Implementation of Numerical Mesostructure Concrete Material Models: A Dot Matrix Method

Abstract

We develop a dot matrix method (DMM) using the principles of computational geometry to place aggregates into matrices for the construction of mesolevel concrete models efficiently and rapidly. The basic idea of the approach is to transform overlap detection between polygons (or polyhedrons) into checking the possibility of any intersection between the point sets within a trial placement aggregate and the already placed ones in mortar. Through the arithmetic operation of integer point sets, the efficiency of the underlying algorithm in the dot matrix method is higher. Our parking algorithm holds several advantages comparing with the conventional placement issues. First, it is suitable for arbitrary-shape aggregate particles. Second, it only needs two sets for examining if the overlap between a trial placement aggregate and the already placed ones. Third, it accurately places aggregates according to aggregate grading curves, by order of reduction, led to more efficiently reducing aggregate placement time. The present method is independent of the size of aggregate particles. Combing with 3D laser scanning technology, the present method can also be used to create mesostructure concrete models conveniently and flexibly. Several examples show that DDM is a robust and valid method to construct mesostructure concrete models.

Meso-concrete modeling based on laser scanning technology

“…制备良好的连续级配骨料是构建数值混凝土细观模型的关键. 20 世纪初由 Fuller 提出的最大密实度曲线(富 勒级配曲线)为目前常见的三维理想级配曲线 [7,15,21,22] , 采用该曲线所确定的级配浇筑的混凝土可以产生最优化的 结构密度和强度, 其表达式为：…”

“…由于使用了离散的点阵代替了连续的空间区域, 上述骨料投放过程不能完全保证没有侵入现象发生, 如图 4(a)所示, 从点阵上看, 投放完成后骨料包围的点阵的状态值都为 1, 但从骨料几何形态上看却存在侵入现象. 为 解决此问题, 在侵入判断时将待投骨料放大 T/2 的长度, 如图 4(b)所示, 其中 T 表示骨料间最小容许间隔, 其取值 大小由公式(4)确定 [21] . 将放大后的待投放骨料与已投放骨料进行侵入判断, 若无侵入发生, 则将放大前的骨料位 置和相关数据进行保存.…”

“…The intrusion judgment between aggregates 在 SDMM 骨料投放算法中, NumX、NumY、NumZ 作为计算域点阵化的重要参数, 对骨料投放效率和所能达 到的最大骨料含量影响较大, 随着点阵中点数的增加程序执行效率随之降低. 在满足普通混凝土骨料含量(粗骨 料体积含量小于 50%) [10] 情况下, 并考虑到骨料投放效率, 给出 NumX、NumY、NumZ 的参考取值为 [21] ： min / ( um 1) / ( um 1) / ( um 1) / 10…”