Collapse Capacity Research Articles

On the collapse of thick-walled steel pipes under coupling initial geometric imperfection and corrosion defect

ABSTRACT Initial geometric imperfections and corrosion defects were considered as two of the most common imperfections for subsea pipes, which could lead to an inevitable reduction of collapse capacity. In this study, the coupling effect of both types of defects on the collapse performance was investigated numerically, with a particular focus on the relative corrosion position as described by defect location angle (DLA). A customised numerical framework was established to efficiently build FE models with various corrosion defects and imperfect geometry. Verification of the finite element (FE) model was performed using existing experiments in the open literature. In addition, extensive sensitivity studies were then conducted for several key problem parameters, including defect length, width, depth, initial ovality, and DLA. The variation of normalised collapse pressure with DLA exhibits two types of trajectories, namely ‘Minor Decrease’ and ‘Constant-Decrease-Constant’ responses. In the first, the normalised collapse pressure decreases slightly with increasing DLA. Among these cases, if the ratio stays above or close to 1.0, the collapse takes the form of classical ovalization mode. In contrast, for cases below 1.0, the collapse occurs in the corroded region. For the latter type of trajectory, the normalised collapse pressure follows a ‘Constant-Decrease-Constant’ path, and the collapse mode involves ovalization, anti-ovalization, non-symmetrical and U-shaped pattern. Subsequently, a series of empirical formulas were proposed upon extensive simulation results to predict the collapse pressure of non-symmetrical defect pipes.

Effectiveness of Instantaneous Power in predicting the collapse responses of structures under pulse-like ground motions by Esra ZENGİN

This study investigates the performance of the Instantaneous Power (IP(T1)) intensity measure (IM) for predicting the structural collapse of structures under near-fault pulse-like ground motions. The efficiency and sufficiency of vector IM consisting of elastic spectral acceleration at the fundamental period of the structure (Sa(T1)) and IP(T1) are compared with those obtained using Sa(T1), average spectral acceleration (Saavg), and spectral shape-based vector IMs. A proportional reduction in error, which quantifies to what extent the other ground-motion parameter eliminates the error in the collapse capacity prediction relative to IM of interest, is used to assess the sufficiency. Our findings reveal that [Sa(T1), IP(T1)] yields better collapse capacity prediction compared to all IMs considered and is found to be sufficient with respect to most of the seismological parameters, duration-related IMs, pulse period, and scale factor.

Post-earthquake fire collapse performance and residual story drift fragility of two-dimensional structural frames

Structural systems have deteriorated seismic performance as they are exposed to thermal effect due to dependency of material properties to temperature. Following an earthquake, once structure has already some residual displacement, fire ignition is very likely to occur. This makes it necessary to evaluate structural response of a building considering the fire event which follows an earthquake to have robust evaluation of structural response. Thus, it is required to model structural systems with consideration of both earthquake and thermal loads to capture multi-hazard behavior. In this study, performance of two-dimensional steel frames in case of fire following an earthquake is evaluated and collapse parameters of frames are calculated. Fragility curves related to collapse and residual story drift demands are given, and comparison of results between earthquake and fire-following-earthquake is illustrated. In addition, collapse probability of frames in fifty years is also given. Results of collapse performance evaluation are adjusted with the consideration of expected seismic hazard on site. Median collapse capacity decreases more than 30% and there is an apparent increase in collapse probability of fire-exposed frames in fifty years, which is more than three times for some frames.

Sidesway collapse capacity of the bottom-story-stiffness-irregular moment-resisting frames

This paper proposes a new procedure to estimate the seismic sidesway collapse capacity of the frame structures including the stiffness irregularity effects at the first (bottom) story. The presented method is based on the pushover analysis procedure and is easy to use. A large number of generic structures with various structural characteristics are developed to simulate the seismic collapse response of the frames. In this study, a comprehensive databank of the seismic demands for the generic structures is first developed by using the Incremental Dynamic Analysis (IDA) and pushover analysis procedures. A simple equation is then presented to estimate the seismic sidesway collapse capacity of the frame structures using multivariate linear regression analysis. After examining different multivariate regression models, a logarithmic equation is proposed to connect the collapse capacities predicted by the exact IDA procedure to the structural parameters derived from an idealized capacity curve. The proposed method is verified by analyzing 45 example frames and comparing its collapse capacities with those given by the exact IDA approach. The results clearly show that the proposed procedure is reliable and can predict the seismic collapse capacity of the regular and the first-story stiffness-irregular frames with sufficient accuracy.

The collapse margin ratio of steel frames considering the vertical component of earthquake ground motions

The FEMA P695 methodology does not consider the application of the vertical component of ground motions in nonlinear response history dynamic analyses for obtaining collapse margin ratios. The vertical component of earthquake affects the demand on the steel moment frame and flexural capacity of the columns in interaction with the fluctuating axial load. This paper investigates the effect of the vertical component of far- and near-field ground motions on the seismic collapse capacity of low-, mid-, and high-rise buildings. Various span lengths, story heights, and seismic mass ratios have been taken into account to cover the significant parameters in amplifying vertical earthquake damages. More than 50,000 nonlinear response history dynamic analyses are performed to obtain seismic collapse margin ratios considering (1) the horizontal components of ground motion, (2) the horizontal plus vertical components of the earthquake, (3) the horizontal components of ground motion along with dead load factors suggested by ASCE7–16 to represent the vertical earthquake loading. Results are compared numerically, and the robustness of the procedure suggested by ASCE7–16 is assessed. It is shown that the adverse effect of the vertical component of the earthquake on the collapse capacity of the considered archetype buildings increases with the increase in the fundamental vertical period of buildings. Finally, adjusting equations using dimensionless parameters are developed for estimating the seismic collapse margin ratio of structures considering the vertical component of the ground motion. The proposed equations adjust the corresponding collapse margin ratio obtained using the horizontal components of ground motion.

Improving anti-progressive collapse capacity of welded connection based on energy dissipation cover-plates

In view of the poor robustness of fully welded connections, energy dissipation cover-plates (EDCs) were proposed in this study with the aim of improving their anti-progressive collapse capacity. First, the stress law and failure modes of the EDCs were revealed through the study of 13 uniaxial tensile test specimens, and the calculation formulas for the collapse resistance and corresponding deformation of the EDC were determined by theoretical analysis. Then, a design method for a fully welded connection with EDCs was proposed according to the forming principle of the double plastic regions and the deformation coordination principle of the EDC and beam flange. The analysis results show that the design method verified by analyzing three series of numerical examples is reasonable. The collapse resistance and deformation of the substructures with EDCs were increased by 78%–120% and 140%–182%, respectively, compared with those of substructures without EDCs. Moreover, the substructures with EDCs formed an obvious resistance improvement stage. The beam members in the substructure with EDCs can yield completely before connection failure, which enhances the catenary mechanism and delays the failure of the connection. The energy generated by the vertical load dissipation in the structure with EDCs can be increased to approximately twice that of the original structure. Therefore, adding EDCs is conducive to the dissipation of the energy generated by vertical loads and to the improvement of the collapse resistance of a fully welded connection.

Hazard-consistent seismic losses and collapse capacities for light-frame wood buildings in California and Cascadia

We evaluate the seismic performance of modern seismically designed wood light-frame (WLF) buildings, considering regional seismic hazard characteristics that influence ground motion duration and frequency content and, thus, seismic risk. Results show that WLF building response correlates strongly with ground motion spectral shape but weakly with duration. Due to the flatter spectral shape of ground motions from subduction events, WLF buildings at sites affected by these earthquakes may experience double the economic losses for a given intensity of shaking, and collapse capacities may be reduced by up to 50%, compared to those at sites affected by crustal earthquakes. These differences could motivate significant increases in design values at sites affected by subduction earthquakes to achieve the uniform risk targets of the American Society of Civil Engineers (ASCE) 7 standard.

Risk-targeted seismic design of reinforced concrete moment-resisting-frame buildings

The seismic design of new structures in Iran is currently based on earthquake hazard maps for a fixed return period of 475 years. However, this can lead to an unequal level of risk due to uncertainty in collapse capacity and differences in hazard curves in different locations. In the work reported in this paper, a risk-targeted approach was used to determine the peak ground acceleration (PGA) for designing reinforced concrete moment-resisting-frame (RC MRF) buildings in four important port cities in southern Iran. The three main parameters considered for determining risk-targeted PGA were the structural fragility curve, the seismic hazard curve and the target annual collapse probability. Nine RC MRF buildings with different geometrical characteristics were evaluated and their fragility curves were extracted. Then, using a risk integral, the annual collapse probability and PGA of the frames were obtained for the studied cities. Comparison of the results showed that an approach proposed in the literature for Europe is in accordance with the results of the approach proposed in this paper.

Effect of bidirectional excitation on seismic performance of regular RC frame buildings designed for modern codes

The existing practice to estimate seismic performance of a regular building is to carry out nonlinear time history analysis using two-dimensional models subjected to unidirectional excitations, even though the multiple components of ground motion can affect the seismic response, significantly. During seismic shaking, columns are invariably subjected to bending in two orthogonal vertical planes, which leads to a complex interaction of axial force with the biaxial bending moments. This article compares the seismic performance of regular and symmetric RC moment frame buildings for unidirectional and bidirectional ground motions. The buildings are designed and detailed according to the Indian codes, which are at par with the other modern seismic codes. A fiber-hinge model, duly calibrated with the biaxial experimental results, is utilized to simulate the inelastic behavior of columns under bidirectional bending. A comparison of the estimated seismic collapse capacity is presented, illustrating the importance of considering the bidirectional effects. The results from fragility analysis indicate that the failure probabilities of buildings under the bidirectional excitation are significantly higher as compared to those obtained under the unidirectional excitation.

Modelling catastrophic degradation of flexural-dominated RC columns at ultimate displacements based on fibre beam-column model

Catastrophic degradation of the mechanical strength of reinforced concrete (RC) columns at ultimate displacements is one of the critical factors for the seismic collapse of structures. Accurately predicting this degradation is critical to assess the seismic collapse capacity of structures. However, the mechanism and theory about the degradation of RC columns are insufficient at present. This study is devoted to revealing the cause of catastrophic degradation and establishing an updated fibre beam-column model for predicting the catastrophic degradation of RC columns at ultimate displacements. First, the de-confinement effect of kernel concrete at ultimate loading displacements is described based on experimental observation and the stress state analysis of the confined concrete. The kernel concrete in the confined zone is shifted from confinement state to de-confinement state during the loading cycles. Next, an updated fibre beam-column model is proposed where a uniaxial stress-strain relation considering the de-confinement effect is introduced to represent the behaviour of kernel concrete during the loading cycles. The validity of the proposed model is confirmed by comparing experimental results and model results. Compared with the classical fibre beam-column model, the detailed discussions about the load-displacement response, moment-curvature, and strain distribution during loading cycles showed that the updated model achieves reasonable prediction of catastrophic degradation of RC columns by capturing the state shift of kernel concrete. At last, the applicability of the proposed model is discussed. Existing models including Panagiotakos and Fardis model, Eurocode 8 model, and ASCE 41 model are used as comparative models to evaluate the model accuracy of predicting the ultimate drift ratio of RC columns.

Seismic collapse safety analysis of performance-based optimally designed reinforced concrete frames considering life-cycle cost

The present paper aims to assess the seismic collapse capacity of reinforced concrete (RC) frames optimized in the context of performance-based design. The proposed methodology in this work consists of two main phases namely, performance-based design optimization and seismic collapse safety assessment. In the first phase, an efficient metaheuristic algorithm is employed to carry out single-objective optimization of RC frames in the framework of performance-based design with two different objective functions including initial construction cost and total cost. In the second phase, the seismic collapse capacity of optimally designed RC frames is evaluated by conducting seismic fragility analysis. Three illustrative examples of 3-, 6-, and 12-story RC frames are presented to demonstrate the capability of the proposed methodology for designing of cost-efficient structures with considerable seismic collapse safety.

Collapse capacity of masonry domes under horizontal loads: A static limit analysis approach

A static limit analysis approach is proposed for assessing the collapse capacity of axisymmetric masonry domes subject to horizontal forces. The problem formulation is based on the sound theoretical framework provided by the classical statics of shells. After introducing the shell stress resultants on the dome mid-surface, integral equilibrium equations are enforced for its typical part. Heyman’s assumptions of infinite compressive and vanishing tensile strengths are made, with cohesive-frictional behavior governing the shear strength, to characterize the admissible stress states in the dome. An original computational strategy is developed to address the resulting static limit analysis problem, involving the introduction of a mesh on the dome mid-surface, the interpolation of the physical components of the shell stress tensors on the element boundaries, and the imposition of equilibrium and admissibility conditions respectively for the elements and at the nodes of the mesh. The descending discrete second-order cone programming problem is solved by standard and effective optimization tools, automatically providing collapse multiplier of horizontal forces, incipient collapse mechanism and expected crack pattern. Convergence analysis, validation with experimental results available in the literature, and parametric analyses with respect to geometric parameters and material shear response, are presented for spherical and ellipsoidal masonry domes, proving the reliability of the proposed approach for estimating the pseudo-static seismic resistance of masonry domes. Finally, as an application to a real structure, the pseudo-static seismic assessment of the central dome of the Taj-Mahal is presented.

Adaptive hysteretic model for reinforced concrete columns including variations in axial force and shear span length

AbstractIn this study, a hysteretic model is developed for simulating the nonlinear response of reinforced concrete columns with strength degradation behavior under cyclic loading. During analysis, the proposed model exhibits the ability to adjust the model parameters assigned to the model continually, based on the monitored element boundary conditions. A semi‐empirical relationship between model parameters and boundary conditions is formulated from experimental evidence, which is used to adjust the model parameters. The boundary conditions that are monitored include the axial load acting on the column section and shear span length; these are known to have a significant effect on capacity in terms of strength and ductility. The developed model was implemented in the widely used research‐oriented structural analysis software, OpenSees. To simulate the nonlinear response of the columns, model parameter predictive equations composed of input parameters such as material strength, reinforcement layout, and specimen geometry were developed using lasso regression. As an application of the proposed column model, an eight‐story code‐conforming frame building was selected to perform incremental dynamic analyses based on 44 far‐field ground motions. The numerical results showed that, without the model parameter adaptation feature, the median collapse capacity and residual story drift can be significantly overestimated.

Seismic fragility of structures with energy dissipation devices for mainshock-aftershock events

This paper presents a mainshock-aftershock seismic fragility and collapse capacity assessment of reinforced concrete (RC) structures retrofitted with a hybrid damper composed of a steel slit plate and friction pads. Three and eight-story RC buildings are designed and assessed before and after retrofit considering the aftershocks effect. Non-linear time-history response analysis (NLTHA) using twelve natural earthquake sequences are used to produce incremental dynamic analysis (IDA) curves to obtain the median collapse capacity of the structures. Three different damage state (DS) levels are used for the mainshock ground excitation to quantify the scale factors required for conducting the aftershock IDAs. The maximum inter-story drift ratio (MIDR) is used as the main engineering demand parameter. The study shows the importance of considering the aftershock in the seismic assessment process of RC structures. The un-retrofitted structures are found to experience a high level of deterioration under aftershock event which is not considered in the design stage. The findings of the study reveal that the mainshock-aftershock sequence responses of the retrofitted structures show better performance in terms of the median collapse capacity and the seismic fragility compared to the un-retrofitted ones.

Development of vehicle body-in-white section optimization framework for crash performance by introducing a combined collapse capacity criterion

Enhancing the stiffness and crash characteristics of the vehicle body structure is among the most important concerns of auto manufacturers. Typically, enhancing these attributes leads to an increase in the vehicle’s mass, and as a result, a suitable optimization scheme is needed. In crash scenarios, collapsing of a section causes the load path to lose its load-carrying capability and degrades the crash safety of the vehicle. As a result, the sections should be designed accordingly, so that their collapse capacities be as high as possible. Although there are some research works that deal with the analysis and optimization of thin-walled members for stiffness or crash objectives, utilization of optimization methods for the design of vehicle sections against collapsing is still absent in the literature. In this regard, the present paper proposes an optimization framework that takes into account the collapse capacity and stiffness of the sections and optimizes their weight. Analytic formulations are derived to calculate the collapse capacity of sections under pure axial force and bending moment. The formulations are verified via finite element (FE) simulations. It is shown that the average absolute difference between the formulation results and explicit FE solver is less than 12%. Considering the highly nonlinear nature of the problem, this is a reasonably accurate approximation. Moreover, a combined collapse capacity criterion (CCCC), as a handy design guide for engineers, is also proposed for the first time to take into account the combination of axial and bending load cases. It is based on the FE analyses of numerous automotive sections in different load cases. To facilitate the optimization process, a new software interface named “JSec Design” is developed and introduced that is much faster than existing FE-based optimizers. Finally, as a case study, an automotive A-pillar section is designed under a combination of axial force and bending moment.

Seismic fragility assessment of self-centering hybrid precast walls subjected to mainshock-aftershock sequences

This study primarily investigates the seismic fragility of mainshock damaged self-centering (SC) hybrid precast walls in aftershocks, and the results are compared with equivalent conventional reinforced concrete (RC) walls. A 5-story case-study structure is selected and designed comparatively using SC walls and RC walls to resist all the lateral seismic forces for design requirements. Thereafter, nonlinear time history incremental dynamic analyses (IDA) are conducted for the two analytical wall models using 44 artificially constructed seismic sequences. In the first step, mainshock IDA analyses are performed followed by aftershock IDA analyses considering different mainshock damages on the considered wall models. Three mainshock damage levels relating to three distinct post-mainshock inter-story drift ratios are induced in both wall models. The IDA curves in terms of maximum inter-story drift and residual drift are produced and comparatively studied for both wall models at predefined mainshock damage levels. The results are investigated and compared regarding seismic collapse capacity, residual drift, and effects of the polarity of aftershocks. It indicates from the study that in a general sense, the SC walls and RC walls exhibit similar collapse capacities for both undamaged conditions (i.e., subjected to mainshock only) and damaged conditions (with distinct mainshock damage levels). However, SC walls are intrinsically designed with significantly reduced residual drifts (proved again in this study), which results in much less influence from the aftershock polarity as compared to RC walls.

A finite difference method for the static limit analysis of masonry domes under seismic loads

The static limit analysis of axially symmetric masonry domes subject to pseudo-static seismic forces is addressed. The stress state in the dome is represented by the shell stress resultants (normal-force tensor, bending-moment tensor, and shear-force vector) on the dome mid-surface. The classical differential equilibrium equations of shells are resorted to for imposing the equilibrium of the dome. Heyman’s assumptions of infinite compressive and vanishing tensile strength, alongside with cohesive-frictional shear response, are adopted for imposing the admissibility of the stress state. A finite difference method is proposed for the numerical discretization of the problem, based on the use of two staggered rectangular grids in the parameter space generating the dome mid-surface. The resulting discrete static limit analysis problem results to be a second-order cone programming problem, to be effectively solved by available convex optimization softwares. In addition to a convergence analysis, numerical simulations are presented, dealing with the parametric analysis of the collapse capacity under seismic forces of spherical and ogival domes with parameterized geometry. In particular, the influence that the shear response of masonry material and the distribution of horizontal forces along the height of the dome have on the collapse capacity is explored. The obtained results, that are new in the literature, show the computational merit of the proposed method, and quantitatively shed light on the seismic resistance of masonry domes.

Effect of Proportioning of Lateral Stiffness in Orthogonal Directions on Seismic Performance of RC Buildings

ABSTRACT Effect of different proportioning of lateral force-resisting system in the orthogonal directions, on seismic collapse capacity and fragility of reinforced concrete buildings is investigated. Buildings with different structural systems and configurations, are designed for a modern seismic design code. To simulate the structural collapse, the hysteretic models of beams, columns, and shear walls are duly calibrated using experimental tests results. Results show that if the buildings of a given height are designed for the same hazard level, these show equal levels of safety against collapse, irrespective of the proportioning of lateral load resisting systems in the orthogonal directions.

Design of computer experiments for developing seismic surrogate models

Surrogate models are growing in popularity within the earthquake engineering community because of their ability to increase the efficiency of computationally intensive tasks. This article examines the design of computer experiments (DoCE) for the purpose of developing seismic surrogate models. Two categories of DoCE approaches are discussed while underscoring the benefits and drawbacks of specific methods. Further insight is provided through an illustrative case study that develops surrogate models to predict the median collapse capacity and expected annual losses in single-family woodframe buildings with cripple walls. The implications of the chosen DoCE method on the predictive performance and efficiency (in terms of the required number of explicit simulations) of the associated surrogate models are closely examined. The results show that both factorial and Latin hypercube designs [Formula: see text] do not perform well when different approaches are used to generate the training and testing sets (i.e. out-of-design-type testing). An efficient hybrid design that combines an orthogonal array-based composite design with a small number of [Formula: see text] samples is shown to produce a surrogate model with superior predictive performance.

Probabilistic Seismic Demand Model and Seismic Fragility Analysis of NPP Equipment Subjected to High- and Low-Frequency Earthquakes

This study presents the Probabilistic Seismic Demand Model (PSDM) and explores optimal intensity measures (IMs) for nuclear power plant (NPP) equipment when subjected to ground motions having high-frequency (HF) and low-frequency (LF) contents. To this end, the PSDM is first constructed in terms of the IM and the corresponding engineering demand parameter, and its outcomes are utilized to select the optimum IMs based on the satisfaction of certain essential properties (i.e., efficiency, practicality, and proficiency). Regarding earthquake excitation, different IMs (i.e., structure-independent and structure-dependent IMs) are studied. The results show that the most appropriate IMs for the seismic performance of the cabinet are velocity spectrum intensity and spectral accelerations for the structure-independent IMs and the structure-dependent IMs, respectively. Moreover, fragility analysis is performed to assess the vulnerability of NPP equipment. The outcomes indicate that the cabinet is highly vulnerable to HF earthquakes as a consequence of response amplification. In addition, the selection of the earthquake IM has an important influence on the collapse capacity of the cabinet, and the fragility curves obtained from structure-dependent IMs are more reliable in comparison to those of structure-independent IMs.