*2.3. DEM Particle Replacement Model Parameter Calibration*

The particle replacement model (PRM) used in this work may be used to describe fragmentation of individual particles under compression or impact. It consists of instantaneously replacing a spherical particle by progeny fragments every time a critical condition for failure is met. Spheres that make up the progeny fragments are allowed to overlap each other at the instant of replacement and a relaxation factor of the repulsive force was applied to prevent them from explosively repelling each other given the large contact forces involved. The version used in the present work is a custom PRM implemented in the software EDEM®, using an Advanced Programming Interface (API). An extended description of the model is presented in the work of Barrios et al. (2020) [19].

The PRM formulation used in the present work has been successfully used previously in DEM simulations describing breakage of individual and beds of particles by impact [17], as well as the interaction of particles and complex geometries in High-Pressure Grinding Rolls [21].

The calibration of the PRM parameters was conducted from uniaxial compression tests of individual unconfined irregular particles using a universal press manufacture by Maekawa with a capacity of 400 kN, applying a methodology similar to that used by Qian et al. [22]. Displacement during compression was measured using a digital camera, and the force was measured using a load cell with a maximum capacity of 5 kN, coupled to an Arduino UNO data acquisition device connected to a laptop (Figure 4). Each test consisted of compressing 30 particles contained in each narrow size range.

**Figure 4.** Uniaxial compression system used in unconfined testing of particles.

#### *2.4. Jaw Crusher DEM Simulations*

Tables 3 and 4 show individual and contact parameters of the materials used in the DEM simulations. These DEM parameters were chosen based on the work of Rodriguez et al. [23], and validated on the basis of repose angle results from the EDEM® software database (Generic EDEM Material Model Database—GEMM).




Material and contact parameters in Tables 3 and 4 were used both in calibration of the PRM parameters and in the DEM simulations of the jaw crusher.

EDEM® 2019 was used in the DEM simulations of the laboratory-scale jaw crusher. The CAD model of the jaw crusher geometry was designed using the software SketchUp (Boulder, CO, USA), based on the Otsuka Iron Works manual, as well as direct measurements of the discharge opening and the jaw wear surfaces. Table 5 shows the ranges of operating variables used in the DEM simulations of the jaw crusher.

The throughput of the simulated jaw crusher was obtained using the "flow sensor" feature of the EDEM® post processing module. The compressive force and the power on the swing and fixed jaws were calculated extracting the force and the torque on each element of the geometry. Finally, the particle size distribution of the product was calculated based on the mass of the particles produced by the PRM.


**Table 5.** Operating conditions adopted in the DEM simulations of the jaw crusher

#### **3. Results**

#### *3.1. Calibration of Particle Replacement Model Parameters*

Figure 5 shows the comparison between the experimental and the DEM simulation set-up of the single particle compression test, used to calibrate the PRM parameters of mother particle fragmentation and breakage force.

**Figure 5.** Experimental (**a**) and DEM simulation (**b**) set up of the single particle uniaxial compression test.

Figure 6a shows a comparison between the experimental and simulated force-deformation profiles of a single particle obtained from a compression test. In the figure, some of the limitations of the PRM, already discussed by Jimenez-Herrera et al. [17], in describing the fine details of the breakage process, are evident. Figure 6b shows the cumulative distribution of specific fracture energies for each size class. From the experimental distribution the median values of breakage force that is used to calibrate the threshold breakage force parameter of the DEM Particle Replacement Model, above which mother particles break and are replaced by daughter particles, is calculated.

**Figure 6.** Force-deformation profile of a single particle compression test (experiment and simulation) (**a**) and distribution of breakage forces for three size classes (**b**).

Figure 7a shows the experimental product size distributions from the jaw crushing tests conducted using the different feeds, including the three different narrow size classes and the particle size distribution. Figure 7b compares results from modeling and calibration of the DEM PRM spherical daughter particle distribution based on the experimental results of the jaw crushing test using a distributed feed. It was fitted using a primary distribution in which every breakage event results in a generation of daughter particle contained in three size classes: 1 particle with a size ratio equal to 0.595 of the mother particle, 8 particles with size ratio equal to 0.354 of the mother particle and the last with 52 particles with size ratio equal to 0.210 of the mother particle. In addition, the value of the relaxation factor bL equal to 0.0524 of the particle replacement model [19] was selected, which is responsible for capping the normal force calculated using the overlap of the daughter particles, so as to prevent the appearance of extremely high velocities of the fragments from breakage which would make simulations unrealistic.

**Figure 7.** Product size distributions from laboratory jaw crushing tests with different feeds (**a**) and DEM PRM daughter spheres distribution modeled (**b**).
