堆石料颗粒破碎模拟的SBFDEM研究及程序研制

发布时间：2019-06-20 19:31

【摘要】：颗粒破碎特性的影响因素有颗粒的强度、大小、圆度、粗糙度、风化程度、相对密度、颗粒级配以及组构等内因和围压大小、应力水平、加载路径、加载速率、含水量、制样方法等外因。揭示颗粒料破碎特性的途径主要有室内试验、数值模拟、原位测试及其间相结合的方法,随着计算机技术的发展和数学、力学理论的进步和日趋完善,近年来,数值模拟方法成为研究堆石体颗粒料力学特性热点课题,并取得了长足的进步,由于该课题的复杂性、不确定性等,但目前尚未形成系统准确的数值模拟体系,仍面临诸多关键科学技术问题亟待解决。鉴于此,论文将围绕堆石体颗粒料复杂形状、破碎的模拟问题开展数值分析方法研究,以期从颗粒层面为研究颗粒料的宏观力学特性探索一条数值模拟途径,该课题研究成果将对建造堆石体工程的分析、设计、施工、维护等都具有十分重要的理论意义和实用价值。论文的主要内容如下:(1)在考虑堆石料复杂颗粒形状的基础上,以凸多边形作为基本单元,建立了二维离散单元的实用算法,并研制了用于模拟堆石料的二维离散单元法程序PDEM,采用本程序对室内试验进行了数值模拟,且与PFC模拟进行了比较,得到了与室内试验一致的应力变形规律;(a)推导了半解析方法计算任意多边形的转动惯量的公式,为牛顿运动定律求解任意多边形单元的转动问题提供了方便;(b)采用线性搜索算法实现了求解多边形间交点坐标,求解任意两个多边形之间的交点最多只要2(n+m)次,且易于编程实现。提出了由近似接触判断到真实接触判断的适用于多边形的接触判断算法;(c)采用基于势能原理的法向接触模型,推导了求解多边形-多边形法向接触力,结合切向摩擦定律构成了一个完整的多边形-多边形接触模型,为多边形颗粒之间的相互作用提供了理论依据;(d)基于以上原理和思路,研制了多边形离散元计算程序PDEM,并对姜景山等的粗粒料二维模型试验进行了数值模拟,且与PFC采用clump技术的模拟进行了比较。通过与PFC模拟结果和试验结果的对比分析了论文方法、程序的可靠性。(2)针对具有尖角的堆石料在外荷载作用下容易发生颗粒破碎的现象,建立了一种将多边形离散元(PDEM)和比例边界有限元(SBFEM)两种方法结合起来的新的模拟颗粒破碎的数值方法(SBFDEM),可以同时发挥这两种方法的优势,从颗粒尺度揭示颗粒破碎机理及其对宏观力学效应的影响。(a)将具有尖角的颗粒用多边形单元表示,用多边形离散单元方法分析颗粒运动及其相互作用规律,采用多边形比例边界有限单元法对单个颗粒进行应力应变分析。每个颗粒既是离散元方法中一个独立的离散单元,又是比例边界有限元分析时的一个多边形单元;(b)应用Hoek-Brown准则判断任意单元中某个点的破坏,假定破坏点达到一定比例时,此单元即破碎;破坏路径假设为直线,对破坏点的分布采用加权最小二乘法进行直线拟合得到破坏路径;根据破坏路径将单元一分为二,新产生的单元直接进入下一步的离散元和比例边界有限元的计算;(c)将相关理论形成了一套系统的用于分析颗粒破碎的方法,并基于MATLAB研制了相应的程序SBFDEM。(3)应用SBFDEM程序对堆石料试样进行了不同围压下的双轴压缩试验数值模拟。分析了颗粒破碎对堆石料在双轴压缩条件下的力链演化、试样变形以及宏观应力应变关系等物理力学行为的影响;分析了不同初始颗粒粒径分布对堆石料在双轴压缩条件下的颗粒破碎行为的影响。论文研究工作丰富和发展了离散单元法、比例边界有限元法,研究成果为数值模拟堆石体颗粒料复杂形状、颗粒破碎等关键问题探索了一条高效、科学的途径。
[Abstract]:The influence factors of the particle breaking property are the strength, the size, the roundness, the roughness, the degree of weathering, relative density, particle grading and the internal and confining pressure, the stress level, the loading path, the loading rate, the water content and the sample preparation method. The method of revealing the breaking property of the granular material mainly includes the indoor test, the numerical simulation, the in-situ test and the combination method, with the development of the computer technology and the progress and the perfection of the mathematics and the mechanics theory, in recent years, The numerical simulation method has been a hot topic in the study of the mechanical properties of the rockfill material, and has made great progress. Due to the complexity and uncertainty of the project, the numerical simulation system of the system has not yet been developed yet, and many key scientific and technical problems still need to be solved. In view of this, the paper studies the numerical analysis method about the complex shape and the broken simulation of the rockfill material, in order to explore a numerical simulation approach from the particle level to the study of the macro-mechanical properties of the granular material, and the research results will be used to analyze the construction of the rockfill. It is of great theoretical and practical value to design, construct, maintain and so on. The main contents of the paper are as follows: (1) On the basis of considering the complex particle shape of the rockfill material, a practical algorithm of two-dimensional discrete unit is established by using convex polygon as the basic unit, and a two-dimensional discrete unit method for simulating the rockfill material is developed, The numerical simulation of the indoor test is carried out by the program, and compared with the PFC simulation, the stress deformation law which is consistent with the indoor test is obtained; (a) the formula for calculating the moment of inertia of any polygon by the semi-analytical method is derived, The method of Newton's motion law is used to solve the problem of the rotation of any polygon element, and (b) a linear search algorithm is adopted to solve the coordinate of the intersection point of the polygon, and the intersection point between any two polygons can be solved by a maximum of 2 (n + m) times, and is easy to be programmed and implemented. In this paper, a contact determination algorithm for polygon based on approximate contact determination is presented, and (c) a normal contact model based on the principle of potential energy is used to derive the normal contact force of the polygon-polygon. In this paper, a complete polygon-polygon contact model is constructed in combination with the law of tangential friction, which provides a theoretical basis for the interaction between polygon particles; and (d) based on the above principles and ideas, a polygon discrete element calculation program (PDEM) is developed. The numerical simulation of the two-dimensional model test of the coarse aggregates such as Jiang Jingshan and the like is carried out and compared with the simulation of the PFC. The reliability of the method and the program is analyzed through the comparison with the results of the PFC simulation and the test results. (2) A new numerical method (SBFDEM), which combines the two methods of the polygonal discrete element (PDEM) and the proportional boundary finite element (SBFEM), is established for the phenomenon that the pile stone with the sharp angle is easy to crack under the action of the external load. The advantages of these two methods can be exerted at the same time, and the mechanism of particle breaking and its effect on the macro-mechanical effect can be revealed from the particle size. (a) the particles with sharp corners are represented by a polygonal unit, the particle motion and the interaction rule are analyzed by a polygon discrete unit method, and the stress and strain analysis of a single particle is carried out by using a polygonal proportional boundary finite element method. each particle is an independent discrete unit in a discrete element method, and is a polygon unit at the time of the finite element analysis of the scale boundary; and (b) the Hoek-Brown criterion is applied to judge the failure of a certain point in an arbitrary unit, and the unit is broken when the failure point is assumed to reach a certain proportion; the failure path is assumed to be a straight line, the distribution of the damage point is subjected to linear fitting by using a weighted least square method to obtain a failure path, and the unit is divided into two according to the failure path, and the newly generated unit directly enters the calculation of the discrete element and the proportional boundary finite element of the next step; (c) The relevant theory is used to form a system to analyze the particle breaking method, and the corresponding program SBFDEM is developed based on MATLAB. (3) The method of SBFDEM is used to simulate the two-axis compression test under different confining pressure. The influence of the particle size distribution on the particle breaking behavior of the rockfill material under biaxial compression was analyzed. In this paper, the discrete element method, the proportional boundary finite element method and the research results are enriched and developed, and a high-efficiency and scientific way is explored for the key problems such as the complex shape of the particle materials of the rockfill and the crushing of the particles.
【学位授予单位】：武汉大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TV41

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