# Creep Model of Weakly Cemented Soft Rock Considering Damage and Secondary Development in FLAC3D
## 5 Conclusions  
Based on the microstructure and creep tests of weakly cemented mudstone from a mine in western China, this study investigated the creep damage degradation mechanism of the material. By incorporating a damage factor derived from an improved Nishihara model, a novel damage-based rheological model was proposed. The model was imple  
Figure 13: Comparison diagram of axial strain between the simulation and test. (**a**) Creep curve (uniaxial condition). (**b**) Mode of failure (uniaxial condition). (**c**) Creep curve (triaxial condition). (**d**) Mode of failure (triaxial condition).  
mented through secondary development, and simulation results demonstrated strong fitting performance. The key conclusions drawn from this study are as follows:  
1. Microstructural analysis revealed that the high clay mineral content (40.4%) and the loose structure characterized by face-to-face and cemented connections are the primary factors contributing to creep in weakly cemented mudstone. Under external forces, the fracture of clay minerals leads to the continuous propagation of microcracks, ultimately resulting in accelerated creep.
2. The proposed damage creep model dynamically captures parameter weakening through a time-dependent damage factor and accurately represents the three stages of creep by incorporating nonlinear winding elements. Its three-dimensional extension enhances its applicability to real-world engineering problems. Parameter inversion using the Levenberg-Marquardt (L-M) algorithm confirmed a fitting accuracy exceeding 98%. Sensitivity analysis indicated that the acceleration stage was significantly affected by the damage coefficients \(\alpha\) and \(\lambda\).
3. The numerical feasibility of the model was validated through secondary development in FLAC3D. The deviation between simulation and experimental results was within 5%, and the model successfully replicated the creep behavior of salt rock, anthracite, and mica-quartz schist, demonstrating strong universality. These findings provide a theoretical foundation for predicting time-dependent deformation and supporting disaster prevention and control in deep underground engineering.  
This study mainly focuses on uniaxial and conventional triaxial stress states, without consideration of true triaxial or dynamic creep behavior. Additionally, the damage factor applied here uniformly affects both elastic and viscoelastic components, which may oversimplify material responses. Future work should explore creep under true triaxial or dynamic loading conditions and investigate the differential effects of damage on various moduli. Although the model was developed and implemented within FLAC3D in the current study, the governing constitutive equations are general and suitable for integration into other numerical platforms such as ABAQUS or ANSYS. Adaptation to discrete frameworks like LEM remains an open research direction, as the current model structure assumes continuum mechanics.  
Conceptualization, J.H.; Software, J.H.; Writing--original draft, J.H.; Supervision, X.L.; Funding acquisition, S.H. and X.L.; Writing--review and editing, X.L., S.H., and C.Z.; data curation, S.G., Z.G., and J.D.; formal analysis, D.Y. and Y.C. All authors have read and agreed to the published version of the manuscript.  
The research described in this paper was financially supported by the National Natural Science Foundation of China (No. 52274087), the Taishan Scholars Project (tsqnz20221140), and the Natural Science Foundation of Shandong Province (ZR2024 ME097).  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare that there are no conflicts of interest regarding the publication of this paper.