## 6 Conclusions  
This study achieved the secondary development of the Nishihara creep model within Abaqus using the Fortran language and the UMAT subroutine. Building on previous laboratory experiment data, the validity and accuracy of the developed subroutine were verified through cube element and laboratory specimen validation. Field measurement data from different-depth sections of the Jinping diversion tunnel further confirmed its engineering applicability. Utilizing this validated model, numerical simulations and predictions were conducted to investigate the long-term mechanical response of the surrounding rock during the Jinping auxiliary tunnel expansion project, enabling preliminary engineering applications. The key conclusions are as follows:  
(1) The numerical implementation of the Nishihara creep model in Abaqus was validated using a Jinping marble sample at a 2400 m depth. Element-level and specimen-scale simulations effectively captured the characteristic creep behavior of both intact marble and fractured rock masses approximated through fracture zone elements. The analyses revealed localized compression-induced tensile cracking and bedding-parallel slippage during the creep process after engineering disturbance conditions. (2) The comparative analysis of the long-term creep deformation calculations in the Jinping diversion tunnel at 1400 m and 2400 m depths highlights the profound influence  
Figure 16: The deformation characteristics of the left sidewall before and after expansion. Figure 17: Creep behavior analysis and prediction for both sidewalls post-expansion. of depth. The creep deformation at the 2400 m depth exceeded that at 1400 m by 46% in vertical strain and 65% in lateral expansion from the stress and strain contours. Excavation-induced creep deformation significantly exceeds instantaneous deformation at both depths. The stress concentration induced by engineering disturbances at the 2400 m depth is 71% higher than that at 1400 m, which increases markedly with depth. These results indicate that deeper rock masses exhibit slower deformation convergence and larger cumulative displacements, necessitating long-term monitoring of tunnel deformation. (3) Following rigorous validation, long-term deformation predictions were made for the Jinping auxiliary tunnel expansion initiated in late 2021. The results indicate that critical stress concentrations increase from 135 MPa to 203 MPa at the left sidewall's top and bottom, marking this zone for priority monitoring. The total rock deformation increases by 5 mm during expansion, accumulating to 14 mm. The deformation converges within 180 days post-expansion, with final creep magnitudes of 2.5-3.5 mm for both sidewalls. The surrounding rock remains stable for three years post-expansion, with no significant deformation changes observed. Future extensions of this model could encompass 3D simulations for complex tunnel geometries, integration with thermo-hydro-mechanical couplings for analyses of deep rock masses, and linkage to real-time monitoring systems to enable predictive infrastructure maintenance. Conceptualization: [PERSON] and M.C. ; methodology: [PERSON]; software: [PERSON]; validation: [PERSON] and Y.Z. ; formal analysis: [PERSON]; data curation: [PERSON] and Z.L. ; writing--original draft preparation: [PERSON]; writing--review and editing: [PERSON]; visualization: [PERSON]; supervision: [PERSON]; funding acquisition: [PERSON] and M.C. All authors have read and agreed to the published version of the manuscript. This research was supported by Beijing Natural Science Foundation (No. 8254049), the National Natural Science Foundation of China (No. 52374139), Fundamental Research Funds for China Academy of Safety Science and Technology (No.2024 JBKY07 and No.2025 JBKY05), and the Deep Earth Probe and Mineral Resources Exploration-National Science and Technology Major Project (No. 2024 ZD1004505). Not applicable. The original contributions of this study are included in the article, and further inquiries can be directed to the corresponding author.