journal article·2020-07-19Open access

Development of Energy-Based Impact Formula—Part I: Penetration Depth

Sanghee Kim, Thomas H.-K. Kang

Applied Sciences· Volume 10· Issue 14

Abstract

Predicting the damage to a concrete panel under impact loading is difficult due to the complexity of the impact mechanism of concrete. Based on the experimental results obtained by various researchers, the energies involved in the impact mechanism are classified into seven categories: Kinetic energy, deformed energy of a projectile, elastic penetration resistance energy of the panel, overall deformed energy of the panel, spalling-resistant energy, tunneling-resistant energy, and scabbing-resistant energy. Using these impact mechanisms and the energy conservation law, a new energy-based penetration depth formula is proposed to predict the penetration depth. This is validated using 402 impact test results, which include those with high-strength concrete, ultra-high-performance concrete (UHPC), or steel fiber-reinforced concrete, those under very high-velocity impact, and those with a very low ratio of target panel thickness to projectile diameter. It is found that the new impact formula predicts the penetration depth quite well.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: High-Velocity Impact and Material Behavior · Structural Response to Dynamic Loads · Geophysical Methods and Applications

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Department of Architectural Engineering, Kyonggi University, Suwon, Gyeonggi 16227, Korea

Department of Architecture and Architectural Engineering, Seoul National University, Seoul 08826, Korea

References (60)

Show source-provided references
1. Composite Flexural Behavior of Full-Scale Concrete Filled Tubes without Axial Loads10.1061/(ASCE)ST.1943-541X.0000241 ↗
2. Shear-Flexure Coupling Behavior of Steel Fiber-Reinforced Concrete Beams
3. Punching of Reinforced and Post-Tensioned Concrete Slab-Column Connections
4. Structural Behavior and Progressive Collapse Prevention under Abnormal Extreme Loading
5. Local Impact Effects of Hard Missiles on Concrete Targets10.1016/j.ijimpeng.2005.04.005 ↗
6. The Strength Properties Activated Granulated Ground Blast Furnace Slag with Aluminum Potassium Sulfate and Sodium Hydroxide10.4334/JKCI.2015.27.2.095 ↗
7. Energy-Based Penetration Model for Local Impact Damaged Concrete Members10.14359/51689868 ↗
8. ACE (1946). Fundamentals of Protective Structures, Army Corps of Engineering. Technical Report No. AT120 AT1207821.
9. NDRC (1946). Effect of impact and explosion. Summary Technical Report of Division 2, National Defense Research Committee.
10. A Review of Procedures for the Analysis and Design of Concrete Structures to Resist Missile Impact Effects10.1016/0029-5493(76)90015-7 ↗
11. Penetration Depth in Concrete for Nondeformable Missiles10.1016/0029-5493(82)90171-6 ↗
12. Local Effect of Solid Missiles on Concrete Structures10.1061/(ASCE)0733-9445(1984)110:5(948) ↗
13. Hard Missile Impact on Reinforced Concrete10.1016/0029-5493(84)90058-X ↗
14. Barr, P. (1990). Guidelines for the Design and Assessment of Concrete Structures Subjected to Impact, UK Atomic Energy Authority, Safety and Reliability Directorate. Technical Report No. SRD-R-439.
15. Reid, S.R., and Wen, H.M. (2001). Predicting Penetration, Cone Cracking, Scabbing and Perforation of Reinforced Concrete Targets Struck by Flat-Faced Projectiles, University of Manchester Institute of Science and Technology (UMIST). Technical Report No. ME/AM/02.01/TE/G/018507/Z.
16. BNFL (2003). Appendix H reinforced concrete slab local damage assessment. R3 Impact Assessment Procedure, Magnox Electric plc & Nuclear Electric Limited.
17. Rigid and Eroding Projectile Penetration into Concrete Targets Based on an Extended Dynamic Cavity Expansion Model10.1016/j.ijimpeng.2016.10.005 ↗
18. The Theory of Indentation and Hardness Test10.1088/0959-5309/57/3/301 ↗
19. Perforation Thickness and Ballistic Limit of Concrete Target Subjected to Rigid Projectile Impact10.1061/(ASCE)0733-9399(2003)129:9(1083) ↗
20. Sneddon, I.N., and Hill, R. (1960). Dynamic expansion of spherical cavities in metal. Progress in Solid Mechanics, North-Holland Publishing Company.
21. Dynamic Spherical Cavity-Expansion in a Compressible Elastic-Plastic Solid10.1115/1.3173672 ↗
22. Penetration into Semi-Infinite Reinforced-Concrete Targets with Spherical and Ogival Nose Projectiles10.1016/0734-743X(87)90096-0 ↗
23. Penetration into Soil Targets10.1016/0734-743X(92)90167-R ↗
24. An Empirical Equation for Penetration Depth of Ogive-Nose Projectiles into Concrete Targets10.1016/0734-743X(94)80024-4 ↗
25. Dimensionless Formulae for Penetration Depth of Concrete Target impacted by a non-deformable Projectile10.1016/S0734-743X(02)00037-4 ↗
26. Deep Penetration of a Non-Deformable Projectile with Different Geometrical Characteristics10.1016/S0734-743X(02)00005-2 ↗
27. Shear Strength Model for Interior Flat Plate-Column Connections10.4334/JKCI.2010.22.3.345 ↗
28. Direct Punching Shear Strength Model for Interior Slab-Column Connections and Column Footings with Shear Reinforcement10.4334/JKCI.2011.23.2.159 ↗
29. Shear Strength Model for Slab-Column Connections10.4334/JKCI.2010.22.4.585 ↗
30. Shear-Strength Model for Slab-Column Connections Subjected to Unbalanced Moment10.14359/51686533 ↗
31. Strain-Based Strength Model for Direct Punching Shear of Interior Slab-Column Connections10.1016/j.engstruct.2010.12.032 ↗
32. fib (2010). Model Code for Concrete Structures 2010 (fib Model Code 2010), Ernst & Sohn.
33. ACI Committee 224 (2001). Control of Cracking in Concrete Structures (ACI 224R-01), American Concrete Institute.
34. ACI Committee 318 (2019). Building Code Requirement for Structural Concrete and Commentary (ACI 318-19), American Concrete Institute.
35. Tensile Strength of Steel Fiber Reinforced Concrete10.12988/ces.2013.3531 ↗
36. Modeling of Local Impact Effects on Plain and Reinforced Concrete
37. Thoma, K. (2009). Predictive Modeling of Dynamic Processes, Springer.
38. Strain-Rate Effects on The Strength and Fragmentation Size of Rocks10.1016/j.ijimpeng.2009.04.008 ↗
39. Dynamic Strength Properties of Concrete and Reinforcing Steel Subject to Extreme Loads10.14359/51688754 ↗
40. Sharpe, W.N. (2008). High rates and impact experiments. Springer Handbook of Experimental Solid Mechanics, Springer.10.1007/978-0-387-30877-7 ↗
41. Finite Deformations and the Dynamic Measurement of Radial Strains in Compression Kolsky Bar Experiments10.1016/0020-7683(95)00206-5 ↗
42. Comité Euro-International du Béton (CEB) (1988). Concrete Structures Under Impact and Impulsive Loading—Synthesis Report, fib International. Technical Report CEB Bulletin No. 187.
43. Über die berührung fester elastischer Körper (On the contact of rigid elastic solids)
44. Johnson, K.L. (1985). Contact Mechanics, Cambridge University Press.10.1017/CBO9781139171731 ↗
45. Contact Mechanics of Fractal Surfaces by Spline Assisted Discretisation10.1016/j.ijsolstr.2015.01.021 ↗
46. The Relation Between Load and Penetration in the Axisymmetric Boussinesq Problem for a Punch of Arbitrary Profile10.1016/0020-7225(65)90019-4 ↗
47. Anderson, J.D. (2006). Hypersonic and High. Temperature Gas. Dynamics, American Institute of Aeronautics and Astronautics. [2nd ed.].
48. Eligenhausen, R., Popov, E.P., and Bertero, V.V. (1983). Local Bond. Stress-Slip Relationships of Deformed Bars under Generalized Excitations, University of California. Earthquake Engineering Research Council Technical Report No. 83/23.
49. Modeling Reinforced-Concrete Beam-Column Joints Subjected to Cyclic Loading10.1061/(ASCE)0733-9445(2003)129:12(1686) ↗
50. Bond-Slip Relationship of Beam Flexural Bars in Interior Beam-Column Joints10.14359/51687708 ↗
51. Evaluation of Impact Resistance of Steel Fiber-Reinforced Concrete Panel Using Design Equations10.14359/51689540 ↗
52. Penetration of Grout and Concrete Targets with Ogive-Nose Steel Projectiles10.1016/0734-743X(95)00048-F ↗
53. Penetration of Concrete Targets with Deceleration-Time Measurements10.1016/S0734-743X(02)00108-2 ↗
54. The Effect of Concrete Target Diameter on Projectile Deceleration and Penetration Depth10.1016/j.ijimpeng.2005.01.012 ↗
55. Penetration of Concrete Targets with Ogive-Nose Steel Rods10.1016/S0734-743X(98)00008-6 ↗
56. Resistance of High-Strength Concrete to Projectile Impact10.1016/j.ijimpeng.2004.04.009 ↗
57. Response of Hybrid-Fiber Reinforced Concrete Slabs to Hard Projectile Impact10.1016/j.ijimpeng.2013.02.005 ↗
58. Impact Resistance of Hybrid-Fiber Engineered Cementitious Composite Panels10.1016/j.compstruct.2013.01.029 ↗
59. Effect of Reinforcement on the Concrete Panels to Impact of Hard Projectiles10.1016/j.ijimpeng.2013.07.005 ↗
60. Kim, S. (2018). Impact Resistance of High Performance Concrete Panels under High Velocity Projectile Collision. [Ph.D. Thesis, Seoul National University].