Damage Evolution Law of Layered Rock Mass Considering Residual Strength
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摘要:
为更加真实准确地描述层状岩体的损伤演化过程，结合横观各向同性材料的弹性理论和损伤力学理论，采用修正的Lemaitre应变等价假设，建立了考虑残余强度的层状岩体损伤本构模型，通过页岩、千枚岩和板岩的三轴试验数据验证了模型的准确性，并分析了不同层理角度岩体的全过程损伤演化规律. 研究表明：模型既可以描述层状岩体的弹性变形，又可以较好地反映峰后应变软化过程；在初期加载过程中岩体的损伤值基本为0，随着应力增加，损伤值呈现出缓慢增长、加速增长、减速增长以及达到残余强度后稳定于1；页岩层理角度为60° 时损伤演化曲线最陡，损伤发展速度最快，最先破坏，千枚岩层厚较薄，强度更低，层理角度为90° 时最先破坏，而板岩相对较厚，强度更高，层理角度为45° 时最先破坏；岩体层理弱面的存在，导致了力学性能和破坏模式的各向异性，损伤演化规律也表现出明显的差异性.
Abstract:In order to describe the damage evolution process of layered rock mass more truly and accurately, a damage constitutive model for layered rock mass considering the residual strength was established, which adopted modified Lemaitre strain equivalence hypothesis, combining the elastic theory of transversely isotropic materials and the damage mechanics theory. The accuracy of the model was verified by the triaxial test data of shale, phyllite, and slate, and the whole process damage evolution law of rock mass with different bedding angles was analyzed. The research results showed that the model could describe the elastic deformation of layered rock mass, but also reflect the post-peak strain softening process well. In the initial loading process, the damage value of rock mass was near zero. With the increase of stress, the damage value showed slow growth, accelerated growth, and decelerated growth, until it reached the residual strength and then stabilized at one. When the bedding angle of the shale was 60°, the damage evolution curve was the steepest, the damage speed was the fastest, and it shale failed first. Because the phyllite was thinner in thickness and lower in strength, it failed first when the bedding angle was 90°. However, the slate was relatively thick and had higher strength, and it failed first when the bedding angle was 45°. The existence of a weak bedding surface of rock mass led to the anisotropy of mechanical properties and failure modes, and the damage evolution law showed remarkable differences.
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Key words:
- layered rock mass /
- anisotropy /
- constitutive model /
- residual strength /
- damage evolution
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图 1 横观各向同性材料坐标示意
Figure 1. Diagram of coordinate system for the transversely isotropic materials
图 3 考虑残余强度与不考虑残余强度对比
Figure 3. Comparison between the considered and unconsidered residual strengths
图 4 弹性模量的理论值与试验值对比
Figure 4. Comparison between theoretical and experimental values of elastic modulus
图 5 页岩应力-应变关系的理论值与试验值对比
Figure 5. Comparison between theoretical and experimental values of stress-strain curves for shale
图 6 千枚岩、板岩应力-应变关系的理论值与试验值对比
Figure 6. Comparison between theoretical and experimental values of stress-strain curves for phyllite and slate
围压/MPa 层理角度/（°） 峰值应力/MPa 峰值应变/% 弹性模量/GPa 残余强度/MPa m ε0/% 0 0 120.87 0.891 14.07 117.1 15.476 0.965 30 108.63 0.687 16.67 95.8 14.929 0.720 60 47.18 0.238 20.53 35.3 11.163 0.275 90 124.07 0.525 24.61 103.3 17.374 0.569 10 0 152.76 0.961 19.50 114.9 5.463 1.190 30 142.62 0.710 24.10 99.5 6.181 0.901 60 80.02 0.282 34.10 38.5 7.013 0.342 90 147.29 0.422 46.64 83.4 3.291 0.513 20 0 173.87 1.042 20.52 99.1 5.770 1.242 30 153.05 0.751 25.57 75.2 5.148 0.925 60 102.59 0.395 33.93 64.7 10.159 0.450 90 204.14 0.485 54.13 132.7 3.841 0.563 30 0 191.47 1.094 21.50 125.5 5.720 1.300 30 180.17 0.872 25.57 96.7 6.979 1.051 60 144.11 0.416 41.05 79.6 11.682 0.479 90 227.50 0.584 56.60 138.9 2.576 0.684 
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表 2 千枚岩、板岩三轴压缩试验的主要参数[22-23] （σ3=10 MPa）
Table 2. Main parameters of triaxial compression test for phyllite and slate [22-23] （σ3 = 10 MPa）
岩性 层理角度/（°） 峰值应力/MPa 峰值应变/% 弹性模量/GPa 残余强度/MPa m ε0/% 千枚岩[22] 0 69.29 0.489 15.7 40.0 20.726 0.547 30 51.55 0.459 14.4 36.0 4.642 0.539 45 53.39 0.362 16.7 33.5 14.487 0.412 90 95.46 0.217 55.0 68.0 4.848 0.253 板岩[23] 0 154.19 0.820 20.0 49.0 42.896 0.887 15 111.41 0.590 20.5 67.5 29.327 0.644 30 70.26 0.384 20.6 45.0 22.803 0.425 45 55.82 0.267 23.5 30.0 50.078 0.285 60 87.26 0.349 30.0 51.0 8.212 0.415 75 121.25 0.400 34.5 100.0 10.882 0.443 90 170.35 0.487 42.0 87.0 17.038 0.505
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