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含孔隙冻融岩石的损伤本构模型

2019-09-10孟祥振张慧梅康晓革

关键词:损伤

孟祥振 张慧梅 康晓革

摘 要:针对现有损伤本构模型所存在的局限与不足,在深入研究孔隙岩石变形破坏特征的前提下,将岩石视为孔隙、损伤与未损伤3部分。以孔隙率反映岩石体积变化,基于weibull随机分布,依据损伤力学原理,确立含孔隙冻融岩石的损伤本构模型,并以理论表达的形式确定模型参数,最后利用冻融岩石的力学特性试验结果验证其合理性。结果表明:推导的本构模型与试验结果吻合较好,且岩石初始阶段时孔隙压密以及应变软化特性都能更好地反映出来;通过峰值条件获得的模型参数表达式,可反映冻融岩石的损伤演化与变形破坏的一般规律,增强了模型的适用性。

关键词:孔隙率;本构模型;模型参数;损伤

中图分类号:TU 452   文献标志码:A

DOI:10.13800/j.cnki.xakjdxxb.2019.0417   文章编号:1672-9315(2019)04-0688-05

Abstract:With the limitations and deficiencies of the existing damage constitutive model in view, the rock was abstracted as three parts of pore, damage and non damage based on weibull random distribution, after having investigated the deformation and failure characteristics of porous rock. Due to the fact that porosity reflects the change of rock volume, the damage constitutive model of porous rock under freeze thaw was established based on the damage mechanics theory, and the model parameters were determined in the form of expressions. Finally, the rationality of the model was verified by using the conventional triaxial freeze thaw text to obtain mechanical parameters. The results of the study show that: The establishment of constitutive model is reasonable, and the pore pressure and softening properties of the rock can be better reflected in the initial period. The expression of the model parameters obtained through the peak conditions can reflect the law of the damage and the deformation of rock under freeze thaw, which enhance the applicability of the model.

Key words:porosity;constitutive model;model parameter;damage

0 引 言

影响寒区岩土工程稳定性不可忽视的因素包括冻融及其所处的应力场等。自然状态下的岩石是由岩石颗粒及其颗粒间的孔隙组合而成,受外界因素的作用,内部孔隙压密与扩展,致使岩石体积不断发生变化,从而表现出不同的力学特性。因此,在研究岩石冻融状态下的损伤本构关系时,岩石体积的变化是必须考虑的重要因素。

目前,针对岩石损伤本构方面的研究取得了一定的成果。ZHOU H W,周辉、CHEN Xin等推导出岩石损伤本构模型,并利用线性回归的方法确定模型参数[1-3];李树春、张慧梅、LI XIANG,袁小清通过峰值点法确定了模型参数,较线性回归法有了较大改进,且参数具有明确的物理意义[4-8];曹文贵、温韬、石崇等采用不同的强度准则建立了岩石的本构模型[9-11];曹文贵在研究岩石空隙率基础上建立了岩石损伤模型[12];张蒙军、陈有亮、刘松明建立了不同环境下的岩石损伤关系式[13-15];张慧梅、ZHOU Shuwei,HUANG Shibing[16-19]等采用弹性模量对岩石冻融损伤进行了表征,确定了冻融和载荷下的统计本构方程。上述模型虽然对岩石变形过程进行了比较好的描述,但对于变形过程中岩石体积变化及凍融环境因素变化的影响并没有很好的综合考虑。

文中基于weibull随机分布,在深入探讨孔隙岩石变形破坏特征的基础上,以孔隙率反映岩石体积的变化,从而确立含孔隙冻融岩石损伤本构模型,并通过峰值条件以理论表达的形式确定模型参数。最后利用冻融岩石的力学特性试验结果验证其合理性。

1 含孔隙岩石的损伤本构模型

1.1 损伤模型的建立

3 模型验证

将式(25)、(30)、(31)代入式(27)之后,通过文献[15]中砂岩冻融循环条件下常规三轴压缩力学特性试验数据,计算得到本构关系的理论曲线,并与试验曲线做对比,如图1所示,以此来证明文中推导的含孔隙冻融岩石本构模型的合理性。

通过比较图1中理论曲线与试验曲线可知,文中确立含孔隙岩石本构模型具有合理性。砂岩的应力-应变曲线初始呈下凹形,斜率即变形模量逐渐增大,岩石有逐渐强化的趋势,这是由于岩石初始受荷,内部原始孔隙被压密所致。一定围压下,随着冻融次数的增加,压密阶段的变形模量减小,弹性模量和峰值点强度降低,岩石塑性增强,分析其原因是冻融作用逐渐导致岩石内部次生孔隙的增加,在宏观上表现为岩石的抗压强度逐渐衰减、应力-应变曲线变缓;一定冻融次数下,随着围压的增加,砂岩压密阶段的变形模量增加,弹性模量及峰值应力变大,表明围压具有抑制岩石损伤破坏的作用。另外,岩石峰后软化阶段应变特性在文中模型中也能更好地反映出来。

4 结 论

1)在深入探讨孔隙岩石变形破坏特征的前提下,以孔隙率反映岩石体积的变化,从而确立含孔隙冻融岩石的损伤本构模型,并获得模型参数表达式。

2)通过试验结果验证了含孔隙冻融岩石损伤本构模型的合理性。该模型对受荷初期时的孔隙压密阶段有较好的描述,且岩石应变软化特性也能更好地反映出来。

3)模型参数少,只需通过常规三轴力学试验即可获得,其理论表达式可反映岩石损伤与变形破坏的一般规律,对寒区岩土工程稳定性的研究具有实际意义。

参考文献(References):

[1] Zhou H W,Wang C P,Han B B,et al.A creep constitutive model for salt rock based on fractional derivatives[J].International Journal of Rock Mechanics & Mining Sciences,2011(48):116-121.

[2]周 辉,李 震,朱国金,等.基于岩石统一能量屈服准则的硬岩损伤模型[J].岩土力学,2016,37(3):609-624.

ZHOU Hui,LI Zhen,ZHU Guo jin,et al.A damage model for hard rock based on unified energy yield criterion of rock[J].Rock and Soil Mechanics,2016,37(3):609-624.

[3]Chen X,Liao Z H,Peng X.Deform ability characteristics of jointed rock masses under uniaxial compression[J].International Journal of Mining Sciences and Technology,2012,22(2):213-221.

[4]李树春,许 江,王 鸿,等.岩石损伤统计本构模型及其参数确定的研究[J].矿业研究与开发,2007,27(2):6-8.

LI Shu chun,XU Jiang,WANG Hong,et al.Research on statistical damage constitutive model of rock and determination of Its parameters[J].Mining Research and Development,2007,27(2):6-8.

[5]张慧梅,雷利娜,杨更社.等围压条件下岩石本构模型及损伤特性[J].中国矿业大学学报,2015,44(1):59-63.

ZHANG Hui mei,LEI Li na,YANG Geng she.Characteristic and representative model of rock damage process under constant confining stress[J].Journal of China University of Mining & Technology,2015,44(1):59-63.

[6]徐银花,徐小丽.高温下岩石损伤本构模型研究[J].广西大学学报,2017,42(1):226-235.

XU Yin hua,XU Xiao li.Study on damage constitutive model of rock under high temperature[J].Journal of Guangxi University,2017,42(1):226-235.

[7]LI Xiang,CAO Wen gui,SU Yong hua.A statistical damage constitutive model for softening behavior of rocks[J].Engineering Geology,2012,143-144:1-17.

[8]袁小清,刘红岩,刘京平.冻融荷载耦合作用下节理岩体损伤本构模型[J].岩石力学与工程学报,2015,34(8):1602-1611.

YUAN Xiao qing,LIU Hong yan,LIU Jing ping.A damaging model of jointed rock under coupling action of freezing and thawing[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(8):1602-1611.

[9]曹文贵,莫 瑞,李 翔.基于正态分布的岩石软硬化损伤统计本构模型及其参数确定方法探讨[J].岩土工程学报,2007,29(5):671-675.

CAO Wen gui,MO Rui,LI Xiang.Study on statistical constitutive model and determination of parameters of rock based on normal distribution[J].Chinese Journal of Geotechnical Engineering,2007,29(5):671-675.

[10]溫 韬,唐辉明,刘佑荣,等.影响因子修正的新型岩石损伤统计本构模型[J].中国矿业大学学报,2016,45(1):141-149.

WEN Tao,TANG Hui ming,LIU You rong,et al.Newly modified damage statistical constitutive model of rock based on impact factors[J].Journal of China University of Mining & Technology,2016,45(1):141-149.

[11]石 崇,蒋新兴,朱珍德,等.基于Hoek Brown 准则的岩石损伤本构模型研究及其參数探讨[J].砂岩力学与工程学报,2011,30(增1):2647-2652.

SHI Chong,JIANG Xin xing,ZHU Zhen de,et al.Study of rock damage constitutive model and discussion of its parameters based on Hoek Brown criterion[J].Chinese Journal of Rock Mechanics and Engineering, 2011, 30 (supp1): 2647-2652.

[12]曹文贵,李 翔,刘 峰.裂隙化岩体应变软化损伤本构模型探讨[J].岩石力学与工程学报,2007,26(12):2488-2494.

CAO Wen gui,LI Xiang,LIU Feng.Discussion on strain softening damage constitutive model for fissured rock mass[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(12):2488-2494.

[13]张蒙军.冻融环境下红砂岩物理力学特性试验研究[D].西安:西安科技大学,2015.

ZHANG Meng jun.The experimental study on the physical and mechanical properties of red sandstone under the environment of freeze thaw environment[D].Xi’an:Xi’an University of Science and Technology,2015.

[14]陈有亮,代明星,刘明亮,等.含初始损伤岩石的冻融损伤试验研究[J].力学季刊,2013,34(1):74-80.

CHEN You liang,DAI Ming xing,LIU Ming liang,et al.Experimental investigation on freezing damage characteristics of granite with initial damage[J].Chinese Quarterly of Mechanics,2013,34(1):74-80.

[15]刘松明,陈有亮,杜 曦,等.酸侵蚀区白砂岩冻融损伤的影响因素研究[J].水资源与水工程学报,2014,25(5):127-131.

LIU Song ming,CHEN You liang,DU Xi,et al.Study on influence factor of freeing thawing damage of white sandstone in acid erosion area[J].Journal of Water Research and Water Engineering,2014,25(5):127-131.

[16]张慧梅,谢祥妙,张蒙军,等.真三轴应力状态下岩石损伤本构模型[J].力学与实践,2015,37(1):75-78.

ZHANG Hui mei,XIE Xiang miao,ZHANG Meng jun,et al.Damage constitutive model of rock under the true triaxial confinement state[J].Mechanics in Engineering,2015,37(1):75-78.

[17]张慧梅,孟祥振,彭 川,等.岩石变形全过程冻融损伤模型及其参数[J].西安科技大学学报,2018,38(2):260-265.

ZHANG Hui mei,MENG Xiang zhen,PENG Chuan,et al.Freeze thaw damage model and parameters of rock deformation in whole process[J].Journal of Xi’an University of Science and Technology,2018,38(2):260-265.

[18]ZHOU Shu wei,XIA Cai chu,ZHAO Hai bin,et al.Statistical damage constitutive model for rocks subjected to cyclic stress and cyclic temperature[J].Acta Geophysica,2017,65(5):893- 906.

[19]HUANG Shi bin,LIU Quan sheng,CHENG Ai ping,et al.A statistical damage constitutive model under freeze thaw and loading for rock and its engineering application[J].Cold Regions Science and Technology,2018,145:142-150.

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