Ductile fracture simulation and risk quantification of buckling-restrained braces under earthquakes

Since their firrst use in Japan in 1980s, Buckling-Restrained Braces (BRBs) have been widely implemented in steel-framed structures throughout the world. A BRB consists of a steel core enclosed by mortar and a steel casing tube. The steel core resists the axial loading applied to the BRB, while the mortar and casing tube prevent the steel core from globally buckling under compressive loading. Since BRBs do not buckle under compressive loads, they display stable and nearly symmetric behavior in tensile and compressive excursions. Thanks to their superior ductility capacity, BRBs have been applied to variety of structures and configurations, such as diagonal braces (i.e. BRBFs), outriggers for high-rise buildings and energy dissipation fuses for rocking-frames. Since the safety of the structures with BRBs heavily relies on the ductility of BRBs, it is important to ensure that BRBs have sufficient ductility capacity as compared with the ductility demand. The ductility capacity of BRBs is usually controlled by fracture of the steel core since BRBs are designed to avoid other failure modes (e.g. global buckling). Under earthquakes, BRBs will experience relatively small number of cyclic loadings (less than 100 cycles) with large deformation amplitudes, which may lead to failure by Ultra-Low Cyclic Fatigue (ULCF). Therefore, to fully understand BRB ductility capacity, evaluating the fracture of the steel core caused by ULCF is essential. To date, most of the development and validation of BRB ductility has relied extensively on full-scale cyclic loading tests. This nearly exclusive reliance on empirical test data is due in part to the limitation of computational methods for evaluating fracture under inelastic cyclic loading. Ductile fracture caused by ULCF has been studied for a few decades, especially after 1994 Northridge Earthquake and 1995 Kobe Earthquake, during which a number of structural steel components and joints fractured due to ULCF. Several ULCF criteria have been proposed and shown to successfully evaluate fracture caused by ULCF under a wide range of stress states. However, previous validations were mostly limited to cyclic loadings with relatively large amplitudes, during which specimens failed in less than 20 cycles. In addition, the loading histories used for the validation of these criteria were usually constant amplitude cyclic loadings or the combination of stepped constant amplitude cycles. Therefore, the applicability of the ULCF criteria under earthquake-induced random loadings has not yet been fully validated. Motivated by the limitations of existing computational iv methods for evaluating BRB capacity, this study develops, validates and applies a computational fracture simulation method using a local ULCF criterion, referred to as Stress-Weighted Damage Model (SWDM), through detailed FE simulations of both coupon-scale tests and full-scale BRB tests. The research objective is accomplished through calibration and validation of the SWDM using an extensive experimental program, and detailed FE simulation techniques to accurately determine the local stress and strain states of BRBs. Typically, this study includes: (1) 71 small-scale loading tests including constant amplitude loadings and random loadings, (2) calibration of material constitutive parameters using an optimization algorithm, so-called Particle Swarm Optimization (PSO), (3) calibration of the SWDM using a probabilistic approach, referred as to Maximum Likelihood Method (MLE), (5) proposal of detailed FE simulation techniques to replicate the buckling-restraining mechanism in BRBs, and (6) detailed numerical studies for BRB ductile fracture evaluation. In addition to evaluating the ductility capacity of individual BRB components, it is also essential to appropriately evaluate BRB ductility demands in BRB framing (i.e. BRBF) systems. Currently, the required ductility capacity of BRBs is specified in terms of a maximum and cumulative ductility demand in AISC341-16 as acceptance criteria of qualifying BRB loading tests. However, these demands are based on relatively limited data from nonlinear response history analyses (NLRHAs) of a few archetype building designs, which may not represent the ductility demands for various sites with varied seismicity. To address questions regarding the ductility demand in BRBF systems, this study develops a framework to evaluate BRB ductility demand and quantify the influence of BRB fracture on building collapse risk. This objective is achieved by extending a existing reliability-based framework, so-called HC-IDA, for collapse risk assessment to evaluate BRB ductility demands and quantification of the fracture risk of BRBs. The small-scale test results validate the applicability of the SWDM to smaller amplitude cyclic loadings (typically the number of cycles to specimen fracture, Nf > 30 cycles) and earthquake-induced random loadings. The calibration of the material constitutive parameters indicates that tests of a single specimen geometry may not be sufficient to obtain a reliable set of parameters for general application to other structural configurations. Including various geometries of specimens and loading amplitudes in the calibration improves the robustness of the calibration. The calibration of the SWDM demonstrates that its accuracy is improved by including a parameter to distinguish between the relative rate of void growth in positive stress triaxiality and shrinkage in negative stress triaxiality. Previously, this parameter was fixed to 1.0 (implying equal rate of void growth and shrinkage). Based on the tests done in this study, the value of is found to be 1.3 (implying a higher rate of void growth than shrinkage), which improves the accuracy of the SWDM, especially under small amplitude cyclic loadings. The proposed FE simulation techniques for BRBs successfully replicate the buckling-restraining v mechanism. The numerical studies reveals that BRB fracture is greatly influenced by several local conditions, specifically (1) existence of mechanical weakness in the BRB core yielding zone, and (2) lower material toughness and elevated yield stress in the Heat-Affected Zone at the edge of the steel core created by plasma cutting. The proposed fracture evaluation method is shown to reliably simulate the observed BRB fracture behavior in full-scale loading tests. Based on the numerical case study using the proposed reliability-based framework, BRB fracture may significantly increase the mean annual frequency (MAF) of collapse of BRBFs by a factor of 1.4 to 3.6, as compared with the side-sway collapse risk (excluding BRB fracture). In addition, BRB ductility demand significantly differs depending on site seismicity. The ratio of median cumulative plastic ductility (CPD) demand for BRBs in a case study building at a site in downtown San Francisco (SFDT) shown to be 1.4 to 1.5 times larger than a site with comparable MCE spectral intensity in downtown Los Angeles (LADT). Furthermore, the case study result indicates that the median CPD demand at the SFDT at MCE is up to 1.7 times larger than the CPD criteria specified in AISC341-16, highlighting that current ductility criteria specified in AISC341-16 may underestimate the ductility demands for some sites in the western U.S.

Advisor: Deierlein Gregory G. (Gregory Gerard)
Kanvinde Amit M.
Miranda Eduardo (Miranda Mijares)