Implementation of the Jones-Wilkins-Lee Equation of State with Solid High Explosives Element into the FDEM Code, Y-Blast 2D
Authors: Wu Di , Li Haibo 
Published: September 2022

ABSTRACT:
Drilling and blasting are the most common and commercial ways in efficient engineering rock fragmentation, which have been widely used in large-scale engineering like hydroelectric stations, nuclear power plant excavations and open-pit mining and tunneling for decades. As one of the novel continuum-discontinuum methods, FDEM (the combined Finite Discrete Element Method) has shown great potential in simulating rock fracturing and rock fragmentation under dynamic load. However, in the previous study of FDEM modeling blasting, the pressure of detonation is usually calculated by an empirical equation describing the pressure-time relationship pre-defined and then applied as surface/edge force onto the surface/edge of the elements, so the detonation process is not properly considered. In this paper, the JWL (Jones-Wilkins-Lee) equation of state and solid high explosives elements are firstly and successfully implanted in the new 2D blasting FDEM code which is called Y-Blast 2D, and the validation of implementation is conducted. The numerical results are comparable with the experimental results of (Dehghan Banadaki and Mohanty, 2012).

1. INTRODUCTION
As one of the most commercial ways in engineering rock fragmentation, drilling and blasting have been widely utilized in rock engineering for centuries. With the rapid development of the hardware and the numerical algorithms, numerical modeling is either economical or efficient in predicting and evaluating the results of blasting. (Cho and Kaneko, 2004; Dehghan Banadaki and Mohanty, 2012; Ma and An, 2008). These numerical methods used for simulating blasting can be generally classified into four categories, consisting of continuum-based methods, discrete element methods, coupled methods, and some meshfree methods.
The continuum-based methods, such as the Finite Element Method (Dehghan Banadaki and Mohanty, 2012) and eXtended Finite Element Method (Bendezu et al., 2017), although they are good at handling the continuum mechanics, they can barely deal with problems with multi-fractures while Peridynamics (Silling et al., 2017, 2007) is suitable for modeling both the continuum and the fractures; The discrete element can be subclassified into particle-based or block-based (Cundall, 1987; Deng et al., 2014), the cracks are represented by the particle-bond or block-bond breakages; The meshfree method, such as smoothed particle hydrodynamics (Gharehdash et al., 2020; Pramanik and Deb, 2015) and cracking particle method (Rabczuk et al., 2010; Rabczuk and Belytschko, 2007) can also deal with blasting-induced fractures problems. As for the coupled methods, coupled FEM-SPH method (Johnson, 1994) is widely used. The combined finite discrete element method, known as FDEM(Munjiza et al., 1995), is getting much attention in the last decade. FDEM has the capacity of simulating the crack and fractures due to the insert of the four-node none-thickness cohesive element (CE4) between the two neighboring three-node triangular elements (TRI3) (left side of Figure 1). The FDEM, raised by Dr. Munjiza (Munjiza, 2004), has been used to investigate many problems such as crack initiation and propagation (Fukuda et al., 2021; Han et al., 2020; Wu et al., 2021a, 2021b), blasting problems (Fukuda et al., 2019) and some multi-physics problems(Yan et al., 2016).