To investigate the dimensional effect on shock wave propagation in jointed rock masses, a 2-D and a 3-D calculation of a site test are performed respectively by using Discrete Element Method, the simulated results are compared with test data. It shows that, in modelling shock wave propagation and attenuation in jointed rock masses, when the explosive along explosion chamber is long enough and the joints are dense enough or uniformly distributed, the model can be considered as plane-strain problem, 2-D results are good enough to fit with test data. 2-D modelling, with much more details of rock masses taken into account, can be applied to make critical engineering judgements instead of 3-D modelling in some cases.
It is well known that all rock masses are three-dimensional (3-D) in consideration of discontinuities, topography as well as constructive structures, and 3-D discontinuum modelling is undoubtedly the most feasible method in revealing the mechanical responses of rock masses (Mckinnon 1999). Nevertheless, due to the limitations of computer memory and running time, only small percentage of joints can be constructed into 3-D models. On the other hand, in modelling dynamic problems, the mesh size must be smaller than 1/10–1/8 of the shortest length of the waves propagating in the rock masses, leading to impossibility for big 3-D models which cover the whole domain of interest (Itasca 1998). This shortage of details in rock masses can sometimes result in lower reliability of the simulated results. Therein, a question is brought forward: can 2-D modelling be a substitute of 3-D modelling?
Discrete Element Method, which is specially designed to simulate discontinuous behaviour of rock masses, has been employed to simulate the dynamic response of rock masses under blast loading these years (Cundall 1971; Lemos 1987; Chen 1999). However, only fewer efforts have been spent on three-dimensional DEM modelling due to the difficulties in operation (Chen et al. 2000; Papantonopoulos et al. 2002).
In this study, by using UDEC and 3DEC, the commonly used commercial codes of discrete element method, a 2-D and a 3-D calculation of a site test are performed respectively to investigate the dimensional effect on shock wave propagation in jointed rock masses, the simulated results are compared with test data.
An in-situ ground shock test was conducted in limestone to investigate the wave propagation and wave attenuation. The exploding chamber, with a dimension of 8 × 4 × 2m, is located at 115m below the ground surface. The effective TNT charge weight is 606kg with a loading density of 10kgm−3 (Ma et al. 1998). By using the test setting up and measured data, a UDEC modelling and a 3DEC modelling are performed to examine the dimensional effect on shock wave propagation and attenuation.
(Figure in full paper)
Figure 1 shows the schematic model of the test. In the calculation, the virgin rock is assumed to be linear elastic, while all joints satisfy Coulomb slip model.