Probabilistic Seismic Performance Evaluation Research Articles

Probabilistic Evaluation of Seismic Performance of Steel Buildings with Torsional Irregularities in Plan and Soft Story under Mainshock-Aftershock Sequence

Due to the tectonic plate movement, numerous aftershocks may occur following an earthquake. There are several real mainshock-aftershock ground motion records in which the peak ground acceleration of aftershock is greater than that of the mainshock. Furthermore, irregularities such as soft story and torsional irregularity may change the structural behavior under the influence of earthquakes. This study investigates the fragility curves associated with the three-, five-, and eight-story models with steel moment-resisting frames under the main earthquake and mainshock-aftershock sequence to probabilistically evaluate the aftershock impacts on the steel structures with irregularities in the plan and height. The seismic fragility curves were calculated for four damage levels by selecting the relative displacement capacity at seismic performance levels of slight, moderate, extensive, and complete damage from the US HAZUS code. The analysis was done using structural reliability relationships and incremental dynamic analysis with the OpenSees software platform. The analytical results showed that the structures with soft-story and torsional irregularity were more vulnerable with an increasing number of stories. Also, aftershocks were found to have a more destructive effect on low-rise models. The probability of structural collapse in a given peak ground acceleration for a damaged state due to the mainshock-aftershock sequence is higher than that of the mainshock sequence.

Probabilistic seismic performance assessment of nuclear containment structure considering statistical uncertainty

Statistical uncertainty is inherently involved in probabilistic seismic performance assessment of containment structure due to heavy computational efforts of nonlinear dynamic analysis. Aiming at the statistical uncertainty involved in seismic fragility and seismic risk evaluation of containment structure, this study proposes a method for quantifying the statistical uncertainty in probabilistic seismic performance assessment of the containment structure. Taking a three story reinforced concrete frame as an example, effectiveness and efficiency of the proposed method for confidence interval estimation of seismic fragility curve is verified. Then, the proposed method is applied to fragility analysis and seismic risk evaluation of the containment structure. Roof drift of the containment structure under different ground motion intensity levels is discussed. Confidence interval for seismic fragility curve and seismic risk of the containment structure considering statistical uncertainty is quantified by the proposed method. The results highlighted the necessity for quantifying the impact of statistical uncertainty involved in probabilistic seismic performance evaluation of the containment structure.

An uncertainty-aware dynamic shape optimization framework: Gravity dam design

Uncertainties such as material randomness, manufacturing anomalies, and external loading play an important role in the design of engineering structures. Therefore, reliability-based design optimization (RBDO) is frequently used as a tool to guarantee economic aspects without compromising safety. In this paper, an uncertainty-aware framework is proposed for seismic optimization of structures. This algorithm is founded on the stochastic dynamic stressor, and therefore, reduces the bias due to the aleatory nature of ground motion. Safety constraints are evaluated in quantiles instead of the exact solution of reliability analysis. Kriging approach approximates the actual model, while a global search algorithm solves the RBDO problem. The proposed algorithm is used for the optimal shape design of gravity dams with a series of local and global time-variant/invariant performance indices. Two sets of deterministic and probabilistic shape optimization algorithms were compared to demonstrate the impact of uncertainty quantification. Finally, the framework is extended to a class of generic dams with different heights, concrete strengths, and foundation-to-concrete flexibility. By probabilistic seismic performance evaluation, system safety is guaranteed using the proposed dynamic RBDO compared to the median response in applying a set of as-recorded ground motions. This paper provides a new paradigm for RBDO of structures with dynamic loading and a robust decision-making during dam design.

Probabilistic seismic performance evaluation of nuclear containment structure subjected to far-fault ground motions

This study presents probabilistic seismic performance evaluation of nuclear containment structure subjected to far-fault ground motions. To achieve this objective, refined finite element model of nuclear containment structure is established and incremental dynamic analysis (IDA) is performed automatically using pre-processing and post-processing scripts. Cracking status, roof drift, damage dissipated energy and floor acceleration of the nuclear containment structure is discussed. Furthermore, probabilistic seismic safety margin of nuclear containment structure is quantitatively evaluated by median value method and confidence interval method. Finally, a closed-form solution for the annual frequency of exceedance for the roof drift of the nuclear containment structure is derived, and the effectiveness of the closed-form solution is verified by the classical direct numerical integration method. Annual frequency of exceedance for the roof drift of the nuclear containment structure corresponding to different performance levels is analyzed. Results indicated that the bottom of nuclear containment structure is the most vulnerable location. In general, nuclear containment structure subjected to far-fault ground motions is dominated by shearing cracks. When the ground motion intensity level is less than 0.4 g, damage dissipated energy of the nuclear containment structure is very small. In general, with the increase of elevation, acceleration amplification factor of the nuclear containment structure increases rapidly. Probabilistic seismic safety margin of the nuclear containment structure evaluated by median value method tends to be conservative. Analytical and classical numerical integration method provides almost the same prediction of the annual frequency of exceedance for the roof drift of the nuclear containment structure, which indicates the effectiveness of the proposed closed-form solution.

Probabilistic seismic performance evaluation of SMA-braced steel frames considering SMA brace failure

This study explores seismic performance of steel frame buildings with SMA-based self-centering bracing systems using a probabilistic approach. The self-centering bracing system described in this study relies on superelastic response of large-diameter cables. The bracing systems is designed such that the SMA cables are always stressed in tension. A four-story steel frame building characterized until collapse in previous research is selected as a case-study building. The selected steel frame building is designed with SMA bracing systems considering various design parameters for SMA braces. Numerical models of these buildings are developed by taking into account the ultimate state of structural components and SMA braces as well as the effect of gravity frames on lateral load resistance. Nonlinear static analyses are conducted to assess the seismic characteristics of each frame and to examine the effect of SMA brace failure on the seismic load carrying capacity of SMA-braced frames. Incremental dynamic analyses (IDA) are performed to compute seismic response of the designed frames at various seismic intensity levels. The results of IDA are used to develop probabilistic seismic demand models for peak inter-story and residual inter-story drifts. Seismic demand hazard curves of peak and residual inter-story drifts are generated by convolving the ground motion hazard with the probabilistic seismic demand models. Results show that steel frames designed with SMA bracing systems provide considerably lower probability of reaching at a damage state level associated with residual drifts compared to a similarly designed steel moment resisting frame, especially for seismic events with high return periods. This indicates reduced risks for the demolition and collapse due to excessive residual drifts for SMA braced steel frames.

Probabilistic seismic performance evaluation of steel moment frame using high-strength and high-ductility steel

To shorten a steel building recovery time after an earthquake, a dual and damaged-controlled system is proposed, in which the seismic energy is absorbed by a highly ductile buckling restrained brace (BRB) and the gravity load is resisted by high-strength column. Because the seismic energy is mainly dissipated by the BRB, to accurately simulate the BRB hysteretic behavior is essential. Thus, kinematic hardening and two surface theories are adopted and coded as an ABAQUS user-defined material (UMAT). Particle swarm optimization (PSO) is used to find the optimal design equivalent to a corresponding traditional structure. The performance of the optimal frame is verified by nonlinear time history and fragility analysis. Based on the found optimum, a practical design guideline is recommended. The performance of high-strength steel and a high-ductility structural system such as the inter-story drift, maximum roof acceleration, property of BRB hysteresis, strength ratio between the main frame and BRB and cumulative fatigue damage are investigated. In addition, the economic feasibility of using high-strength steel in the structural system is compared to that using traditional steel materials.

Convex model-based calculation of robust seismic fragility curves of isolated continuous girder bridge

The convex model approach is applied to derive the robust seismic fragility curves of a five-span isolated continuous girder bridge with lead rubber bearings (LRB) in China. The uncertainty of structure parameters (the yield force and the post-yield stiffness of LRB, the yield strength of steel bars, etc.) are considered in the convex model, and the uncertainty of earthquake ground motions is also taken into account by selecting 40 earthquake excitations of peak ground acceleration magnitudes ranging from 0.125 to 1.126 g. A 3-D finite element model is employed using the software package OpenSees by considering the nonlinearity in the bridge piers and the isolation bearings. Section ductility of piers and shearing strain isolation bearings are treated as damage indices. The cloud method and convex model approach are used to construct the seismic fragility curves of the bridge components (LRB and bridge piers) and the bridge system, respectively. The numerical results indicate that seismic fragility of the bridge system and bridge components will be underestimated without considering the uncertainty of structural parameters. Therefore, the failure probability P f,max had better be served as the seismic fragility, especially, the fragility of the bridge system is largely dictated by the fragility of LRB. Finally, the probabilistic seismic performance evaluation of the bridge is carried out according to the structural seismic risk estimate method.

Eurocode conforming design of BRBF – Part I: Proposal for codification

Buckling Restrained Braces (BRB) are innovative displacement dependent devices having balanced hysteretic behavior. Frames equipped with such devices are known as Buckling Restrained Braced Frames (BRBF). Application of BRB elements in Europe is seriously limited by the lack of a standardized European design procedure for BRBF.In the first part of this paper the authors propose a Eurocode conforming design procedure for BRBF and provide the seismic design parameters and capacity design rules by enhancing Eurocode 8 specifications on steel Concentrically Braced Frames. Major extensions concern rules for static and dynamic analyses, calculation of material and structural overstrength, unbalanced loads, braced frame column sections and a BRBF-specific behavior factor. Brief examples explain the motivation for each modification and justify the proposed regulations. The complete design procedure is illustrated through the design of a sample six-story BRBF.The authors developed a probabilistic seismic performance evaluation environment on the basis of the methodology in FEMA P-695. The second part of this paper shows how the performance of the proposed design procedure was evaluated with that environment. Results confirmed the applicability of the proposed design procedure in Europe.

Probabilistic Seismic Performance Evaluation of Vertically Irregular Steel Building Considering Soil–Structure Interaction

In this paper, the probabilistic seismic performance of vertically irregular steel buildings, considering soil–structure interaction effects, is evaluated. Various irregular distributions of structural properties, including mass, stiffness and strength along the height of three-dimensional moment resisting steel frames were intended. The finite element model of soil medium was created with solid elements below the structure. The nonlinear material behavior of soil was considered as well. Nonlinear incremental dynamic analysis was performed to evaluate the flexible-base structural performance in the framework of probabilistic performance-based earthquake engineering. According to the median curves of intensity demand of structures, it is concluded that non-uniform height-wise distribution of lateral resistance properties of steel structures varies the displacement demand and the seismic capacity of the irregular frames, compare to the regular structure. The capacity variation of most irregular frames is more obvious at the nonlinear phase of structural behavior. Due to the foundation flexibility, the damage concentration raises in the bottom floor and the irregularity increases the seismic demands of the lower floors of the system. Among all the irregular steel frames, the average increase of the displacement demand and reduction of the seismic capacity are maximal for the strength and concurrent variation of stiffness and strength irregularity models, respectively. Additionally, mass irregularity shows minor influence in the seismic demand and capacity variations of the steel frames. The predominant influence of stiffness and strength irregularities (soft and weak story) is observed in reduction of the structural ductility factor and the mean annual frequency of exceeding limit states.

Finite element model development, validation and probabilistic seismic performance evaluation of Vincent Thomas suspension bridge

Based on recent findings, the main span of the Vincent Thomas suspension bridge crosses directly over the Palos Verdes fault, which has the capacity to produce a devastating earthquake. In spring 2000, the bridge underwent a major retrofit using visco-elastic dampers. This study focuses on seismic vulnerability of the retrofitted bridge. Three-dimensional member-based detailed and panel-based simplified finite element models of the bridge are developed. In order to show the appropriateness of these models, eigenproperties of the bridge are evaluated and compared with the system identification results obtained using ambient vibration data. In addition, a model validation is performed by simulating the dynamic response during the 1994 Northridge earthquake and comparing with the measured response. Finally, considering a set of strong ground motions in the Los Angeles area, nonlinear time history analyses are performed and the ductility demands of critical sections are presented in terms of fragility curves. The study shows that a ground motion with peak ground acceleration of 0.9 g or greater will result in plastic hinge formation at one or more locations with a probability of exceedance of 50%. Also, it is found that the effect of dampers is minimal for low to moderate earthquakes and high for strong earthquakes.

Probabilistic seismic performance evaluation of non-geometric vertically irregular steel buildings

The seismic performance of structures with irregular distribution of mass, stiffness and strength along the height, may be significantly different compared to regular structures, depending on the limit-state or the level of seismic intensity considered. In the framework of probabilistic performance based earthquake engineering, it is possible to quantify the effects of vertical irregularities on the seismic performance of structures. In this study, the seismic performance of different non-geometric vertical irregular structures is compared to a regular structure at various performance levels with a probabilistic approach. The results show that the non-uniform distribution of lateral resisting properties over the height of structure influences the seismic performance, especially at the limit-states close to collapse until global dynamic instability. These effects may be on the seismic intensity capacity and/or on the ductility capacity of the structure, based on the type and the position of vertical irregularities. Also from the standpoint of a probabilistic seismic performance based design, the vertical irregularities increase the mean annual frequency of exceeding the GI performance level by about 5% to 30%.

Probabilistic seismic performance evaluation of non-seismic RC frame buildings

In this paper, probabilistic seismic performance assessment of a typical non-seismic RC frame building representative of a large inventory of existing buildings in developing countries is conducted. Nonlinear time-history analyses of the sample building are performed with 20 large-magnitude medium distance ground motions scaled to different levels of intensity represented by peak ground acceleration and 5% damped elastic spectral acceleration at the first mode period of the building. The hysteretic model used in the analyses accommodates stiffness degradation, ductility-based strength decay, hysteretic energy-based strength decay and pinching due to gap opening and closing. The maximum inter story drift ratios obtained from the time-history analyses are plotted against the ground motion intensities. A method is defined for obtaining the yielding and collapse capacity of the analyzed structure using these curves. The fragility curves for yielding and collapse damage levels are developed by statistically interpreting the results of the time-history analyses. Hazard-survival curves are generated by changing the horizontal axis of the fragility curves from ground motion intensities to their annual probability of exceedance using the log-log linear ground motion hazard model. The results express at a glance the probabilities of yielding and collapse against various levels of ground motion intensities.

Probabilistic evaluation of seismic performance of 3‐story 3D one‐ and two‐way steel moment‐frame structures

AbstractThis paper presents the results of a probabilistic evaluation of the seismic performance of 3D steel moment‐frame structures. Two types of framing system are considered: one‐way frames typical of construction in the United States and two‐way frames typical of construction in Japan. For each framing system, four types of beam–column connections are considered: pre‐Northridge welded‐flange bolted‐web, post‐Northridge welded‐flange welded‐web, reduced‐beam‐section, and bolted‐flange‐plate connections. A suite of earthquake ground motions is used to compute the annual probability of exceedence (APE) for a series of drift demand levels and for member plastic‐rotation capacity. Results are compared for the different framing systems and connection details. It is found that the two‐way frames, which have a larger initial stiffness and strength than the one‐way frames for the same beam and column volumes, have a smaller APE for small drift demands for which members exhibit no or minimal yielding, but have a larger APE for large drift demands for which members exhibit large plastic rotations. However, the one‐way frames, which typically comprise a few seismic frames with large‐sized members that have relatively small rotation capacities, may have a larger APE for member failure. The probabilistic approach presented in this study may be used to determine the most appropriate frame configuration to meet an owner's performance objectives. Copyright © 2008 John Wiley & Sons, Ltd.