Collapse Limit State Research Articles

Seismic drifts of buildings through deep neural networks circumventing incremental dynamic analysis: Aims and pitfalls for robust and reliable predictions

In the field of seismic response assessment, simplified procedures have long been pursued to circumvent the rigorous, state-of-the-art nonlinear response history analysis (NRHA) and incremental dynamic analysis (IDA) that typically require tedious computations. To this end, this study investigates artificial neural networks (ANN) as prediction models to bypass IDA and quickly and reliably determine the structural drift responses of buildings, without employing surrogate models or analysis techniques that lower the quality of the estimates. Three designs of such prediction models are identified in terms of their scope, implementation and corresponding database, commonly employed in research, while identifying common pitfalls in their design. The investigations involve ten steel-frame multi-story structures, considering cyclic and in-cycle material deterioration and P-Delta phenomena. More than 17-thousand recorded ground motions (GM) are employed to perform IDA on these frame-building models, resulting in a unique database of responses ranging from linear to collapse, with more than 3-million NRHA. Based on this database, a prediction model is developed for each building, capable of predicting the IDA under a GM excitation not included in the database. Additionally, another prediction model is developed that can predict the IDA of a building under a GM excitation, both of which are not included in the database. These investigations show that ANN are excellent tools to circumvent IDA and capture the record-to-record uncertainty by rapidly and reliably predicting structural drifts ranging from linear responses to the collapse limit state, while building-to-building predictions are additionally feasible if the employed database is appropriate.

Test on progressive collapse of steel moment-resisting frame with upper-and-lower flange angle steel connection

Both of test and numerical simulation methods are employed to study the vertical progressive collapse and collapse assessment methods of steel frame under accidental loads. Firstly, a steel frame collapse test model with a geometric similarity ratio of 1:1.5 is designed and manufactured. The ends of column of test model is fixed. The upper and lower flange angle steel connection is used. The far end of the beam is constrained by a controllable sliding hinge support. The various stages of vertical progressive collapse of structures are simulated by a large displacement loads applied at the far end of the beam. The main focus of the testing is to examine the stress and deformation of beam and joint at various stages, particularly the development of stress and deformation in the angle steel attached to the beam-column connection. The development law of collapse load-displacement curve, joint rotation, beam strain, and angle steel strain are analyzed. The structural resistance mechanism and the transformation relationship between resistance mechanisms during collapse are studied. Subsequently, the relationship between the structural dynamic increase factor curve and the structural collapse process is analyzed using finite element method. The results show that the strain of angle steels can better reflect the destruction and deformation process of substructure during the collapse, the collapse resistance mechanism of structure, and the transition between resistance mechanisms.With the help of the characteristic points on the structural dynamic increase factor curve, the collapse limit state of structure can be reliably determined.

A novel approach for quantifying dynamic impacts on steel frames induced by instantaneous interior column loss

This research presents an innovative approach to accurately quantify dynamic impacts on the steel frame structure resulting from the instantaneous loss of an interior column. This methodology effectively calculates the dynamic amplification factor (DAF) when the steel frame reaches its collapse limit state and predicts the structure's deformation under such a scenario. Central to this approach is the conversion of the static load-deformation curve, pertinent to a scenario of interior column loss, into a dynamic force load-deformation curve using the concept of energy balance. A comprehensive parametric analysis was conducted to study how different structural parameters, such as beam depth, span, slab thickness, rebar diameter, and slab aspect ratio, affect the enhancement factor (i.e., the ratio of collapse resistance to yield resistance). A pragmatic formula for determining enhancement factor was subsequently suggested. Moreover, this study delved into how these structural parameters influence the dynamic amplification factor at the collapse state, revealing a notable dependency of dynamic amplification factor on the slab aspect ratio that an increasing aspect ratio correlates with a rising dynamic amplification factor trend. The manuscript also presented a detailed methodology for computing the dynamic deformation of frame structures in the event of an instantaneous interior column loss. The results of the case study show that the proposed method closely matches the accuracy of numerical analyses, with differences falling within a 15% range.

Determination of dynamic collapse limit states using the energy-based method for multi-story RC frames subjected to column removal scenarios

The Alternative Load Path method is widely adopted to perform progressive collapse analyses for reinforced concrete (RC) frame structures subjected to column removal scenarios. Considering that the progressive collapses are usually dynamic phenomena, nonlinear dynamic analyses can yield the most accurate results. However, the associated computational cost is high. Alternatively, the energy-based method (EBM) can be employed to efficiently calculate the maximum dynamic responses. Unfortunately, collapse or dynamic limit states (DLS) cannot be directly determined when the EBM is adopted for the progressive collapse analyses, because it is essentially a quasi-static approach. To tackle this issue, in this paper an EBM-Intersection Point-based (EBM-IP-based) method is proposed to effectively determine the DLS. The method is considering that the dynamic instability will occur once the dynamic capacity curve exceeds the corresponding static capacity curve. Hence, it is possible to determine the DLS by making a correction on the intersection point of the aforementioned two curves without performing nonlinear dynamic time-history analyses. Compared with the other energy components, the kinetic energy at the moment of the peak displacement response is relatively small and the effectiveness of the EBM is verified. Through both static pushdown analyses and incremental dynamic analyses for 48 column removal scenarios of six different multi-story RC frames, the effectiveness of the proposed EBM-IP-based method is verified and the associated coefficients are calibrated. Statistical information and (joint) probabilistic density functions (PDF) of the coefficients are identified. Further, stochastic analyses are carried out in order to quantify the model uncertainties when adopting the EBM-IP-based method. On the basis of all the calculation results, a Gumbel distribution is adopted to capture the PDF of the model uncertainty in relation to displacements, while a lognormal distribution is adopted to fit the PDF of the model uncertainty in terms of resistances. Moreover, a multi-variate Gaussian distribution model with two components is employed to fit the joint PDF.

Hybrid simulation of a steel frame with Dissipative Replaceable Link Frames

In the last decades, high priority has been given to enhancing the seismic resilience of structures by reducing the damage of structural and non-structural elements after a disaster. In this context, the European Research Fund for Coal and Steel (RFCS) project DISSIPABLE was funded to perform large demonstration tests of steel frames equipped with easily repairable seismic dissipative devices. The paper extensively describes the experimental campaign carried out at the University of Trento on a steel frame equipped with innovative Dissipative Replaceable Link Frame (DRLF) systems, composed of two rigid columns connected by weakened beams at their ends. Hybrid Simulation was employed, enabling to physically test the first floor of the building yet allowing for considering the response of the remaining five floors, which were numerically simulated. A bidimensional frame was tested under increasing seismic intensity levels: Damage Limitation, Significant Damage and Near Collapse limit states. The experimental results proved that the DRLF system was able to dissipate energy and protect the primary elements of the structure from plasticisation. Moreover, the structure's re-centring capability was verified to ensure the components' replaceability. Finally, the calibration of the nonlinear model was performed following the tests, which allowed to develop a high-fidelity model suitable for further numerical investigation.

Seismic Fragility Reduction for Base Isolated RC Frame Buildings by Curved Surface Sliding Bearings with Over-Stroke Displacement Capacity

ABSTRACT Recently, experimental studies on failure conditions of buildings equipped with curved surface sliding isolators have shown that when no displacement restraining elements are employed and the concave plates feature a flat rim, the inner slider can run on the edge of the sliding surfaces producing lateral displacement larger than the nominal isolator capacity. The over-stroke displacement capacity reduces the probability of seismic collapse of code-conforming base-isolated buildings for earthquake stronger than the design one. In order to quantify the benefit of the over-stroke displacement capacity of double concave curved surface slider (DCCSS) bearings on the seismic fragility of base isolated buildings, four case studies of six-storey reinforced concrete framed structures, consisting of new constructions and retrofit of existing structures located in high and medium hazard seismic sites, have been investigated in this paper. In all cases, two configurations of the isolation system have been considered, with end-stop displacement or with over-stroke displacement capacity. The seismic performance of the buildings has been investigated by multi-stripe nonlinear time-history analysis. The results of the nonlinear dynamic analysis at the collapse limit state have been compared with nonlinear static analysis in terms of maximum displacement and corresponding base shear. Fragility curves highlight a higher safety margin against collapse for seismic intensities beyond the design limit state of the isolation system with over-stroke capacity.

Rapid Visual Screening Feature Importance for Seismic Vulnerability Ranking via Machine Learning and SHAP Values

Structures inevitably suffer damage after an earthquake, with severity ranging from minimal damage of nonstructural elements to partial or even total collapse, possibly with loss of human lives. Thus, it is essential for engineers to understand the crucial factors that drive a structure towards suffering higher degrees of damage in order for preventative measures to be taken. In the present study, we focus on three well-known damage thresholds: the Collapse Limit State, Ultimate Limit State, and Serviceability Limit State. We analyze the features obtained via Rapid Visual Screening to determine whether or not a given structure crosses these thresholds. To this end, we use machine learning to perform binary classification for each damage threshold, and use explainability to quantify the effect of each parameter via SHAP values (SHapley Additive exPlanations). The quantitative results that we obtain demonstrate the potential applicability of ML methods for recalibrating the computation of structural vulnerability indices using data from recent earthquakes.

Performance Assessment of Reinforced Concrete Bridges Under Coupled Horizontal and Vertical Ground Motions Using Fragility Surfaces

ABSTRACT The objective of this study is to explore the seismic fragility of reinforced concrete bridges, specifically in response to the vertical components of ground motions, utilizing fragility surfaces. The examination of bridge responses involves the application of optimally selected intensity measures through three-dimensional nonlinear time-history analyses, encompassing uncertainties in both superstructure materials and soil–structure interaction effects. In this investigation, an extended Probabilistic Seismic Demand Model (e-PSDM) is employed, leveraging fragility surfaces to concurrently consider vertical and horizontal excitations. The results obtained from this approach are compared with traditional fragility curves. This study emphasizes Pile-cap displacement and drift ratio as pivotal engineering damage parameters, acknowledging their sensitivity to the influences of both soil–structure interaction effects and vertical ground motion. The fragility surfaces derived from the study reveal a correlation between increased vertical spectral accelerations and elevated probabilities of surpassing both slight damage and collapse limit states. These observations underscore the critical significance and practical utility of fragility surfaces in the context of performance-based seismic assessment and design for reinforced concrete bridges. The findings from this research contribute valuable insights into the nuanced behaviour of reinforced concrete bridges under seismic conditions, emphasizing the relevance of incorporating vertical components in fragility assessments for a more comprehensive understanding of structural vulnerability.

Post-earthquake fire performance of a steel moment-resisting frame

The effects of earthquakes and fires are typically analyzed separately in structural design. However, historical events highlight that fires following earthquake (FFE) can cause significantly more damage than an earthquake alone. The 1906 San Francisco earthquake exemplifies this, with fires destroying 80% of the city. Other major FFE events include Tokyo (1923), Kobe (1995), and Tohoku (2011) earthquakes. Earthquakes can damage infrastructure, leading to potential ignitions and structural fire performance deterioration. This paper focuses on the post-earthquake fire performance of a four-story five-bay steel frame using a probabilistic FFE framework to develop FFE fragility functions and consider uncertainties in the ground motions, compartmentation measures, fire development, and material properties. Damage to structural and non-structural components is considered. In this respect, the probabilistic FFE framework generates the fire scenarios based on seismic response. The seismic response is assessed through nonlinear time-history analyses. Then, post-earthquake fire ignitions in specific compartments are assessed based on the structural damage, determined by inter-storey drift ratio (IDR) and peak floor acceleration (PFA). Compartmentation and opening characteristics as well as the potential for fire spread are considered based on seismic damage in windows, doors, and partition walls following seismic fragility functions found in the literature. Finally, thermomechanical analyses are performed, and failure criteria based on displacement and displacement rate are applied to the beams and columns. The results of the probabilistic analyses were used to produce fragility functions to evaluate the probability of exceeding a limit state conditioned on an intensity measure in the context of FFE. A higher probability of exceeding the collapse limit state with shorter times to collapse was observed when the structure was subjected to higher values of spectral acceleration.

Behavior factor estimation for seismic design of unreinforced masonry buildings

The use of new geo-sourced construction materials in seismic areas requires the assessment of the structure ductility in order to properly design the building. This research aims to propose a procedure for behavior factor estimation in case of using a new construction material. In particular, in this paper, the proposed methodology is applied to an unreinforced masonry building in an average-risk seismic zone. Before application for seismic design, the reliability of the selected equivalent frame modeling approach is validated by comparison of dynamic features obtained from both numerical and operational modal analysis. An existing stone masonry building is selected as case study to validate the modeling approach. A measurement campaign provides the structural response to ambient vibrations and structural damping. After validating the model in elastic conditions, the building ductility capacity is estimated using a numerical pushover analysis, for different load combinations and distributions, according to the European design code, under the assumption of perfect plasticity. The proposed procedure provides a behavior factor obtained specifically for the analyzed building, using a relationship between ductility demand and behavior factor deduced from dynamic analysis. The average ductility demand is estimated numerically, for a set of synthetic acceleration signals compatible with the Eurocode elastic response spectrum and a given behavior factor. Finally, it is suggested to verify the near collapse limit state of the building structure not only in terms of target to capacity displacement ratio but also in terms of load ratio, since it can be more restrictive in some instances.

Seismic assessment of the steel Moment Resisting Frame equipped with friction beam‐to‐column joints

AbstractSupplementary dissipative devices are viable solutions to enhance the seismic response of building structures. In particular, friction devices are low‐cost and easy‐to‐maintain systems that can be easily inserted into moment‐resisting beam‐to‐column joints of steel Moment Resisting Frames. The effectiveness of dissipative friction joints has been widely demonstrated in many research project. In Europe, the first building equipped with such devices will be fabricated in Italy within the framework of the ongoing RFCS DREAMERS project. The preliminary seismic assessment of this prototype building using the framework of performance‐based earthquake engineering method at different performance levels is summarized in the present paper. To this end, nonlinear dynamic analyses are carried out on three‐dimensional (3‐D) models of the prototype developed in “OpenSees”. The results show that this type of structure can be free of damage under earthquakes corresponding to significant damage and near collapse limit states.

Prediction of the cyclic rotation capacity of steel members with cold‐formed hollow cross‐section

AbstractCold formed Hollow Structural Sections (HSS) are widely used in structural applications, especially in multi‐storey buildings located in seismic areas because of their high strength‐to‐weight ratio and torsional stiffness. However, the current version of the European seismic code provides limited rules and guidance to evaluate the ductility and the plastic rotation capacity of HSS members. The research activity carried out in this study aims to develop formulations to predict both the deformation capacity and the overstrength of cold formed HSS beams and columns at significant damage and near collapse limit states. Therefore, parametric finite element simulations have been carried out on a large set of members with different cross section (i.e., both square and rectangular HSSs), local and global slenderness, shear span and axial load ratio (from 0 to 0.5). The adopted finite element models have been calibrated against results of cyclic experimental tests available from the literature. The accuracy of the proposed equations has been statistically verified and discussion of practical applications is also provided.

Influence of uncertainties on the seismic performance assessment of chevron braced frames

In the framework of the probabilistic seismic response assessment of buildings, a key aspect is the evaluation of the influence of uncertainties on the mean annual frequency of exceedance of assigned limit states. In this regard, this study is focused on the seismic performance of concentrically braced frames in the chevron configuration. Out of the possible sources of uncertainties related to the numerical model (e.g. modelling of infills, soil-structure interaction), the effects of modelling of connections at the ends of braces are investigated by considering three different models: a model with pinned braces, a model with braces connected to beams and columns by means of rigid links simulating the gusset plates and a model with braces connected to beams and columns by means of elements with axial and flexural stiffnesses based on the real size of the gusset plates. In the two latter models out of plane buckling of braces is allowed. All the considered models are first validated against an experimental test and then used to estimate the fragility curves and the mean annual frequency of exceedance of Damage Limitation, Significant Damage and Near Collapse limit states of four case-study buildings. In addition to the uncertainty in the main characteristics of the seismic input, the uncertainties in the yield strength of material, equivalent viscous damping ratio, permanent and variable loads are also considered. The effects of these additional sources of uncertainty on the structural response are determined by comparing results provided by numerical models with random values of the uncertain variables with results provided by a single model with median values of the same variables. Finally, a simplified approach is proposed to simulate the effects of the additional uncertain variables in analyses of models with only variability in the seismic input.

Multi-hazard assessment of transmission line systems subjected to independent non-concurrent turbulent winds and ground accelerations

The design of transmission lines is based on the Load and Resistance Factor Design approach, considering that their collapse limit state is governed by climatic actions (wind and ice). Even so, accident reports indicate the regular observation of moderate to severe damage of towers after strong ground motions, affecting the structure’s capacity to withstand future load events. Therefore, integrating the concepts of Performance-Based and Multi-Hazard Design, successfully applied to buildings and still embryonic to transmission lines, seems to be promising. With such performance-based multi-hazard approaches, intermediate performances can be evaluated even when they are controlled by a non-dominant hazard. Hence, the present paper aims at performing an original multi-hazard assessment of a Chilean 230kV transmission line segment. For this purpose, direct geometric and material nonlinear time history analysis, using a finite element suitable for eccentrically loaded angle profiles (L-shaped cross-sections), is employed to construct the fragility curves. In addition, uncertainties in loads and material properties are accounted for to address the transmission line system failure probability. In the existing literature, fragility analysis has been performed through pushover approaches, whereas reliability has been assessed for a single structure rather than for the transmission line system, as recommended by line codes. Contrary to design practice, the results show that seismic loads control all limit states in TLs located from central to northern Chile. Numerical results presented in this paper are based on 5000 h of total computation time.

Effect of serviceability limit state and over-strength mechanism on seismic performance of self-centring low damage structures with friction connections

Low damage design is an alternative to conventional seismic design, where earthquake-induced damage in the building is controlled and minimised. The most common approach to implement this concept is to design the structural system in a way that damage occurs in a series of specified components. This makes the designer able to predict the performance of the building under earthquakes by deliberately designing these components weaker than the other parts of the structure. These components can be replaced, repaired, or even designed to remain functional after earthquakes. Therefore, the performance of such components (e.g. weak links) is critical for evaluting the performance of the building as a whole.The New Zealand standard defines two extra limit states in addition to the design level earthquake (Ultimate Limit State (ULS)). First is the Serviceability Limit State (SLS), where the system is expected to remain linear and elastic, and the second is the collapse limit state (also known as MCE limit state), where damage is accepted, but the building should not collapse. For a low damage system, the weak links should be designed to remain linear and elastic under SLS actions. Also, they should have adequate reserve capacity to not completely fail under MCE actions. The latter is also called the over-strength mechanism (or the upper bound design level) for designing the low damage components. This study investigates the effect of the over-strength and serviceability limit state on the overall seismic performance of low damage systems. Two types of generic structural responses are considered for the study, self-centring braced frames and self-centring rocking wall systems. Numerical models for both concepts are developed and subjected to nonlinear dynamic time-history analysis with different intensities up to large, rare events (MCE). The results showed that braced frames' appropriate over-strength capacity is relatively smaller than rocking walls. The findings of this study help designers and engineers to perform more efficient and optimised designs for low damage systems. Also, this research helps them to have a better understating of the performance of such systems under large, rare earthquake events.

Influence of the modelling approach on the seismic assessment of RC structures by nonlinear static analyses

Different modelling approaches are available for the evaluation of the nonlinear response of structures. The goals of this paper are to determine the implications of two frame modelling strategies, one based on lumped plasticity and the other on distributed plasticity combined with a fibre section modelling, to assess the differences in predicting the structural response of existing RC framed buildings, and to provide guidelines on the range of applicability of the two different modelling approaches. The study is carried out using two RC framed buildings as studies. Both buildings are characterized by seismic deficiencies typical of existing buildings belonging to the Mediterranean building stocks, but with different ductility capacities and collapse mechanisms. For each case study, two 3D numerical models are built in OpenSees, considering the above mentioned models. For each plan direction, two pushover analyses are run on each numerical model with two distributions of forces. The seismic response is assessed at the Damage Limitation (DL), Significant Damage (SD) and Near Collapse (NC) limit states. The seismic responses assessed by the two numerical models showed that the lumped phenomenological plastic hinge model tends to provide more conservative results than the distributed plasticity, fibre-section model, leading to relevant differences especially in case of structures with a low ductile behaviour.

Experimental analysis of a full-scale steel frame with replaceable dissipative connections

This work presents the experimental campaign performed on a full-scale 6-storey steel concentrically braced frame equipped with the so-called Dissipative Replaceable Braced Connection (DRBrC) made with plates of mild steel and high-strength steel. Such component, constituting the brace-column joint, is capable of dissipating large amounts of energy through wide hysteretic loops, while providing the possibility of being easily replaced after the building undergoes medium-high intensity earthquakes. To reduce the costs and, at the same time to obtain a representative response of the full frame, hybrid simulation tests were employed, in which only the ground floor was physically built in the laboratory. In contrast, the remainder of the structure was numerically simulated. The innovative frame was subjected to three different natural ground motions at the Damage Limitation (DL), Significant Damage (SD) and Near Collapse (NC) limit states, respectively. The outcomes highlighted the high potential of the DRBrC component in dissipating large amounts of energy and, at the same time, in protecting the remaining parts of the structure, by exhibiting very small residual displacements that enhance self-centring and repairability capabilities. Moreover, the numerical models were calibrated by including the non-negligible effect introduced by the bolt-hole clearances. All results are thoroughly described in the manuscript.

Evaluation of modelling uncertainties impact in older infilled frame RC structures

The seismic response of infilled frame reinforced concrete structures is affected by different sources of aleatory and epistemic uncertainties and is particularly sensitive to the modeling parameters evidenced by reported numerical and analytical studies. In the current study, a probabilistic sensitivity analysis is performed by nonlinear static (PNSA) and nonlinear dynamic analyses (PNDA) on a base-case infilled frame structure incorporating structural (beam, column) and non-structural (masonry infill) components behavior. Therefore, the state-of-the-art models of the most effective sources of nonlinear response employed herein as fiber section to depict the axial-moment interaction in frame components, bi-diagonal eccentric strut to capture the cracking and crushing of masonry infill, and the shear failure in columns caused by infill-frame interaction. Finally, results are illustrated by tornado plots incorporating probabilistic sensitivity to material and component parameters for operational (O), damage (D), life safety (L), and collapse (C) limit states. Results state that the building response is significantly affected by the modeling parameters of infill characteristics, mass source, and the damping of the structure.

Seismic Performance Assessment of Girder Bridges with Composite Rubber Bearings

The objective of this study is to analytically assess the effectiveness of a novel composite rubber bearing (CRB), which is proposed to enhance both the displacement and damping capacities of the laminated natural rubber bearing (LNB), in improving the seismic performance of girder bridges. Four numerical bridge models respectively with the unbonded and bonded LNBs and CRBs (i.e. ULNB, BLNB, UCRB, BCRB) are established based on the bearing restoring force models. Then, incremental dynamic analyses (IDAs) are performed to obtain the fragility functions and the estimated economic costs. The results show that the bearing fragilities of the two CRB bridges are between those of the two LNB ones, but the pier damage is obviously mitigated by the CRBs, leading to the lower system vulnerabilities and economic costs. Allowing bearing sliding can further reduce the damage probability of the piers, but enlarge that of the bearings especially for the collapse limit state.

Load and resistance factor design for bamboo reinforced concrete beam in ultimate flexural limit state

Building sustainable infrastructure brings back the idea of using environmentally friendly materials, such as bamboo, for reinforcing concrete structures. However, a design framework for bamboo reinforced concrete (BRC) structures is still in its early stages due to the inherent uncertainties in the properties of bamboo. The present work focuses on developing a load and resistance factor design (LRFD) framework for BRC beams subjected to flexure. Before developing the design framework, the major variables affecting the behaviour of BRC beams are identified — the tensile properties of bamboo, the compressive properties of concrete, the bond strength between them, and the load. BRC beams, with various reinforcement percentages, are investigated through real-life experiments and finite element (FE) based numerical experiments. We show that the FE models provide good agreement with the real-life experiments if the major variables are chosen as per their descriptive statistics. The FE model is used to generate a synthetic dataset, using which Monte Carlo simulations are performed. The BRC beam is assumed to be governed by the limit state of collapse in flexure. The partial safety factors for bamboo with different dead and live load combinations are calibrated to different target reliability. Designers can make use of the proposed partial safety factors for designing BRC flexural members.