Simulation of Concrete Wall Subjected to Airblast by Developing an Elastoplastic Spring Model in Modelica Modelling Language

Authors: Leo Laine, Morgan Johansson

Abstract:

To meet the civilizations future needs for safe living and low environmental footprint, the engineers designing the complex systems of tomorrow will need efficient ways to model and optimize these systems for their intended purpose. For example, a civil defence shelter and its subsystem components needs to withstand, e.g. airblast and ground shock from decided design level explosion which detonates with a certain distance from the structure. In addition, the complex civil defence shelter needs to have functioning air filter systems to protect from toxic gases and provide clean air, clean water, heat, and electricity needs to also be available through shock and vibration safe fixtures and connections. Similar complex building systems can be found in any concentrated living or office area. In this paper, the authors use a multidomain modelling language called Modelica to model a concrete wall as a single degree of freedom (SDOF) system with elastoplastic properties with the implemented option of plastic hardening. The elastoplastic model was developed and implemented in the open source tool OpenModelica. The simulation model was tested on the case with a transient equivalent reflected pressure time history representing an airblast from 100 kg TNT detonating 15 meters from the wall. The concrete wall is approximately regarded as a concrete strip of 1.0 m width. This load represents a realistic threat on any building in a city like area. The OpenModelica model results were compared with an Excel implementation of a SDOF model with an elastic-plastic spring using simple fixed timestep central difference solver. The structural displacement results agreed very well with each other when it comes to plastic displacement magnitude, elastic oscillation displacement, and response times.

Keywords: Airblast from explosives, elastoplastic spring model, Modelica modelling language, SDOF, structural response of concrete structure.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.2571920

References:

[1] K-J. Bathe, Finite Element Procedures, Prentice-Hall, Englewood Cliffs, New Jersey, USA, 1996.
[2] J. M. Biggs, Introduction to Structural Dynamics, McGraw-Hill, New-York, USA, 1964.
[3] Eurocode 2: Design of Concrete Structures – Part 1-1: General rules and rules for buildings, European Committee for Standardization, Brussels, Belgium, 2004.
[4] ConWep – Collection of conventional weapons effects calculations based on TM 5-855-1, Fundamentals of Protective Design for Conventional Weapons, U.S. Army Engineer Waterways Experiment Station, Vicksburg, USA, 1992.
[5] Structures to Resist the Effects of Accidental Explosions. UFC 3-340-02, Department of Defense, USA, 2008.
[6] J. Ekström, Blast and Impact Loaded Concrete Structures. Engineering, Chalmers University of Technology, PhD Thesis, Göteborg, Sweden, 2017.
[7] M. Johansson, Structural Behaviour in Concrete Frame Corners of Civil Defence Shlters: Non-linear Finite Element Analyses and Experiments, Department of Concrete Structures, Chalmers University of Technology, PhD Thesis, Publication 00:2, Göteborg, Sweden, 2000.
[8] J. Johansson, Central differensmetod (Central difference method. In Swedish.), Swedish Civil Contingencies Agency, B03-102, 2012-10-15, Karlstad, Sweden, 2012.
[9] J. Johansson, Luftstötvåg (Air shockwave. In Swedish.), Swedish Civil Contingencies Agency. Publ.no. MSB448, Karlstad, Sweden, 2012.
[10] J. Johansson and L. Laine, Bebyggelsens motståndsför¬måga mot extrem dynamisk belastning, Del 1: Last av luftstötvåg (The resistance of housing settlement subjected to extreme dynamic loading. Part 1: Load of shock wave in air. In Swedish.), Swedish Civil Contingencies Agency, Publ. no. MSB449, Karlstad, Sweden, 2012.
[11] J. Johansson and L. Laine, Bebyggelsens motståndsför¬måga mot extrem dynamisk belastning, Del 2: Explosion i gatukorsning (The resistance of housing settlement subjected to extreme dynamic loading. Part 2: Explosion at an urban intersection. In Swedish.), Swedish Civil Contingencies Agency, Publ. no. MSB450, Karlstad, Sweden, 2012.
[12] J. Johansson and L. Laine, Bebyggelsens motståndsför¬måga mot extrem dynamisk belastning, Del 3: Kapacitet hos byggnader (The resistance of housing settlement subjected to extreme dynamic loading. Part 3: Building capacity. In Swedish.), Swedish Civil Contingencies Agency, Publ. no. MSB142, Karlstad, Sweden, 2012.
[13] L. Laine, Markstötvåg (Ground shock wave. In Swedish.), Swedish Civil Contingencies Agency, Publ.no. MSB344, Karlstad, 2012.
[14] J. Leppänen, Concrete Structures Subjected to Fragment Impacts – Dynamic Behaviour and Material Modelling, Department of Concrete Structures, Chalmers University of Technology, PhD Thesis, Publication 04:4, Göteborg, Sweden, 2004.
[15] J. Leppänen, Splitterverkan (Splinter effects, In Swedish.), Swedish Civil Contingencies Agency, Publ.nr MSB345, Karlstad, Sweden, 2012.
[16] U. Nyström, Modelling of Concrete Structures Subjected to Blast and Fragment Loading. Division of Structural Engineering, Chalmers University of Technology, PhD Thesis, no. 3486, Göteborg, Sweden, 2013.
[17] J. Johansson, Strukturrespons vid impulsbelastning (Structural response at impulse loading. In Swedish.), Swedish Civil Contingencies Agency, B03-101, 2014-04-16, Karlstad, Sweden, 2014.
[18] Modelica - A Unified Object-Oriented Language for Systems Modeling, Modelica Association, language specification and relevant documents can be freely downloaded at https://www.modelica.org, 2019.
[19] OpenModelica, an open-source Modelica-based modeling and simulation environment intended for industrial and academic usage, Open Source Modelica Consortium, can be freely downloaded at https://www.openmodelica.org, 2019.
[20] A. Öshcner, Elasto-Plasticity of Frame Structure Elements Modeling and Simulation of Rods and Beams, Springer Verlag, p588, DOI 10.1007/978-3-662-44225-8, 2014.
[21] L. Petzold, A Description of DASSL: A Differential/Algebraic System Solver, SAND82-8637, Applied Mathematics Division, Sandia National Laboratories, Livermore, CA, USA, 1982.
[22] Swedish Civil Contingencies Agency (MSB) documents can be freely downloaded at https://www.msb.se/skyddsrum, 2019.