基于八面体理论的岩石循环加-卸载本构模型及修正

罗吉安; 刘丰茂; 刘之喜; 马雷鸣; 陈烨开; 李欣慰

doi:10.11858/gywlxb.20190797

基于八面体理论的岩石循环加-卸载本构模型及修正

doi: 10.11858/gywlxb.20190797

1.
安徽理工大学力学与光电物理学院，安徽淮南　232001
2.
安徽理工大学土木建筑学院，安徽淮南　232001

基金项目: 国家自然科学基金（51404013）；安徽高校自然科学重大研究项目（KJ2018ZD010）；深部岩土力学与地下工程国家重点实验室开放基金（SKLGDUEK1212）

详细信息

作者简介:
罗吉安（1978－），男，博士，副教授，主要从事矿山工程力学的理论与应用研究.E-mail: 19552433@qq.com

通讯作者:
刘丰茂（1995－），男，硕士研究生，主要从事岩石蠕变与损伤本构研究. E-mail: liufmaust@163.com

中图分类号: O347.3; TU457
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出版历程
- 收稿日期: 2019-06-26
- 修回日期: 2019-07-10

Study and Correction of Cyclic Loading-Unloading Constitutive Model of Rock Based on Octahedral Theory

1.
School of Mechanics and Optoelectronics Physics, Anhui University of Science and Technology, Huainan 232001, Anhui, China
2.
School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, Anhui, China

摘要

摘要: 探究岩石的受力特点及破坏特性是研究岩石地下工程安全性的关键，诸多学者都期望能在岩石本构模型的研究上取得突破性进展。在此背景下，提出了一种能够描述循环加-卸载条件下岩石的本构模型。首先，假设岩石的微元强度服从八面体剪应力理论并且微元破坏服从Weibull概率公式，将岩石本构中的损伤变量以及岩石微元强度表达式里包含的损伤因子进行本构变换，得到关于应力、应变等其他表现加-卸载下岩石损伤本构模型的参数，表示出岩石微元强度和损伤变量，再将得到的岩石微元强度和损伤变量代入所提出的岩石本构模型中，并进行等式变换得到一个函数表达式。通过将其与实验数据进行拟合对比分析，得出修正后的拟合参数，将其代入函数式中，得到损伤本构模型的修正式。最后将拟合参数进行必要的敏感性分析，得出各拟合参数的实际物理意义。
- 循环加-卸载 /
- 本构模型 /
- 八面体剪应力理论 /
- 岩石
Abstract: Exploring the stress and failure characteristics of rock is the key to study the safety of rock underground engineering, thus many scholars expect to make breakthrough in the study of rock constitutive model. In this paper, a constitutive model is proposed to describe the rock under cyclic loading and unloading. Firstly, it is assumed that the micro-unit strength of rock obeys Octahedral shear stress theory and the micro-unit failure of rock obeys Weibull probability formula, and the damage variables in rock constitution and the damage factors contained in micro-unit strength of rock expression are transformed into the constitutive equation. Then the parameters such as stress, strain and others representing the damage constitutive model of rock under loading and unloading can be obtained and are used to express the micro-unit strength and damage variables. Substituting the micro-unit strength and damage variables into the proposed rock constitutive model, a function expression can be carried out by an equation transformation. Through the comparison and analysis of the fitting data with the experimental results, the modified fitting parameters are acquired, and can be substituted into the function to revise the damage constitutive model. Finally, the necessary sensitivity analysis of the fitting parameters is implemented to obtain the practical physical significance of each fitting parameter.
- cyclic loading and unloading /
- constitutive model /
- octahedral shear stress theory /
- rock

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图 1 循环加-卸载试验机

Figure 1. Cyclic loading and unloading test machine

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图 2 标准岩石试件

Figure 2. Standard rock specimens

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图 3 试验应力-应变曲线

Figure 3. Stress-strain curve of the tests

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图 4 加载阶段B-A曲线拟合

Figure 4. B-A fitting curve during loading stage

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图 5 卸载阶段B-A曲线拟合

Figure 5. B-A fitting curve during unloading stage

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图 6 Weibull分布参数F₀与正应力σ₁的关系

Figure 6. Relation between Weibull distribution parameter F₀ and the normal stress σ₁

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图 7 Weibull分布参数m与正应力σ₁的关系

Figure 7. Relation between Weibull distribution parameter m and the normal stress σ₁

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图 8 参数F₀的敏感性分析情况

Figure 8. Sensitivity analysis of parameter F₀

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图 9 参数m敏感性分析情况

Figure 9. Sensitivity analysis of parameter m

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表 1 加-卸载等级参数

Table 1. Parameters of each loading and unloading level

Loading and unloading grade	m	F₀	R²
Grade 1, loading	–0.483 01	29.691 94	0.932 97
Grade 2, loading	–0.737 97	30.952 10	0.983 45
Grade 3, loading	–0.840 34	32.264 57	0.984 80
Grade 4, loading	–0.890 04	33.767 98	0.988 36
Grade 5, loading	–0.920 34	36.484 55	0.991 11
Grade 6,loading	–0.938 51	40.468 44	0.993 62
Grade 1, unloading	–1.001 48	32.181 62	0.972 66
Grade 2, unloading	–1.135 50	34.403 39	0.975 51
Grade 3, unloading	–1.183 00	36.806 63	0.973 74
Grade 4, unloading	–1.252 52	39.700 14	0.976 53
Grade 5, unloading	–1.297 34	43.966 39	0.978 54

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参考文献(16)

[1]	徐志英. 岩石力学 [M]. 北京:水利电力出版社, 1986. XU Z Y. Rock mechanics [M]. Beijing: Water Conservancy and Electricity Press, 1986.
[2]	刘佑荣, 唐辉明. 岩体力学 [M]. 北京:中国地质大学出版社, 1999. LIU Y R, TANG H M. Rock mass mechanics [M]. Beijing: China University of Geosciences Press, 1999.
[3]	曹文贵, 方祖烈, 唐学军. 岩石损伤软化统计本构模型之研究 [J]. 岩石力学与工程学报, 1998, 17(6): 628–633. doi: 10.3321/j.issn:1000-6915.1998.06.004 CAO W G, FANG Z L, TANG X J. A study of statistical constitutive model for soft and damage rocks [J]. Journal of Rock Mechanics and Engineering, 1998, 17(6): 628–633. doi: 10.3321/j.issn:1000-6915.1998.06.004
[4]	曹文贵, 赵明华, 唐学军. 岩石破裂过程的统计损伤模拟研究 [J]. 岩土工程学报, 2003, 25(2): 184–187. doi: 10.3321/j.issn:1000-4548.2003.02.013 CAO W G, ZHAO M H, TANG X J. Study on simulation of statistical damage in the full process of rock failure [J]. Journal of Geotechnical Engineering, 2003, 25(2): 184–187. doi: 10.3321/j.issn:1000-4548.2003.02.013
[5]	曹文贵, 张升. 基于Mohr-Coulomb 准则的岩石损伤统计分析方法研究 [J]. 湖南大学学报(自然科学版), 2005, 32(1): 43–47. CAO W G, ZHANG S. Statistical analysis of rock damage based on Mohr-Coulomb criterion [J]. Journal of Hunan University (Natural Science Edition), 2005, 32(1): 43–47.
[6]	袁小平, 刘红岩, 王志乔. 基于 Drucker-Prager 准则的岩石弹塑性损伤本构模型研究 [J]. 岩土力学, 2012, 33(4): 1103–1108. doi: 10.3969/j.issn.1000-7598.2012.04.021 YUAN X P, LIU H Y, WANG Z Q. Study of elastoplastic damage constitutive model of rocks based on Drucker-Prager criterion [J]. Geotechnical Mechanics, 2012, 33(4): 1103–1108. doi: 10.3969/j.issn.1000-7598.2012.04.021
[7]	李西蒙, 刘长友, 鲁岩, 等. 单轴分级循环加载条件下砂岩疲劳变形特性与损伤模型研究 [J]. 中国矿业大学学报, 2017, 46(1): 8–17. LI X M, LIU C Y, LU Y, et al. Fatigue deformation characteristics and damage model of sandstone subjected to uniaxial step cyclic loading [J]. Journal of China University of Mining and Technology, 2017, 46(1): 8–17.
[8]	王者超, 赵建纲, 李术才, 等. 循环荷载作用下花岗岩疲劳力学性质及其本构模型 [J]. 岩石力学与工程学报, 2012, 31(9): 1888–1900. doi: 10.3969/j.issn.1000-6915.2012.09.021 WANG Z C, ZHAO J G, LI S C, et al. Fatigue mechanical behavior of granite subjected to cyclic load and its constitutive model [J]. Journal of Rock Mechanics and Engineering, 2012, 31(9): 1888–1900. doi: 10.3969/j.issn.1000-6915.2012.09.021
[9]	何明明, 陈蕴生, 李宁, 等. 单轴循环荷载作用下砂岩变形特性与能量特征 [J]. 煤炭学报, 2015, 40(8): 1805–1812. HE M M, CHEN Y S, LI N, et al. Deformation and energy characteristics of sandstone subjected to uniaxial cyclic loading [J]. Journal of Coal Mine, 2015, 40(8): 1805–1812.
[10]	张平阳, 夏才初, 周舒威, 等. 循环加-卸载岩石本构模型研究 [J]. 岩土力学, 2015, 12(36): 3354–3359. ZHANG P Y, XIA C C, ZHOU S W, et al. A constitutive model for rock under cyclic loading and unloading [J]. Geotechnical Mechanics, 2015, 12(36): 3354–3359.
[11]	夏才初, 张平阳, 周舒威, 等. 大规模压气储能洞室稳定性和洞周应变分析 [J]. 岩土力学, 2014, 35(5): 1391–1398. XIA C C, ZHANG P Y, ZHOU S W, et al. Stability and tangential strain analysis of large-scale compressed air energy storage cavern [J]. Geotechnical Mechanics, 2014, 35(5): 1391–1398.
[12]	徐卫亚, 韦立德. 岩石损伤统计本构模型的研究 [J]. 岩石力学与工程学报, 2002, 21(6): 787–791. doi: 10.3321/j.issn:1000-6915.2002.06.006 XU W Y, WEI L D. Study on statistical damage constitutive model of rock [J]. Journal of Rock Mechanics and Engineering, 2002, 21(6): 787–791. doi: 10.3321/j.issn:1000-6915.2002.06.006
[13]	章清叙, 葛修润, 黄铭, 等. 周期荷载作用下红砂岩三轴疲劳变形特性试验研究 [J]. 岩石力学与工程学报, 2006, 25(3): 473–478. doi: 10.3321/j.issn:1000-6915.2006.03.006 ZHANG Q X, GE X R, HUANG M, et al. Testing study on fatigue deformation law of ren-sandstone under triaxial compression with cyclic loading [J]. Journal of Rock Mechanics and Engineering, 2006, 25(3): 473–478. doi: 10.3321/j.issn:1000-6915.2006.03.006
[14]	葛修润, 卢应发. 循环荷载作用下岩石疲劳破坏和不可逆变形问题的探讨 [J]. 岩土工程学报, 1992, 14(3): 56–60. doi: 10.3321/j.issn:1000-4548.1992.03.007 GE X R, LU Y F. Discussion on fatigue failure and irreversible deformation of rock under cyclic loading [J]. Journal of Geotechnical Engineering, 1992, 14(3): 56–60. doi: 10.3321/j.issn:1000-4548.1992.03.007
[15]	葛修润, 蒋宇, 卢允德, 等. 周期荷载作用下岩石疲劳变形特性试验研究 [J]. 岩石力学与工程学报, 2003, 22(10): 1581–1585. doi: 10.3321/j.issn:1000-6915.2003.10.001 GE X R, JIANG Y, LU Y D, et al. Testing study on fatigue deformation law of rock under cyclic loading [J]. Journal of Rock Mechanics and Engineering, 2003, 22(10): 1581–1585. doi: 10.3321/j.issn:1000-6915.2003.10.001
[16]	刘树新, 刘长武, 韩小刚, 等. 基于损伤多重分形特征的岩石强度Weibull 参数研究 [J]. 岩土工程学报, 2011, 33(11): 1786–1791. LIU S X, LIU C W, HAN X G, et al. Weibull distribution parameters of rock strength based on multi-fractal characteristics of rock damage [J]. Journal of Geotechnical Engineering, 2011, 33(11): 1786–1791.