工程力学 ›› 2019, Vol. 36 ›› Issue (1): 32-43.doi: 10.6052/j.issn.1000-4750.2017.11.0790

• 基本方法 • 上一篇    下一篇

多相非饱和多重孔隙介质的有效应力定律

高彦芳, 陈勉, 林伯韬, 金衍   

  1. 油气资源与工程国家重点实验室, 中国石油大学(北京)石油工程学院, 北京 102249
  • 收稿日期:2017-11-01 修回日期:2018-04-20 出版日期:2019-01-29 发布日期:2019-01-10
  • 通讯作者: 陈勉(1962-),男,辽宁人,教授,博士,博导,主要从事石油工程岩石力学研究(E-mail:chenmian@vip.163.com). E-mail:chenmian@vip.163.com
  • 作者简介:高彦芳(1991-),男,山东人,博士生,主要从事石油工程岩石力学研究(E-mail:yanfang_gao@163.com);林伯韬(1983-),男,福建人,副教授,博士,博导,主要从事石油工程地质力学研究(E-mail:linbotao@cup.edu.cn);金衍(1972-),男,浙江人,教授,博士,博导,主要从事石油工程岩石力学、井壁稳定、井筒完整性等研究(E-mail:jiny@cup.edu.cn).
  • 基金资助:
    国家自然科学基金重大项目(51490651);国家科技重大专项(2017ZX05037-004)

GENERALIZED EFFECTIVE STRESS LAW FOR MULTI-POROSITY MEDIA UNSATURATED WITH MULTIPHASE FLUIDS

GAO Yan-fang, CHEN Mian, LIN Bo-tao, JIN Yan   

  1. State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum-Beijing, Beijing 102249, China
  • Received:2017-11-01 Revised:2018-04-20 Online:2019-01-29 Published:2019-01-10

摘要: 多孔介质的有效应力定律广泛应用于流固耦合变形分析问题。该文考虑孔隙的重数、孔隙流体的相数、各向异性、非饱和、基质吸力等条件,提出了广义多相非饱和多重孔隙介质的有效应力定律。在固体相及各流体相线弹性变形的假设下,首先通过应力状态分解、边界条件叠加方法,得到了不考虑基质吸力的多相等效饱和各向异性多重孔隙介质的有效应力。考虑到非饱和多孔介质中两相界面张力引起的基质吸力,在线弹性变形基础上,叠加了基质吸力引起的变形部分,推导得到非饱和多孔介质的有效应力定律的一般形式。将所得公式根据实际需要进行简化处理,可以得到目前常用的有效应力定律的表达形式,充分说明了该文所得结论的合理性。

关键词: 多相流体, 非饱和, 多重孔隙介质, 有效应力定律, 叠加原理

Abstract: The effective stress law for porous media is widely employed in the analysis of fluid-solid coupling problems. This paper proposed a generalized effective stress law for multi-porosity media unsaturated with multiphase fluids, considering the porosity multiplicity, phase numbers of porous fluids, anisotropy, saturation degree, and metric suction. Under the hypothesis that the solid and liquid phases both only undergo liner elastic deformations, the effective stress law for the anisotropic multi-porous media unsaturated with multi-phase liquid (without the consideration of matric suction) was proposed by the approaches of stress separation and superposition of boundary conditions. The solid's linear elastic deformation and the deformation induced by the matric suction occurring on phase interfaces in an unsaturated porous media were contemplated to attain a generalized form of the effective stress law for unsaturated porous media. Most of expression formats of the effective stress laws in literatures can be obtained from corresponding reduced forms of the generalized law proposed, which proves its reasonableness.

Key words: multiphase fluids, unsaturated, multi-porosity media, effective stress law, superposition principle

中图分类号: 

  • TU43
[1] 汤连生, 颜波, 张鹏程, 等. 非饱和土中有效应力及有关概念的解说与辨析[J]. 岩土工程学报, 2006, 28(2):216-220. Tang Liansheng, Yan Bo, Zhang Pengcheng, et al. Defination and exploration for effective stress and related conception in unsaturated soil[J]. Chinese Journal of Geotechnical Engineering, 2006, 28(2):216-220. (in Chinese)
[2] 汤连生, 王思敬. 湿吸力及非饱和土的有效应力原理探讨[J]. 岩土工程学报, 2000, 22(1):83-88. Tang Liansheng, Wang Sijing. Absorbed suction and principle of effective stress in unsaturated soils[J]. Chinese Journal of Geotechnical Engineering, 2000, 22(1):83-88. (in Chinese)
[3] Fjar E, Holt R M, Raaen A M, et al. Petroleum related rock mechanics, 2nd edited[M]. New York:Elsevier Science, 2008:33.
[4] Terzaghi K. The shearing resistance of saturated soils and the angle between the planes of shear[C]//Proceedings of 1st International Conference on Soil Mechanics and Foundation Engineering. Cambridge, MA, USA:Harvard University Press, 1936:54-56.
[5] Biot M A. General theory of three-dimensional consolidation[J]. Journal of Applied Physics, 1941, 12(2):155-164.
[6] Nur A, Byerlee J D. An exact effective stress law for elastic deformation of rock with fluids[J]. Journal of Geophysical Research, 1971, 76(26):6414-6419.
[7] Skempton A W. Effective stress in soils, concrete and rocks[C]//Aitchison G D, Bishop A W T. Proceedings of Pore Pressure and Suction in Soils. London:Butterworth, 1961:4-16.
[8] 陈勉, 陈至达. 多重孔隙介质的有效应力定律[J]. 应用数学与物理学, 1999, 20(11):1121-1127. Chen Mian, Chen Zhida. Effective stress laws for multi-porosity media[J]. Applied Mathematics and Mechanics, 1999, 20(11):1121-1127. (in Chinese)
[9] 赵颖, 陈勉, 张广清. 各向异性双重孔隙介质有效应力定律[J]. 科学通报, 2004, 49(21):2252-2255. Zhao Ying, Chen Mian, Zhang Guangqing. Effective stress laws for anisotropic dual-porosity media[J]. Chinese Science Bulletin, 2004, 49(21):2252-2255. (in Chinese)
[10] 陈勉, 金衍, 张广清. 石油工程岩石力学[M]. 北京:科学出版社, 2008:42-43. Chen Mian, Jin Yan, Zhang Guangqing. Petroleum related rock mechanics[M]. Beijing:Science Press, 2008:42-43. (in Chinese)
[11] 蔡新树, 陈勉, 金衍, 等. 各向异性多重孔隙介质有效应力定律[J]. 工程力学, 2009, 26(4):57-67. Cai Xinshu, Chen Mian, Jin Yan, et al. An effective stress laws for anisotropic multi-porosity media[J]. Engineering Mechanics, 2009, 26(4):57-67. (in Chinese)
[12] 赵成刚, 韦昌富, 蔡国庆. 土力学理论的发展和面临的挑战[J]. 岩土力学, 2011, 32(12):3521-3540. Zhao Chenggang, Wei Changfu, Cai Guoqing. Development and challenge for soil mechanics[J]. Rock and Soil Mechanics, 2011, 32(12):3521-3540. (in Chinese)
[13] Bishop A W. The principle of effective stress[J]. Teknisk Ukeblad, 1959,106(39):113-143.
[14] Bishop A W, Blight G E. Some aspects of effective stress in saturated and partly saturated soils[J]. Géotechnique, 1963, 13(3):177-197.
[15] Blight G E. A study of effective stress for volume change[C]//Aitchison G. Moisture Equilibria and Moisture Changes in Soils Beneath Covered Areas. Sydney:Butterworth, 1965:259-269.
[16] Jennings J E B, Burland J B. A revised effective stress law for use in the prediction of the behavior of unsaturated soils[C]//Aitchison G D, Bishop A W T. Proceedings of Pore Pressure and Suction in Soils. London:Butterworth, 1961:26-30.
[17] Aitchison G D, Donald I B. Some preliminary studies of unsaturated soils[C]//New Zealand Institute of Engineering. Proceedings of 2nd Australia-New Zealand Conference on Soil Mechanics and Foundation Engineering. Wellington:Technical Publications for the New Zealand Institution of Engineers, 1956:192-199.
[18] Jennings J E B. Limitations to the use of effective stress in unsaturated soils[J]. Géotechnique, 1962, 12(2):125-144.
[19] Burland J B. Some aspects of the mechanical behaviour of partly saturated soils[C]//Aitchison G. Moisture Equilibria and Moisture Changes in Soils Beneath Covered Areas. Sydney:Butterworth, 1965:270-278.
[20] Aitchison G D. Soils properties, shear strength, and consolidation[C]//Associate Committee on Geotechnical Research. Proceedings of 6th International Conference on Soil Mechanics and Foundation Engineering. Toronto:University of Toronto Press, 1965:319-321..
[21] Matyas E L, Radhakrishna H S. Volume change characteristics of partially saturated soils[J]. Géotechnique, 1968, 18(4):432-448.
[22] Brackley I J A. Partial collapse in unsaturated expansive clay[C]//Associate Committee on Geotechnical Research. Proceedings of 5th Regional Conference on Soil Mechanics and Foundation Engineering. Luanda, Angola:Laboratório de Engenharia de Angola, 1971:23-30.
[23] Frelund D G, Morgenstern N R. Stress state variables for unsaturated soils[J]. Journal of the Geotechnical Engineering Division, ASCE, 1977, 103(5):447-466.
[24] Khalili N, Geiser F, Blight G E. Effective stress in unsaturated soils:Review with new evidence[J]. International Journal of Geomechanics, 2004, 4(2):115-126.
[25] Coleman J D. Stress-strain relations for partly saturated soils[J]. Géotechnique, 1962, 12(4):348-350.
[26] Bishop A W, Blight G E. Some aspects of the effective stress in saturated and partially saturated soils[J]. Géotechnique, 1963, 13(3):177-197.
[27] Blight G E. Effective stress evaluation for unsaturated soils[J]. Journal of the Soil Mechanics and Foundations Division, ASCE, 1967, 93(2):125-148.
[28] Wheeler S J, Sharma R S, Buisson M S R. Coupling of hydraulic hysteresis and stress-strain behavior in unsaturated soils[J]. Géotechnique, 2003, 53(1):41-54.
[29] Fredlund D G. Unsaturated soil mechanics in engineering practice[M]. Hoboken:John Wiley & Sons, 2012:80-83.
[30] Houlsby G T. The work input to a granular material[J]. Géotechnique, 1979, 29(3):354-358.
[31] Houlsby G T. The work input to an unsaturated granular material[J]. Géotechnique, 1997, 47(1):193-196.
[32] Jommi C. Remarks on the constitutive modeling of unsaturated soils[C]//Tarantino A, Mancuso C. Experimental Evidence and Theoretical Approaches in Unsaturated Soils:Proceedings of An International Workshop on Unsaturated Soils. Trento, Italy:A. A. Balkema, 2000:139-154.
[33] Vaunat J, Romero E, Jommi C. An elastoplastic hydromechanical model for unsaturated soils[C]//Tarantino A, Mancuso C. Experimental Evidence and Theoretical Approaches in Unsaturated Soils:Proceedings of An International Workshop on Unsaturated Soils. Trento, Italy:A. A. Balkema, 2000:121-138.
[34] 赵成刚, 张雪东. 非饱和土中功的表述以及有效应力与相分离原理的讨论[J]. 中国科学(E辑:技术科学), 2008, 38(9):1453-1463. Zhao Chenggang, Zhang Xuedong. Expression of work in unsaturated soil and discussion of the principle of effective stress and phase separation[J]. Science in China (Series E:Technological Sciences), 2008, 38(9):1453-1463. (in Chinese)
[35] 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. (in Chinese)
[36] 赵成刚, 蔡国庆. 非饱和土广义有效应力原理[J]. 岩土工程, 2009, 30(11):3232-3236. Zhao Chenggang, Cai Guoqing. The principle of generalized effective stress for unsaturated soils[J]. Rock and Soil Mechanics, 2009, 30(11):3232-3236. (in Chinese)
[37] 黄义, 张引科. 非饱和土本构关系的混合物理论(I)-非线性本构方程和场方程[J]. 应用数学与力学, 2003, 24(2):111-123. Huang Yi, Zhang Yinke. Constitutive relation of unsaturated soil by use of the mixture theory (I)-Nonlinear constitutive equations and field equations[J]. Applied Mathematics and Mechanics, 2003, 24(2):111-123. (in Chinese)
[38] 黄义, 张引科. 非饱和土本构关系的混合物理论(Ⅱ)-线性本构方程和场方程[J]. 应用数学与力学, 2003, 24(2):124-137. Huang Yi, Zhang Yinke. Constitutive relation of unsaturated soil by use of the mixture theory (Ⅱ) -Linear constitutive equations and field equations[J]. Applied Mathematics and Mechanics, 2003, 24(2):124-137. (in Chinese)
[39] Loret B, Khalili N. A three-phase model for unsaturated soils[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2000, 24(11):893-927.
[40] Carroll M M. An effective stress law for anisotropic elastic deformation[J]. Journal of Geophysical Research, 1979, 84(B13):7510-7512.
[41] Coussy O. Mechanics and physics of porous solids[M]. Hoboken:John Wiley and Sons, 2010:68-71.
[42] 费康, 张建伟. ABAQUS在岩土工程中的应用[M]. 北京:中国水利水电出版社, 2013:169. Fei Kang, Zhang Jianwei. Applied rock and soil mechanics with ABAQUS application[M]. Beijing:China Water & Power Press, 2013:169. (in Chinese)
[43] 吴意谦, 朱彦鹏. 考虑疏干带非饱和土影响下基坑降水引起地面沉降的计算[J]. 工程力学, 2016, 33(3):179-187. Wu Yiqian, Zhu Yanpeng. Calculation of settlement considering unsaturated soil influence on the dewatering of foundation pits[J]. Engineering Mechanics, 2016, 33(3):179-187. (in Chinese)
[44] 杨骁, 蒋志云, 张敏. 爆炸荷载作用下深埋圆形隧洞饱和土-衬砌系统的动力响应[J]. 工程力学, 2015, 32(5):138-146. Yang Xiao, Jiang Zhiyun, Zhang Min. Dynamical analysis of a saturated soil-lining system with a deeply buried circular tunnel subjected to a blast load[J]. Engineering Mechanics, 2015, 32(5):138-146. (in Chinese)
[45] 邸元, 康志江, 代亚非, 等. 复杂多孔介质多重介质模型的表征单元体[J]. 工程力学, 2015(12):33-39. Di Yuan, Kang Zhijiang, Dai Yafei, et al. Representative elementary volume of the multiple-continuum model for complex porous media[J]. Engineering Mechanics, 2015(12):33-39. (in Chinese)
[46] Saurabh S, Harpalani S. The effective stress law for stress-sensitive transversely isotropic rocks[J]. International Journal of Rock Mechanics & Mining Sciences, 2018, 101:69-77.
[47] Ma J. Wetting collapse analysis on partially saturated oil chalks by a modified cam clay model based on effective stress[J]. Journal of Petroleum Science and Engineering, 2018, 167:44-53.
[1] 吴意谦, 朱彦鹏. 考虑疏干带非饱和土影响下基坑降水引起地面沉降的计算[J]. 工程力学, 2016, 33(3): 179-187.
[2] 欧阳煜,卞海涛,杨峥. FRP布加固具有中心裂纹板条的断裂疲劳性能[J]. 工程力学, 2015, 32(3): 158-166.
[3] 张亚国,李镜培,饶平平. 倾斜坡体中圆孔扩张的弹性应力分析[J]. 工程力学, 2014, 31(7): 23-28.
[4] 杨钢, 杨庆, 孔纲强. 平衡饱和度差异性产生机理及其对非饱和土力学特性的影响[J]. 工程力学, 2014, 31(6): 151-158.
[5] 陈炜昀,夏唐代,黄睿,周新民. P1波在非饱和土地基表面的反射特性[J]. 工程力学, 2013, 30(9): 56-62.
[6] 许兆棠. 直升机传动系统扭转振动的分析[J]. 工程力学, 2012, 29(9): 330-336.
[7] 李顺群,郑刚,王英红. 预留土对非饱和基坑支护结构的影响[J]. 工程力学, 2012, 29(5): 122-127.
[8] 金 旭;赵成刚;蔡国庆;陈铁林. 基于扰动变量的非饱和原状土本构模型[J]. 工程力学, 2011, 28(9): 149-156,.
[9] 徐明江;魏德敏. 非饱和土地基的三维非轴对称动力响应[J]. 工程力学, 2011, 28(3): 78-085.
[10] 张智卿;王奎华;李 强;卢萌盟. 非饱和土中端承桩纵向振动问题简化解[J]. 工程力学, 2010, 27(5): 159-165,.
[11] 蔡新树;;陈 勉;金 衍;赵 颖. 各向异性多重孔隙介质有效应力定律[J]. 工程力学, 2009, 26(4): 57-060,.
[12] 许兆棠. 传动比对直升机尾传动系统扭转振动影响的分析[J]. 工程力学, 2009, 26(12): 249-256.
[13] 李顺群;柴寿喜;王 沛;刘双菊;. 非饱和土的系列强度试验研究[J]. 工程力学, 2009, 26(11): 140-144.
[14] 褚卫江;徐卫亚;苏静波. 变形多孔介质流固耦合模型及数值模拟研究[J]. 工程力学, 2007, 24(9): 0-064.
[15] 师俊平;解敏;王静. 无限大平面中斜裂纹的压剪断裂分析[J]. 工程力学, 2006, 23(12): 59-62,5.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] 李天娥, 孙晓颖, 武岳, 王长国. 平流层飞艇气动阻力的参数分析[J]. 工程力学, 2019, 36(1): 248 -256 .
[2] 管俊峰, 姚贤华, 白卫峰, 陈记豪, 付金伟. 由小尺寸试件确定混凝土的断裂韧度与拉伸强度[J]. 工程力学, 2019, 36(1): 70 -79,87 .
[3] 高良田, 王键伟, 王庆, 贾宾, 王永魁, 石莉. 破冰船在层冰中运动的数值模拟方法[J]. 工程力学, 2019, 36(1): 227 -237 .
[4] 于潇, 陈力, 方秦. 一种量测松散介质对应力波衰减效应的实验方法及其在珊瑚砂中的应用[J]. 工程力学, 2019, 36(1): 44 -52,69 .
[5] 罗大明, 牛荻涛, 苏丽. 荷载与环境共同作用下混凝土耐久性研究进展[J]. 工程力学, 2019, 36(1): 1 -14,43 .
[6] 袁驷, 蒋凯峰, 邢沁妍. 膜结构极小曲面找形的一种自适应有限元分析[J]. 工程力学, 2019, 36(1): 15 -22 .
[7] 高山, 郑向远, 黄一. 非高斯随机过程的短期极值估计:复合Hermite模型[J]. 工程力学, 2019, 36(1): 23 -31 .
[8] 白鲁帅, 李钢, 靳永强, 李宏男. 一种隔离损伤的桁架结构性态识别方法[J]. 工程力学, 2019, 36(1): 53 -60 .
[9] 崔兆彦, 徐明, 陈忠范, 王飞. 重组竹钢夹板螺栓连接承载力试验研究[J]. 工程力学, 2019, 36(1): 96 -103,118 .
[10] 贾布裕, 颜全胜, 余晓琳, 杨铮. 考虑行人随机性的人行桥人致横向振动稳定性分析[J]. 工程力学, 2019, 36(1): 155 -164 .
X

近日,本刊多次接到来电,称有不法网站冒充《工程力学》杂志官网,并向投稿人收取高额费用。在此,我们郑重申明:

1.《工程力学》官方网站是本刊唯一的投稿渠道(原网站已停用),《工程力学》所有刊载论文必须经本刊官方网站的在线投稿审稿系统完成评审。我们不接受邮件投稿,也不通过任何中介或编辑收费组稿。

2.《工程力学》在稿件符合投稿条件并接收后会发出接收通知,请作者在接到版面费或审稿费通知时,仔细检查收款人是否为“《工程力学》杂志社”,千万不要汇款给任何的个人账号。请广大读者、作者相互转告,广为宣传!如有疑问,请来电咨询:010-62788648。

感谢大家多年来对《工程力学》的支持与厚爱,欢迎继续关注我们!

《工程力学》杂志社

2018年11月15日