2. Numerical modelling strategy

as a sudden, rapid rupture of the rock mass with a violent, explosive release of elastic/strain energy from the surface of an excavation, which is generally associated with a seismic event and produces rock particle ejections [1–5]. The coal burst source is the mechanism that triggers or induces the damage mechanism visible on the excavation surface. The coal burst source is generally associated with a seismic event that can be performed at a wide range of local magnitudes, normally ranging from undetectable up to 5 [6]. Indeed, mining-induced seismicity can reach moderate values of ground velocity and acceleration, and in some cases its effects on the surface can be compared with low-intensity earthquakes [7]. The mechanism that produces the seismic event is a sudden release of the strain energy that has been stored above a critical level within the rock/coal mass. Some portion of this energy is demolished by crack development, and the rest of the energy is converted into the kinetic energy [8, 9]. When the energy source is located near the roadway, the released energy may lead to coal fragmentation. At the place of the source of the energy, where it is located in a plane of weakness inside the coal mass, the released energy provokes shear displacement along the plane, which in revolve generate vibrations that persuade coal ejections when they are situated near the excavation boundaries [7]. Tarasov and Randolph [6] have explained a number of special and inconsistent behaviours of hard rock at the significant depth that are directly related to rock failure mechanisms in deep excavations. They determined that the procedures of the shear failure, with respect to the significant low friction, can be classified as the main reason to release energy. Based on the suggested frictionless mechanism, the level of the brittleness of the confined rock/coal masses might be increased under high stress conditions. This may result in reducing the overall ductility which would in line with the abrupt fracture failure. Under an energy-balance approach, the methods to predict coal burst risk are based on energy indexes such as energy release rate (ERR) [8–10], energy storage rate (ESR), strain energy storage index (WET) [11], potential energy of elastic strain (PES) or strain energy density (SED) (i.e., the elastic strain energy in a unit volume of the coal mass, which can be computed by the uni-axial compressive strength of the coal and the relevant unloading tangential modulus), and burst potential index (BPI). A combination of both analytical as well as numerical methods, where they can comprehensively evaluate the structural performance of the mine scale, would be broadly addressed in the current

208 Finite Element Method - Simulation, Numerical Analysis and Solution Techniques

research. Thus, the following aims explicitly will be addressed.

loading will be exclusively examined.

the different contact/joint properties.

mining activities.

1. Develop a full 2D and 3D finite element as well as discrete element models to compute the inducted energies in a single pillar with different high to width ratios. In this approach, different loading conditions varying from the static, quasi-static as well as dynamic

2. Considering the effect of the energy transformations between the rock/coal layers due to

3. Suggest empirical equations to predict the amount of the released strain energy due to the

The main novelty of this research is to simulate the effect of the failure and post-failure of the

engaged material as well as joint/contact properties on the energy transformation.

Numerical simulations can be considered as an individual tool to predict possible failure modes and the actual capacity of the mining setting. It is mostly useful to undertake parametric and sensitivity analyses to gain better understanding the nature and level of indecision, or remaining hazard, associated with design process.

First, a finite element model is developed by taking advantage from the commercial software package ABAQUS/Explicit. All the geotechnical components, including the rock and coal, were modelled by the eight-node linear brick element (C3D8R) available in the ABAQUS library. Element C3D8R relies on reducing integration and hourglass control. The assigned meshes were established by using the structured technique available in ABAQUS. The solution to the nonlinear problem was sought using the explicit dynamic analysis procedure available in ABAQUS. In the current study, Figure 1 presents a quarter of a single pillar.

Thus, by taking advantage from the symmetrical boundary conditions, a finer mesh was assigned to the model. Finding the right input material properties would be a significant assumption, which has not been appropriately studied in the available literature. Modelling of mechanical behaviour of the coal under both compression and shear stresses would be very complicated, since there are no articulated reports which might be concerned with the uni-axial and tri-axial behaviour of coal under both static and dynamic loading conditions. According to

Figure 1. Illustration of a typical single pillar model using ABAQUS/Explicit.

the elastic analysis, the stress analysis and energy computations were organised in line with the linear relationship between the stress and the strain in coal and overburden properties. The peak and post-peak behaviour of coal and surrounding rock masses will be ignored. Therefore, in the current literature, the computed stress, strain and kinetic energy have been noticeably overestimated. At the second stage, a combination of the 2D and 3D discrete element models using UDEC and 3DEC was developed. Figure 2 illustrates the pillar model incorporating half of coal, roof and floor along the symmetrical centre-line of the pillar. The height of the roof and floor was 20 m and the mining height was fixed at 3 m, while the pillar widths varied in order to simulate the pillars with width to height (w/h) ratios from 1 to 5.

A Mohr-Coulomb (MC) material that presents a constant strength after failure and a Mohr-Coulomb strain-softening material that can reach the peak strength and then decrease to a residual strength have been considered. A quasi-static loading condition as a velocity was applied on the top and bottom of the model. The applied velocity was started with a very small, constant velocity to represent a relative loading system to promote a model of a coal failure that progresses slowly. Simulating a proper loading/displacement condition is significantly crucial, specifically, gaining a sound understanding of the structural reaction of a single

coal sample under dynamic or quasi-static loading conditions. Consideration was also given to defining a joint interface. A Coulomb Slip (CS) joint interface property, where it is represented by displacement softening parameters, was taken into account to simulate the interface prop-

Numerically and Analytically Forecasting the Coal Burst Using Energy Based Approach Methods

http://dx.doi.org/10.5772/intechopen.71879

211

The uniform zone size of 0.1 m was applied to the coal, and a smooth variation of zoning from the coal to the boundaries was used for roof and floor with appropriate aspect ratios to avoid numerical instability. Roller boundaries were applied along the side of the roof and floor, the bottom of the floor and the vertical line. The same trend was applied to develop the

An analytical method is developed to evaluate shear stress and strain distributions between the engaged surfaces throughout different joint layers by considering the beam theory

three-dimensional discrete element using 3DEC (see Figure 3).

erties between the different joints.

Figure 3. Geometry and zoning of coal pillar model using 3DEC.

3. Analytical approach

Figure 2. Geometry and zoning of coal pillar model using UDEC.

Numerically and Analytically Forecasting the Coal Burst Using Energy Based Approach Methods http://dx.doi.org/10.5772/intechopen.71879 211

Figure 3. Geometry and zoning of coal pillar model using 3DEC.

coal sample under dynamic or quasi-static loading conditions. Consideration was also given to defining a joint interface. A Coulomb Slip (CS) joint interface property, where it is represented by displacement softening parameters, was taken into account to simulate the interface properties between the different joints.

The uniform zone size of 0.1 m was applied to the coal, and a smooth variation of zoning from the coal to the boundaries was used for roof and floor with appropriate aspect ratios to avoid numerical instability. Roller boundaries were applied along the side of the roof and floor, the bottom of the floor and the vertical line. The same trend was applied to develop the three-dimensional discrete element using 3DEC (see Figure 3).
