为准确描述岩石蠕变变形破坏全过程,引入连续损伤和分数阶微积分理论建立全面、简练的蠕变本构模型。首先基于弹性模量随时间衰减规律,根据能量损伤的方式定义损伤变量,构建考虑时效损伤的弹性体,并验证该损伤演化方式的可行性。采用Riemann-Liouville型分数阶微积分算子理论,构建具有非线性特征的分数阶软体元件,利用该软体元件作为分数阶黏滞体描述岩石黏弹性应变,在该软体元件的基础上进行损伤演化,得到考虑时效损伤的分数阶黏塑性体。联合分数阶黏滞体、考虑时效损伤的弹性体和分数阶黏塑性体,建立一个新的考虑时效损伤的分数阶蠕变本构模型。给出参数解析方法,利用泥质板岩蠕变数据验证模型合理性和优越性。分析损伤发展过程,判断模型参数敏感度,并通过红砂岩、千枚岩单轴压缩各向异性蠕变特性试验研究蠕变试验数据验证模型适用性。研究成果为岩石蠕变全过程辨识及岩体工程长期稳定性研究提供一定参考。
Abstract
To accurately describe the whole process of creep deformation and failure of rock, a comprehensive and concise creep constitutive model is established by introducing continuous damage and fractional calculus theory. First of all, damage variable is defined according to the energy damage mode, and the elastic body in consideration of aging damage is constructed based on the attenuation law of elastic modulus with time, and the feasibility of the damage evolution mode is verified. The fractional order software components with nonlinear characteristics are constructe based on the Riemann-Liouville type fractional calculus operator theory, and the viscoelastic strain of rock is described with the aforementioned software components as a fractional viscous body. On such basis, the fractional order viscoplastic body in consideration of aging damage is obtained via damage evolution. Hence, a new fractional creep constitutive model in consideration of aging damage is established. The parameter analysis method is given, and the rationality and superiority of the model are verified by the creep data of argillaceous slate. Moreover, the damage development process is analyzed to determine the sensitivity of the model parameters, and the applicability of the model is verified by creep test data of red sandstone and phyllite. The research results offer reference for identifying the whole creep process and the long-term stability of rock mass.
关键词
岩石 /
分数阶 /
蠕变 /
时效损伤 /
本构模型
Key words
rock /
fractional order /
creep /
aging damage /
constitutive model
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参考文献
[1] 刘文博, 张树光. 基于应力和时间双重影响下岩石蠕变模型研究[J]. 中南大学学报:自然科学版, 2020, 51(8): 2256-2265.
[2] HUANG X, LIU Q, LIU B,et al. Experimental Study on the Dilatancy and Fracturing Behavior of Soft Rock under Unloading Conditions[J]. International Journal of Civil Engineering, 2017, 15(6): 921-948.
[3] 孙 钧.岩石流变力学及其工程应用研究的若干进展[J].岩石力学与工程学报,2007,26(6):1081-1106.
[4] 肖欣宏,王 静,谢小帅, 等. 水岩作用下红层泥岩蠕变特性[J]. raybet体育在线
院报, 2020, 37(9): 100-105, 113.
[5] MOGHADAM S N, MIRZABOZORG H, NOORZAD A. Modeling Time-dependent Behavior of Gas Caverns in Rock Salt Considering Creep, Dilatancy and Failure[J]. Tunnelling & Underground Space Technology, 2013, 33(1): 171-185.
[6] GÜNTHER R M, SALZER K, POPP T,et al. Steady-State Creep of Rock Salt: Improved Approaches for Lab Determination and Modelling[J]. Rock Mechanics and Rock Engineering, 2015, 48(6): 2603-2613.
[7] 王艳春, 王永岩. 深部三场环境下页岩蠕变模型的建立与试验[J]. 科技导报, 2014, 32(27): 60-65.
[8] 黄方勇. 低温下岩土体非整数阶元件组合蠕变模型研究[D]. 合肥:安徽理工大学, 2016.
[9] 张 玉, 王亚玲, 俞 缙, 等. 深层膏质泥岩蠕变特性及非线性蠕变模型研究[J]. 岩土力学, 2018, 39(增刊1): 105-112.
[10]金俊超,佘成学,尚朋阳.基于应变软化指标的岩石非线性蠕变模型[J]. 岩土力学,2019,40(6):2239-2246.
[11]张亮亮,王晓健,周瑞鹤.一种新的岩石非线性黏弹塑性蠕变模型研究[J].力学季刊,2020,41(1):120-128.
[12]蔡 煜, 曹 平. 基于Burgers模型考虑损伤的非定常岩石蠕变模型[J]. 岩土力学, 2016, 37(增刊2):369-374.
[13]张强勇, 杨文东, 张建国,等. 变参数蠕变损伤本构模型及其工程应用[J]. 岩石力学与工程学报, 2009, 28(4): 732-739.
[14]许宏发. 软岩强度和弹模的时间效应研究[J]. 岩石力学与工程学报, 1997, 16(3): 246-246.
[15]LEMAITRE J. A Continuous Damage Mechanics Model for Ductile Fracture[J]. Journal of Engineering Materials & Technology, 1985, 107:83-89.
[16]周激流, 蒲亦非, 廖 科. 分数阶微积分原理及其在现代信号分析与处理中的应用[M]. 北京:科学出版社, 2010.
[17]BLAIR G W S. Analytical and Integrative Aspects of the Stress-Strain-Time Problem[J]. Journal of Scientific Instruments, 1944, 21(5): 80-84.
[18]陈小磊. 分数阶理论在BP神经网络中的应用[D]. 南京:南京林业大学, 2013.
[19]苏国韶, 冯夏庭. 基于粒子群优化算法的高地应力条件下硬岩本构模型的参数辨识[J]. 岩石力学与工程学报, 2005, 24(17): 3029-3034.
[20]赵宝云, 刘东燕, 郑颖人, 等. 红砂岩单轴压缩蠕变试验及模型研究[J]. 采矿与安全工程学报, 2013, 30(5): 744-747.
[21]袁 泉, 谭 彩, 李列列. 千枚岩单轴压缩各向异性蠕变特性试验研究[J]. 水电能源科学, 2019, 37(11): 84, 154-157.
基金
中建股份科技研发计划资助项目(CSCEC-2018-Z-23)
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