Deformation Simulation for Rock in Consideration of Initial Damage and Residual Strength
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摘要: 针对现有损伤模型的不足，提出同时反映岩石初始损伤和残余强度的岩石变形过程模拟方法.将岩石材料分为未损伤部分、损伤部分和微缺陷，未损伤部分和损伤部分共同承担岩石所受的应力.通过岩石材料几何条件及微观受力分析建立未损伤部分的应变分析.再考虑岩石的形变比能只与损伤部分材料相关，从而建立损伤部分的应变分析.然后探讨岩石损伤和耗散能的关系，提出了可以反映岩石初始损伤的损伤演化方程，基于各部分应变分析建立模拟岩石变形过程的损伤本构模型，同时给出模型各参数的确定方法.结果表明：损伤演化方程不仅表现了岩石的初始损伤特征，也可以完整地体现岩石变形破坏过程的5个阶段；与前人模型相比，提出的岩石变形模拟方法与试验曲线更加吻合，体现了岩石的变形全过程，特别是更加直观地反映了岩石的初始损伤和残余强度特征.综合体现了本文模型在模拟岩石变形全过程时的优势.Abstract: Aiming at the limitations of previous rock damage constitutive models, a comprehensive simulation method of rock deformation to present simultaneously initial damage and residual strength is developed. With consideration of the initial damage of rock and the fact that the damage portion still can bear certain stress, deformation mechanism models of each portion are established by decomposing rock materials into three portions, undamaged material, damaged material and micro-defects. Firstly, on the basis of geometry conditions and micro-force for rocks, the strain analysis for undamaged material is proposed. Meanwhile, considering that the deformation energy of rock is only related to damaged material, the strain analysis for damaged material is developed. Then, discussing the relationships between damage evolution and energy dissipation, and putting forward a damage evolution model to reflect the initial damage for rocks, a rock damage constitutive model to simulate the complete processes of deformation for rocks is established based on the strain analysis and the determination methods of model parameters are also provided. The results show that damage evolution model not only reflects the initial damage for rocks, but also presents the rock deformation stages. Compared with previous models, the proposed damage constitutive model is more consistent with the experimental curve. In addition, the proposed model reflects the complete processes of deformation for rocks, and presents intuitively the characteristics of the initial damage and the residual strength. Thus, the superiority of the model is validated.
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Key words:
- rock /
- closure stage /
- initial damage /
- residual strength /
- constitutive model
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图 1 含微缺陷的岩石损伤模型
a.损伤岩石材料；b.未损伤部分；c.损伤部分；d.微缺陷部分
Fig. 1. Rock damage model including micro-defects
图 2 压缩情况下典型的岩石损伤演化曲线
a.前人的理论曲线；b.本文的理论曲线
Fig. 2. Typical rock damage curves under loading conditions
图 4 岩石损伤演化曲线
a.σ3=5 MPa; b.σ3=10 MPa; c.σ3=20 MPa; d.σ3=30 MPa
Fig. 4. Rock damage evolution curves
图 5 试验曲线与理论曲线的比较
a.σ3=5 MPa; b.σ3=10 MPa; c.σ3=20 MPa; d.σ3=30 MPa
Fig. 5. The comparison of experimental curves and theoretical curves
表 1 不同围压下确定损伤模型所需的参数
Table 1. The damage model parameters under different confining pressures
σ3(MPa) ε10(10-3) γ β U0d(mJ/mm3) R2 5 2.61 9.92×10-8 1.48 137.69 0.99 10 1.80 3.55×10-6 1.03 154.62 0.99 20 1.87 6.88×10-8 1.27 270.68 0.99 30 1.78 9.55×10-20 3.39 466.80 0.99 
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表 2 不同损伤变量对应的强度参数值
Table 2. The strength parameters corresponding to different damage variables
D 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 φ(°) 36.65 37.82 36.73 35.48 34.13 32.77 31.31 29.73 28.02 26.29 24.10 c(MPa) 7.72 6.55 5.89 4.95 4.77 4.67 4.60 4.47 4.40 4.26 4.19
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表 3 不同围压下的δ和γ的值
Table 3. The values of δ and γ under different confining pressures
σ3(MPa) 5 10 20 30 δ(10-3) 2.448 1.721 1.411 1.277 γ 2.194 1.387 1.084 1.722
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表 4 岩石各部分的变形参数
Table 4. Mechanical parameters of each portion of rock
σ3(MPa) E1(GPa) μ1 E2(GPa) μ2 E3(MPa) μ3 5 2.502 0.14 2.085 0.23 1.133 0.47 10 3.377 0.16 2.598 0.25 1.634 0.47 20 3.657 0.18 2.709 0.26 1.643 0.48 30 3.75 0.19 2.778 0.26 1.681 0.49
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