基于颗粒接触模型的砂土剪切波速研究
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摘要
砂土的剪切波速是一个重要的土动力学参数,它能够反映出砂土骨架的结构性,对砂土剪切波速的研究一直是土动力学及岩土工程中的核心课题。在过去的几十年中,许多学者得到了很多具有重要意义的研究成果,但是这些研究成果大多集中在宏观范畴,而对于砂土甚至所有土体的细观结构的研究逐渐成为土动力学的研究重点。本文从砂土颗粒间的接触入手,在颗粒接触理论的基础上对砂土剪切波速进行研究。
考察分析了实际砂土颗粒的表观特征。对福建标准砂、杭州黄砂和人工石英砂进行筛分取样,从每个样本抽取一定数量的颗粒进行电镜扫描获得颗粒二维图像,计算出砂土样本颗粒性质的平均参数。砂土颗粒的粒径在0.75-2mm之间,用肉眼是无法对其颗粒表观特征进行观察的,借助于场发射电镜扫描仪,砂颗粒可以被放大几百至几万倍并形成扫描图像被记录下来。对这些图像进行数学处理可以对砂颗粒的表观特征进行定量的描述,为后续的砂颗粒间接触模型的推导提供必要的参数。
处于不同地层深度的砂土由于自重应力、附加应力以及孔隙比(密实度)的变化而使砂土颗粒间的接触压力不同,而颗粒的表观特征的差异又会导致在接触面上的接触应力的分布形式不同。综合前人在对金属球体的接触问题上的研究成果,对砂土颗粒间的接触模型进行探讨。在砂土颗粒表观特征研究的基础上,借助理论分析或数值模拟研究砂土颗粒间真实接触面、接触应力分布在不同接触压力及粗糙度下的表达式,然后推导法向变形量、切向变形量的计算方法和表达式。在砂土颗粒接触模型的基础上推导出砂土颗粒法向接触刚度、切向接触刚度的表达式。
在宏观上将砂土介质视为连续介质,推导出砂土的等效剪切模量和剪切波速计算公式。对颗粒间接触力、颗粒接触点数、颗粒粒径等等参数进行平均化处理,在散粒体介质的组构及本构关系研究的基础上,将砂土颗粒接触模型与砂土的宏观物理量联系起来。
通过试验和工程实例对本文提出的计算公式或者关系式进行验证,并考察应用效果。采用弯曲元剪切波速测试仪对不同类型的砂土进行室内试验,对比其颗粒表观特征对剪切波速的影响,并对理论公式进行补充和修正。提出了一种剪切波速的简化计算方法并应用到工程中的实例中,将本文方法计算结果与实测数据对比,分析本文方法应用的可行性和效果。
Shear wave velocity of sand, which represents the structure of sand skeleton, is an important parameter in soil dynamic mechanics. Research on shear wave velocity of sand has been always one of primary problems in soil dynamic mechanics and geotechnical engineering. A lot of meaningful researches have been obtained in the past several decades, which mostly focus on macro-scope. Recently, researches on micro structures of sand turn to be more and more important in soil dynamics. In this dissertation, the contact of sand particles is taken to be the breakthrough point, and the shear wave velocity of sand is studied based on particle contact theory.
Firstly, the surface characteristic of sand particles is analyzed. Several sand samples are made through filtration and screening of Fujian standard sand, Hangzhou sand and man-made quartz sand. Afterwards a few sand particles which are picked up randomly from every sample are scanned by electron microscope.2-D photos of sand particles obtained by scan are analyzed to calculate the average values of surface characteristic parameters of every sand sample. Diameters of sand particles are mostly ranged in 2-0.75mm, which means people can't observe sand particles with naked eyes. By using scanning electron microscope, the images of sand particles can be magnified hundreds or thousands times. Then some graphical and mathematical treatments are taken based on these images to describe the surface characteristic of sand particles, which provides some essential parameters for the deriving of sand particles contact model.
For sands in different depths, contact forces between sand particles vary with gravity stress, additional stresses and porosity (compactness), and the distribution of contact stress is greatly influenced by surface characteristic of sand particles. According to previous researches on metal particle contacting, the contact model of sand particles is discussed. Subsequently, on the basis of research on sand particles surface characteristic, the formulas of real contact area and distribution of contact stress under different contact force and roughness are derived using theoretical analysis and numerical simulation. At the same time, the calculation method and formulas of normal deformation and shear deformation are obtained. Then, normal contact stiffness and shear contact stiffness of sand particles are derived according to researches above.
Equivalent shear modulus and shear wave velocity are derived by considerirg sand as continuous media macroscopically. With average treatment on contact forces, contact points and particle radius, the relationships between macro parameters and contact model of sand are established according to fabric and constitutive research of granular media.
Formulas and relationships established in this dissertation are verified by experiment and measured data, and the effect of application is also evaluated. An experimental research concerning the influence of particle surface characteristic on shear wave velocity is taken by using bender element testing equipment, which provides addition and correction to theoretical formulas above. A simplized calculation method for shear wave velocity is established which can be used to predict shear wave velocity of sand in projects. The application feasiblity and effect of this method is analyzed by comparing calculated results of simplized method with measured data.
考察分析了实际砂土颗粒的表观特征。对福建标准砂、杭州黄砂和人工石英砂进行筛分取样,从每个样本抽取一定数量的颗粒进行电镜扫描获得颗粒二维图像,计算出砂土样本颗粒性质的平均参数。砂土颗粒的粒径在0.75-2mm之间,用肉眼是无法对其颗粒表观特征进行观察的,借助于场发射电镜扫描仪,砂颗粒可以被放大几百至几万倍并形成扫描图像被记录下来。对这些图像进行数学处理可以对砂颗粒的表观特征进行定量的描述,为后续的砂颗粒间接触模型的推导提供必要的参数。
处于不同地层深度的砂土由于自重应力、附加应力以及孔隙比(密实度)的变化而使砂土颗粒间的接触压力不同,而颗粒的表观特征的差异又会导致在接触面上的接触应力的分布形式不同。综合前人在对金属球体的接触问题上的研究成果,对砂土颗粒间的接触模型进行探讨。在砂土颗粒表观特征研究的基础上,借助理论分析或数值模拟研究砂土颗粒间真实接触面、接触应力分布在不同接触压力及粗糙度下的表达式,然后推导法向变形量、切向变形量的计算方法和表达式。在砂土颗粒接触模型的基础上推导出砂土颗粒法向接触刚度、切向接触刚度的表达式。
在宏观上将砂土介质视为连续介质,推导出砂土的等效剪切模量和剪切波速计算公式。对颗粒间接触力、颗粒接触点数、颗粒粒径等等参数进行平均化处理,在散粒体介质的组构及本构关系研究的基础上,将砂土颗粒接触模型与砂土的宏观物理量联系起来。
通过试验和工程实例对本文提出的计算公式或者关系式进行验证,并考察应用效果。采用弯曲元剪切波速测试仪对不同类型的砂土进行室内试验,对比其颗粒表观特征对剪切波速的影响,并对理论公式进行补充和修正。提出了一种剪切波速的简化计算方法并应用到工程中的实例中,将本文方法计算结果与实测数据对比,分析本文方法应用的可行性和效果。
Shear wave velocity of sand, which represents the structure of sand skeleton, is an important parameter in soil dynamic mechanics. Research on shear wave velocity of sand has been always one of primary problems in soil dynamic mechanics and geotechnical engineering. A lot of meaningful researches have been obtained in the past several decades, which mostly focus on macro-scope. Recently, researches on micro structures of sand turn to be more and more important in soil dynamics. In this dissertation, the contact of sand particles is taken to be the breakthrough point, and the shear wave velocity of sand is studied based on particle contact theory.
Firstly, the surface characteristic of sand particles is analyzed. Several sand samples are made through filtration and screening of Fujian standard sand, Hangzhou sand and man-made quartz sand. Afterwards a few sand particles which are picked up randomly from every sample are scanned by electron microscope.2-D photos of sand particles obtained by scan are analyzed to calculate the average values of surface characteristic parameters of every sand sample. Diameters of sand particles are mostly ranged in 2-0.75mm, which means people can't observe sand particles with naked eyes. By using scanning electron microscope, the images of sand particles can be magnified hundreds or thousands times. Then some graphical and mathematical treatments are taken based on these images to describe the surface characteristic of sand particles, which provides some essential parameters for the deriving of sand particles contact model.
For sands in different depths, contact forces between sand particles vary with gravity stress, additional stresses and porosity (compactness), and the distribution of contact stress is greatly influenced by surface characteristic of sand particles. According to previous researches on metal particle contacting, the contact model of sand particles is discussed. Subsequently, on the basis of research on sand particles surface characteristic, the formulas of real contact area and distribution of contact stress under different contact force and roughness are derived using theoretical analysis and numerical simulation. At the same time, the calculation method and formulas of normal deformation and shear deformation are obtained. Then, normal contact stiffness and shear contact stiffness of sand particles are derived according to researches above.
Equivalent shear modulus and shear wave velocity are derived by considerirg sand as continuous media macroscopically. With average treatment on contact forces, contact points and particle radius, the relationships between macro parameters and contact model of sand are established according to fabric and constitutive research of granular media.
Formulas and relationships established in this dissertation are verified by experiment and measured data, and the effect of application is also evaluated. An experimental research concerning the influence of particle surface characteristic on shear wave velocity is taken by using bender element testing equipment, which provides addition and correction to theoretical formulas above. A simplized calculation method for shear wave velocity is established which can be used to predict shear wave velocity of sand in projects. The application feasiblity and effect of this method is analyzed by comparing calculated results of simplized method with measured data.
引文
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