A New Numerical Simulation Method for Three-Dimensional Mesoscale Analysis of Concretes

Abstract

This paper presents a method for generating a region with a lot of randomly distributed ellipsoids. Using the parametric expression of an ellipsoid, the criterion for determining if a spatial point is in the interior or exterior of the ellipsoid is established. Then the computation of the distance between a point and the ellipsoid is converted into finding the solution to an optimization problem, which can be efficiently approximated by the searching method. Based on these facts, the proposed method is able to make the distance between generated ellipsoids very small and then successfully improve the content of ellipsoids grains in the region. Numerical results show that the proposed method can generate simulation of specimens in which the content of ellipsoids is higher than 55% according to four-graded aggregates, 50% according to three-graded aggregates, and 45% according to two-graded aggregates, respectively, in relatively short time.

Features of the Morphology of the Shear Failure Surfaces of Coarse-Grained Slip Zone Soils

“…The established space size is consistent with the test shear box size, which is 200 mm × 200 mm, and the area is denoted as "A." According to the particle size gradation in the test scheme, the diameter range of each particle interval and the proportion of particles in each particle interval is set, and the proportion coefficient is recorded as "p." The principle is as follows: First, the sequence randomly picks a point "O" in the space, with the point as the center of the ellipse [12]. An ellipse with the length of the long semi-axis "a" and the length of the short semi-axis "b" is generated.…”

“…If the distance is less than the maximum radius of the particle size interval, then a new point is picked, and if the distance is greater than the maximum radius of the particle size interval, then a particle is generated according to the above steps. The distance from any point in the plane to the boundary of the particle is shown in the literature [12][13].…”