1.1 Background
Since the construction of reinforced concrete (RC) structures has been widely increased in recent decades, the need for recognizing different behavioral aspects of such structures from micro (materials) to macro scales (structural responses) under various types of loadings from static to dynamic and impulsive loadings is the topic of importance nowadays. As reported by Buth et al. [1], the collapse of bridge superstructures in several cases, such as due to the collision of trucks with bridge piers, from 1965 to 2008 was observed in the United States. Harik et al. [2] classified the bridge failures that occurred due to various causes in the United States during the period of 1951–1988. It was reported that 42 out of 79 (i.e., about 53%) bridges collapsed due to collisions in which 19 cases (≈24%) caused by ships, 11 cases (≈14%) by trucks, and 6 cases (≈8%) by trains. Moreover, in 4 cases (≈5%), the bridges collapsed due to exploding or burning of fuel-tanker trucks. Based on a study done by Wardhana and Hadipriono [3], during 1989–2000 in the United States, 12% of the total bridge failures occurred due to lateral impact forces (arising from the collision of trucks, barges, ships, and trains) and 3% of the failures caused by fire and explosions. For the period of 2000–2008, Hersi [4] revealed that 24% of bridge failures in the United States were occurred due to collision and lateral impact loads, whereas fire and explosions caused only 1% of bridge failures during a similar time period. In addition, Cook [5] reported that 12% of collapsed bridges in the United States during 1987–2011 were occurred due to collision, and 3% of them failed due to explosions and the combination of fire and collision. According to a study by Lee et al. [6] during 1980–2012 in the United States, 15.3% and 2.8% of failures were occurred due to collisions, and fire and explosions, respectively. Comparing to bridge failure studies in the United States, Scheer [7] classified the causes of bridge failures that occurred all over the world. It was found that 13% of 440 failure cases were due to ship collisions and 5% of them failed due to fire or explosion.
The effects of extreme loads such as impact and blast loads on RC structures and infrastructures have been notably studied since the 1960s. In 1964, the dynamic principles and analyses for structures under impulsive load were proposed by Biggs [8]. A comprehensive treatment of explosion hazard mitigation free field by Baker [9] and Clough and Penzien [10] adopted a more systematic and advanced theory for structural dynamics. Subsequently, Hetherington and Smith [11] presented the design of structures to resist weapon effects. The Structural Engineering Institute (SEI) of the American Society of Civil Engineers (ASCE) published a state-of-the-practice report to provide guidance to structural engineers in the design of civil structures to resist the effects of terrorist bombings. More recently, Krauthammer [12] addressed a broad range of scientific and technical issues involved in mitigating the extreme loading effect associated with blast, shock, and impact. In addition, a few design manuals can be referred to, e.g., the Tri-service manual TM-5-1300 [13], Army Technical Manual TM-5-855-1 (US Department of the Army, 1986) [14], ASCE Manual 42 [15], ASCE guidelines for blast-resistant buildings in petrochemical facilities [9], UFC 3-340-02 [16], GSA [17] criteria, DOE/TIC-11268 [18], and FEMA Reference Manual [19].
The effects of blast loads are directly related to stress-wave propagation in the structure which are generally applied to the surface of target structures. On the basis of the interactions and relationships between blast loading pressure (P) and its impulse (I) response on target structure, known as P-I diagrams, blast loads are divided into three classes, including (i) impulsive (in which loading duration, td , is very short relative to structure period time, T), (ii) dynamic (td ≈ T), and (iii) quasi-static (td > T). Another common criterion to classify the intensity of blast loadings based on Hopkinson-Cranz law [20] is known as the scaled distance (Z) of detonation from the target defining a relationship between equivalent weight (W) and standoff distance (R) of the explosive charge. According to this criterion, blast loads can be categorized into near-field and far-field detonations. There exist different definitions in classifying blast loads on scaled distance. According to the American Society of Civil Engineers (ASCE SEI 59-11) [21], blast loads with scaled distances less than 1.2 m/kg1/3 are identified as close-in detonations. Gel'fandetal et al. [22] defined another criterion based on the dimension of the charge r0 . According to this criterion, blast loads with standoff distance Rn between the ranges 0 and 20r0 (0 < Rn < 20r0 ) are recognized as close-in detonations. In addition, UFC 3-340-02 [23] considered a scaled distance equal to 0.4 m/kg1/3 as the sensitive level for scaling of blast loads. As such, blast loads with a scaled distance less than this value were considered close-in explosions.
The analysis of structures under explosions has been widely carried analytically, numerically, and experimentally in the literature. Krauthammer et al. [24, 25] proposed an analytical method to analyze RC beams under idealized blast loadings uniformly distributed on the theoretical Timoshenko beam. Most of the design codes and guidelines listed previously employ simplified approaches to idealized blast loads and predict the resistance of structures by considering dynamic increase factors. The occurrence of concrete spallation is the most probable failure mode in RC structures under explosions. The basic theory of spallation of RC structures associated with the concept of stress-wave propagation under blast loadings was proposed by McVay [26] and the intensity damage states of RC structures based on the spallation were classified. Although the global failure behaviors of structures on displacement-based damage criterion can be predicted by simplified methods, they are unable to capture brittle shear failures and spallation. Moreover, these approaches cannot take into account the effects of structural dimensions, material dynamic properties, stress-wave propagation, and interlock resistance forces in the cross section. Therefore, many research works utilized experimental and numerical finite element (FE) methods to realistically analyze the failure behaviors and dynamic responses of structures under explosions. There exist several approaches to conduct experimental field and laboratory tests of blast loads on structures using different facilities such as (i) free-air bursts using explosive charges [27], (ii) shock tube facilities [28], (iii) the University of California, San Diego (UCSD) simulator [28], (iv) Gas Blast Simulator (GBS) [29–33]. Owing to expensive costs and security limitations and difficulties of experimental tests, numerous research studies focused on the simulation of blast loads on structures using high-fidelity FE software codes such as ABAQUS [34], LS-DYNA [35], and AUTODYN [36].
Impact loading is another type of dynamic and extreme loadings in which its duration may reach 1,000 times shorter than earthquakes. Impact loads can be characterized into three types based on their intensity and duration (td ). These types are (i) quasi-static loading in which the structure reaches its maximum response before ending of the impact duration, (ii) dynamic loading in which the structure reaches its maximum response almost at the same time with the ending of the impact duration, and (iii) impulsive loading in which impact duration ends before reaching the structure its maximum response. Accordingly, structural components can demonstrate different behaviors under concentrate lateral impact loads, including localized and overall responses. When a structural member is subjected to high-rate impact loading with very short duration relative to the structure natural period (T), the stress-wave propagation and inertia resistance of the structure are predominant on the responses. Under this loading condition, it is more expected to observe localized failure in the structure. However, when this ratio (td/T) is large, the structural responses and failure modes are dependent on the stiffness of the structure and the structure tends to fail in overall modes [37]. Another classification of impact loadings based on their dissipative mechanism was proposed by Eurocode [38], including (i) hard impact in which the initial kinetic energy was dissipated by striking objects such as colliding of vessels and vehicles with deformable bows with concrete structures and (ii) soft impact in which the major part of the initial kinetic energy was dissipated by the impacted structure such as impacting the rocks and rigid objects on concrete structures. However, concrete structures might suffer localized failure modes and damages such as brittle spalling, scabbing, perforation, and punching shear failure [39, 40] under high-rate impact loads, or overall failure modes under rather low-rate impact loads that cannot capture using simplifie...