Analytical Collapse Study of Lightly Confined Reinforced Concrete Frames Subjected to Northridge Earthquake Ground Motions

Review of older non seismically detailed reinforced concrete building collapses shows that most collapses are triggered by failures in columns, beam-column joints, and slab-column connections. Using data from laboratory studies, failure models have previously been developed to estimate loading conditions that correspond to failure of column components. These failure models have been incorporated in nonlinear dynamic analysis software, enabling complete dynamic simulations of building response including component failure and the progression of collapse. A reinforced concrete frame analytical model incorporating column shear and axial failure elements was subjected to a suite of near-fault ground motions recorded during the 1994 Northridge earthquake. The results of this study show sensitivity of the frame response to ground motions recorded from the same earthquake, at sites of close proximity, and with similar soil conditions. This suggests that the variability of ground motion from site to site (so-called intra-event variability) plays an important role in determining which buildings will collapse in a given earthquake.     

DEM Algorithm for Progressive Collapse Simulation of Single-Layer Reticulated Domes under Multi-Support Excitation

In this paper, the Member Discrete Element Method (MDEM) is modified and perfected for three aspects: the algorithm itself, loading and computational efficiency, and to accurately and quantitatively simulate the progressive collapse for large-span spatial steel structures. In addition, the corresponding computational programs are compiled. First, from the perspective of the method, a meshing principle for discrete element models is determined, a treatment for material nonlinearity and strain rate effect is proposed, and a damping model is established. Next, the Displacement Method is introduced to determine the multi-support excitation for the MDEM, and then motion equations of particles under multi-support excitation are derived. On this basis, the specific process of gravitational field loading is presented. Furthermore, parallel implementation strategies for the MDEM based on OpenMP are constructed. Finally, the collapse simulation of a 1/3.5-scaled single-layer reticulated dome shaking table test model under multi-support excitation is carried out. The comparison demonstrates that the ultimate load and failure mode as well as the complete collapse time of the numerical results are consistent with the experimentally measured responses, and the configuration variations from member buckling and local depression until collapse failure are fully captured. Moreover, the displacement time-history curves obtained using MDEM are almost identical to the experimental measurements, and there is a nuance only in the amplitude. It is verified that MDEM is capable of precisely addressing the collapse failure for large-span spatial steel structures. Additionally, the failure mechanism for structures of this type is naturally revealed.     

Successive Earthquake-Tsunami Analysis to Develop Collapse Fragilities

Over the last half century, scientists and engineers have developed methods to better understand and mitigate the damage caused by tsunamis. According to U.S. Federal Emergency Management Agency (FEMA) P646, buildings in many regions, including the U.S. Pacific Northwest, will experience substantial ground shaking from an offshore earthquake that precedes a tsunami and then experience the tsunami forces themselves. Thus, both hazards should be considered in computing the damage and collapse risk to buildings. This article summarizes a basic approach to numerically consider the successive seismic and tsunami risk to buildings in near-field tsunami regions such as the U.S. Pacific Northwest.     

Sensitivity of the Earthquake Response of Tall Steel Moment Frame Buildings to Ground Motion Features

The seismic response of two tall steel moment frame buildings and their variants is explored through parametric nonlinear analysis using idealized sawtooth-like ground velocity waveforms, with a characteristic period (T), amplitude (peak ground velocity, PGV), and duration (number of cycles, N). Collapse-level response is induced only by long-period, moderate to large PGV ground excitation. This agrees well with a simple energy balance analysis. The collapse initiation regime expands to lower ground motion periods and amplitudes with increasing number of ground motion cycles.     

The Variance of Collapse Capacity of Symmetric and Asymmetric Low-Rise RC-SMF Buildings

This study primarily investigates if the building asymmetry changes the variance of collapse capacity. The example models are five-story reinforced concrete buildings. The variance of collapse capacity is evaluated by first-order-second-moment method. There is a difference between the results of symmetric and asymmetric building models, independent of torsional behavior. The influence of record-to-record variability is more important than the effects of modeling uncertainty on the variance of collapse capacity. Plastic rotation capacity is the most important contributor to the variance of collapse capacity of high ductile buildings independent of the asymmetry.     

Assessment of Numerical and Experimental Errors in Hybrid Simulation of Framed Structural Systems through Collapse

Hybrid simulation can provide significant advantages for large-scale experimental investigations of the seismic response of structures through collapse, particularly when considering cost and safety of conventional shake table tests. Hybrid simulation, however, has its own challenges and special attention must be paid to mitigate potential numerical and experimental errors that can propagate throughout the simulation. Several case studies are presented here to gain insight into the factors influencing the accuracy and stability of hybrid simulation from the linear-elastic response range through collapse. The hybrid simulations were conducted on a four-story two-bay moment frame with various substructuring configurations. Importantly, the structural system examined here was previously tested on a shake table with the same loading sequence, allowing for direct evaluation of the hybrid simulation results. The sources of error examined include: (1) computational stability in numerical substructure; (2) setup and installation of the physical specimen representing the experimental substructure; and (3) the accuracy of the selected substructuring technique that handles the boundary conditions and continuous exchange of data between the subassemblies. Recommendations are made regarding the effective mitigation of the various sources of errors. It is shown that by controlling errors, hybrid simulation can provide reliable results for collapse simulation by comparison to shake table testing.     

Experimental Study and Numerical Model Calibration for Earthquake-Induced Collapse of RC Frames with Emphasis on Key Columns,Joints, and the Overall Structure

A thorough investigation of earthquake-induced collapse of reinforced concrete frames is presented. The inherent correlation between the nonlinear behavior of key components and the collapse mechanism of overall frame is examined through concurrent collapse tests of both frame and key components. Important issues in the component models are investigated through calibration against experiments, leading to a comprehensive structural system model. Both test and simulation indicate that the seismic performance are predominately governed by the key columns, whereas the energy dissipation capacity is somewhat affected by the joints. This study offers systematic experimental data and numerical models for future collapse assessments.     

Simplified Seismic Sidesway Collapse Capacity-Based Evaluation and Design of Frame Buildings with Linear Viscous Dampers

This article describes a simplified procedure for estimating the seismic sidesway collapse capacity of frame building structures incorporating linear viscous dampers. The proposed procedure is based on a robust database of seismic peak displacement responses of viscously damped nonlinear single-degree-of-freedom systems for various seismic intensities and uses nonlinear static (pushover) analysis without the need for nonlinear time history dynamic analysis. The proposed procedure is assessed by comparing its collapse capacity predictions on 272 different building models with those obtained from incremental dynamic analyses. A straightforward collapse capacity-based design procedure is also introduced for structures without extreme soft story irregularities.     

OUT-OF-PLANE SEISMIC RESISTANCE OF MASONRY WALLS

Seismic vulnerability of unreinforced masonry buildings is studied by means of simplified out-of-plane collapse mechanisms that take into account connections with transversal walls. According to experimental evidence, the analysis assumes that failure is reached with a rigid body motion of a part of the facade that falls down. Two classes of mechanism are examined: the overturning of the facade due either to a vertical crack at the connection or a diagonal crack on the transversal wall, both defined resorting to a simple model of masonry fabric, viewed as a regular assembly of rigid blocks and elastic plastic joints with friction but no cohesion. The use of simplified mechanisms give rise to an explicit evaluation of the seismic resistance to changes in the geometry and in the masonry fabrics, that could be used by practising engineers. This formulation is developed for both static horizontal actions and ground velocity peak, in the belief that the latter probably gives a better approximation of seismic action, while also providing, by comparison with the results of static forces, an estimate of the behaviour factor for unreinforced masonry. Eventually, the analytical forecasts are compared with numerical results obtained by means of the distinct element method.     

A High-Performance Quadrilateral Flat Shell Element for Seismic Collapse Simulation of Tall Buildings and Its Implementation in OpenSees

Shear walls are important lateral force-resistant components of tall buildings. Hence, a reliable numerical model that can accurately represent the mechanical characteristics and large deformations of shear walls is critical for realistic collapse simulation of tall buildings. Based on the theory of generalized conforming element, a high-performance quadrilateral flat shell element, NLDKGQ, accounting for the large deformation using the updated Lagrangian formulation, is proposed herein and implemented in OpenSees. The reliability of NLDKGQ is validated using classical benchmark problems and reinforced concrete specimens. In addition, its capability in simulating the collapse of a tall building is also demonstrated.     

Modification of Ductility Reduction Factor for Strength Eccentric Structures Subjected to Pulse-Like Ground Motions

This article investigates the ductility reduction factors for RC eccentric frame structures subjected to pulse-like ground motions. The structural models are with the strength eccentricities which are much disadvantageous than the stiffness eccentricities during the inelastic response range. A method to determine the ductility reduction factors of the strength eccentric structures is suggested by modifying those of reference symmetric structures through an eccentricity modification factor. The four factors of strength eccentricity ratio, ductility ratio, story number and velocity pulse of ground motions, are investigated to gain insight into this modification factor. It shows that the ductility reduction factors of the eccentric structures are clearly smaller than those of the symmetric structures. The eccentricity modification factor is mainly affected by the strength eccentricity and the ductility ratio, decreasing with the increment of the eccentricity or the decrement of the ductility ratio in a medium eccentricity range. The earthquake pulse-like effect and the eccentricity have coupling influence on the modification factor, while the effect of story number is not apparent. Based on the results of a comprehensive statistical study a simplified expression is suggested, which can estimate the eccentricity modification factors for both pulse-like and nonpulse-like ground motion cases.     

State Collapse and Fresh Starts: Some Critical Reflections

In examining the incidence of state collapse, two central themes emerge, one concerned with the search for causalities and the other concerned with appropriate responses. There is often a misplaced tendency to look for single causes and explanations of state collapse, and similarly to propose single, preferably ‘quick–fix’ solutions. Instead, what seems to be called for is a more nuanced scrutiny which differentiates the factors leading to collapse in specific instances, and a reconsideration, in the light of this scrutiny, of responses and possible external actor involvement. This article addresses these two themes. Firstly, it takes a preliminary look into the complex web of conditioning and facilitating factors that may or may not set in motion a chain reaction eventually leading to state collapse, examining the extent to which any emerging patterns can be identified. Secondly, it looks more closely at the response side to incidences of state collapse, specifically external responses. Whilst external actors, notably the ‘donor community’, are trying to better prepare themselves for the eventualities of crises of governance and state collapse in various countries, and to design more effective strategies and instruments, it remains to be seen to what extent there is a ‘fit’ between the determinants and dynamics of state collapse and the responses and solutions for restoration which are offered.     

Optimal Spectral Acceleration-based Intensity Measure for Seismic Collapse Assessment of P-Delta Vulnerable Frame Structures

This study proposes an “optimal” spectral acceleration-based intensity measure (IM) to assess the collapse capacity of highly inelastic frame structures vulnerable to the P-delta effect. The IM is derived from the geometric mean of the spectral pseudo-acceleration over a certain period interval. The lower bound period of the averaging interval is related to the mode in which 95% of the effective modal mass is exceeded. The upper bound period is 1.6 times the fundamental period. This IM provides minimum, or close to the minimum, dispersion for frames with different fundamental periods of vibration, or number of stories.     

YIELDING OSCILLATOR UNDER TRIANGULAR GROUND ACCELERATION PULSE

An analytical solution is presented for the response of a bilinear inelastic simple oscillator to a symmetric triangular ground acceleration pulse. This type of motion is typical of near-fault recordings generated by source-directivity effects that may generate severe damage. Explicit closed-form expressions are derived for: (i) the inelastic response of the oscillator during the rising and decaying phases of the excitation as well as the ensuing free oscillations; (ii) the time of structural yielding; (iii) the time of peak response; (iv) the associated ductility demand. It is shown that when the duration of the pulse is long relative to the elastic period of the structure and its amplitude is of the same order as the yielding seismic coefficient, serious damage may occur if significant ductility cannot be supplied. The effect of post-yielding structural stiffness on ductility demand is also examined. Contrary to presently-used numerical algorithms, the proposed analytical solution allows many key response parameters to be evaluated in closed-form expressions and insight to be gained on the'response of inelastic structures to such motions. The model is evaluated against numerical results from actual near-field recorded motions. Illustrative examples are also presented.     

What Maya Collapse? Terminal Classic Variation in the Maya Lowlands

Interest in the lowland Maya collapse is stronger than ever, and there are now hundreds of studies that focus on the era from approximately A.D. 750 to A.D. 1050. In the past, scholars have tended to generalize explanations of the collapse from individual sites and regions to the lowlands as a whole. More recent approaches stress the great diversity of changes that occurred across the lowlands during the Terminal Classic and Early Postclassic periods. Thus, there is now a consensus that Maya civilization as a whole did not collapse, although many zones did experience profound change.     

Spatial Autocorrelation and the Classic Maya Collapse: One Technique, One Conclusion

A pair of articles appearing recently in this journal (Whitley & Clark, Journal of Archaeological Science12, 377-395, 1985; Kvamme, Journal of Archaeological Science17, 197-207, 1990) apply spatial autocorrelation analysis to the distribution of terminal long-count dates from southern Lowland Classic Maya monuments. The authors employ similar techniques yet arrive at contradictory conclusions regarding the presence of geographical patterning in the collapse of the Classic Maya civilization in this region. Kvamme's contention, however, that Whitley & Clark conducted an inappropriate analysis and arrived at an erroneous conclusion is unsubstantiated. Both articles present appropriate analyses and report results which support the presence of spatial patterning in the Lowland Maya dates.     

State Collapse and its Implications for Peace–Building and Reconstruction

At the beginning of the twenty–first century, terms such as state collapse and failed states are becoming familiar, regularly used in international politics to describe a new and frightening challenge to international security. The dramatic events of September 11 have pushed the issue of collapsed states further into the limelight. This article has two aims. Firstly, it explains the contextual factors that gave rise to the phenomenon of state collapse. In the early post–Cold War period, state collapse was usually viewed as a regional phenomenon, and concerns were mainly limited to humanitarian consequences for the local population and destabilizing effects on neighbouring countries. Now, state collapse is seen in a more global context, and concerns are directed at the emergence of groups of non–state actors who are hostile to the fundamental values and interests of the international society such as peace, stability, rule of law, freedom and democracy. Secondly, the article offers some observations about the normative implications of the phenomenon of state collapse for peace–building and reconstruction.     

Nothing Lasts Forever: Environmental Discourses on the Collapse of Past Societies

The study of the collapse of past societies raises many questions for the theory and practice of archaeology. Interest in collapse extends as well into the natural sciences and environmental and sustainability policy. Despite a range of approaches to collapse, the predominant paradigm is environmental collapse, which I argue obscures recognition of the dynamic role of social processes that lie at the heart of human communities. These environmental discourses, together with confusion over terminology and the concepts of collapse, have created widespread aporia about collapse and resulted in the creation of mixed messages about complex historical and social processes.     

Cumulative Ductility Spectra for Seismic Design of Ductile Structures Subjected to Long Duration Motions: Concept and Theoretical Background

A seismic design procedure that does not take into account the maximum and cumulative plastic deformation demands that a structure will likely undergo during severe ground motion could lead to unreliable performance. Damage models that quantify the severity of repeated plastic cycling through plastic energy are simple tools that can be used for practical seismic design. The concept of constant cumulative ductility strength spectra, developed from one such model, is a useful tool for performance-based seismic design. Particularly, constant cumulative ductility strength spectra can be used to identify cases in which low-cycle fatigue may become a design issue, and provides quantitative means to estimate the design lateral strength that should be provided to a structure to adequately control its cumulative plastic deformation demands during seismic response. Design expressions can be offered to estimate the strength reduction factors associated to the practical use of constant cumulative ductility strength spectra.     

Allowing Traffic Over Mainshock-Damaged Bridges

A criterion is proposed for deciding whether, after a damaging mainshock, a bridge can still be open for either emergency or ordinary traffic. The criterion is based on the comparison between the collapse risk of the mainshock-damaged structure and the pre-mainshock risk of the intact structure. The approach requires fragilities for multiple damage states for the intact structure, and transition probabilities from these states to collapse for the damaged structure. The aftershock risk decreases with time, hence a decision for reopening might have to wait until the risk level goes down to an acceptable value. A realistic application demonstrates the approach.