Review on quick safety assessment of building structures in complex urban environment after extreme explosion events

Abstract

Extreme explosion events result in demands for emergency rescue service. From the civil engineering perspective, a quick safety assessment of building structures in the explosion’s vicinity will provide the emergency rescue committee with concrete support to make scientific decisions. In this paper, three primary issues, namely, inverse analysis of explosive characteristics, blast wave propagation in complex urban areas and blast-induced damage identification, are reviewed. These are often performed stepwise and form a multi-step whole to assist the emergency rescue service. The paper begins by introducing the inverse analysis of explosives based on craters, building damages and seismic or acoustic records. In this step, explosive characteristics, for example, charge type, original time, yield and location, could be produced and input into blast load calculation in the next step. Then, the existing literature on blast wave propagation and blast load determination is presented with close attention to complex urban environments. It shows that the current study remains in its infancy and relies on advancement in computational fluid dynamics (CFD). Besides, pressure–impulse (P-I) diagrams which predict the structural damage based on the calculated blast loads are illustrated. Onsite damage detection techniques, such as visual inspection, non-destructive testing (NDT) and vibration-based methods, are also discussed. The paper ends with a discussion of the shortcomings of previous work and the outlooks of further work.

Keywords

Quick safety assessment complex urban environment explosive characteristics blast loads blast-induced damage

Highlight

Three post-blast issues for quick safety assessment of buildings are reviewed;

The explosive inversion is based on crater, building damage and vibration signals;

Blast wave propagation in urban areas is affected by surrounding environments;

Structural damage identification uses pressure–impulse diagram and onsite detection;

Discussions and recommendations for further studies are provided.

Introduction

Extreme events, such as typhoon, earthquake, tsunami, fire and explosion, are continual threats to urban safety, which often lead to heavy casualties, property losses and adverse effects on political aspects. Human beings have been fighting against various natural disasters since ancient times. In contrast, from the 1940s onward, research on explosion-proof structures started attracting attention from scientists’ and engineers’ communities, especially after the occurrence of several terrorist bomb attacks.

The destructive power of an explosion is quite impressive and overwhelming. For example, on April 19, 1995, a truck loaded with nearly 5000 pounds of ammonium nitrate fuel oil (ANFO) was detonated in front of the Murrah Federal Building in Oklahoma City. It was reported as the biggest terrorist attack on the mainland of the United States before the 911 event. The malevolent bombing killed 168 people, including 19 children, and caused the full collapse of half of the reinforced concrete building (Osteraas, 2006). Later, on June 25, 1996, another vehicle bomb attack against the Khobar Towers compound in Dhahran, Saudi Arabia, broke out, taking 19 US airmen’s lives and leaving 420 injured (Donald et al., 2004). Both explosion attacks caused significant damage to the surrounding buildings.

Worse of all, because of outdated planning of urban areas, city scale has gradually expanded with residential areas or commercial areas getting closer to the industrial zones. In this circumstance, the situation would be catastrophic if industrial processes were not well supervised. Recently, a devastating chemical explosion caused by about 2750 metric tons of ammonium nitrate and many fireworks precariously stored in the warehouse struck Beirut Port in Lebanon. The accident resulted in almost 200 fatalities, over 6000 injuries and more than 100 missing. It destroyed numerous houses and facilities, leaving nearly 300,000 people homeless, and the economic loss exceeded 10 billion dollars (El Sayed, 2020). Shortly after the explosion, the United States Geological Survey (USGS) declared an earthquake with a local magnitude of 3.3. Also, a crater with a diameter of about 120 m was observed in situ. In China, hundred-ton-scale chemical explosion accidents occurred several times too, for example, the ‘8·12’ Tianjin Port Explosion Event in 2015 and the ‘3·21’ Xiangshui Explosion Event in 2019, in which the energy released was equivalent to almost 450 tons and 260 tons of TNT, respectively (Ministry of Emergency Management of the People’s Republic of China, 2017, 2019). One noticeable observation is that ammonium nitrate was often present in historical bomb attacks and chemical accidents, as is illustrated in the above cases. Ammonium nitrate is a common and essential material in industrial manufacturing, generally used for producing fertilizers and fireworks. Preventive measures, such as strict regulation on the purchase, transportation, storage and fabrication of ammonium nitrate, could be implemented to prevent explosion incidents. However, just in case of malfunction of preventive measures, an effective post-blast emergency response system is desirable to mitigate the blast effects.

The emergency response to catastrophic explosion events is a comprehensive project, which demands multi-disciplinary coordination and cooperation involving but not being limited to medicine, meteorology, environmental science, civil engineering and forensic technique. It is a race against the clock. However, the tremendous energy released by an explosion would cause severe casualties and leave a mess on the scene, which is usually fraught with great dangers such as secondary explosions and poisonous ingredients. Besides, the blast wave and ground motion induced by the high-volume explosives will continue to propagate and interact with the surrounding buildings, leading to local damages or even collapse of the building structures. It was reported that up to 154 rescuers sustained trauma in the Khobar Towers compound (Donald et al., 2004). Therefore, the rescue service must be prepared carefully before being executed to minimize the harm from potential risks.

For civil engineering communities, the main task is to provide reliable information on the blast-surviving structures. However, the accompanying contradiction is the balance between time and accuracy. The aid community believes there is a ‘golden 72-hour window’ after a disaster, during which victims are most likely to survive. As a result, assessment methods using complicated models are not cost-effective. A practical solution to this dilemma is to develop a quick safety assessment methodology for the structure buildings under blast attacks, and it should be a compromise proposal between time and accuracy. In this regard, a multi-step approach, which mainly contains three primary elements, namely, inverse analysis of explosives, blast waves propagating in complex geometries and blast-induced damage identification of building structures, is advised. The above three elements are executed stepwise and combined to produce a reliable evaluation of the residual bearing capacity and remaining useful life of buildings against external interferences.

A quick safety assessment will also underlie the following reconstruction stage, in which time is no longer limited, and accuracy is the first concern. Detailed identification and classification of building structures require thoroughly preparing to provide scientific support for the ultimate disposal of buildings, such as reservation (without any repair), repair (with slight or heavy repair) and total removal. Then, different actions corresponding to different disposals are undertaken. For damaged buildings to be removed, the subsequent work is relatively simple without much extra effort. For those to be repaired, a more specific scheme is required, in which new materials and advanced technologies are preferred.

This paper presents a literature review on the quick safety assessment of building structures in complex urban environments after extreme explosion events. Three primary issues, inverse analysis of explosives, blast wave propagation and blast-induced damage identification of buildings, are reviewed in order. Given the state of the art, in this paper, the inverse analysis of explosives based on craters, seismic or acoustic records, and building damage is introduced at first. Then, existing studies on the main blast effects and shock waves in complex geometries are discussed. The inverse analysis of explosives produces the explosive characteristics, such as location, original time and TNT equivalency, which will be entered into the blast wave propagation in specific areas to estimate the blast loads on structural facades. Besides, the pressure–impulse diagram (P-I diagram) is presented to indicate the blast-induced damage of building structures based on the calculated blast loads. The feasibility of onsite damage detection techniques, such as visual inspection, non-destructive testing (NDT) and vibration-based methods, are also discussed. These three issues constitute the entire body of the quick safety assessment of post-blast structures. The paper ends with a discussion of shortcomings of current researches and outlooks for further work.

Inverse analysis of explosives

Inverse analysis of explosives mainly refers to the identification of explosive characteristics such as contents, yield, original time and detonated location using various blast-induced effects. It is primarily intended for forensic investigation, for example, criminal tracking in deliberate bombing attacks. For civil engineering communities, inverse analysis of explosives is necessary for acquiring the inputs of blast load calculation and structural damage prediction. For practical uses, studies on this issue are currently focusing on three pieces of evidence: crater, damaged structures and seismic or acoustic records.

Craters

The crater is the direct evidence for deriving explosive characteristics since it is seated in the explosion centre. Figure 1 depicts a typical blast-induced crater profile caused by a buried explosion. As is shown in Figure 1, the crucial dimensions of craters include the radius (apparent or true), the depth and the expelled soil volume measured from the original ground surface.

For buried explosions, in the past, for a long time, most experimental results showed the crater dimensions conformed to the cubic-root scaling rule. Later studies found that in large-scale explosions, the quarter-root law was more accurate. Based on the statistical analysis of the experimental data from the underground blast in Nevada desert alluvium, the 3/10 root similarity law was advised by Chabai (1965). Further, Baker et al. (1991) proposed a theoretical explanation for different similarity laws through the dimensional analysis and obtained a unified similarity law for the underground explosion crater, as shown in equations (1) and (2).

R / d = f (\frac{W^{1 / 3}}{σ^{1 / 3} d}, \frac{W^{1 / 4}}{K^{1 / 4} d})

(1)

R / d = f (\frac{W^{7 / 24}}{σ^{1 / 6} K^{1 / 8} d})

(2)

Where R represents the radius of the crater, d denotes the buried depth of explosive, W is the explosive energy, σ is a parameter related to soil strength (in unit consistent with pressure) and K denotes the parameter associated with the gravitational field (in the unit consistent with the unit weight).

The first term in parentheses of equation (1) represents the soil strength effect, and the second term stands for the effect of the gravitational field. Cubic-root similarity law can be obtained if the influence of gravity field is ignored, while neglecting the effect of soil strength will lead to the quarter similarity law. Chabai’s work indicates that equation (1) could be facilitated by simply multiplying the two terms in parentheses, as shown in equation (2). The formulae show an acceptable deviation in case of large charge mass or shallow buried depth.

The buried explosion is not the case of inverse analysis considering that almost all explosion incidents, deliberate and accidental, occur on or above ground level. For unburied explosions, Kinney and Graham (1985) established an empirical relationship between the crater’s diameter and TNT equivalency (c.f., Equation (3)), and the coefficient of variance of the empirical equation is about 30%. They also concluded that the crater depth approximately equalled one-quarter of the crater diameter.

D = 0.8 W^{1 / 3}

(3)

Ambrosini et al. (2002) proposed empirical formulae for explosions below, on and above the ground surface, as shown in equations (4) and (5). It should be noted that the formulae have certain limitations for large-scale explosions since they were derived from some small-scale experiments (1–10 kg).

l o g (R / | d |) = 1.241 l o g (W^{1 / 3} / | d |) - 0.818

(4)

D / H_{2} = 5.78 + 5.05 | d |

(5)

The United States and the former Soviet Union have conducted many large-scale surface explosions under different geological conditions (Adushkin and Khristoforov, 2004; Chabai, 1965). The former had a TNT equivalency between 4 kilos and 5000 tons, and the latter ranged from 1 to 5000 tons. These experiments collected a large body of crater dimension data and resulted in a series of power functions, which showed approximate results to equation (3). In most cases, the power functions showed approximative exponents and coefficients, and the coefficient of the chemical explosion is slightly greater than that of the nuclear tests.

Many other types of experiments, such as laboratory tests (Pacheco-Vázquez et al., 2017) and centrifuge tests (Brownell and Charlie, 1992; Kutter et al., 1988; Schmidt and Holsapple, 1980), were also available as complements to outdoor tests. Meanwhile, the numerical technique was also developed and its high fidelity was highlighted in parametric studies (Ambrosini et al., 2004; Ambrosini and Luccioni, 2008; Bjelovuk et al., 2015a, 2015b; De, 2012; Luccioni et al., 2009; Nagy et al., 2007; Nagy, 2015; Wang et al., 2018). The emerging artificial intelligent algorithms also provide an insight into the inverse analysis of explosives (Zhou et al., 2017). These advancements are continuously motivating the development of inverse analysis of explosives based on craters.

The correlations based on the dimensions of the crater are dependent on several parameters, such as soil properties, explosive configuration and geological conditions. Recent observation on the Beirut explosion incident has reported a large deviation if using these correlations. According to the hydrographic survey by the Lebanese Navy (Aouad et al., 2021), the diameter and depth of the crater by the explosion in Beirut are about 120 m and 4.0 m, respectively, and thereby, the estimated yield by Kinney and Graham’s correlation is about 3375 tons, which is significantly overestimated since the ammonium nitrate illegally stored was only 2750 metric tons. Further, the observed depth/diameter ratio is about 0.033, which is also much smaller than 1/4 declared by Kinney and Graham. Similar observations had also occurred in the ‘8·12’ explosions in Tianjin Port, China (97 m in diameter and 2.7 m in depth, 450 t) and the ‘3·21’ explosion in Xiangshui, Jiangsu Province, China (75 m in diameter and 1.7 m in depth, 260 t).

Building damage (window breakage included)

Craters only provide a little information, and the yield derived from one crater often contains error as much as one order of magnitude. Sometimes, it is even worse that there is no crater found in sites, and inverse analysis based on crater evidence is not applicable. In this situation, structural damages, such as damaged buildings and window breakage, could be utilized to perform the inverse analysis of explosives. For damaged buildings, there are two different methodologies. The first methodology is based on the relationship between charge mass and average circle radius (W-R relationship or theory of safety stand-off distance). An example is given in equation (6) (Gilbert, 1994). The inverse form can be employed for the inverse calculation of explosive mass if given the distribution of damaged buildings, as shown in equation (7).

A C R / R B = \frac{k \cdot W^{1 / 3}}{{[1 + {(W_{0} / W)}^{2}]}^{1 / 6}}

(6)

W = \sqrt{\frac{1}{2} {(\frac{A R C}{R B \cdot k})}^{3} \cdot [{(\frac{A R C}{R B \cdot k})}^{3} + \sqrt{{(\frac{A R C}{R B \cdot k})}^{6} + 4 M_{0}^{2}}]}

(7)

Where W is the charge mass,

k = 7.1 {m / kg}^{1 / 3}

and

W_{0} = 3175 kg

. ACR and RB are the average circle radius and the modified constant for different damage levels, as listed in Table 1 (Gilbert, 1994). For damage level B, the ACR is defined as the radius of a circle drawn around an explosion centre, inside which the number of damaged buildings of level C is equal to that of level B outside.

Table 1.

Specification of damage levels and RB ratios (Gilbert, 1994).

Damage level	RB	Description
A	0.675	Houses are demolished
B	1.00	Houses are so badly damaged that they are beyond repair and must be demolished
Cb	1.74	Houses are uninhabitable and need extensive repairs
Ca	3.0	Houses are uninhabitable but can be repaired quickly
D	6.0	Houses remain habitable with sustained damage to ceilings and tiling, battens and roof coverings, and minor fragmentation effects on walls and window glazing

Van Der Voort et al. (2015a, 2015b) re-analysed the observed data and showed the accumulative normal distribution law for the number of damaged buildings against stand-off distance for each damage level. Their applications of the theory to the Enschede firework accident showed reliable results consistent with the technical reports. However, the above work is based on the statistical analysis of air raid cases of UK brick dwellings during WWII. It may not be applicable for other types of buildings or explosives.

Another method is relatively intuitive and straightforward. In this methodology, a series of three-dimensional numerical models with different explosive charges and locations are established to simulate the blast wave propagation in city streets, and apposite pressure–impulse diagrams (c.f., the latter section titled with Blast-induced damage identification) are selected for structural damage assessment. By comparing the simulations with the forensic records, the best fitting one is accepted to represent the explosion case. Ambrosini et al. (2005) and Luccioni et al. (2005) once applied this method to the AMIA (Israel–Argentina Mutual Association) building attack. The strategy of inverse analysis based on window breakage is similar but uses probabilistic P-I diagrams (Van Der Voort et al., 2015a, 2015b).

Normally, these two methods based on damaged buildings give more reliable results than that of crater evidence. However, these methods are of lower efficiency and higher cost because they require a laborious investigation of damaged buildings and window breakage. For emergent rescue services, they are not economical, especially in complex urban environments.

Seismic and acoustic records

Craters and structure damages are only available inside the explosion sites, and it is very tough to collect the evidence as soon as possible. Outside the explosion sites, the enormous energy released by an explosion will cause the ground and air to vibrate and spread energy outward in the forms of seismic waves and acoustic waves. By digging into the records from seismic stations and acoustic arrays, analysts can further determine the origin time, the location and the magnitude of an explosion. The research is still in the exploratory stage and focuses on case studies. In 2008, two main chemical explosions occurred successively in Tianjin Port, China, and the seismic and acoustic data were recorded and analysed. Then, the original time, relative position and earthquake magnitude were determined (Deng et al., 2018; Li and Tian, 2015; Ren et al., 2016; Zhao et al., 2016). Further case studies on the combined analysis of infrasound and ground motion are available (Ceranna et al., 2009; Ottemöller and Evers, 2008; Schneider et al., 2018).

At present, inverse analysis of seismic and acoustic records is quite successful for predicting the explosion’s original time and location but fails to capture a reliable prediction of TNT equivalency. The reason is that the empirical formula for calculating TNT equivalency arises from statistical analysis of underground explosion cases (such as underground nuclear explosions and mine explosions). Studies on surface explosions, especially those with small yields, are still rarely reported.

Remarks

The inverse analysis of explosives based on craters, building damages and seismic and acoustic records shapes the foundation of identifying explosive characteristics. A few works on the casualties, photographs, videos and debris are also occasionally reported. Following the Beirut explosion on August 4, 2020, there was a burst of efforts in the field of new-fashioned methods for explosive inversion. For instance, by analysing the fireball images from social media videos, Diaz (2021) reported an estimation of 300–900 tons’ TNT equivalency through Taylor’s method (1950a, 1950b), while Aouad et al. (2021) claimed a yield of 120–280 tons. Besides, by using the arrival time of blast wavefront through social media, Rigby et al. (2020) declared a TNT equivalency of 550–1120 tons, while a predicted yield of 407–936 tons TNT was determined by Stennett et al. (2020). The estimations basically agree with the predicted 130–2000 tons using seismic and infrasound data (Pilger et al., 2021).

The disadvantages of using a single blast effect for explosive inversion are considerable since each method has its own advantages and drawbacks. Although empirical approaches through crater data and seismic records are relatively easy to perform compared to inverse methods using building damages and social videos; however, the range of predicted results is normally too large for blast load estimation. Besides, in the case of vapour cloud explosion (VCE) or small-scale explosion on firm ground, no crater is observed. The information of ground motion and infrasound depends on the array arrangement around and instrument capacity, and the ideal record is affected during its transmission. The inversion analysis of explosives based on building damages requires extensive in-site surveys, which is time consuming and laborious, thus reducing the inversion efficiency. Therefore, a union of multiple factors is inevitable for common usages. The Netherlands Organization for Applied Scientific Research (TNO) developed a soft program called IEA (Inverse Explosion Analysis) using various observed damages to estimate the charge location and equivalency (Van Der Voort et al., 2015a, 2015b). Zhou (2014) used the so-called ‘data-driven’ method to combine crater, ground motion and window debris for a comprehensive inverse analysis, which declared that the multi-factor inversion method had a higher superiority. Fang et al. (2017) also combined seismic wave, crater and building damage radius to estimate the TNT equivalency of the two major explosions in the Tianjin Port explosion on August 12, 2015, and the results by the evidence show good consistency. So far, the explosive inversion techniques are continuously developing. There are still many technical problems to be solved, for example, the error of the current inverse analysis and the viability of TNT equivalency in gaseous and dust explosions. There is still a long path to desirable outcomes.

Blast wave propagating in complex urban areas

The tremendous energy released by an explosion will spread outward as shock waves. A typical pressure history of a fixed point around the free explosion scenario is described in Figure 2, which is named the Friedlander waveform (Smith and Hetherington, 1994). The all-important characteristics of a blast wave mainly include peak overpressure, duration, positive impulse and negative impulse. The Hopkinson–Cranz similarity law or the cubic-root scaling rule indicates that in the atmospheric environment, two unrestrained explosives with similar shapes will generate the proportional quantities at the same scaled distance $Z = R / \sqrt[3]{W}$ (R is the distance from explosive centre to the measuring point and W is the charge mass), for example, the pressure scale is one, and the scales of time and impulse are equal to the geometric scale (Baker et al., 1983).

Blast wave propagation in urban areas is strongly affected by terrains and structures. As a result, buildings with an identical stand-off distance from the explosion centre might suffer different blast loads and damage levels. Clear evidence emerged in many explosion cases during the past decades. If buildings are coded with different colours corresponding to different damage levels, non-circular colour shapes would be observed. Empirical models (Hyde, 1992; UFC 3-340-02, 2014) derived from free-field tests or an isolated structure are no longer appropriate for predicting blast loads in densely built-up environments since no confining effect or shielding effect on blast wave propagation is included. There are many experimental and numerical works performed to narrow the gap. Two literature reviews on this issue are also available (Li et al., 2006; Smith and Rose, 2006).

The explosion test is a necessary means to inspect the external effects on blast wave propagation. However, all explosion tests are currently reduced scale because of the limitations of cost, safety requirements and site conditions. Many experimental studies indicated that the confining or shielding effects on blast wave propagation could be pronounced. A laboratory test on a straight street with a simple T-junction at both ends (as is depicted in Figure 3) suggested that the dimensionless peak, overpressure (defined as the ratio of reflected peak overpressure to that produced in free-field tests) could even reach four or five where the scaled distance was in the interval between 2 and 10 kg/m^1/3 (Smith et al., 2001). Smith et al. (2001) discussed the positive impulse enhancement using a series of reduced-scale experiments on five typical street configurations (crossroads, T-interaction, right angle, straight and dead-end, as shown in Figure 4). Their experiments showed that the dimensionless positive impulse (defined as the ratio of the reflected positive impulses to that in free-field tests) would go up as the scaled distance increased. Among these five road layouts, the dead-end road showed the maximum confining effects, with the right angle, straight street, T-intersection and crossroad arranged in descending order. It is reasonable considering the change of closure properties. A gram-range (about 1.0 g) charge experiment further confirmed the confining and shielding effects of city streets, and preliminary discussions on the impacts of street width and height were given (Fouchier et al., 2017).

A large body of small-scale explosive trials has provided a reliable understanding of structure effects on blast wave propagation. Meanwhile, in most cases, especially for parametric analysis, researchers might prefer numerical studies, and they usually adopt experimental records for validity. Rose and Smith (2002) worked on the quantitative effects of street width and building height on both positive and negative blast impulse by implementing a series of numerical simulations with varying street widths and building heights. It showed that positive phase impulse would monotonously converge to its maximum with increasing building heights. Buildings higher than one-fifth of the maximum scaled distance were effectively tall. In a straight street composed of sufficiently tall buildings, positive impulse varied inversely as street width changed. Unlike positive phase impulse, the negative phase impulse first increased to a maximum at a scaled building height ranging from 3.2 to 12.8 m/kg^1/3 and then decreased as the scaled height of buildings went up. Another important observation was that the positive impulse exhibits like the negative phase impulse if building facades were absent. Otherwise, as scaled height increased, the positive phase impulse became significantly larger inside a region where the scaled distance was less than about 2.0 m/kg^1/3. The negative phase impulse would capture its predominance, where the scaled distance was beyond 2.0 m/kg^1/3. This rule was said to account for the glazing elements drawn out into the streets in some explosion cases.

The numerical technique is a useful tool for predicting blast loads in complex environments. Remennikov (2003), Remennikov and Rose (2005) used the Air3D program to investigate the shielding and enhancement factor of adjacent structures on blast loads. Their analysis of numerical results showed consistency with that of Smith et al. Programs like LS-DYNA and AUTODYN were also widely utilized to investigate the blast wave propagation in several city configurations (Codina et al., 2013; Fedorova et al., 2016; Johansson et al., 2007; Shi et al., 2007; Sklavounos and Rigas, 2004). During the last two decades, the rapid development of high-performance computers and various commercial programs have boosted the numerical simulating analysis on this topic, but numerical studies had stayed on several relatively simple street layouts. It was because in actual situations, especially in modern city areas, numerical modelling and calculating still consume massive computer resources. As is expected, the efficiency of numerical simulations mainly depends on the capacity of computers and hydrocodes. The set-up and modification of numerical models also take time and demand specialities. Manual manipulation is only acceptable in some studies involving a small group of buildings or several typical street layouts. The complexities of numerical techniques have strongly limited their application in the emergent rescue stages, especially in urban areas hit by large-scale explosions. From this, a multi-stage strategy, in cooperation with geographic information system (GIS), grid refinement and data remapping technique, was introduced (Cowler et al., 2004). The multi-stage analysis comprises two steps. The first step is the initial expansion stage, starting from the ignition of explosives to the interaction with obstacles. In this stage, although the high frequency of blast waves demands a small grid size as a guarantee of accuracy, the blast wave propagation can be simplified as spherical symmetry and modelled in a one-dimensional (1D) way. The second step starts from the contact with obstacles, and a three-dimensional (3D) model follows to account for the boundary influence. Because of the decrease in the frequency of the blast waves, the second stage can further be divided into several substages and enlarge the grid size accordingly. Recently, the multi-stage analysis strategy got popularized for blast load prediction in large-scale urban areas.

There were still many other strategies for improving numerical efficiency, for instance, new computational fluid dynamics (CFD) code (Hanka et al., 2014), hierarchical adaptive mesh refinement (HAMR) technique (Coirier and Bayyuk, 2002) and adaptive virtual cell embedding (VCE) method (Tang, 2007, 2008). Wang et al. (2017) proposed an overset grid meshing strategy based on a component view, which allows for idealized meshes in an automated fashion. Mohr et al. (2019) developed a 3D reconstruction method by combining geo-referenced aerial images and semantic information through deep neural networks. An advanced computational package specialized in rapid assessment and accurate prediction of the blast waves in complex scenarios was also reported (Cullis et al., 2016).

Most studies assumed that the ground and structures experiencing blast were perfectly rigid with no ventilation or deformation. However, light glazing and cladding elements were often observed destroyed in explosion sites, which enabled the ingress of the blast wave into the buildings to cause further casualties inside buildings and reduced the blast loads in the distance. Smith et al. (2003) employed the so-called ‘porosity effect’ to depict the influence of building facade failure on blast wave propagation. However, the small-scale experiments provided few promising results, and they continued to accomplish their work through numerical simulations. According to the numerical results, blast impulse would decrease obviously as the building facade porosity goes up from 0 to 100%, and the decreasing rate depends on the scaled distance. Meanwhile, the blast wave would interact with the ground and structures, whereby the energy dissipates by creating craters, generating ground motion and causing plastic deformation of structures. The calculating result would be conservative if not considering these effects, but the overestimation may lead to an unsatisfactory evaluation. Till now, the influence of deformation of ground and structures on blast wave propagation is still rarely reported.

Current studies on blast wave propagation in the complex urban environment are limited to some simplified models containing several building blocks and do not cover the actual city environment. This embarrassment is largely attributed to the limitations of computer hardware and numerical algorithms. In the present study, there are still three challenges, namely, an improved automatically numerical model based on the GIS technique to cover as many cities blocks as possible, a highly efficient numerical algorithm for the propagation of blast wave in a large-scale urban complex environment and at last, a more reliable load model depicting the blast loads on buildings in the complex city environment.

Blast-induced damage identification

The blast-induced damage in civil structures roughly represents the loss of load-carrying capacity caused by explosion attacks. Blast-induced damage will continue to deteriorate the structural operating condition during the remaining service cycle, and damage identification is of great importance for blast-surviving structures. According to the adopted strategies, there are two methods available for blast damage identification of concrete structures: damage prediction using pressure–impulse (P-I) diagram based on the given blast load and onsite damage detection techniques.

P-I diagram

The P-I diagram was initially constructed for brick houses by bombing attacks during World War II. Then, it was introduced and modified to present a visual perception of the damage extent of concrete structures and human casualties under blast loads (Jarrett, 1968). The diagram depicts all possible combinations of peak overpressure and impulse given a specific damage level, as illustrated in Figure 5. In the figure, the hyperbolic curve accompanied with two asymptotes in the plane is related to a specific damage level, which is defined as the ratio of the proper mechanical index (e.g. maximum deflection, maximum rotation, maximum principal strain and loss of bearing capacity) to that at critical limit state. The diagram can be split into three districts that indicate different loading regimes, namely, impulse loading district, dynamic loading district and quasi-static loading district. Particularly, for some brittle materials, such as glass, masonry and plain concrete, the blast-induced damage can be categorized into several distinct levels and assigned with corresponding thresholds of peak overpressure (Federal Emergency Management Agency, 2006; Pape et al., 2009; Stephens, 1970).

The derivation of the P-I diagram is an elaborate and sophisticated procedure for scientists and engineers. Theoretically, physical tests, analytical deduction utilizing the single-degree-of-freedom (SDOF) method and numerical simulations could be used to produce the P-I diagram. However, due to the limitations of the experimental cycle, cost and security, in most cases, the physical experiment is mainly conducted for the validation of the latter two solutions. In this respect, analytical and numerical models are commonly used to generate data points in the P-I plane, and regression analysis is performed to delineate the targeted iso-damage curves. Some load combination strategies, literately called search algorithms, are also designed to avoid aimless calculations (Chernin et al., 2019). A general formula that describes certain blast-induced damage is listed in equation (8).

(P - P_{c r}) (I - I_{c r}) = C

(8)

where P and I represent the peak overpressure and the impulse alongside the blast duration, while P_cr and I_cr are the reference values of the horizontal and vertical asymptotes. C is a constant value that depends on a specific damage level. Equation (8) could be reorganized as equation (9) if C = P_crI_cr is assumed (Abrahamson and Lindberg, 1976). Shi et al. (2008) proposed an estimation for C based on numerical analysis of numerous reinforced concrete columns under idealized triangular decay pulse load, as shown in equation (10).

(P / P_{c r} - 1) (I / I_{c r} - 1) = 1

(9)

(P - P_{c r}) (I - I_{c r}) = 12 {(P_{c r} / 2 + I_{c r} / 2)}^{1.5}

(10)

Many studies indicated that the pulse load shape has a pronounced influence on the P-I diagram. A common settlement scheme to include this effect is the employment of the equivalent rectangular load in which the impulse value remains unchanged. The equivalent pulse duration and overpressure are calculated as follows (Youngdahl, 1970).

t_{0} = \frac{2}{I} \int τ P (τ) d τ

(11)

P_{0} = I / t_{0}

(12)

To generalize a unified formula for different damage levels, dimensionless analysis followed by normalized form is commonly accepted to derive the P-I diagram. Li and Meng (2002a) gave a normalized P-I diagram based on the SDOF analysis of the linearly elastic system under idealized impulse loads, as shown in equation (13).

(p - 0.5) {(i - 1)}^{n 2} = n 1

(13)

Where p and i are normalized pressure and impulse, respectively, while n1 and n2 are the two parameters that depend on the blast loads. Li and Meng (2002b) also offered a normalized formula for an elastic–perfectly plastic SDOF system.

A similar formula for simply supported beams under idealized pulse load is given in equation (14) (Fallah et al., 2013), where c equals 1.0 for elastic beams and 10 for elastic–perfectly plastic beams. Normalized formulae resembling equation (10) were also recommended by Oswald and Sherkut (1994) (equation (15)) and Krauthammer et al. (2008) (equation (16)).

(p - c) (i - c)^{n 2} = n 1

(14)

(p - p_{c r}) (i - i_{c r}) = 0.4 {(p_{c r} / 2 + i_{c r} / 2)}^{1.5}

(15)

(p - 0.5) (i - 1) = 0.01 {(p_{c r} + i_{c r})}^{1.0} for rectangular pulse load

(16a)

(p - 0.5) (i - 1) = 0.08 {(p_{c r} + i_{c r})}^{0.3} for triangular pulse load

(16b)

Relevant publications showed that the quasi-static (horizontal) asymptote in a normalized P-I diagram usually varies from 0.5 to 1.0, with the inertia effect decreasing accordingly (Chernin et al., 2016). For instance, when the impulse load increases slowly or rapidly, the asymptote gets close to 1.0 or 0.5. For ductile materials, the quasi-static asymptote approaches 1.0 easier compared to some brittle materials. The P-I diagrams in the dynamic and impulsive districts are also sensitive to various influencing factors. Many attempts have been implemented to tackle the variation of the P-I diagram, such as the piecewise equations regarding multiple failure modes (Huang et al., 2017; Li and Hao, 2014; Xu et al., 2014), the pressure–impulse band (PIB) covering the reinforcing details and eccentric actions (El-Dakhakhni et al., 2009), and the probabilistic diagrams using the Monte Carlo method (Parisi, 2015). Meanwhile, there were also many diagrams for steel structures (Al-Thairy, 2016; Shi et al., 2017), polyvinyl butyral (PVB)–laminated float glass window (Zhang et al., 2013), brick masonry (Elliot et al., 1992) and some new-fashioned structural forms made of advanced materials (Liao et al., 2019; Zhang et al., 2017). Up to now, the sensitivity problem of the P-I diagram stays knotty, and the current researches are not extensive and intensive to fix the gap.

Moreover, most existing P-I diagrams were developed and fabricated for the structural components rather than the entire building. The P-I diagram for the entire building is less reported. Chee et al. (2020) combined the SDOF approach and numerical technique to construct the P-I diagrams for shallow buried box-type building structure, in which the effects of roof’s failure modes and the soil–structure interaction (SSI) were included. A mapping methodology of blast-induced damage of components onto reinforced concrete frame structure was also presented for progressive collapse assessment (Gombeda et al., 2017). A decision-based framework to calculate the consequent magnitude of blast-induced local damage and to evaluate the structural resilience was also provided (Quiel et al., 2016).

The P-I diagram offers a brand-new insight into the quantitative relation between blast loads and structural behaviours. Like the response spectrum in seismic design, the P-I curve has already played a significant role in blast resistance design. However, due to the sensitivity of structural response to material properties, load characteristics and analysis methods, no universal formula is available yet, and extensive and intensive efforts are imperative in further work.

Blast damage detection techniques

In the passing decades, advanced progress on structural health monitoring (SHM) has gradually promoted and deepened the application of structural damage identification (Tadeusz and Staszewski, 2013). These results provide necessary tools for the investigation of blast-induced damage assessment of reinforced concrete structures. In-situ damage detection is a complementary element to the P-I diagram approach, and it has been implemented in structural health monitoring (SHM) for years. In terms of blast-induced damage investigation, practical applications mainly involve visual inspection, non-destructive detection testing (NDT) and vibration-based methods. For clarity, there are five distinct levels for blast damage identification: (1) emergence of the damage, (2) damage localization, (3) damage type (e.g. cracks, steel yielding and concrete spalling), (4) severity or extent of the damage and (5) structural prognosis to predict the remaining useful life (Chen and Ni, 2018; Tadeusz and Staszewski, 2013).

Visual inspection is a primitive method in structural damage detection. It provides an intuitive understanding of blast damage and structural failure mechanism, and it is also effective in damaged building classification. For instance, by reviewing the existing literature, Sorensen and McGill (2011) presented a summary list of blast-induced damage characteristics and failure modes for five conventional construction materials: reinforced concrete, masonry, steel, glass and timber. Using the photographic evidence collected in an LPG explosion case, Turgut et al. (2013) explained the blast-induced damages of reinforced concrete members and their mechanisms under close-in blast loads. However, these visual inspection references only describe some external structural damage qualitatively, and they are greatly dependent on specialities and experiences. For these reasons, visual inspection has a limited application range and less research attraction. In recent years, several efforts have been implemented to enhance the quantitative capacity of the visual inspection approach. Cui et al. (2015) proposed a formula to identify the loss of bearing capacity of the reinforced concrete columns under close-in explosion by measuring the relative residual deflection. It is an effective attempt to develop quantitative visual inspection techniques.

Modern structural damage detection mainly adopts advanced instruments and algorithms, and it is generally divided into local detection methods and global detection methods (Chen and Ni, 2018; Tadeusz and Staszewski, 2013). The former generally adopts non-destructive testing (NDT), such as acoustic emission (AE), ultrasonic testing (UT), eddy-current testing (ECT) and radiation testing (RT). The global detection technique usually refers to various dynamic detection methods called vibration-based detection. The non-destructive testing technology is mainly used for detecting slight local damage, such as concrete cracks and steel corrosion. It has strict requirements on the number and arrangement of sensors, leading to a higher cost than the dynamic testing methods. In contrast, the vibration-based detection method is not sensitive to slight structural damage, but it demands a lower budget and does not need cumbersome sensor configuration. The theoretical basis of the vibration-based detection method is simple: the structural damage will change the mass, stiffness and damping properties, and make the modal parameters such as natural vibration frequency, damping ratio and mode shape deviate from the normal states, and ultimately affect the vibration signals such as displacement, velocity and acceleration.

According to the vibration signal processing method, vibration-based detection methods can further be categorized into model-based damage assessment methods and data-based damage assessment methods. Conventional vibration-based detection techniques prefer to employ model-based damage assessment methods. In this method, a structural model or modal model is established, and then the damage location and damage extent are determined by analysing the changes of the natural frequency, mode shape, flexibility and stiffness matrix. Recently, Shi et al. (2021) proposed a linear equation between the fundamental frequency loss and the blast damage of reinforced concrete columns through extensive numerical simulations and parametric analysis. The data-based method directly processes the vibration signal using some pattern recognition methods through various algorithms. This process does not involve any physical or mechanical properties of the building structures. In most cases, some statistical models are derived through several artificial intelligence techniques such as backpropagation neural network (BPNN) and genetic algorithm (GA) (Yan et al., 2007). The data-based method is gradually becoming popular because of the emerging artificial intelligence technique. Current research on the onsite detection of blast-induced damage is still less reported, and there is still a long journey to go until reliable engineering application.

Discussions

In the passing decades, scientists and engineers have centred their interest in the field of vulnerability and progressive collapse of building structures under explosion events. As a result, a large body of knowledge and data are accessible to make a comprehensive understanding of structural behaviours under blast loads. In contrast, the literature on the post-blast assessment of buildings remains less reported, especially on the quick safety assessment of in-service building structures in complex geometries. In this paper, three primary issues that formulate the post-blast assessment method of blast-surviving buildings were reviewed. The idea was enlightened given that deliberate bomb attacks or accidental chemical explosions in complex urban environments may become a catastrophe if not properly handled in the emergent rescue stage. The inverse analysis based on a variety of evidence is performed to identify the explosive characteristics. The numerical simulations or empirical formulae fulfil the function of revealing the actual behaviour of blast wave propagating in complex geometries, whereby blast loads on building facades are measured. Given the blast loads, the structural damage comes into view by referring to the proper P-I diagram. Also, the detection techniques are included as supplementary tools for more precise results. Through years, fruitful works are accessible to the public to enrich the knowledge in this area, as can be seen in the previous sections, but there are still many crucial problems remaining unsolved:

(1) Existing studies on the inverse analysis of explosives show deviation from the true values up to one order of magnitude. Further work is imperative for a reliable estimation of explosives with few errors. Besides, most of these methods mainly focus on determining the TNT equivalency, which may be unreliable in some kinds of explosions, such as gaseous or dust explosions. Also, many explosion cases, deliberate or accidental, show that ammonium nitrate and its products (fertilizer and fireworks) deserve a systematic study;

(2) The complexity of urban environments brings trouble to the accurate assessment of blast loads on building structures. Currently, numerical simulations are used to predict the blast wave propagation and interaction with buildings in complex geometries. However, current practice in numerical modelling of blast wave propagation in modern city areas is still very time consuming because of the mesh size dependency of the numerical results. Thus, improving the efficiency of the numerical method is one crucial issue. Improvement of automatic establishment of numerical models of building structures in a complex urban environment based on the GIS technique is the other. Besides, current work on blast wave propagation does not pay sufficient attention to the influence of buildings’ and ground’s deformation;

(3) For blast damage identification of buildings, there are various damage criteria for different structural components, and they are not consistent with one another. In the quick safety assessment of building structures, the damage degree and progressive collapse potential of the entire building are much more critical. However, the relationship between the local failure of structural members/connections and the performance of the entire building remains vague. Therefore, it is necessary to develop a cost-effective model based on the damage assessment of structural members/connections. Meanwhile, visual inspection, non-destructive detection techniques and vibration-based methods are still in their developing stages and demand extensive and intensive studies on the quick blast-induced damage assessment of building structures.

Footnotes

Acknowledgements

The authors gratefully acknowledge the support from the National Natural Science Foundation of China under grant numbers 51878445, 51938011, 52178498 and Natural Science Foundation for Distinguished Young Scholars of Tianjin under grant number 17JCJQJC43900.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China under grant numbers 51878445, 51938011, 52178498, and Natural Science Foundation for Distinguished Young Scholars of Tianjin under grant number 17JCJQJC43900.

ORCID iD

Zhongxian Li

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