PSI - Issue 68

551 5

Koji Uenishi et al. / Procedia Structural Integrity 68 (2025) 547–553 Uenishi et al. / Structural Integrity Procedia 00 (2025) 000–000

a

5.0 ´ 10 -5

Reinforcing

Cartridges

- 5.0 ´ 10 -5

b

c

Compression

Tension due to the vertical free surface

d

e

Tension due to reinforcing steel bars

Relatively larger tension in vertical virtual interface

Fig. 3. (a) Cartridges containing the self-reactive liquid and reinforcing steel bars implemented to simulate EDI-induced wave evolution inside the RC block indicated in Fig. 2. (b-e) Snapshots of dynamic disturbances developing in a RC block with three cartridges, numerically generated by a finite difference numerical simulation. Contours of volumetric strain (a strain invariant; tension positive) approximately at time (b) 20, (c) 60, (d) 100, and (e) 140 µ s after the simultaneous application of EDI are illustrated for the lower half part. (b) Initially, regions in compression appear around the cartridges due to the application of EDI. Shortly later, in (c) and (d), regions of dynamic tension quickly emerge by wave reflection at the front free surface of the RC block. In (d), the additional tension “captured” by the vertical rebars can be clearly identified. This tension-capturing characteristic of rebars contributes to the vertical “virtual interface” effect. In (e), due to the vertical “virtual interface” effect, relatively larger tension develops in the region in front of the vertical virtual interface indicated by the broken lines. simpler than that behind other effects, including the horizontal “virtual interface” effect, that make use of reflection and diffraction at empty dummy holes. Here, we briefly consider this mechanics behind the vertical “virtual interface” effect by numerically tracing the evolution of EDI-induced waves in the RC block (Fig. 2) with our finite difference simulator having the second-order spatiotemporal accuracy. The material properties employed for the simulation remain the same as those found in Uenishi et al. (2024) and listed in Table 1. As before, both concrete material and rebars are assumed to be homogeneous, isotropic and linear elastic, and according to Table 1, the longitudinal (P) and shear (S) wave speeds in the concrete (1) and the rebars (2) are calculated to be c P 1 » 4,200 m/s, c S 1 » 2,400 m/s and c P 2 » 5,900 m/s and c S 2 » 3,100 m/s, respectively. Also as before, for the simple identification of the fundamentals of the problem considered, the simulation is performed without specific fracture criterion and the stemming material is assumed to have the same material properties as concrete, with the pressure acting on the blast hole wall due to EDI given by A sin 2 ( p t / T ) (for 0 £ t £ T ) and 0 (otherwise) ( t : time, T = 260 µ s, and A = 1 GPa) and a fixed time step D x /(2 c P 2 ) and constant grid spacing D x = 10 mm. Figure 3(a) illustrates the positions of the EDI