Page 291 - The Combined Finite-Discrete Element Method

274 FLUID COUPLING

in general greater for a larger amount of explosive, and this is also true for the duration
of the pressure. It can be observed that the pressure-time curve obtained shows at first
instance a relatively slow decrease in pressure (up to 0.02 ms). This is due to the inertia of
the rock. Once the solid domain of the rock acquires an initial velocity field, the pressure
drop is rapid. This rapid pressure drop continues for approximately 0.02 ms. After that
the pressure becomes so small that it can almost be neglected. However, it continues
decreasing, although at much slower rate.
When this time-scale is compared to the time-scale of fracture and fragmentation pro-
cesses, it is evident that a significant pressure drop occurs much before the completion of
the fracture and fragmentation processes.

8.4.1 Scaling of coupled combined finite-discrete element problems

Linear problems such as linear elasticity problems are relatively easy to scale. This means
that if a solution for, say, a 2 m block is available, a solution for a 0.2 m block can be
obtained analytically using the scaling laws. Coupled combined finite-discrete element
analysis is highly nonlinear, and simple scaling laws do not apply. This is demonstrated
by the coupled problem shown in Figure 8.11.
The problem comprises a 0.2 × 0.2 × 0.01 m square block. The amount of explosive
supplied is 5.5 g per 0.1 m of thickness, i.e. (5.5/0.1)0.01 = 0.55 g. All the other param-
eters are the same as those given for the 2 × 2 m block. The stress wave propagation and
transient fracture patterns are shown in Figure 8.12.
The kinetic energy of the rock fragments as a function of time is shown in Figure 8.13.
The figure also shows the pressure of the detonation gas as calculated by the model. The
initial pressure drop is relatively rapid. The kinetic energy peaks twice, and the second
peak coincides with an intensive fragmentation taking place, together with a significant

0.1 0.1

0.1 m Bore-hole

0.1 m

Figure 8.11 A 0.2 m square block of thickness 0.01 m and 0.55 g explosive charge: wave fronts
at 0.018 ms and 0.032 ms.