含缺陷砂岩轴压能量本构关系的离散元模拟研究

郭永成; 陈冰; 李建林; 邓华锋

doi:10.11858/gywlxb.20251142

含缺陷砂岩轴压能量本构关系的离散元模拟研究

doi: 10.11858/gywlxb.20251142

郭永成^{1, 2, 3,*, ,},
陈冰³,
李建林^{1, 2, 3},
邓华锋^{1, 2, 3}

1.
三峡大学三峡库区地质灾害教育部重点实验室, 湖北宜昌　443002
2.
三峡大学防灾减灾湖北省重点实验室, 湖北宜昌　443002
3.
三峡大学土木与建筑学院, 湖北宜昌　443002

基金项目: 国家自然科学基金（52009069）；国家自然科学基金重点项目（U22A20600）

详细信息

通讯作者:
郭永成（1980－），男，博士，副教授，主要从事岩石力学及多尺度数值模拟研究. E-mail：gyc@ctgu.edu.cn

中图分类号: TU452; O521.9
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出版历程
- 收稿日期: 2025-07-25
- 修回日期: 2025-09-18
- 网络出版日期: 2025-09-18

Discrete Element Simulation of Axially Compressed Energy Constitutive Relations in Defective Sandstone

GUO Yongcheng^{1, 2, 3,*
, ,},
CHEN Bing³,
LI Jianlin^{1, 2, 3},
DENG Huafeng^{1, 2, 3}

1.
Key Laboratory of Geological Hazards on Three Gorges Reservoir Area of Ministry of Education, China Three Gorges University, Yichang 443002, Hubei, China
2.
Hubei Key Laboratory of Disaster Prevention and Mitigation, China Three Gorges University, Yichang 443002, Hubei, China
3.
College of Civil Engineering and Architecture, China Three Gorges University, Yichang 443002, Hubei, China

摘要

摘要: 为探究单轴压缩下缺陷砂岩的能量演化和力学行为，通过离散元法数值模拟，分析了不同岩桥倾角和岩桥距离对缺陷砂岩的影响，结合能量耗散建立了损伤本构方程。结果表明：岩桥倾角和岩桥距离显著影响缺陷砂岩的力学响应和破坏机制，大倾角（60°、90°）促进裂纹沿最大主应力方向扩展，而小倾角（0°、30°）增加剪切裂纹比例，导致不同的破坏形态；弹性模量和抗压强度随岩桥倾角和岩桥距离的变化呈“U”形非线性特征。能量演化规律对岩桥倾角具有依赖性，总能量和耗散能量随岩桥倾角的增加先降低后升高，并在90°时达到最大。岩桥距离对能量的影响随岩桥倾角的变化而变化，当岩桥倾角小于45°时，能量随岩桥距离的增加而减少，当岩桥倾角大于45°时，能量随岩桥距离的增加先增加后减少。弹性能耗比的三阶段特征可作为缺陷砂岩失稳的预测指标。基于耗散能理论构建的能量耗散损伤本构模型能够准确地描述不同岩桥参数下缺陷砂岩的变形和破坏行为。该模型在实际工程中具有重要的应用潜力，但需要针对具体应力条件进行调整以优化预测准确性。研究结果可为岩土工程的灾害防治提供理论参考。
- 单轴压缩 /
- 缺陷砂岩 /
- 离散元方法 /
- 裂纹演化 /
- 能量本构
Abstract: In order to investigate the energy evolution and mechanical behavior of defective sandstone under uniaxial compression, the discrete element method (DEM) is employed. Effects of different rock bridge inclination angles and distances on the mechanical behavior of defective sandstone are systematically studied by DEM, and established a damage constitutive equation based on energy dissipation. The results indicate that the rock bridge inclination angle and distance significantly affect the mechanical response and failure modes of defective sandstone. Large inclination angles (60°, 90°) facilitate crack propagation along the direction of maximum principal stress, while small inclination angles (0°, 30°) increase the proportion of shear cracks, leading to different failure patterns. Additionally, the elastic modulus and compressive strength exhibit a “U” -shaped nonlinear characteristic with the variation of inclination angle and distance. Moreover, the energy evolution pattern depends on the rock bridge inclination angle. The total energy and dissipated energy first decrease and then increase with increasing rock bridge inclination angle, and peaking at 90°. The influence of rock bridge distance on energy varies with inclination angle. For angles less than 45°, the two types of energy decrease with increasing distance. For angles greater than 45°, the two types of energy first increase and then decrease. The three-stage characteristic of the elastic energy dissipation ratio can serve as a predictive indicator of the instability of defective sandstone. Furthermore, the energy dissipation damage constitutive model constructed based on dissipated energy can accurately describe the deformation and failure behavior of defective sandstone under different rock bridge parameters. This model has significant application potential in practical engineering, but it needs to be adjusted according to specific stress conditions to optimize prediction accuracy. The research results can provide theoretical references for disaster prevention in geotechnical engineering.
- uniaxial compression /
- defective sandstone /
- discrete element method /
- crack evolution /
- energy ontology

HTML全文

图 1 砂岩的数值模型及平行黏结模型^[20–21]

Figure 1. Numerical model of sandstone and parallel bond model^[20–21]

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图 2 试验与模拟验证

Figure 2. Verification of test and simulation

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图 3 缺陷砂岩的数值模型

Figure 3. Numerical modeling of defective sandstone

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图 5 缺陷砂岩应力-应变曲线阶段划分示意图

Figure 5. Schematic diagram of the phases of stress-strain curves for defective sandstone

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4 不同岩桥倾角及岩桥距离条件下缺陷砂岩的应力-应变曲线

4. Stress-strain curves of defective sandstone at different rock bridge inclinations and distances

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图 6 抗压强度和弹性模量随岩桥倾角及岩桥距离变化的三维响应曲面

Figure 6. Three-dimensional response surface of compressive strength and elastic modulus with different rock bridge inclinations and rock bridge distances

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图 7 砂岩能量转换过程^[28]

Figure 7. Energy conversion process of sandstone^[28]

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图 8 不同岩桥倾角及岩桥距离下缺陷砂岩的能量演化规律

Figure 8. Energy evolution laws of defective sandstone at different rock bridge inclinations and distances

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图 9 不同岩桥倾角下缺陷砂岩的弹性能耗比曲线

Figure 9. Elastic energy ratio curves for defective sandstone at different rock bridge inclinations

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图 10 数值模型的本构关系验证

Figure 10. Verification of numerical model constitutive relation

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表 1 试验^[19]与数值模拟得到的力学参数对比

Table 1. Comparison of mechanical parameters between test^[19] and simulation

σ_max			ε_max			E
Test/MPa	Sim./MPa	Error/%	Test/10⁻³	Sim./ 10⁻³	Error/%	Test/GPa	Sim./GPa	Error/%
84.96	85.68	0.8	4.62	4.71	1.9	20.01	18.84	5.8

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表 2 砂岩的细观参数

Table 2. Microscopic parameters of sandstone

E_c/GPa	$ {\overline{E}}_{\rm c} $/GPa	k	σ_b/MPa	τ_b/MPa	Damp value	$ \overline{\varphi } $/(°)	μ
15	15	1.33	10	9	0.7	70	0.2

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表 3 数值模拟方案

Table 3. Numerical simulation scheme

Specimen No.	e/mm	β/(°)	Specimen No.	e/mm	β/(°)	Specimen No.	e/mm	β/(°)
10-0	10	0	20-0	20	0	30-0	30	0
10-30	10	30	20-30	20	30	30-30	30	30
10-45	10	45	20-45	20	45	30-45	30	45
10-60	10	60	20-60	20	60	30-60	30	60
10-90	10	90	20-90	20	90	30-90	30	90

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表 4 含缺陷砂岩的力学参数

Table 4. Mechanical parameters of defective sandstone

Specimen No.	β/(°)	σ_c/MPa	E/GPa	Specimen No.	β/(°)	σ_c/MPa	E/GPa
10-0	0	56.9959	17.10	20-60	60	59.6775	17.95
10-30	30	50.6317	17.54	20-90	90	75.0862	18.60
10-45	45	62.1072	17.26	30-0	0	57.7452	17.39
10-60	60	68.5561	18.13	30-30	30	55.4792	17.29
10-90	90	66.7174	18.25	30-45	45	55.6131	17.06
20-0	0	56.3965	17.26	30-60	60	66.3709	18.04
20-30	30	56.0322	17.29	30-90	90	76.4695	18.31
20-45	45	60.5541	17.63

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表 5 本构方程参数及拟合精度

Table 5. Constitutive equation parameters and fitting accuracy

Specimen No.	m	ω	λ	ϕ	R²
10-0	0.001	−0.364	78.839	−0.242	0.999
10-30	−0.632	−0.145	29.205	−0.116	0.999
10-45	−1.021	−0.374	108.360	−0.460	0.999
10-60	−0.032	−0.027	6.610	−0.018	0.999
10-90	−0.515	−0.322	89.375	−0.381	0.999
20-0	−0.212	−0.066	15.181	−0.062	0.999
20-30	−0.016	−0.040	7.050	−0.019	0.998
20-45	−0.290	−0.225	53.109	−0.139	0.998
20-60	−4.647	−1.272	316.756	−1.196	0.999
20-90	−0.060	−0.020	7.033	−0.017	0.999
30-0	−0.672	−0.496	103.613	−0.432	0.999
30-30	−0.933	−0.785	168.428	−0.640	0.999
30-45	1.174	−3.509	547.213	−1.085	0.998
30-60	0.001	−0.025	6.504	−0.020	0.999
30-90	0.065	−0.082	28.310	−0.089	0.999

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