journal article·2026-01-05Open access

An Improved Damage–Plasticity Constitutive Model Capturing Rock Softening Behavior Under Various Confining Pressures

Wei Huang, Juntao Ren, Peiyong Wang, Bingxiang Yuan, Junxuan Long, Haiqing Zhou, Rui Chen, Hao Li

Applied Sciences· Volume 16· Issue 1

Abstract

With the gradual depletion of shallow high-grade mineral resources, global mining activities are shifting toward deeper regions with more complex geological conditions. Rocks exhibit significantly different mechanical responses under high confining pressure environments, posing new challenges to deep mining safety. To address this, this study proposes an optimized rock damage constitutive model that characterizes the influence of confining pressure on rock mechanical behavior, incorporating its peak strength enhancement effect and regulatory mechanism on post-peak softening behavior. The core innovation lies in establishing an inverse relationship between softening parameters and confining pressure, as confining pressure increases, softening parameters decrease. This inverse relationship enables the model to reasonably reflect the inhibitory effect of confining pressure on the rock softening process, meaning that under higher confining pressure, the material exhibits slower stress decay and more pronounced ductile characteristics. This model can consistently describe brittle responses under low confining pressure and ductile responses under high confining pressure. The findings provide reliable theoretical support for predicting rock mass failure and conducting stability analysis under deep mining conditions.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Rock Mechanics and Modeling · Geotechnical Engineering and Soil Mechanics · Nonlocal and gradient elasticity in micro/nano structures

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

School of Civil and Hydraulic Engineering, Chongqing University of Science and Technology, Chongqing 401331, China

Chongqing Key Laboratory of Facility Damage Mechanism and Protection in Highland Mountain Environment, PLA Joint Logistics Support Force University of Engineering, Chongqing 401331, China

School of Civil and Transportation Engineering, Guangdong University of Technology, Guangzhou 510006, China

Funding

National Natural Science Foundation of China · Chongqing Municipal Education Commission Science and Technology Research Project · Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering Safety · Opening Fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection · Science and Technology Innovation Project Fund of Chongqing University of Science and Technology · Open Fund of Chongqing Key Laboratory of Energy Engineering Mechanics & Disaster Prevention and Reduction

References (42)

Show source-provided references
1. Triaxial mechanical behaviour and energy conversion characteristics of deep coal bodies under confining pressure10.1016/j.energy.2022.126443 ↗
2. Effects of confining pressure on acoustic emission and failure characteristics of sandstone10.1016/j.ijmst.2021.08.003 ↗
3. Experimental study on rock mechanical behavior retaining the in situ geological conditions at different depths10.1016/j.ijrmms.2020.104548 ↗
4. An experimental study on deformation and failure mechanical behavior of granite containing a single fissure under different confining pressures10.1007/s12665-017-6696-4 ↗
5. Confinement effects for damage and failure of brittle rocks10.1016/j.ijrmms.2006.03.015 ↗
6. Mechanical behavior of brittle-ductile transition in rocks at different depths
7. Experimental investigation and micromechanical modeling of the brittle-ductile transition behaviors in low-porosity sandstone10.1016/j.ijmecsci.2020.105654 ↗
8. Mechanical Deformation, Acoustic Emission Characteristics, and Microcrack Development in Porous Sandstone During the Brittle–Ductile Transition10.1007/s00603-023-03533-7 ↗
9. The Brittle–Ductile Transition and the Formation of Compaction Bands in the Savonnières Limestone: Impact of the Stress and Pore Fluid10.1007/s00603-022-02963-z ↗
10. Brittle-Ductile Transition and Hoek–Brown mi Constant of Low-Porosity Carbonate Rocks10.1007/s10706-021-01995-6 ↗
11. Triaxial Compression Testing at Constant and Reducing Confining Pressure for the Mechanical Characterization of a Specific Type of Sandstone10.1007/s00603-020-02357-z ↗
12. Experimental study on mechanical behavior, permeability, and damage characteristics of Jurassic sandstone under varying stress paths10.1007/s10064-021-02214-5 ↗
13. Mechanical behavior and damage constitutive model of granodiorite in a deep buried tunnel10.1007/s10064-022-02619-w ↗
14. Characterization and mesosimulation of the triaxial compression failure of rock-like materials10.1088/1755-1315/570/2/022030 ↗
15. Zhang, J., Li, L., Chen, X., Cui, Z., Jin, C., Shen, C., Su, Z., Li, S., and Liang, J. (2025). Study on Microcracks Propagation of Shale Under Tensile and Shear Loading at Different Confining Pressures. Appl. Sci., 15.10.3390/app152111546 ↗
16. Damage mechanism of rock induced by microcrack evolution: A multi-dimensional perspective10.1016/j.engfracmech.2024.110420 ↗
17. Timely spread characteristics of micro- and meso-scale fractures based on SEM experiment10.1007/s12665-020-09224-8 ↗
18. Microcracking Behavior of Gabbro During Monotonic and Cyclic Loading10.1007/s00603-021-02381-7 ↗
19. Zhao, L., Cui, Z., Peng, R., and Si, K. (2022). Numerical Simulation and Evaluation on Continuum Damage Models of Rocks. Energies, 15.10.3390/en15186806 ↗
20. A Continuous Damage Statistical Constitutive Model for Sandstone and Mudstone Based on Triaxial Compression Tests10.1007/s00603-022-02924-6 ↗
21. Assessment of Tensorial and Scalar Damage Models for an Isotropic Thermally Cracked Rock Under Confining Pressure Using Experimental Data: Continuum Damage Mechanics Versus Effective Medium Theory
22. Causes, characterization, damage models, and constitutive modes for rock damage analysis: A review10.1007/s12517-020-05755-3 ↗
23. A Simple 3D Damage-Plasticity Model with Energy-Based Regularisation in SPH for Modelling Fractured Quasi-brittle Rocks10.1007/s00603-025-04638-x ↗
24. Study on the damage-softening constitutive model of rock and experimental verification10.1007/s10409-018-00833-y ↗
25. Constitutive model of rock triaxial damage based on the rock strength statistics10.1177/1056789520923720 ↗
26. An experimental investigation and mechanical modeling of the combined action of confining stress and plastic strain in a rock mass10.1007/s10064-022-02716-w ↗
27. A damage mechanics based on the constitutive model for strain-softening rocks10.1016/j.engfracmech.2019.106521 ↗
28. Statistical damage constitutive model based on the Hoek–Brown criterion10.1007/s43452-021-00270-y ↗
29. Triaxial compression experiment and damage constitutive model of microbially modified strongly weathered phyllite10.1016/j.conbuildmat.2023.131962 ↗
30. Deformation failure and damage evolution law of weathered granite under triaxial compression10.1080/10589759.2023.2283710 ↗
31. Constitutive model to simulate full deformation and failure process for rocks considering initial compression and residual strength behaviors10.1139/cgj-2018-0178 ↗
32. Evolution models of the strength parameters and shear dilation angle of rocks considering the plastic internal variable defined by a confining pressure function10.1007/s10064-020-02040-1 ↗
33. SPH-based modelling of the entire rock caving process: Insights into failure mechanisms10.1016/j.ijrmms.2025.106228 ↗
34. Stress–Energy Mechanism for Rock Failure Evolution Based on Damage Mechanics in Hard Rock10.1007/s00603-019-01953-y ↗
35. Energy Damage Evolution Mechanism of Rock and Its Application to Brittleness Evaluation10.1007/s00603-018-1681-0 ↗
36. Controlling behaviour of constitutive models for rocks using energy dissipations10.1016/j.ijplas.2024.104196 ↗
37. Capturing pressure- and rate-dependent behaviour of rocks using a new dam-age-plasticity model10.1016/j.ijimpeng.2017.01.006 ↗
38. Post-yield Strength and Dilatancy Evolution Across the Brittle–Ductile Transition in Indiana Limestone10.1007/s00603-017-1195-1 ↗
39. A study of the behaviour of brittle rocks under plane strain and triaxial loading conditions10.1016/0148-9062(95)00025-C ↗
40. Method for Determining Hoek-Brown Softening Parameters of Rocks Based on Triaxial Compression Tests
41. Elastoplastic Damage Behavior of Rocks: A Case Study of Sandstone and Salt Rock10.1007/s00603-023-03349-5 ↗
42. A damage plasticity model for different types of intact rock10.1016/j.ijrmms.2015.09.012 ↗