Author Contributions
Conceptualization, X.Z. and L.X.; methodology, X.Z. and Y.W.; software, C.Z.; validation, X.Z., C.Z. and S.L.; formal analysis, X.Z.; investigation, X.Z.; resources, L.X.; data curation, X.Z.; writing—original draft preparation, X.Z. and C.Z.; writing—review and editing, G.Z.; project administration, X.Z.; funding acquisition, X.Z. and Y.W. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Geometric model of the protective structure: (a) separation modeling of steel reinforced concrete, (b) composite model, and (c) size and finite element mesh division of the projectile.
Figure 1.
Geometric model of the protective structure: (a) separation modeling of steel reinforced concrete, (b) composite model, and (c) size and finite element mesh division of the projectile.
Figure 2.
Frontal damage to the target surface in the penetration test: (a) simulation results, and (b) experimental results.
Figure 2.
Frontal damage to the target surface in the penetration test: (a) simulation results, and (b) experimental results.
Figure 3.
Curves of the depths of projectile penetration into the target versus time obtained by numerical model.
Figure 3.
Curves of the depths of projectile penetration into the target versus time obtained by numerical model.
Figure 4.
Numerical simulation image of the damage process inside the target during the internal explosion experiment of prefabricated holes in concrete.
Figure 4.
Numerical simulation image of the damage process inside the target during the internal explosion experiment of prefabricated holes in concrete.
Figure 5.
Internal explosion experiment of prefabricated holes in concrete: (a) numerical simulation results, (b) experimental results, and (c) details of explosion pit.
Figure 5.
Internal explosion experiment of prefabricated holes in concrete: (a) numerical simulation results, (b) experimental results, and (c) details of explosion pit.
Figure 6.
Distribution of measurement points in the model.
Figure 6.
Distribution of measurement points in the model.
Figure 7.
Volume of damage for different qualities of concrete.
Figure 7.
Volume of damage for different qualities of concrete.
Figure 8.
Penetration depth of the projectile under (a) Case 1 and (b) Case 2.
Figure 8.
Penetration depth of the projectile under (a) Case 1 and (b) Case 2.
Figure 9.
Damage of protective structures: (a) 3D image for plain concrete; (b) 3D image with reinforcement layers; (c) top-view image for plain concrete; and (d) top-view image with reinforcement layers.
Figure 9.
Damage of protective structures: (a) 3D image for plain concrete; (b) 3D image with reinforcement layers; (c) top-view image for plain concrete; and (d) top-view image with reinforcement layers.
Figure 10.
Maximum principal stress distribution on the upper surface of the internal use area of the protective structure.
Figure 10.
Maximum principal stress distribution on the upper surface of the internal use area of the protective structure.
Figure 11.
3D damage images of protective structures with different diameters of steel bars.
Figure 11.
3D damage images of protective structures with different diameters of steel bars.
Figure 12.
Damage information of protective structures with different diameters of steel bars: (a) penetration depth; (b) damage volume; and (c) diameter of damage hole formed by EPW.
Figure 12.
Damage information of protective structures with different diameters of steel bars: (a) penetration depth; (b) damage volume; and (c) diameter of damage hole formed by EPW.
Figure 13.
(a) Maximum principal stress distribution of the protective structure after penetration–blasting damage; and evolution of maximum principal stress at each measuring point versus time with reinforcement diameters of (b) 8 mm, (c) 12 mm, (d) 16 mm, (e) 20 mm, and (f) 24 mm.
Figure 13.
(a) Maximum principal stress distribution of the protective structure after penetration–blasting damage; and evolution of maximum principal stress at each measuring point versus time with reinforcement diameters of (b) 8 mm, (c) 12 mm, (d) 16 mm, (e) 20 mm, and (f) 24 mm.
Figure 14.
3D damage images of protective structures with different spacing of steel reinforcement mesh.
Figure 14.
3D damage images of protective structures with different spacing of steel reinforcement mesh.
Figure 15.
(a) Maximum principal stress distribution of the protective structure after penetration–blasting damage; and evolution of maximum principal stress at each measuring point versus time with reinforcement mesh spacing of (b) 12 cm, (c) 15 cm, (d) 18 cm, (e) 21 cm, and (f) 24 cm.
Figure 15.
(a) Maximum principal stress distribution of the protective structure after penetration–blasting damage; and evolution of maximum principal stress at each measuring point versus time with reinforcement mesh spacing of (b) 12 cm, (c) 15 cm, (d) 18 cm, (e) 21 cm, and (f) 24 cm.
Figure 16.
Relationship curve between the proportion of steel reinforcement volume and penetration depth.
Figure 16.
Relationship curve between the proportion of steel reinforcement volume and penetration depth.
Figure 17.
Concrete damage and steel layer penetration effect of protective structures under the same reinforcement ratio for steel rebar with (a) diameter of 16 mm, 8 layers; (b) diameter of 17.1 mm, 7 layers; (c) diameter of 18.5 mm, 6 layers; (d) diameter of 20.2 mm, 5 layers; and (e) diameter of 22.6 mm, 4 layers.
Figure 17.
Concrete damage and steel layer penetration effect of protective structures under the same reinforcement ratio for steel rebar with (a) diameter of 16 mm, 8 layers; (b) diameter of 17.1 mm, 7 layers; (c) diameter of 18.5 mm, 6 layers; (d) diameter of 20.2 mm, 5 layers; and (e) diameter of 22.6 mm, 4 layers.
Figure 18.
Protective structures with the same reinforcement ratio: (a) maximum principal stress distribution after penetration–blasting damage; evolution of maximum principal stress at each measuring point versus time for steel reinforcement with (b) diameter of 16 mm, 8 layers; (c) diameter of 17.1 mm, 7 layers; (d) diameter of 18.5 mm, 6 layers; (e) diameter of 20.2 mm, 5 layers; and (f) diameter of 22.6 mm, 4 layers.
Figure 18.
Protective structures with the same reinforcement ratio: (a) maximum principal stress distribution after penetration–blasting damage; evolution of maximum principal stress at each measuring point versus time for steel reinforcement with (b) diameter of 16 mm, 8 layers; (c) diameter of 17.1 mm, 7 layers; (d) diameter of 18.5 mm, 6 layers; (e) diameter of 20.2 mm, 5 layers; and (f) diameter of 22.6 mm, 4 layers.
Table 1.
Result comparison.
Table 1.
Result comparison.
Velocity (m/s) | Test Results (cm) | Simulation Results (cm) | Relative Error (%) |
---|
860 | 54 | 52.9 | 2.0 |
981 | 65 | 64.1 | 1.3 |
1183 | 98 | 96.2 | 1.8 |
Table 2.
Design parameters of steel reinforcement layers in various cases.
Table 2.
Design parameters of steel reinforcement layers in various cases.
Case | Diameter (mm) | Mesh Spacing (cm) | Number of Layers |
---|
1 | — | — | — |
2 | 16 | 18 | 8 |
3 | 8 | 18 | 8 |
4 | 12 | 18 | 8 |
5 | 20 | 18 | 8 |
6 | 24 | 18 | 8 |
7 | 16 | 12 | 12 |
8 | 16 | 15 | 10 |
9 | 16 | 21 | 7 |
10 | 16 | 24 | 6 |
11 | 17.1 | 18 | 7 |
12 | 18.5 | 18 | 6 |
13 | 20.2 | 18 | 5 |
14 | 22.6 | 18 | 4 |
Table 3.
Damage information of protective structures with different spacing of reinforcement mesh.
Table 3.
Damage information of protective structures with different spacing of reinforcement mesh.
| Spacing of Steel Reinforcement Mesh (cm) |
---|
12 | 15 | 18 | 21 | 24 |
---|
Penetration depth (m) | 1.08 | 1.14 | 1.15 | 1.17 | 1.2 |
Damage volume (cm3) | 8616 | 9712 | 9368 | 10,096 | 9560 |
Max. diameter of damage hole (mm) | 920 | 1160 | 724 | 960 | 727 |
Min. diameter of damage hole (mm) | 686 | 645 | 705 | 766 | 685 |
Table 4.
Damage parameters and steel content parameters under different cases.
Table 4.
Damage parameters and steel content parameters under different cases.
Case | Penetration Depth (m) | Damage Volume (cm3) | Volume Ratio of Steel Bars | Ratio of the Number of Layers of Penetrated Steel Bars | Volume Ratio of Effective Steel Bars |
---|
1 | Penetrated | 16,736 | — | — | — |
2 | 1.15 | 8640 | 8.68% | 75% | 6.51% |
3 | 1.34 | 10,248 | 2.17% | 87.5% | 1.90% |
4 | 1.25 | 9880 | 4.88% | 87.5% | 4.27% |
5 | 1.06 | 10,128 | 13.6% | 75% | 10.20% |
6 | 0.98 | 10,552 | 19.5% | 62.5% | 12.19% |
7 | 1.08 | 8616 | 13.0% | 66.7% | 8.67% |
8 | 1.14 | 9712 | 10.9% | 70% | 7.63% |
9 | 1.17 | 10,096 | 7.60% | 71.4% | 5.43% |
10 | 1.20 | 9560 | 6.51% | 83.3% | 5.42% |
Table 5.
Damage information of protective structures with the same reinforcement ratio.
Table 5.
Damage information of protective structures with the same reinforcement ratio.
| Reinforcement Diameter Size (mm) |
---|
16 | 17.1 | 18.5 | 20.2 | 22.6 |
---|
Penetration depth (m) | 1.15 | 1.13 | 1.08 | 1.07 | 1.05 |
Damage volume (cm3) | 9368 | 9368 | 9560 | 9008 | 10,880 |
Max. diameter of damage hole (mm) | 724 | 766 | 727 | 700 | 687 |
Min. diameter of damage hole (mm) | 705 | 741 | 686 | 688 | 644 |