Spatial reliability analysis of explosive blast load damage to reinforced concrete columns
Introduction
Accidental or malevolent explosions can cause serious damage to civilian and military infrastructure as well as inflicting personal injury or death. Blast loads and its impact on safety and performance of structures have received considerable attention in recent years. The US Army, Navy and Air Force combined manual TM5-1300 [1] contains a comprehensive background and empirical relationships for blast load to predict structural performance developed from extensive experimental data. Since reinforced concrete (RC) is the principal material used for civil and military engineering structures [2], many investigations have been conducted on the dynamic response of RC structures subject to blast loading. Wu [3] investigated the dynamic response of simply supported RC slabs subject to explosive blast loading, using finite difference analysis. Remennikov [4] conducted research on predicting the effectiveness of blast wall barriers using experimental data and a neural network-based model.
Columns are the key load-bearing elements in frame structures and exterior columns are probably the most vulnerable structural components to terrorist attack. Failure of a critical column can lead to progressive collapse and large loss of life. The preferred method of attack continues to be Improvised Explosive Devices (IEDs), often through suicide tactics, against buildings and transport infrastructure. Moreover, military planners are under greater scrutiny to ensure that unintended damage or injury to civilians (collateral damage) by targeted ordnance is minimised. Hence, predicting the likelihood and extend of infrastructure damage and casualties due to explosive blast loading is topical focus for research, for both terrorist attack and targeted ordnance delivery. In recent years, much research is conducted on RC columns subject to explosive blast loading. Shi et al. [5] proposed a numerical method to generate pressure-impulse diagrams for RC column damage to blast loads. Bao and Li [6] and Wu et al. [7] conducted field tests using near-field explosive charges on two RC column specimens to validate their numerical simulations, then an extensive parametric study was developed to investigate the relationship between residual axial capacity and structural and loading parameters. Fujikake and Aemlaor [8] qualitatively and quantitatively investigated the damage of RC column by blast tests. Hao et al. [9] developed numerical simulation of blast wave interaction with RC columns, using AUTODYN 3D. Li et al. [10] analysed progressive collapse of RC frame structures by considering failure of columns induced by blast loading.
However, there are considerable uncertainties associated with material properties, dimensions, structural response, blast loading and expected damage which are not considered in those deterministic studies. Structural reliability and the inclusion of stochastic methods in structural simulations have been well developed, but there are few applications in explosive blast loading. Low and Hao [11], [12] considered the stochastic parameters describing explosive loads and computed probabilities of failure for RC slabs. Stewart et al. [13] described a general framework for probabilistic and structural reliability analysis of structural systems. Stewart and Netherton [14], [15] and AI-Habahbeh and Stewart [16], using probabilistic analysis, modelled the damage and safety risks of monolithic glazing and unreinforced masonry to explosive blast loads. Hao et al. [17] conducted a structural reliability analysis of RC columns using regression functions to correlate changes in parameter values to changes in RC resistance. Eamon [18] developed a procedure to assess the reliability of concrete masonry unit infill walls subjected to blast loading. Recently, Kelliher and Sutton-Swaby [19] combined Monte Carlo methods with a simplified but conservative progressive collapse RC structural model. However, many of these studies used simplified probabilistic blast loading models and finite element models, and all assumed homogeneous material and dimensional properties. Due to the spatial variability of workmanship, environmental and other factors, it is recognised that the material and dimensional properties of a concrete structures will not be homogeneous (eg. [20], [21]).
In this paper, Monte-Carlo simulation iterations and numerical methods are used to predict the damage of RC columns subjected to blast loading based on the explicit FEM software LS-DYNA. The prediction of damage is based on load-bearing capacity of the structure. The structural reliability analysis calculates: (i) variability of structural response and (ii) damage and collapse risks for RC columns subject to various explosive threat scenarios. Concrete compressive strength and cover are taken as spatial variables in this research and the reliability analysis of both non-spatial and spatial models are compared. The variability of blast loading is also taken into consideration. A terrorist VBIED (Vehicle Borne Improvised Explosive Device) scenario is considered to reflect the concerns and reality of current terrorist threats [22]. Therefore the blast scenarios considered herein are 50 kg (small VBIED), 100 kg (car-size) and 1000 kg (truck-size) of home-made ANFO (Ammonium Nitrate Fuel Oil) detonated at various stand-off distances from a typical RC column. The reliability analysis allows Blast Reliability Curves (BRC) to be generated – these represent damage and collapse risks as a function of stand-off.
If protective measures, such as bollards or other perimeter security measures, allow the stand-off to be increased, then BRCs obtained from structural reliability and probabilistic methods may be used to assess risk reduction due to these protective measures. A decision analysis can then consider threat likelihood, cost of security measures, risk reduction and expected losses to compare the costs and benefits of security measures to decide which security measures are cost-effective, and those which are not. For additional and wider-ranging assessments of the issues raised and the approaches used, see Stewart [23], [24], [25] and Mueller and Stewart [26], [27].
Section snippets
Structural reliability
The probability of damage to infrastructure conditional on the occurrence of a specific threat iswhere G(X) is the limit state function, and X is the vector of all relevant variables. Structural systems damage or collapse takes place when load effects (S) exceeds resistance (R), so G(X) = R−S where G(X) = 0 defines the boundary between the ‘unsafe’ and ‘safe’ domains [28]. The limit state functions can be expressed in terms of structural damage, safety hazards or casualties.
Probabilistic modelling of structural response
The RC
Random field analysis
Reinforced concrete construction involves various processes including concrete batching, onsite dimensional set out, reinforcement placement, compaction of the concrete and curing. The nature of these processes introduces the potential for substantial variability of concrete quality due to variations in work practices and environment. In order to predict more accurately RC reliability, the spatial variability of concrete strength and concrete cover are incorporated.
The midpoint method is used
Probabilistic blast load model
Clearly, structural reliability is sensitive to the variability of loads. Therefore, quantifying the variability of blast load is important in order to realistically assess structural reliability. It is observed from field testing that the blast load experienced by a target structure, for apparently similar circumstances, will not always be the same. The variability in blast loading can be traced to:
- (a)
Parameter uncertainty,
- (b)
Inherent variability – natural, intrinsic, irreducible uncertainty of a
Structural reliability analysis
The reliability analysis is complicated since the structural system failure modes are neither statistically independent nor fully dependent. Load and resistance are not statistically independent, and structural response will be calculated from a non-linear FEA. So a closed form solution is not readily tractable. Hence, the probability of damage will be obtained from a stochastic FEA which will utilise event-based Monte-Carlo simulation (MCS) analysis. This will enable the progression of damage
Results
The VBIED blast scenario considered is three masses of ANFO (50 kg, 100 kg, 1000 kg) detonated from R = 0 m to R = 30 m from the front face of the RC column. Due to high computational demand associated with LS-DYNA, N = 100 simulation runs for each scenario were used to generate distribution of residual load-carrying capacity and Damage Index of the post-blast column, and estimates of probability of damage and collapse. Stochastic analyses were conducted for (i) resistance parameters without spatial
Further work
The spatial reliability model developed in this research makes use of new and existing models to predict the probability of damage of RC columns subjected to explosive blast loading. There exist several areas for further work in the improvement and validation of these models. In this paper, the peak pressure was applied on one face of the column. If pressure on side faces and rear face of the column are considered, the prediction will be more accurate. The estimation for the scale of
Conclusions
This paper has described the process and models used for a stochastic analysis of the damage of RC columns subject to explosive blast loading due to considerable uncertainties associated with structural response and blast loading, and spatial variability of concrete compressive strength and concrete cover. Monte-Carlo simulation methods are used to quantify the probability of damage of RC columns based on the explicit FEM software LS-DYNA. The prediction of damage is based on axial
Acknowledgements
The authors acknowledge support for this research provided by the Australian Research Council. The first author also appreciates the financial support provided by the China Scholarship Council and The University of Newcastle. Dr Michael Netherton is also gratefully acknowledged for advice about probabilistic blast loading.
References (52)
- et al.
Dynamic response of a reinforced concrete slab subjected to air blast load
Theor Appl Fract Mech
(2011) - et al.
Predicting the effectiveness of blast wall barriers using neural networks
Int J Impact Eng
(2007) - et al.
Numerical derivation of pressure-impulse diagrams for prediction of RC column damage to blast loads
Int J Impact Eng
(2008) - et al.
The effects of explosive mass ratio on residual compressive capacity of contact blast damaged composite columns
J Constr Steel Res
(2011) - et al.
Reliability analysis of reinforced concrete slabs under explosive loading
Struct Saf
(2001) - et al.
Reliability analysis of direct shear and flexural failure modes of RC slabs under explosive loading
Eng Struct
(2002) - et al.
Security risks and probabilistic risk assessment of glazing subject to explosive blast loading
Reliab Eng Syst Safe
(2008) - et al.
The effects of explosive blast load variability on safety hazard and damage risks for monolithic window glazing
Int J Impact Eng
(2009) - et al.
Stochastic representation of blast load damage in a reinforced concrete building
Struct Saf
(2012) Spatial variability of pitting corrosion and its influence on structural fragility and reliability of RC beams in flexure
Struct Saf
(2004)
Spatial time-dependent reliability analysis of corrosion damage and the timing of first repair for RC structures
Eng Struct
Risk-informed decision support for assessing the costs and benefits of counter-terrorism protective measures for infrastructure
Int J Crit Infrastruct Prot
Uniformity of in situ properties of self-compacting concrete in full-scale structural elements
Cem Concr Compos
Finite difference analysis of simply supported RC slabs for blast loadings
Eng Struct
Residual strength of blast damaged reinforced concrete columns
Int J Impact Eng
Damage of reinforced concrete columns under demolition blasting
Eng Struct
Numerical simulation of blast wave interaction with structure columns
Shock Waves
A new method for progressive collapse analysis of RC frames under blast loading
Eng Struct
Terrorism risks and blast damage to built infrastructure
Nat Hazards Rev
RC column failure probabilities to blast loads
Int J Protective Struct
Reliability of concrete masonry unit walls subjected to explosive loads
J Struct Eng
Blast load variability and accuracy of blast load prediction models
Int J Protective Struct
Acceptable risk criteria for infrastructure protection
Int J Protective Struct
Cost-effectiveness of risk mitigation strategies for protection of buildings against terrorist attack
J Perform Constructed Facil
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