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为定量描述砂土的细观组构,基于非球形颗粒空间排列的数率统计规律及其组构理论定义,推导了新的土体三维组构定量描述公式。将非球形颗粒长轴方向在三维空间的方向分量用2个独立变化的角度描述,颗粒长轴方向在3个正交面上的方向分量就可用这2个角度定量计算,计算公式即为3个正交面上组构的各向异性幅值的表达式。基于数学概率统计方法,颗粒的离散特性用幅值计算公式转化为组构特性在平面上的可测参量,3个幅值参量中独立变化量只有2个,用任意2个幅值可以推导出三维空间组构的正交各向异性表达式。结果表明:随细观颗粒几何物理特性的变化,该组构三维表达式可以自然描述材料的各向同性、横观各向同性和正交各向异性,正交各向异性组构可以用1个或者2个标量参数描述;考虑非球形颗粒的三维空间排列几何关系,该组构可以描述土体颗粒几何尺寸对组构的影响,克服了现有组构的诸多不足;几种特殊非球形颗粒排列组构的分析表明该组构表达式具有描述范围广、物理意义清晰的特点。
In order to quantitatively describe the meso-structure of sand, a new quantitative description formula of three-dimensional structure of soil is derived based on the statistical rule of number-rate distribution of non-spherical particles and the theory of structure theory. The long axis direction of non-spherical particles in the three-dimensional space with two separate components of the angle of change, the long axis direction of the particles in the three orthogonal plane can be used to calculate the direction of these two angles, the formula is 3 An Anisotropic Amplitude Expression of the Configurations on an Orthogonal Plane. Based on the mathematical probability statistical method, the discrete characteristic of particles is transformed into the measurable parameters of the structural characteristics on the plane by the amplitude calculation formula. There are only two independent variations in the three amplitude parameters, and any two amplitudes can be used to derive Orthotropic Expression of Three - dimensional Space Structure. The results show that the three-dimensional expression of the structure can describe the isotropy, transverse isotropy and orthotropic anisotropy of the material naturally with the change of the geometrical and physical properties of the mesoporous particle. The orthotropic structure can be expressed as 1 Or two scalar parameters. Considering the geometrical relationship of non-spherical particles in three-dimensional space, the structure can describe the effect of soil particle geometry on the structure and overcome many shortcomings of the existing structure. Several special non-spherical The analysis of the arrangement of the particles shows that the structure expression has the characteristics of wide range of description and clear physical meaning.