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Ph.D. Thesis Introduction

Blast resistance assessment of structures: explicit finite element simulations and fragility analyses

In the mid-twentieth century Abraham Maslow wrote a paper on the hierarchy of the human needs [Maslow 1943].  Considering for instance the physiological needs (see Figure 1‑1) the humans should have employment, health, and property; in other words the human needs security.  In general, security is guaranteed by a secure shelter, such as a secure residence, a secure office, and a secure city.  Without security a society cannot develop and prosper.  

Having security means to be protected by adverse environmental conditions, daily human activities, animals, and man-made attacks.  Moreover the perception of a risk due to each one of the mentioned hazards is not perceived with the same intensity by the community [Pidgeon 1998] and the perception of the risk is generally variable.  In particular the hazard due to man-made attacks is mostly perceived in the beginning of the twenty-first century. 

The protection of buildings and critical infrastructures against man-made attacks is a priority for a stable and secure society.  A failure of the security system of a community leads to a socio-economic instability and consequently to a decline of the community.  Nowadays like in the past a protective design [Krauthammer 2008a] against man-made attacks is imperative, especially considering that the free world is constantly engaged by terrorism that aims at the destabilization of the community. 

Figure 1‑1: Maslow’s hierarchy of needs [Maslow 1943]

In fact, terrorism is the new kind of warfare.  Records of terrorism activities provided by the U.S. Department of State report that 85 % of terrorist attacks is conducted by explosives devices [DoS 2003, DoS 2004, DoS 2005, and DoS 2006].  This fact leads to the need to design buildings and critical infrastructures against explosions.  Moreover, also accidental explosions in explosive storage facilities (military or civil) and in the urban contest are considered to be a serious threat for the security of a community. 

Briefly designing structures for blast load is a security’s prerogative of the community.  Without an adequate level of protection a prosperous community cannot withstand the threat of the terrorism and a socio-economic decline is inevitable. 

A protective construction should principally guarantee the maximum reasonable survivability of the occupants.  If the prevention strategies of defense (e.g. intelligence and police activities) fail, the design for blast is the only chance to limit the consequences of an explosion. 

Approaches to design for blast can be divided in either deterministic or probabilistic.  Generally a facility is designed based on a standard threat so a deterministic approach is used.  However if the statistics of the threat and of the mechanical properties of the structure are known a probabilistic approach is preferred. 

A generic structure is composed by several structural elements (components) forming an organized structural scheme.  The structural response of the components is identified as “local response” (e.g. the structural response of a column); instead, the structural response of the overall structural scheme is identified as “global response” (e.g. the stability of a building after a column failure). 

The resistance of a generic structure subjected to a blast load is measured in terms of collapse resistance defined as the exceeding of a performance limit concerning the global and/or the local response.  

The collapse resistance can be assessed directly by applying the blast demand to the structure (un-decomposed approach) or by decomposing the collapse resistance (decomposed approach) in three components: the hazard mitigation (hazard), the local resistance (vulnerability), and the global resistance (structural robustness).  In the latter case the collapse resistance is determined quantifying the three components by a deterministic or probabilistic approach. 

Looking at the probabilistic approach the collapse probability is given by the product of each conditional probability of the collapse probability’s components.  In probabilistic terms commonly used in earthquake engineering (see [Bazzurro et al. 1998, Fragiadakis et al. 2013, and Kennedy et al. 1984]) the decomposed approach is called conditional approach and expressed formally by Eq. (1‑1).

 

Where H_i is the hazard related to the blast scenario “i” (where the scenario is defined by the parameters determining the intensity of the blast action), also known as Intensity Measure (IM) in other engineering fields [Whittaker et al. 2003, Ciampoli et al. 2011, and Reed et al. 1994], LD is the structural local damage, C is the collapse event, P[∙|∙] indicates a conditional probability, P[∙] indicates a probability, and the summation ∑ is extended to all scenarios. 

Following the decomposed approach, the left part of Figure 1‑2 shows the three components of the collapse resistance.  On the right part of Figure 1‑2 instead, there are the investigated methods for a quantitative assessment of the collapse resistance’s components and practical applications are presented for each component of the collapse resistance.

Figure 1‑2: Collapse resistance decomposition

Concerning the hazard mitigation, this Thesis focuses on the gas explosions in civil buildings.  Deterministic Computational Fluid Dynamic (CFD) simulations are carried out for assessing the influence of three crucial parameters determining the severity of the blast load due to the deflagration of a gas cloud.  These parameters are the room congestion, the failure of non-structural walls and the location of the ignition.  Each of these parameters can change drastically the blast demand on the structure.  Usually the room congestion is present in a building and it should be considered in the simulations; the failure of non-structural walls should be taken into account for not overestimating the overpressures generated by the explosion; instead the effect of the location of the ignition should be investigated by performing several simulations with different locations of the ignition (see section 2.3). 

The local resistance is investigated both deterministically and probabilistically.  As mentioned previously, with the term local resistance is intended the resistance of the single component of the structural system subjected to the blast load.  The fragility analysis, see [Bazzurro et al. 1998, Fragiadakis et al. 2013, and Kennedy et al. 1984], is carried out with two different intensity measures, and two different applications are proposed. 

• First a terroristic attack carried out by a probabilistically defined vehicle bomb is considered and a method for computing the fragility curves is provided for a concrete cladding wall panel subjected to blast loads.  The probabilities of exceeding the defined limit states are computed by both the uncoupled and coupled approaches [Reed et al. 1994] for testing both the proposed method for computing the fragility curves and the selected intensity measure (see section 3.1).

• After that, the accidental explosion of mortar rounds in a military facility engaging a steel built-up door is considered probabilistically.  In addition, a safety factor for carrying out deterministic analyses of steel built-up blast doors subjected to accidental explosions of mortar ammunitions is proposed.  Also for this second application the fragility analysis is validated by confronting the obtained results in terms of probability of exceeding a limit state with the results obtained with the uncoupled approach [Reed et al. 1994] (see section 3.2). 

The probabilistic study of the local resistance is developed in collaboration with the Prof. Charis Gantes and the Prof. Dimitrios Vamvatsikos of the National Technical University of Athens (NTUA) during the spring/summer 2013. 

The local resistance is also investigated deterministically by detailed explicit finite element simulations performed using LS-Dyna [LSTC 2012].  The blast generated demands can be categorized into far design range and close-in design range.  In the far design range the blast generated pressure demands can be considered uniform on the structure, while in the close-in design range blast pressures are non-uniform and the pressure magnitudes can be very high. 

• Concerning the far design range the National Science Foundation (NSF) funded a study made by the University of Missouri Kansas City (UMKC) to perform a batch of blast resistance tests on reinforced concrete slabs.  Based on these results, a Blast Blind Simulation Contest was being sponsored in collaboration with American Concrete Institute (ACI) Committees 447 (Finite Element of Reinforced Concrete Structures) and 370 (Blast and Impact Load Effects), and UMKC School of Computing and Engineering.  The goal of the contest was to predict, using simulation methods, the response of reinforced concrete slabs subjected to a blast load.  The blast response was simulated using a Shock Tube (Blast Loading Simulator) located at the Engineering Research and Design Center, U.S. Army Corps of Engineers at Vicksburg, Mississippi.  A team for participating at the contest has been formed by the author of this Thesis Pierluigi Olmati (Sapienza University of Rome), Patrick Trasborg (Lehigh University), Dr. Luca Sgambi (Politecnico di Milano), Prof. Clay J. Naito (Lehigh University), and Prof. Franco Bontempi (Sapienza University of Rome).  The submitted prediction of the slab’s deflection was declared The Winner of The Blast Blind Simulation Contest (http://sce.umkc.edu/blast-prediction-contest/ - accessed August 2013) for the concurring category (see section 3.3). 

• Regarding the close-in design range, concrete elements exhibit localized damage in the form of spalling and/or breach.  When the depth of the spall exceeds half of the element thickness breach often occurs.  The resistance to spall and breach in concrete elements is an important design consideration when close-in detonations of high explosives are possible.  Spall on the interior face of the structural element can result in the formation of small concrete fragments which can travel at hundreds of feet per second [DoD 2008] causing serious injuries and equipment damages.  In this Thesis, the spall and breach resistance is investigated for insulated concrete wall panels by detailed explicit finite element analyses performed using LS-Dyna [LSTC 2012].  The spall and breach resistance is assessed to be dependent by the thickness of the insulation that guarantees a gap between the exterior and interior concrete wythes (see section 3.4).  Moreover experimental tests were conducted at the Air Force Research Laboratory in Panama City, FL.  The report of the experimental test has to be approved for the “Statement A - for public realize and unlimited distribution” following the rules of the United State Department of Defense for being published (see section 3.4.3). 

The study on the spall and breach resistance of insulated concrete cladding wall panels was developed at the Lehigh University during the winter/spring 2012 in collaboration with Prof. Clay J. Naito (Lehigh University). 

Finally the global resistance of a structure is investigated by two methods.  As mentioned before, with global resistance is intended the resistance of a structural system against a failure of one or more structural components. 

• The first method is based on the consequence factor obtained confronting the elastic stiffness matrices of the damaged and undamaged structure.  This methodology takes into account the consequences of extreme loads on structures, focusing on the influence that the loss of primary elements has on the structural load bearing capacity.  Briefly a method for the evaluation of the structural robustness of skeletal structures is presented and tested in simple structures.  Following that, an application focuses on a case study bridge, the extensively studied I-35W Minneapolis steel truss bridge.  The bridge, which had a structural design particularly sensitive to extreme loads, recently collapsed for a series of other reasons, in part still under investigation.  The applied method aims, in addition to the robustness assessment, at increasing the collapse resistance of the structure by testing alternative designs (see section 4.1). 

• The second proposed method take account the non-linear dynamic behavior of a structure for assessing its structural robustness.  The method is developed for buildings and it is based on the hypothesis of the removal column scenario.  The column is suddenly removed and a non-linear dynamic analysis is carried out for assessing if the disproportionate collapse occurs, if not a non-linear static pushover is carried out on both the damaged and undamaged configuration of the building for estimating the residual capacity of the building.  This procedure is repeated both increasing the number of the removed columns and for several scenarios.  The robustness is so assessed for a steel tall building (see section 4.2). 

The following sections contain the carried out studies on the collapse resistance of structures under man-made or accidental explosions following the decomposition of the collapse resistance shows in Figure 1‑2.