Methods for progressive collapse analysis of building structures under blast and impact loads

Progressive collapse is defined as the spread of an initial local failure from a key element to adjacent elements, eventually resulting in the collapse of the whole structure or a disproportionately large part of it. As an abnormal dynamic load, blast load has the characteristic of rapid propagation, high peak value and short duration. And it is also one of the main reasons that might cause the progressive collapse of building structures. Based on the existing research achievements on the progressive collapse of building structures, in this paper the classification method for structural progressive collapse analysis is put forward. Then the current methods for progressive collapse analysis are further divided into two categories, i.e., the method for evaluation of structural progressive collapse resistance and the method for whole process analysis of structural progressive collapse. Recent progress on the evaluation of structural progressive collapse resistance and the method for whole process analysis of structural progressive collapse are presented from literatures. Finally, the conceptual design method, structural detailing and the procedure for progressive collapse resistant design of building structures against blast loading are put forward.

The growing need for blast-resistant designs in structural engineering is driven by the rising threat of terrorism, accidental explosions, and the significant risk of progressive collapse. This study presents a numerical procedure for analyzing the progressive collapse of Reinforced Concrete (RC) framed structures due to blast loads, addressing the gap in current methodologies. Traditional approaches such as the Alternate Load Path method, which are code-based and threat-independent, mainly focus on sudden column loss scenarios but do not fully capture the dynamic nature of blast-induced, threat-dependent collapses. Hence this study addresses the need for a computationally efficient and reliable method to predict and model progressive collapse under blast loading. This study employs a comprehensive numerical investigation using Finite Element Method where a seven-storeyed RC building is assessed for progressive collapse under blast loading. Progressive collapse analysis was executed using a commercially available Finite Element Analysis software, adhering to the Linear Static Procedure specified in the General Services Administration (GSA) guidelines, while blast load scenarios were examined through a nonlinear direct integration time history analysis. Different blast parameters, including charge weight and standoff distances, are varied to evaluate their impact on the structural integrity of the building. The study differentiates between threat-independent analysis, considering four column removal locations, and threat-dependent (blast-induced) scenarios with three distinct column removal positions. The scope of this study delves only into the perimeter blast scenarios neglecting the internal explosions. Demand Capacity Ratios (DCR) of columns were calculated to determine the susceptibility of the building to progressive collapse, with a DCR greater than 1 indicating failure. The numerical model was validated against the GSA baseline model. In threat-independent analysis, 30%, 60%, 22%, and 44% of the considered columns under corner, long side, short side, and interior column removal scenarios respectively exceeded the acceptable DCR criteria. In threat-dependent analysis, 100% of the considered columns under each blast induced column removal scenario exceeded the acceptable DCR criteria. This emphasizes the need for scenario-based planning in structural design to reduce collapse risks. The identification of critical columns, for threat-independent analysis as those directly above the removed column and on the topmost floor and for threat-dependent analysis as ground floor columns adjacent to the removed column, reveals potential weak points for progressive collapse initiation. The analysis of blast-induced progressive collapse reveals significantly higher DCR values than threat-independent assessments. Even the minimum percentage increases of DCRs when transitioning from threat-independent to threat-dependent analysis reaches high values up to 995%, 325%, and 981% for corner, long side, and short side column removal scenarios respectively. This specifies the importance of integrating blast resistance into the structural design of high-risk buildings. As a result, this study contributes to the understanding of structural dynamics under blast loads and offers a framework for the analysis of progressive collapse in RC buildings.

One of the research focus areas of the Structural Engineering Group in the School of Civil and Resource Engineering at the University of Western Australia (UWA) is analysis and design of structures against blast and impact loads. Our research activities spread in a wide spectrum related to structure protections against blast and impact loads, including modelling shock wave propagation and prediction of blast loads on structures; quantification of dynamic material properties and development of dynamic material models; developing fibre-reinforced polymer (FRP) materials with new fibre types; development of theoretical and numerical approaches to predict blast fragmentation; numerical simulation, laboratory impact tests and field blast tests to quantify the effectiveness of FRP strengthening of reinforced concrete structures; and simulation of damage and progressive collapse of building and bridge structures to blast load. The research approaches include theoretical derivations, numerical simulations, and laboratory impact and field blasting tests. These researches are funded by a few ARC Discovery projects. Some of them are carried out with collaborations with researchers in other universities in Australia and other countries. This paper summarises a few research projects, and demonstrates the research capabilities related to protective structures in UWA.

Sandwich plates with grid-core structures possess extensive applications, and non-uniform grid plates (NUGPs) show enhanced potential under varied loading modes. The current study embarks on an investigation into NUGPs by adjusting the dimensions of transverse and longitudinal grid walls. This comprehensive analysis explores the dynamic responses of these plates when subjected to impact and blast loads, focusing on deformation patterns, damage, and the underlying processes. The findings are illustrated as follows. 1) NUGPs, specifically those with an optimized configuration of grid walls termed the d2 structure, display improved resistance to blast and impact loads compared to their uniformly distributed grid plate counterparts. Notably, designs featuring a less dense grid in the central area yield a more evenly distributed damage pattern under impact loads and a lesser severity of damage from blast loads. 2) The study also reveals that under impact loads, the sandwich structure showcases distinct behaviors through three stages evident in the load-displacement curves: initial localized indentation, followed by overall deformation, and ending with deformation recovery. 3) Moreover, when facing blast loads, the initial response involves rapid plastic deformation of the upper skin, succeeded by compression and buckling of the core. This sequence effectively dissipates energy, acting as a protective shield for the lower skin. 4) The optimized NUGPs design achieves a perfect balance between stiffness and ductility, reducing displacement through adequate stiffness while ensuring the effective absorption of dynamic forces through significant ductility, thus preventing catastrophic failure. This research significantly advances topology optimization for sandwich plates, providing essential insights for designing lightweight structures resilient under various modes.

Progressive collapse is defined as the spread of an initial local failure of a critical load bearing structural element to the remaining structure, ultimately leading to the collapse of the entire building or of a large portion of it. After the partial collapse of the Ronan Point apartment tower in 1968, when a localised gas explosion ultimately led to the collapse of the whole corner of the building, progressive collapse firstly drew public attention due to its catastrophic consequences on human casualties and economic losses. Other recent collapse events, such as those of the Murrah Federal Building in 1995, Sampoong department store in 1995 and World Trade Centre towers in 2001, have further highlighted the importance of this topic and made engineering communities aware of the necessity to prevent the occurrence of progressive collapse in building structures. In the past decades, considerable research has been devoted to investigate progressive collapse of building structures. These research typically followed an alternate load path approach. This approach allows an initial failure to occur, while the remaining structure needs to seek alternate load paths to dissipate damage and prevent progressive collapse. In practice, the progressive collapse resistance of building structures is generally evaluated by notionally removing one or more load bearing structural elements, representing the initial failure. Despite all research efforts made, they have predominately focused on frame systems. Relevant investigations on reinforced concrete (RC) flat plate structures, a commonly used structural system, are still scarce. The flat plate system contains slabs, of uniform thickness, directly supported by columns without using beams, drop panels and column capitals. This provides structures with increased storey height, architectural convenience and significant savings in construction costs. Nevertheless, the slab-column connection is prone to punching shear failure, which may propagate to the vicinity of connections, potentially leading to progressive collapse. The present study aims at filling some of the current knowledge gap with comprehensive experimental, analytical and numerical investigations on RC flat plate structures. The experimental program consists of four quasi-static large-deformation tests performed on three 1/3-scale, 2×2-bay RC flat plate substructures subjected to critical column removal scenarios. The test specimens included one specimen tested under two consecutive corner column removal scenarios, one specimen under an edge column removal and one specimen under the scenario of concurrently removing both an edge and an interior column. For the loading scheme, a multi-point loading system was specially designed to simulate an increasing uniformly distributed load (UDL). The loading points of this system were equally positioned on the bays adjacent to the removed column(s) to apply the load until failure of the slab. Throughout each test, the structural behaviour of the slab was monitored by extensive apparatuses mounted to the slab both internally and externally. Failure and post-failure behaviours, failure modes, and collapse resisting mechanisms were observed and analysed. Additionally, a complement of analytical studies to the experimental tests, based on the observed yield lines, was carried out to estimate the flexural capacity of the test specimens. To numerically investigate the progressive collapse behaviour of RC flat plate structures, a set of 3D nonlinear finite element modelling approaches, using LS-DYNA software, was established. A total of five numerical models were explicitly created based on the four experimental tests in present research and one from the literature. The proposed modelling approach was basically composed of appropriate definitions of element types, bond-slip relationships, loadings and boundary conditions, and more importantly development of the material models for concrete and reinforcements and calibration of failure criteria for element erosion. A quasi-static loading scheme in displacement control in the numerical models was adopted, the same as that in the conducted tests, through explicitly modelling the multi-point loading system in order to replicate the true test conditions. The numerical models were respectively validated by comparing the load displacement responses, failure modes, crack patterns, and displacement and strain results against the experimental ones, which confirmed the appropriateness and reliability of the proposed models. The validated modelling techniques could be applied to further perform parametric studies of the progressive collapse resistance of RC flat plate substructures and prototype structures. In summary, the significant and original contribution of this research is to (1) obtain a solid understanding of the collapse behaviour of RC flat plate structures under critical column removal scenarios, (2) examine the analytical solution using the yield line theory to predict the flexural capacity of RC flat plate structures, (3) establish a set of numerical modelling techniques which can reasonably replicate the experimental process and provide valuable references of numerically analysing progressive collapse of RC flat plate structures, and (4) give design insights into Australian and international Standards in mitigating progressive collapse of RC flat plate structures.

Progressive collapse studies generally assess the performance of the structure under gravity and blast loads, while earthquakes may also lead to the progressive collapse of a damaged structure. In this study, the progressive collapse response of concentrically braced dual systems with steel moment-resisting frames was assessed under seismic loads through pushover analysis using triangular and uniform lateral load patterns. Two different bracing types (X and inverted V braces) were considered, and their performances were compared under different lateral load patterns using the nonlinear static alternate path method recommended in the Unified Facilities Criteria (UFC) guideline. Eventually, the seismic progressive collapse resistance of models was compared to their progressive collapse response under gravity loads. These studies showed that models under the seismic progressive collapse loads satisfied UFC acceptance criteria and limited rehabilitation objective. The structures had better performance under seismic progressive collapse than models under gravity loads because of more resistance, ductility, suitable load redistribution, and more structural elements that participated in load redistribution. Furthermore, despite studies on progressive collapse under gravity loads, the dual system with X braces showed better progressive collapse performance (more resistance, residual reserve strength ratio and ductility) under seismic loads than the model with inverted V braces.

This paper investigated the blast behavior of a low‐rise composite steel structure of three stories subjected to internal and external explosions for the same explosive charge of 250 kg TNT. A comparison of three various blast scenarios is aimed at better understanding how blast waves propagate in confined risk zones and their damage effects on far and exposed elements to an explosive charge. Evaluation of the damage level and the overall response of the proposed numerical model is done by estimating the adequacy of structural members subjected to blast loading using general limits in attempting to check the structure's strength and regularity. The analysis was based on load combinations and damage criteria according to the Unified Facilities Criteria which are general design approaches suitable for civil design applications in forecasting blast loads and structural system responses. The overall behavior of this structure was simulated based on a dynamic analysis by the direct simulation approach, which was chosen for modeling blast loads using the Friedlander blast load equation, and the simpler, less expensive, more accurate, and realistic A.T.‐BLAST model to deduce the simplified blast‐wave overpressure profile. The material nonlinearity at a high strain rate using the Johnson‐Cook strength and concrete plasticity damage model is studied dynamically using ABAQUS finite element code to simulate the explicit dynamic nonlinear analysis. The overall response of the proposed numerical model was evaluated by estimating the adequacy of structural members, considering the blast load as the initial cause of failure, such as axial plastic strain, internal forces limits, maximum deformation, support rotation, demand‐capacity‐ratio (DCRshear/moment), drift index and material damage model. The position of the explosive charge played an important role in determining the rate at which the structural element begins to plastic strains, displacements, moments, or rotations beyond the limits, and then key elements should be considered in structural design against progressive collapse. Results showed that steel members exhibit early indicators of failure, such as buckling necking, shear tearing, or plastic hinges, whereas concrete slabs break up immediately due to brittleness. DCRmoment values successfully showed the columns in which the first plastic joint can occur, whereas DCRshear values signaled the onset of shear failure at connections. Besides, plastic hinges played an important role in dissipating energy and preventing total structural collapse via the Strong Column‐Weak Beam design concept, which appears repeatedly in this study. The structure is a well‐designed and ductile building capable of supporting higher loads and is considered to be repairable and intact.

Progressive collapse is a persistent spread and enlargement of initial local failure of structures characterized by inconsistency between the initial failure and its resulting extensive collapse. Although, great contributions have been made towards the progressive collapse of building structures, comparably small attention has been paid to bridge structures. In this study, the procedure of progressive collapse of bridges with concrete prestressed voided slab under earthquakes and effects of other parameters on propagation of collapse of regular, semiregular, and irregular bridges are investigated. At first, a bridge specimen, which its shake table test results were provided by previous researchers, was modeled and verified using the applied element method. Then, the progressive collapse of the box girder bridge was investigated. In the next step, progressive collapse process of the same bridge with posttensioned voided slab under earthquakes was studied using nonlinear time history analysis. Irregularities of the piers were analyzed parametrically. The results show that domino‐type progressive collapse happens in bridges with voided slab after the initial failure of the deck at the seating of bridge abutment. Also, it is concluded that, type of the deck, height of the piers, and ground slope have a great effect on the progressive collapse procedure of both regular and irregular bridges with voided slab deck.

Although much research focuses on investigating the responses of reinforced concrete (RC) structures under sole impact or blast loads, the responses of RC structures under a combination of impact and blast loads currently represent a gap in our knowledge. The combined actions of impact and blast loadings may be applied to RC structures during accidental or intentional collision of vessels, vehicles, etc., carrying explosive materials. A comprehensive study on the vulnerability of various structural members is carried out using finite element (FE) simulations under combination of impact and blast loads with the variations of various loading- and structural-related parameters and key parameters. This book introduces various structural analysis approaches for concrete structures when subjected to extreme loads such as impact and blast loadings. The theory of the combinations of impact and blast loads is proposed that can provide primary insights to the specific readers to develop new ideas in impact and blast engineering, including combined actions of extreme loads arising from real-world intentional or accidental events. This book will be of value to students (undergraduate or postgraduate), engineers, and researchers in structural and civil engineering, and specifically, those who are studying and investigating the performances of concrete structures under extreme loads.

Idealized structural unit method (ISUM) is now well recognized as one of the most efficient methods to analyze nonlinear behavior of large-sized structures under extreme or even accidental actions. This paper presents some techniques of ISUM modeling and surveys the literature on the ultimate limit state assessment of ship structures using ISUM. Theoretical formulations of ISUM elements for the progressive hull girder collapse analysis of ships that were implemented into ALPS/HULL computer code are outlined. Some benchmark studies are made by a comparison with physical test data and ALPS/HULL analyses on a frigate ship hull model under sagging moment tested by UK Royal Navy and on two double-skin tanker hull models under sagging or hogging moments tested by US Navy. Some ALPS/HULL application examples to progressive collapse analysis of a double-skin shuttle tanker hull under combined vertical and horizontal bending moments are then demonstrated. It is concluded that ISUM is very useful for the progressive hull girder collapse analysis of ships because it provides very accurate results while the computing time is very short.

In current practice, the analysis of progressive collapse in building structures widely employs the alternate load path method. However, there are very few collapse tests that can be utilized under blast loads, especially for investigating the degradation mechanism of progressive collapse resistance in post-blast building structures. In this study, the degradation mechanisms and methods for damage assessment of reinforced concrete structures under blast loads were investigated through numerical analysis. A substructure model derived from explosion loads based on a drop-hammer testing machine was validated by comparing with test results, and the established model accurately captured three typical failure modes in the substructure columns and confirmed the axial tensile effects of the columns on the adjacent components. A substructure damage assessment method was used to assess the degree of damage in a 5-story reinforced concrete frame structure under different explosion scenarios. The results show that the degree of damage distribution of the reinforced concrete frame structure exhibited an S-shaped distribution under corner column blast scenarios while an arch-shaped distribution was observed for middle column blast scenarios. Furthermore, empirical formulas based on the explosive mass and distance ( M - R ) curves were established. These empirical formulas can help to rapidly predict the damage levels of RC frame structures for a given explosion scenario within a certain scope.

Occurrence of progressive collapse events invariably leads to significant economic and human-life losses. Progressive collapse analysis and design of building structures have become a research hotspot worldwide. Existing studies have proved that development of extra load-carrying mechanisms could significantly improve the resistance of structures to progressive collapse. However, limited research has been conducted to quantitatively analyze these mechanisms. This study proposed a new and unified division method for mechanisms for resisting progressive collapse; furthermore, it provides a basis for their quantitative analysis. In addition, the progressive collapse behavior of a 1/3-scaled two-story, one-bay-by-two-bay reinforced concrete (beam–slab–column) frame with an edge column lost was experimentally investigated. Additionally, a 3 D solid finite element model was established and validated based on the test results. The effects of different extensive parameters, including ideal lateral constraints, slab thickness, and beam–slab interaction, on each resisting mechanism were quantitatively investigated. Finally, a new simple method for predicting the first peak load was proposed based on the contribution of each mechanism. The results from the simple method were in agreement with the simulation results of beam–slab–column structures.

Numerical analysis of axially loaded RC columns subjected to the combination of impact and blast loads

Blast effects on structures and blast mitigation strategies have been vigorously studied in the world. The alternate path method, or common progressive collapse analysis method, of structures assumes the threat-independent removal of vertical load-carrying elements. However, in reality, a blast-induced column-missing event will produce the damage on adjacent structural elements and the rapid dynamic response of the structures. In this study, the strain rate effects on the dynamic collapse behavior of steel moment frames are investigated by performing the blast-induced sequential progressive collapse analysis. Then, the improvement of the progressive collapse analysis method is discussed based on the numerical results.

Numerical evaluations of codified design methods for progressive collapse resistance of precast concrete cross wall structures