砂土的动态空间滑动面及其强度准则适应性研究
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摘要
在砂土真三轴试验的基础上根据传统强度准则建立空间滑动面的原理,提出了多种动态空间滑动面并建立相应的强度准则;对比分析传统强度理论和新建立的强度准则与真三轴砂土试验资料之间的差异和优劣,定量指出各个准则的强度误差。结果表明,砂土在复杂应力条件下各个强度准则在描述砂土复杂应力条件下均能体现一定的规律性,但各个强度准则均存在一定误差,其常数项均表现出一定的变化,3σ动态空间滑动面准则表现出较好的一致性。
In practical geotechnical engineering,widely used strength criteria include the MohrCoulomb,Drucker-Prager,and Matsuoka-Nakai criteria.These guidelines define the laws that should be obeyed by the stress on a certain spatially mobilized plane when geotechnical materials are damaged.These planes have different characteristics.The spatially mobilized plane of the Mohr-Coulomb criterion is orthogonal with large and small principal stress planes,and the angle between the major principal stress planes is 45°+φ/2.It is assumed that the ratio between the shear stress and the normal stress on the plane is constant;then,the Mohr-Coulomb criterion can be obtained.The Drucker-Prager criterion describes the law that should be obeyed by the principal stress on an octahedral plane when geotechnical material is damaged.That is,the ratio between shear stress and normal stress on an octahedral plane is constant when the geotechnical material is damaged.The plane with the same normal stress is orthogonal with the tendency of geometric space,and the angle between the axes is the same.If a corner of the orthogonal hexahedral principal stress unit is located in the origin of the axes of a three-dimensional geometric space,then a45°angle is present between the sliding surfaces in the space of three orthogonal planes intersecting the line with the axis.Based on the Mohr-Coulomb criterion,the Matsuoka-Nakai criterion presents a spatially mobilized plane(SMP)with non-fixed normal stress.The SMP is changed with the changes in principal stress.The intersection between the unit of main stress in the spatially mobilized plane and the axis of three-dimensional geometric space is respectively σ1,k σ2and k σ3,if the intersection is respectively k( σ1)n、k( σ2)n and k( σ3)n.Then,the spatially mobilized plane can be expanded to different dynamic spatially mobilized planes and different spatially mobilized plane strength criteria.On the basis of true triaxial tests on sand and the traditional principle of the spatially mobilized space,a variety of dynamic spatially mobilized spaces and appropriate strength criteria have been introduced.In this paper,the first-power dynamic spatially mobilized plane(σ),the quadratic-power dynamic spatially mobilized plane(σ),and the third-power dynamic spatially mobilized plane(3σ)are proposed.The essence of the quadratic dynamic spatially mobilized plane(σ)is same as the Matsuoka-Nakai criterion based on the SMP.If the ratio of the shear stress and normal stress on the surface of the dynamic spatially mobilized plane is equal to constant and has the same shear strength criterion as the axisymmetric triaxial compression failure of the Mohr-Coulomb criterion,the criterion of dynamic spatially mobilized plane can be obtained.On the basis of the true triaxial test data of sand,comparative analysis of the theoretical strength and the traditional strength as well as the newly established strength criterion and the actual strength of true triaxial test data is conducted.Through the analysis and comparison,the quantitative strength error of each criterion is determined.Comparative analysis shows that for the sand under complex stress conditions,each criterion can reflect certain regularity.However,certain errors are present,and the constant term changes with complex stress conditions.The3σ)dynamic spatially mobilized space strength criterion showed the best consistency.
In practical geotechnical engineering,widely used strength criteria include the MohrCoulomb,Drucker-Prager,and Matsuoka-Nakai criteria.These guidelines define the laws that should be obeyed by the stress on a certain spatially mobilized plane when geotechnical materials are damaged.These planes have different characteristics.The spatially mobilized plane of the Mohr-Coulomb criterion is orthogonal with large and small principal stress planes,and the angle between the major principal stress planes is 45°+φ/2.It is assumed that the ratio between the shear stress and the normal stress on the plane is constant;then,the Mohr-Coulomb criterion can be obtained.The Drucker-Prager criterion describes the law that should be obeyed by the principal stress on an octahedral plane when geotechnical material is damaged.That is,the ratio between shear stress and normal stress on an octahedral plane is constant when the geotechnical material is damaged.The plane with the same normal stress is orthogonal with the tendency of geometric space,and the angle between the axes is the same.If a corner of the orthogonal hexahedral principal stress unit is located in the origin of the axes of a three-dimensional geometric space,then a45°angle is present between the sliding surfaces in the space of three orthogonal planes intersecting the line with the axis.Based on the Mohr-Coulomb criterion,the Matsuoka-Nakai criterion presents a spatially mobilized plane(SMP)with non-fixed normal stress.The SMP is changed with the changes in principal stress.The intersection between the unit of main stress in the spatially mobilized plane and the axis of three-dimensional geometric space is respectively σ1,k σ2and k σ3,if the intersection is respectively k( σ1)n、k( σ2)n and k( σ3)n.Then,the spatially mobilized plane can be expanded to different dynamic spatially mobilized planes and different spatially mobilized plane strength criteria.On the basis of true triaxial tests on sand and the traditional principle of the spatially mobilized space,a variety of dynamic spatially mobilized spaces and appropriate strength criteria have been introduced.In this paper,the first-power dynamic spatially mobilized plane(σ),the quadratic-power dynamic spatially mobilized plane(σ),and the third-power dynamic spatially mobilized plane(3σ)are proposed.The essence of the quadratic dynamic spatially mobilized plane(σ)is same as the Matsuoka-Nakai criterion based on the SMP.If the ratio of the shear stress and normal stress on the surface of the dynamic spatially mobilized plane is equal to constant and has the same shear strength criterion as the axisymmetric triaxial compression failure of the Mohr-Coulomb criterion,the criterion of dynamic spatially mobilized plane can be obtained.On the basis of the true triaxial test data of sand,comparative analysis of the theoretical strength and the traditional strength as well as the newly established strength criterion and the actual strength of true triaxial test data is conducted.Through the analysis and comparison,the quantitative strength error of each criterion is determined.Comparative analysis shows that for the sand under complex stress conditions,each criterion can reflect certain regularity.However,certain errors are present,and the constant term changes with complex stress conditions.The3σ)dynamic spatially mobilized space strength criterion showed the best consistency.
引文
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[7]陈昌禄.真三轴条件下结构性黄土的强度规律与强度准则的适应性研究[D].西安:西安理工大学,2012.CHEN Chang-lu.Study on the Law of Different Structural Loess and the Adaptability of Strength Criterion under True Triaxial Conditions[D].Xi’an:Xi’an University of Technology,2012.(in Chinese)
[8]邵生俊,罗爱忠,邓国华,等.一种新型真三轴仪的研制与开发[J].岩土工程学报,2009,31(8):1172-1179.SHAO Sheng-jun,LUO Ai-zhong,DENG Guo-hua,et al.Development of a New True Tri-axial Apparatus[J].Chinese Journal of Geotechnical Engineering,2009,31(8):1172-1179.(in Chinese)
[9]Lade P V,Duncan J M.Elasto-plastic Stress-strain Theory for Cohesionless Soil[J].Journal of the Geotechnical Engineering Division,American Society of Civil Engineers,1975,101(10):1037-1053.
[10]Nakai T,Matsuoka H.Shear Behaviors of Sand and Clay Under Three-dimensional Stress Condition[J].Soils and Foundations,1983,23(2):16-42.
[11]邵生俊,许萍,陈昌禄.土的剪切空间滑动面分析及各向异性强度准则研究[J].岩土工程学报,2013,35(3):421-435.SHAO Sheng-jun,XU Ping,CHEN Chang-lu.Several Shear Spatially Mobilized Planes and Anisotropic Strength Criteria of Soils[J].Chinese Journal of Geotechnical Engineering,2013,35(3):421-435.(in Chinese)
[12]王桃桃.新型真三轴仪改进及饱和砂土力学特性测试分析[D].西安:西安理工大学,2010.WANG Tao-tao.Improvement of the New True Triaxial Apparatus and Mechanical Characteristic Analysis of Saturated Sand[D].Xi’an:Xi’an University of Technology,2010.(in Chinese)
[2]俞茂宏.强度理论百年总结[J].力学进展,2004,34(4):529-560.YU Mao-hong.Advances in Strength Theories for Materials Under Complex Stress State in the 20th Century[J].Advances in Mechanics,2004,34(4):529-560.(in Chinese)
[3]俞茂宏,M Yoshimine,强洪夫,等.强度理论的发展和展望[J].工程力学,2004,21(6):1-20.YU Mao-hong,M Yoshimine,QIANG Hong-fu,et al.Advances and Prospects for Strength Theory[J].Engineering Mechanics,2004,21(6):1-20.(in Chinese)
[4]黄文熙.土的工程性质[M].北京:水利电力出版社,1983.HUANG Wen-xi.The Basic Properties of the Soil[M].Beijing:China Water Power Press,1983.(in Chinese)
[5]齐吉琳,谢定义,石玉成.土结构性的研究方法及现状[J].西北地震学报,2001,23(1):99-103.QI Ji-lin,XIE Ding-yi,SHI Yu-cheng.Status Quo and Method of Quantitative Study on Soil Structure[J].Northwestern Seismological Journal,2001,23(1):99-103.(in Chinese)
[6]陈昌禄,邵生俊,方娟.不同结构性黄土的强度规律及传统强度准则适应性分析[J].地震工程学报,2013,35(4):851-857.CHEN Chang-lu,SHAO Shen-jun,FANG Juan.Analysis of Strength Variation of Different Kinds of Structural Loess and Adaptability of Traditional Strength Criterion[J].China Earthquake Engineering Journal,2013,35(4):851-857.(in Chinese)
[7]陈昌禄.真三轴条件下结构性黄土的强度规律与强度准则的适应性研究[D].西安:西安理工大学,2012.CHEN Chang-lu.Study on the Law of Different Structural Loess and the Adaptability of Strength Criterion under True Triaxial Conditions[D].Xi’an:Xi’an University of Technology,2012.(in Chinese)
[8]邵生俊,罗爱忠,邓国华,等.一种新型真三轴仪的研制与开发[J].岩土工程学报,2009,31(8):1172-1179.SHAO Sheng-jun,LUO Ai-zhong,DENG Guo-hua,et al.Development of a New True Tri-axial Apparatus[J].Chinese Journal of Geotechnical Engineering,2009,31(8):1172-1179.(in Chinese)
[9]Lade P V,Duncan J M.Elasto-plastic Stress-strain Theory for Cohesionless Soil[J].Journal of the Geotechnical Engineering Division,American Society of Civil Engineers,1975,101(10):1037-1053.
[10]Nakai T,Matsuoka H.Shear Behaviors of Sand and Clay Under Three-dimensional Stress Condition[J].Soils and Foundations,1983,23(2):16-42.
[11]邵生俊,许萍,陈昌禄.土的剪切空间滑动面分析及各向异性强度准则研究[J].岩土工程学报,2013,35(3):421-435.SHAO Sheng-jun,XU Ping,CHEN Chang-lu.Several Shear Spatially Mobilized Planes and Anisotropic Strength Criteria of Soils[J].Chinese Journal of Geotechnical Engineering,2013,35(3):421-435.(in Chinese)
[12]王桃桃.新型真三轴仪改进及饱和砂土力学特性测试分析[D].西安:西安理工大学,2010.WANG Tao-tao.Improvement of the New True Triaxial Apparatus and Mechanical Characteristic Analysis of Saturated Sand[D].Xi’an:Xi’an University of Technology,2010.(in Chinese)
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