基于介观结构的饱和与非饱和多孔介质有效应力

李锡夔; 杜友耀; 段庆林

doi:10.6052/0459-1879-15-289

基于介观结构的饱和与非饱和多孔介质有效应力

大连理工大学工业装备结构分析国家重点实验室, 大连 116024

基金项目: 国家自然科学基金(11372066),国家重点基础研究发展计划(2010CB731502)资助项目.

详细信息

通讯作者:
李锡夔,教授,主要研究方向:计算力学,颗粒材料力学,多孔介质力学.E-mail:xikuili@dlut.edu.cn

中图分类号: O354.4
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出版历程
- 收稿日期: 2015-07-29
- 修回日期: 2015-12-02
- 刊出日期: 2016-01-17

MESO-STRUCTURE INFORMED EFFECTIVE STRESSES IN SATURATED AND UNSATURATED POROUS MEDIA

The State key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, China

摘要

摘要: 基于描述含液颗粒材料介观结构的Voronoi 胞元模型和离散颗粒集合体与多孔连续体间的介-宏观均匀化过程, 定义饱和与非饱和多孔介质有效应力. 导出了计及孔隙液压引起之颗粒体积变形的饱和多孔介质广义有效应力. 用以定义广义有效应力的Biot 系数不仅依赖于颗粒材料的多孔连续体固体骨架及单个固体颗粒的体积模量(材料参数),同时与固体骨架当前平均广义有效应力及单个固体颗粒的体积应变(状态量) 有关. 提出了描述非饱和多孔介质中非混和固体颗粒、孔隙液体和气体等三相相互作用的具介观结构的Voronoi 胞元模型.具体考虑在低饱和度下双联(binary bond) 模式的摆动(pendular) 液桥系统介观结构. 导出了基于介观水力-力学模型的非饱和多孔介质的各向异性有效应力张量与有效压力张量. 考虑非饱和多孔介质Voronoi 胞元模型介观结构的各向同性情况,得到了与非饱和多孔连续体理论中唯象地假定的标量有效压力相同的有效压力形式.但本文定义的与确定非饱和多孔介质有效应力和有效压力相关联的Bishop 参数由基于三相介观水力-力学模型, 作为饱和度、孔隙度和介观结构参数的函数导出,而非唯象假定.
- 饱和与非饱和多孔连续体 /
- 含液离散颗粒集合体 /
- 介观结构的Voronoi 胞元模型 /
- 有效应力 /
- Biot 系数 /
- Bishop 参数
Abstract: Based on the meso-strucrured Voronoi cell model and the meso-macro homogenization procedure between the discrete particle assembly and the porous continuum for wet granular materials, the e ective stresses in saturated and unsaturated porous media are defined. The generalized e ective stress for saturated porous continua taking into account the volumetric deformation of solid grains due to pore liquid pressure are derived. The Biot coe cient introduced to define the generalized e ective stress depends on not only the bulk moduli of both the porous media and the solid grains (material parameters), but also the current mean stress of solid skeleton of porous media and the current volumetric strains of the individual grain due to the hydrostatic pressure (state variables). The wet meso-structured Voronoi cell model, consisting of three immiscible and interrelated (i.e., solid grains, interstitial liquid and gas) phases, is proposed. The meso-structural pattern with the binary bond mode of pendular liquid bridges valid at low bulk saturation is particularly assumed to derive the meso-hydro-mechanically informed anisotropic e ective pressure and e ective stress tensors for unsaturated porous media. As the isotropic case of the wet meso-structured Voronoi cell model is considered, the meso- hydro-mechanically informed e ective pressure tensor degrades to the scalar variable in the form as same as that given in the theory of unsaturated porous continua. The proposed meso-hydro-mechanically informed Bishop's parameter is derived and obtained as a function of the saturation, the porosity, meso-structural parameters, while without the need to introduce any phenomenological assumptions.
- saturated and partially saturated porous continua /
- wet discrete particle assembly /
- meso-structured Voronoi cell model /
- e ective stress /
- Biot coe cient /
- Bishop parameter

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参考文献(33)

1 Terzaghi K von. The shearing resistance of saturated soils. Proc 1st ICSMFE, 1936, 1: 54-56

2 Biot MA. General theory of three-dimensional consolidation. J Appl Phys, 1941, 12: 155-164

3 Biot MA. Theory of propagation of elastic waves in a fluid saturated porous solid. J Acoust Soc Am, 1956, 28: 168-191

4 Biot MA. Mechanics of deformation and acoustic propagation in porous media. J Appl Phys, 1962, 33: 1482-1498

5 Biot MA. Generalized theory of acoustic propagation in porous media. J Acoust Soc of America, 1962, 34: 1254-1264

6 Zienkiewicz OC, Shiomi T. Dynamic behavior of saturated porous media:the generalized Boit formulation and its numerical solution. Int J Numer Anal Meth Geomech, 1984, 8: 71-96

7 Kytomaa H, Kataja M, Timonen J. On the e ect of pore pressure on the isotropic behavior of saturated porous media. J Appl Phys,1997, 24: 7148-7152

8 Bishop AW. The principle of e ective stress. Teknisk Ukeblad, 1959,106(39): 859-863

9 Bishop AW, Blight GE. Some aspects of e ective stress in saturated and partly saturated soils. G'eotechnique, 1963, 13(3): 177-197

10 Skempton AW. E ective stress in soils, concrete and rock.//Proc. Conf. on Pore Pressure and Suction in Soils, Butterworth, 1960.4-16

11 Li XK, Zienkiewicz OC. Multiphase flow in deforming porous media and finite element solutions. Comput. Struct., 1992, 45(2): 211-227

12 Zienkiewicz OC, Chan AHC, Pastor M, et al. Computational Geomechanics with Special Reference to Earthquake Engineering. Chichester: Wiley, 1999

13 邵龙潭,郭晓霞. 有效应力新解. 北京: 中国水利水电出版社,2014 (Shao Longtan, Guo Xiaoxia. New Insight on the E ective Stress. Beijing: China Water & Power Press, 2014 (in Chinese))

14 Gray WG, Schrefler BA. Thermodynamic approach to e ective stress in partially saturated porous media. Eur J Mech A: Solids,2001, 20(4): 521-538

15 Gray WG, Miller TC. Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems. Switzerland: Springer, 2014

16 Gray WG, Schrefler BA. Analysis of the solid phase stress tensor in multiphase porous media. Int J Numer Anal Meth Geomech, 2007,31(4): 541-581

17 陈正汉, 秦冰. 非饱和土的应力状态变量研究. 岩土力学, 2012,33(1): 1-11 (Chen Zhenghan, Qin Bing. Onstress state variables of unsaturated soils. Rock and Soil Mechanics, 2012, 33(1): 1-11 (in Chinese))

18 赵成刚, 蔡国庆. 非饱和土广义有效应力原理. 岩土力学, 2009,30(11): 3232-3236 (Zhao Chenggang, Cai Guoqing. Principle of generalized e ective stress for unsaturated soils. Rock and Soil Mechanics,2009, 30(11): 3232-3236 (in Chinese))

19 刘艳, 赵成刚, 蔡国庆等. 非饱和土力学理论的研究进展. 力学与实践, 2015, 37(4): 457-465 (Liu Yan, Zhao Chenggang, Cai Guoqing, et al. Research progress of unsaturated soil mechanics. Mechanics in Engineering, 2015, 37(4): 457-465 (in chinese))

20 Scholtes L, Hicher PY, Nicot F, et al. On the capillary stress tensor in wet granular materials. Int J Numer Anal Meth Geomech, 2009,33: 1289-1313

21 Li XS. E ective stress in unsaturated soil: a microstructural analysis. G'eotechnique, 2003, 53: 273-277

22 Hicher PY, Chang CS. A microstructural elastoplastic model for unsaturated granular materials. Int J Solids Struct, 2007, 44: 2304-2323

23 Hicher PY, Chang CS. Elastic model for partially saturated granular materials. J Eng Mech, 2008, 134(6): 505-513

24 Coussy O. Mechanics of Porous Continua. Chichester: Wiley, 1995

25 Ehlers W, Ramm E, Diebels S, et al. From particle ensembles to Cosserat continua: homogenization of contact forces towards stresses and couple stresses. Int J Solids Struct, 2003, 40: 6681-6702

26 Pasternak E, Muhlhaus HB. Generalised homogenisation procedures for granular materials. J Eng Math, 2005, 52: 199-229

27 Chang CS, Kuhn MR. On virtual work and stress in granular media. Int J Solids Struct, 2005, 42: 3773-3793

28 Li XK, Liu QP, Zhang JB. A micro-macro homogenization approach for discrete particle assembly-Cosserat continuum modeling of granular materials. Int J Solids Struct, 2010, 47: 291-303

29 Alonso-Marroquin F. Static equations of the Cosserat continuum derived from intra-granular stresses. Granul Matter, 2011, 13: 189-196

30 Li XK, Du YY, Duan QL. Micromechanically informed constitutive model and anisotropic damage characterization of Cosserat continuum for granular materials. Int J Damage Mech, 2013, 22(5): 643-682

31 El Shamy U, Groger T. Micromechanical aspects of the shear strength of wet granular soils. Int J Numer Anal Meth Geomech,2008, 32: 1763-1790

32 Souli'e F, Cherblanc F, El Youssoufi MS, et al. Influence of liquid bridges on the mechanical behaviour of polydisperse granular materials. Int J Numer Anal Meth Geomech, 2006, 30: 213-228

33 杜友耀,李锡夔. 二维液桥计算模型及湿颗粒材料离散元模拟. 计算力学学报, 2015, 32: 496-502 (Du Youyao, Li Xikui. 2D computational model of liquid bridge and DEM simulation of wet granular materials. Chinese Journal of Computational Mechanics, 2015,32: 496-502 (in Chinese))

施引文献(6)

期刊类型引用(2)

1.	李锡夔，张松鸽，楚锡华. 非饱和颗粒材料的多孔连续体有效压力与有效广义Biot应力. 力学学报. 2023(02): 369-380 . 本站查看
2.	刘艳，赵成刚，李舰，蔡国庆. 相间交界面对非饱和土应力状态的影响. 力学学报. 2017(02): 335-343 . 本站查看