time, couples the effects of discrete surface loads with the stiffness contribution of pavement-hardened layers in predicting shield tunnel deformation. A synergistic deformation mechanism is proposed to simultaneously account for segmental rotation and misalignment, improving physical realism over conventional continuous-load models. The model is formulated using enhanced elasticity theory for granular soils and validated through PLAXIS 3D simulations and field monitoring. It offers a practical, validated tool for optimizing construction load arrangements above operational tunnels, addressing a critical gap in urban tunneling deformation prediction and safety assessment.
Wang et al. (Wed,) studied this question.