## 2 Methods and Materials  
### Experimental Model  
The activities in this part correspond to: selection of rocks and sands, determination of the physical and mechanical properties of the materials, transformation of rocks into coarse aggregates of spherical particles, mixture of the materials, and finally, compression tests with the measurement of deformations. The selection of rocks was carried out in 5 calcareous zones of the country, and for this specific work, the area of the municipality of Tolu viejo in the Department of Surec, Colombia was selected. Samples were extracted in fragments from the existing rock in quarry areas that had limestones dating from the Eocene period. The estimations of physical, mechanical, and elastic properties were carried out on cores, with a section of 100 mm \(\times\) 200 mm obtained from the original rocks. The transformation of the original rocks (Figure 1) into spherical particles began with the cutting of the rock in sheets of thickness (_i_) corresponding to each sieve opening (_i_) in order to extract cylinders of diameter \(i\). These cylinders were worked with a concave head to convert them into spheres. In this way, all the particles required to complete the weight were retained in each sieve (_i_). The number of particles was controlled by the apparent density of the limestone and also by the weight retained on each sieve (_i_) of a reference or a pattern gradation. Thus, it was necessary to reproduce the mass retained in each sieve (_i_) by means of \(n\) spheres. In this way, it was necessary to reproduce a total of 1527 particles that also needed to be generated at the time in the computational model, as listed in Table 1. To obtain the reference gradation or pattern, the gradations used in commercialization were used, as well as the crushed aggregates used for concrete throughout the Colombian territory and standardized (by the ASTM C33/C33M-18 standard), a standard in which the selected gradation is called sieve gradation 56; within the text onwards, it has been given the name of gradation referential (Figure 2). Figure 1: Sequence of transformation activities: (**a**) original rocks of limestones, (**b**) cutting cores for mechanical and elastic tests, (**c**) laminar cutting of rock, (**d**) spherical shaping of particles, and (**e**) grouping of shaped particles to make a cylinder of 100 mm \(\times\) 200 mm. The sand used for the mix was fluvial, with a fineness modulus MF of 2.93. Both coarse and fine aggregates are used commercially to produce concrete in the region. The gradations of both materials were in accordance with the limits established in the ASTM C33/C33M-18 standard. Under a proportioning mixture and attending to a required resistance of \(\mathrm{f^{r}_{c}}\) = 28 MPa, the materials were provided for a design resistance of \(\mathrm{f^{r}_{cr}}\) = 28 + 8.3 MPa, corresponding to 36.3 MPa. It is necessary to note that there is no referential history of works about aggregates with this type of spherical particles; thus, the materials were provided according to what is listed in Table 2, without using any types of additives, to produce 100 mm \(\times\) 200 mm cylinders for mechanical and elastic tests. The cement used corresponded to the commercial type for general use. To complete the required tests and finish the experimental model, the manufactured specimens were subjected to curing in a submerged condition for 28 days (specimens were tested according to ASTM C39/C39M-21 and ASTM C469/C469M-14). The 6 cylinders built were categorized as follows: 3 for compression test, 2 for elastic modulus, and 1 to