基于球形颗粒接触理论考虑频率影响的砂土剪切波速研究

发布时间：2018-01-04 23:14

本文关键词：基于球形颗粒接触理论考虑频率影响的砂土剪切波速研究　出处：《浙江大学》2017年博士论文　论文类型：学位论文

【摘要】：一般来说,自然界中的砂土是由随机堆积的微小砂颗粒以及填充于颗粒间孔隙内的液相与气相组成的三相集合体,它在本质上是非均匀的。当弹性波在砂土介质中传播时,相比于压缩波,剪切波不能在液相和气相中传播,仅能沿由砂土颗粒组成的骨架传播,因此,剪切波能更好地表征砂土结构性,反映砂土颗粒的排列和联结特征,是砂土的一个重要动力学参数。同时,研究砂土的剪切波速还具有重要的工程意义。在地震工程中,砂土剪切波速是反映砂土抗液化性能的重要指标,可用于判别场地的动力响应以及抗震动液化能力。前人对于砂土剪切波速的研究多集中在宏观尺度,近年来从微观尺度对其的研究又多关注于砂土颗粒本身的性质,没有涉及到剪切波自身的性质。本文从微观尺度入手,基于球形颗粒接触理论,考虑频率的影响,关注剪切波传播过程中引起的砂土颗粒旋转,对砂土介质中的剪切波速进行理论研究。本文的主要工作和研究成果如下:(1)给出了本文的三个基本假设,对所研究的砂土介质进行了模型化处理。根据微观尺度下球形颗粒接触理论,考虑剪切波传播过程中引起的颗粒旋转,推导出散粒体介质中的剪切波速公式,对其中不易直接量测的相关参数进行了再参数化处理,最终得到了引入频率参数的砂土剪切波速公式。当各参数在实际工程砂土介质常用的取值范围内变动时,利用推导出的砂土剪切波速公式进行定量参数分析。通过参数分析,研究了砂土颗粒弹性模量、砂土颗粒泊松比、砂土颗粒密度、砂土颗粒半径、砂土介质孔隙率、砂土介质有效内摩擦角、砂土体单元所受到的竖向有效应力、频率等8个因素对砂土剪切波速的影响,并分析了各因素对砂土剪切波速的影响效果。(2)根据推导出的砂土剪切波速公式,采用参数计算的方法,得到了剪切波在砂土介质中传播的频散曲线,分析出剪切波在砂土介质中传播的频散特性,并认为当剪切波长为12倍的砂土颗粒半径,也就是等于颗粒粒径的6倍时,剪切波速开始随频率的增加而显著增大。根据频散特性,定义了砂土介质中的临界频率。经过数学推导,给出了临界频率的精确表达式,确定砂土介质中临界频率的影响因素以及各因素的影响效果。为方便工程应用,在临界频率精确表达式的基础上,进行合理的数学处理,得到了砂土介质中临界频率的简化表达式。(3)使用等效介质理论,引入颗粒形状修正系数,不考虑颗粒旋转,推导散粒体介质等效剪切模量,进而得到基于等效介质理论的砂土介质中理论最大剪切波速公式。同时对使用本文方法得到的砂土剪切波速公式进行合理的数学简化,得到了便于工程应用的砂土剪切波速简化公式。将本文方法与等效介质理论方法进行比较,在此基础上,对使用等效介质理论推导出的砂土剪切波速公式进行了修正。(4)选用室内弯曲元试验和下孔法现场实测剪切波速对本文所提出的理论和公式进行验证。将使用本文方法的计算结果分别与12组室内弯曲元剪切波速试验数据和50组现场剪切波速实测数据进行对比分析,验证了本文理论和所推导公式的合理性、正确性以及适用性。
[Abstract]:In general, the sand in nature are tiny sand particles by three-phase aggregate random stacking and filling in the pores among the particles in the liquid phase and gas phase composition, it is not uniform in nature. When the elastic wave propagation in sand medium when compared to the compressional wave, shear wave cannot propagate in liquid and gas phase, can only be spread along the skeleton is composed of sand particles, therefore, shear wave can better characterize the structure of sand, reflect the arrangement and connection characteristics of sand particles, is one of the important dynamic parameters of sand. At the same time, the shear wave velocity of sand also has important engineering significance. In earthquake engineering, the shear wave velocity of sand is an important indicator of sand liquefaction performance, can be used to distinguish dynamic response and resistance to liquefaction site ability. Research on shear wave velocity of sand before focused on the macro scale in recent years, from the micro The concept of nature of scale on its research is more focused on sand particles themselves, not related to the properties of the shear wave itself. This paper starts from the micro scale, contact theory based on spherical particles, considering the effect of frequency on sand particles shear wave propagation caused by the process of rotation, the theoretical research of the shear wave velocity of sand medium. The main work and research results are as follows: (1) three basic assumptions are given in this paper, the sand medium have been studied through model processing. According to the contact theory of spherical particles of micro scale particles, considering the shear wave propagation caused by rotation, shear wave velocity dispersion formula of particle medium is derived the related parameters of which can not be directly measured for the re parameterized, finally get the formula of the shear wave velocity of sand into the frequency parameters. When the parameters in practical engineering sand medium Quality common range changes, quantitative parameter analysis with shear wave velocity of sand are derived. Through the parametric analysis, the elastic modulus of sand particles of sand particles, Poisson's ratio, sand particle density, sand particle radius, sand medium porosity, medium sand effective internal friction angle, the vertical sand unit effective stress, impact frequency of 8 factors on the shear wave velocity of sand, and analyzed the effect of various factors on the shear wave velocity of sand. (2) according to the formula of the shear wave velocity of sand is deduced, using the method of parameter calculation, obtain the shear wave propagation in sand medium dispersion curve, analysis of powder the characteristics of shear wave propagation in sand medium frequency, and that when the sand particle radius shear wavelength is 12 times, which is equal to the particle size of 6 times, and began to show the shear wave velocity with increasing frequency Increases. According to the dispersion characteristics, the definition of critical frequency of sand medium. Through mathematical derivation, exact expressions for the critical frequency are given, the effect to determine the influence of critical frequency of sandy soil medium factors and factors. For the convenience of engineering application, based on the critical frequency of accurate expression, mathematical treatment the simplified formula of the critical frequency of sand medium is obtained. (3) using the equivalent medium theory, the introduction of particle shape correction coefficient, without considering the particle rotation, derivation of equivalent shear modulus of granular materials, and then get the maximum shear wave velocity formula of medium sand equivalent medium theory based on the formula and the shear wave velocity of sand. To use this method to simplify the reasonable mathematical, simplified formula of the shear wave velocity of sand for the engineering application. The method and the equivalent medium theory. By comparison, on this basis, the shear wave velocity of sand using the formula deduced from the equivalent medium theory is modified. (4) the theory and formula of indoor test and on-site bending element under the hole method of shear wave velocity measured in this paper to verify the use of this method. The calculation results respectively with 12 groups of indoor bending element shear wave velocity test data and 50 groups of shear wave velocity field measured data were analyzed to verify the rationality of the theory and formulas, correctness and applicability.

【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TU441

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