PSI - Issue 46

Koji Uenishi et al. / Procedia Structural Integrity 46 (2023) 136–142

139

4

Koji Uenishi et al. / Structural Integrity Procedia 00 (2019) 000–000

dowels are generated (indicated by pink lines in Fig. 2(a) bottom). To our surprise, the concrete material above the heads of the stud dowels with the four “cups” can be lifted and taken away as one block. The remaining concrete parts can be removed by hand or an electric pick without difficulty, and equally importantly, the stud dowels seem to be dynamically undeformed. If the stud dowels are double in number, in the specimen B (  L = 100 mm), two horizontal fracture planes, one linking the heads of the stud dowels and the other connecting the cartridges develop (illustrated in pink), and the concrete material above the heads of the stud dowels can be lifted and removed as a more rectangular block without “cups” (Fig. 2(b) bottom). In other parts of the reinforced concrete slab, due to the action of a larger number of EDIs, the concrete is fragmented into smaller pieces, most of which can be taken away by hand or with a crowbar. Again, however, the stud dowels themselves seem undeformed. Obviously, this observed dissimilarity of the final disintegration patterns in the specimens A and B is owing to the relative positions of the structural discontinuities associated with the specimens, such as the blast holes (cartridges), the stud dowels and the free surfaces. 3. Numerical speculations The above experimental findings can be possibly explained physically through three-dimensional finite difference calculations with the second-order spatiotemporal accuracy. As seen in Fig. 3 top, in the numerical simulations, for simplicity, the steel girder is excluded except for the upper plate (flange) having a thickness of 20 mm. This upper steel plate is assumed to be perfectly bonded to the concrete slab above, forming a welded interface. The concrete material as well as the steel is considered to be homogeneous, isotropic and linear elastic. The density, Young’s modulus and Poisson’s ratio are 2,320 kg/m 3 , 34.2 GPa and 0.25 for the concrete, and 7,800 kg/m 3 , 200 GPa and 0.3 for the steel. These physical properties give the longitudinal and shear wave speeds as c P 1  4,200 m/s and c S 1  2,400 m/s for the concrete, and c P 2  5,900 m/s and c S 2  3,100 m/s for the steel. Although it can be included without difficulty, for visual clarification, the existence of steel bars and fracture criteria is ignored at this point, and the physical properties of the stemming are presumed to be the same as those of the concrete material. The number of orthogonal grid points is 91  91  23 with the grid point spacing  x = 10 mm and a fixed time step being  x /(2 c P 2 ). The temporal ( t -) profile of the pressure P ( t ) produced by each cartridge has not been thoroughly measured yet, but here, a sine-squared form P ( t ) = A sin 2 (  t / T ) (for 0  t  T ) and 0 (otherwise) is employed, where the maximum amplitude A is 1 GPa and the duration T is 260 microseconds (  s) (Uenishi et al., 2014). Furthermore, each cartridge is now placed precisely at the center between the two neighboring stud dowels in the central row (Fig. 3 top). By setting up the models in this way, every model becomes symmetric with respect to the vertical plane containing the cartridges and the stud dowels in the central row, and the whole dynamic wave field can be envisaged more simply by observing a limited section of the model. As in our earlier study, the development of waves and its relation with dynamic fracture are traced in terms of the volumetric strain (strain invariant) evolving in the specimens. In the lower section of Fig. 3, the distributions of dynamic volumetric strain are illustrated for a half part of the specimen A ((a):  L = 200 mm) and specimen B ((b):  L = 100 mm). At 20  s after the activation of the cartridges, in the second row of Fig. 3, compressive spherical waves, radiated from the cartridges and indicated in bluish and greenish colors corresponding to negative volumetric strains, can be identified in both cases (a) and (b). At 60  s, in the third row of Fig. 3(a), because of the reflection of the initial compressive waves at the free surfaces of the specimen, regions of tensile (positive) volumetric strains, depicted in yellowish and reddish colors, can develop rather independently above each cartridge. The volumetric tension in these regions above the cartridges becomes larger at a later stage, at 100  s in the fourth row of Fig. 3(a) and at 140  s in the bottom row, and tensile fracture can be generated on the boundaries between the compressive (plus smaller tensile) regions around the cartridges and the regions of larger tension exceeding the fracture strength (indicated by the pink broken lines in the figure). In the field experiments (Fig. 2(a)), the specimen A had cup-shaped fractures linking the cartridges to the heads of the stud dowels, and this numerical speculation well explains the experimental finding. On the other hand, in the specimen B, upon reflection of the initial compressive waves at the free surfaces, a single larger region of tension develops above the group of the stud dowels (and the cartridges), which is identifiable at 60  s in the third row of Fig. 3(b). Like in the case of the specimen A, the tension in this region increases at a later stage, at 100  s in the fourth row and at 140  s in the bottom row of Fig. 3(b). Interestingly, however, regions of larger tension do not develop inside the group of the stud dowels itself except for the bottom section of each stud dowel below the cartridges (Fig. 3(b) bottom). Thus, tensile cracks can emerge on a (initially virtual) horizontal plane