| Civil and Traffic Engineering |
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| Thermodynamics-based constitutive theory for unsaturated porous rock |
| HU Ya yuan |
| Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou, 310058, China |
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Abstract An engineering mechanics of unsaturated porous rock was proposed in order to consider the nonlinear and irreversible deformations of both rock material and porous rock. Firstly, with using the volume fraction concept and mixture theory, the equation of energy balance in terms of five state variables was obtained in virtue of the mixture homogenous response principle, which were called void strain tensor, degree of saturation and the material volume strain of each constituent. The five elastic equations which were determined by free energy and the one equation that the sum of all volume fractions was equal to unity compose six constitutive equations. Based on these equations, all six unknown variables (three displace vectors and three volume fractions) could be solved in the constitutive model of unsaturated rock. Secondly, according to the irreversible thermodynamics, the potential of dissipative rate in terms of internal variables was proposed on the basis of entropy production formula. Thus, the dissipative constitutive equations were derived to describe the irreversible deformation behaviors such as viscosity or plasticity. Results show that, the two potential functions of free energy and dissipative rate can depict the discipline of elastic and inelastic deformations, respectively, which both form the constitutive theoretical framework of unsaturated porous rock.
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Published: 06 March 2017
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Cite this article:
HU Ya yuan. Thermodynamics-based constitutive theory for unsaturated porous rock. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2017, 51(2): 255-263.
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非饱和多孔岩石的热力学本构理论
为了在本构模型中同时考虑岩石材料和多孔岩石的非线性和不可逆变形,提出非饱和多孔岩石工程力学理论.应用体积分数概念和混合物理论,凭借均匀化响应原理,获得由孔隙应变张量、饱和度和各组分材料体应变5个状态变量表示的能量平衡方程.利用自由能确定的5个弹性方程,加上体积分数之和等于1这个方程组成6个本构方程.根据这些方程可以求解非饱和岩石本构模型的全部6个未知变量（3个位移矢量和3个体积分数）.根据不可逆热力学理论,基于熵产公式提出用内变量表示的耗散率势函数,获得能够反映黏性和塑性不可逆变形特性的耗散本构方程.结果表明,自由能和耗散率2个势函数分别反映了岩石弹性和非弹性变形规律,共同构成了非饱和多孔岩石的热力学本构理论框架.
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| ［1］ LI X S. Thermodynamicsbased constitutive framework for unsaturated soils［J］. Géotechnique, 2007, 57(5): 411-422．
［2］ 缪林昌.非饱和土的本构模型研究［J］.岩土力学,2007,28(5): 855-860．
MIAO Linchang. Research of constitutive model of unsaturated soils ［J］. Rock and Soil Mechanics, 2007, 28(5): 855-860．
［3］ 孙德安,高游.不同制样方法非饱和土的持水特性研究［J］.岩土工程学报,2015,37(1): 91-97.
SUN Dean, GAO You. Water retention behaviour of soils with different preparations ［J］. Chinese Journal of Geotechnical Engineering, 2015, 37(1): 9197．
［4］ MA T T, WEI C F, WEI H Z, et al. Hydraulic and mechanical behavior of unsaturated silt: experimental and theoretical characterization ［J］. International Journal of Geomechanics, 2015, D40150071D401500713.
［5］ 胡亚元.考虑吸附水的非饱和土耗散本构关系研究［J］.岩土力学,2015,36(S1): 14-18.
HU Yayuan, Study on the dissipative constitutive relation of unsaturated soil considering adsorbed water［J］. Rock and Soil Mechanics, 2015,36(S1): 1418．
［6］ 韩同春,豆红强,马世国,等.考虑雨水重分布对均质无限长边坡稳定性的研究［J］.浙江大学学报:工学版,2013,47(10): 1824-1829．
HAN Tong chun, DOU Hong qiang, MA Shiguo, et al. Rainwater redistribution on stability of homogen ous infinite slop［J］. Journal of Zhejiang University: Engineering Science, 2013, 47 (10): 1824-1829．
［7］ 周创兵,陈益峰,姜清辉,等.复杂岩体多场广义耦合分析导论［M］.北京,中国水利水电出版社,2008: 152187; 328-363．
［8］ 赵阳升.多孔介质多场耦合作用及其工程响应［M］.北京,科学出版社,2010: 171310.
［9］ SKEMPTON A W. Effective stress in soils, concrete and rocks［M］. London, UK: Butterwoths, 1961: 416．
［10］ SUKLJE L. Rheological aspects of soil mechanics ［M］. Interscience, New York, 1969: 123．
［11］ DE BUHAM P, DORMIEUX L. On the validity of the effective stress concept for assessing the strength of saturated porous materials: A homogenization approach［J］. Journal of the Mechanics and Physics of Solids,1996, 44(10): 1649-1667．
［12］ WALSH J, BROWN S, DURHAM W. Effective media theory with spatial correlation for flow in fracture［J］. Journal. Geophysical Resiews, 1997,102 (B10): 22587-22594．
［13］ CARIOU S, DUAN Z, DAVY C, et al. Poromechanics of partially saturated COx argillite ［J］. Applied Clay Science, 2012,56: 36-47．
［14］ 陈正汉.非饱和土与特殊土力学的基本理论研究［J］.岩土工程学报,2014, 36(2): 201-272.
CHEN Zhenghan. On basic theories of unsaturated soils and special soils ［J］. Chinese Journal of Geotechnical Engineering, 2014, 36(2): 201-272.
［15］ BORJA R I. On the mechanical energy and effective stress in saturated and unsaturated porous continua［J］.International Journal of Solids and Structures, 2006, 43: 1764-1786．
［16］ BISHOP A W. The principle of effective stress［J］. Teknisk Ukeblad, 1959, 106(39): 113-143．
［17］ 陈卫忠,谭贤君,伍国军,等.非饱和岩石温度渗流应力耦合模型研究\[J\].岩石力学与工程学报,2007, 26(12): 2395-2403．
CHEN Wei zhong, TAN Xian jun, WU Guo jun,et al. Study on thermo-hydro-mechanical coupling model for unsaturated rock \[J\]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26 (12): 2395-2403．
［18］ 赵成刚,刘艳.连续孔隙介质土力学及其在非饱和土本构关系中的应用\[J\].岩土工程学报,2009,31(9):1324-1335.
ZHAO ChengGang, LIU Yan. Continuum porous medium soil mechanics and its application in constitutive relationship of unsaturated soils［J］. Chinese Journal of Geotechnical Engineering, 2009, 31(9): 1324-1335．
［19］ BOWEN R M 著,徐慧己,张志新,李如庆等译.混合物理论［M］.南京：江苏科学技术出版社,1983: 148．
［20］ GEERTSMA J. The effect of fluid pressure decline on volumetric changes of porous rocks［J］. Petroleum Transactions, 1957, 210: 331-339．
［21］ 李如生,非平衡态热力学和耗散结构.北京：清华大学出版社,1986, 76-106．
［22］ BOIT, M.A. Theory of stressstrain relations in anisotropic viscoelasticity and relaxation phenomena ［J］. Journal of Applied Physics,1954, 25,1385-1391．
［23］ HOULSBY G T, PUZRIN A M. Rate-dependent plasticity models derived from potential functions［J］. Journal of Rheology, 2002, 46(1): 113-126．
［24］ HILL R. The mathematical theory of plasticity \[M\]. \[S.l.\]: Oxford University Press, 1950, 50-52． |
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