A Unified Constitutive Model for the Static Tensile Behavior of Constant-Resistance Anchor Bolts in Deep Underground Roadways

Constant-resistance and large-deformation (CRLD) anchor bolts have evolved into two generations comprising six structural models (1G and 2G CRLD), and have been widely used in underground engineering under complex geological conditions. However, the absence of a unified constitutive model has limited both the efficiency of support system design and the depth of mechanical understanding, particularly regarding their static tensile performance. To address this issue, this study proposes a unified constitutive model for the static tensile behavior of CRLD bolts. The model integrates a generalized hardening function with the Mises yield criterion and associated plastic flow rule. It is numerically implemented via a user-defined subroutine in a finite element software and validated through theoretical solutions, numerical simulations, and experimental tests. Furthermore, model performance is quantitatively assessed using the Akaike Information Criterion (AIC), showing an average reduction of 53.7% for 1G CRLD and 37.6% for 2G CRLD compared to existing models, indicating enhanced accuracy with lower complexity. Finally, a field-scale case study involving a deep underground roadway with high stress and large deformation confirms the model’s applicability in simulating axial force–displacement responses. The unified model provides a practical and extensible tool for the analysis and design of support systems in complex underground engineering environments. • A unified hardening function for CRLD has been proposed • Derive a unified constitutive model for the static tensile of CRLD • Implement the numerical calculations of the constitutive model using ABAQUS • Utilizing engineering case studies for model validation.