A large number of models to predict shear strength of structural walls have been proposed in the literature to replace models adopted in codes and standards. Evaluation of the predictive performance of new models relative to existing models is often difficult because the models were developed using different databases and a model may have substantially different performance (high, versus low variance) when evaluated against a different database. In addition, more complex models are expected to have less variance than relatively simple models and target performance metrics for models of different complexity do not exist. To address these issues, a study was conducted applying statistical and machine learning approaches to establish target model performance for different model complexities. The methodology is demonstrated by addressing the problem of assessing wall shear strength using a comprehensive database of 333 walls reported to have failed in shear.

Wall shear strength equations reported in the literature and used in building codes are assessed using a comprehensive database of reinforced concrete wall tests reported to have failed in shear. Based on this assessment, it is concluded that mean values varied significantly, and coefficient of variations were relatively large (> 0.30) and exceeded the target error for a code-oriented equation defined in the companion paper. Therefore, a methodology employing statistical and machine learning methods was used to develop a new equation with form similar to that currently used in ACI 318-19. The proposed equation is applicable to walls with rectangular, barbell, and flanged cross-sections and includes additional parameters not considered in ACI 318-19, such as axial stress and quantity of boundary longitudinal reinforcement. Parameter limits, e.g., on wall shear and axial stresses, and an assessment of the relative contributions to shear strength also are addressed. Finally, a reliability analysis is performed to study the relationship between probability of failure and strength reduction factor applicable to the proposed equation.

Based on a substantial amount of research on the seismic performance of reinforced concrete structural walls (shear walls), modern design provisions for mid-rise and high-rise shear wall buildings have been developed with the goal of achieving significant ductility in the event of strong earthquake ground shaking. Observations following recent earthquakes in Chile (2010) and New Zealand (2011) have demonstrated that shear wall buildings designed according to modern seismic design codes for tension-controlled action may be vulnerable to brittle compression failure. For walls designed to yield in compression, current reinforced concrete design standards in the United States (ACI 318-14) assume that ductility is ensured if code-prescribed confinement provisions are satisfied at wall boundaries; however, recent laboratory tests suggest that thin, code-compliant walls may be susceptible to compression failure prior to achieving the inelastic deformation capacity assumed by current U.S. design codes (i.e., ASCE 7-10, ASCE 41-13).

Seven, approximately one-half scale, ACI 318-14 compliant wall specimens (designated WP1-WP7) were subjected to reversed cyclic lateral loads and constant axial load. The specimens represented approximately the bottom 1.5 stories of an eight story cantilever wall. The first phase of testing (WP1-WP4) was conducted to identify potential deficiencies in current provisions. Test variables for the phase 1 specimens included the configuration of boundary longitudinal reinforcement, quantity and arrangement of boundary transverse reinforcement, and compression depth (influence by axial load, quantity of longitudinal reinforcement, and wall cross-section). For the second phase of testing (WP5-WP7), walls were designed either with thicker cross-sections, improved boundary transverse reinforcement details (i.e., continuous transverse reinforcement detail rather than hoop and cross-tie detail), or both. Phase 2 specimens were constructed with improved web details whereby longitudinal reinforcement was placed inside of transverse reinforcement and, in some cases, cross-ties were used to provide lateral restraint to longitudinal reinforcement.

Abrupt compression failures occurred at plastic rotations as low as 1.1% for the thinnest walls. Plastic rotations greater than 2.5% were observed for walls that were 25% and 50% thicker and/or constructed with more stringent confinement detailing than required by ACI 318-14. Based on experimental results, it is suggested to improve the deformation capacity of thin walls by avoiding the use of cross-tie confinement, and using overlapping hoops or continuous transverse reinforcement instead. Within the web region of walls, it is recommended to provide transverse reinforcement for web longitudinal reinforcement within the plastic hinge region. A lateral drift capacity prediction equation was developed in a displacement-based design format and was shown to agree with experimentally measured drift capacities for a small database of slender wall laboratory tests. It was demonstrated that, in addition to provided boundary transverse reinforcement, drift capacity of slender walls is most impacted by compression depth (c), wall thickness (b), and wall length (lw). Based on experimental data, drift capacities greater than 2% may be expected for code compliant walls designed such that c/b<2.5, while drifts lower than 1% are expected when c/b>5.0.

ABSTRACT OF THE DISSERTATION

Experimental Study of a Non-Ductile Concrete Moment Frame Building Subjected to Biaxial Quasi-Static Seismic Loading

by

Elham MooreDoctor of Philosophy in Civil Engineering University of California, Los Angeles, 2021 Professor John Wright Wallace, Chair

The ability of reinforced concrete (RC) columns to continue to deform with reduced capacity depends on the ability of the floor system to redistribute some of the axial load from heavily damaged element to adjacent members to prevent the collapse of the structure when that happens. Physical testing of columns, although does not fully capture the behavior of the building as a system, is the closest approach to simulate behavior of columns that undergo high constant or varying axial forces. That is by choosing boundary conditions that are representative of actual conditions, as accurately as possible. However, physical testing of a building subassembly is a more powerful tool to provide realistic information on the performance level of existing buildings under seismic loads, as well as to better demonstrate the governing failure modes of the system working together, rather than evaluating members individually. Two large-scale beam-column-slab subassemblies were tested under biaxial quasi-static, reversed cyclic loading are discussed in this report. The test specimens are replicas of elements from a non-ductile concrete moment frame building located on the UCLA campus, the Franz Tower (currently named the Pritzker Hall). The reinforced concrete building originally constructed in the late 60s consists of six levels with closely spaced perimeter columns supported on a transfer girder, with two open lower levels supported on a widely spaced column grid. The lateral force resisting system at the upper six levels consists of trapezoidal columns spaced at 4 ft. (1219 mm) on center along the perimeter of the structure, with trapezoidal beams spanning between the columns. Traditional retrofit techniques in accordance with the governing building codes and the University of California Seismic Performance Rating (UCSPC), suggested a high cost retrofit scheme with significant disruption to the architecture of the building. This is believed to be attributed to these main reasons: 1- The governing standard for seismic evaluation and rehabilitation of existing buildings, ASCE/SEI 41-13 Seismic Evaluation and Retrofit of Existing Buildings, herein referred to as ASCE 41-13, was conservative in predicting deformation capacity of building components when subjected to lateral (seismic) loading, especially when the building components fell under the non-conforming criteria, hence underestimating their performance. 2- The cross sections of the frame beams and columns were not rectangular which is the common type of cross section for typical moment frames. As a result, there was an inherent ambiguity in the capability of the non-linear modeling parameter offered by ASCE 41-13 to predict the performance achieved by the moment frames in the Franz Tower. 3- Another uncommon characteristic of this building was the aspect ratio of the moment frames (bay width/story height), which is less than 0.3 (with the beam span of 4 ft. (1219 mm) and column height of about 12. ft 9 in. (3886 mm), while aspect ratios of more than or equal to 1 are more common. Therefore, the beams were rigid and would not be able to sustain a double curvature deformation, as common in the moment frame beams. 4- The repetitive frame system around the perimeter of the building provided a high level of redundancy that was not observed in typical buildings, nor in the test data used to derive the ASCE 41-13 modeling parameters. To evaluate all the issues mentioned above, a detailed physical testing program was designed with an emphasis on obtaining the overall force-deformation backbone curve for the subassembly. In order to use the data obtained from the physical testing, it was imperative to recreate the experimental backbone curve in Perform-3D, by making necessary modifications to the modeling parameters of the building components. These modifications were based on the observed damage at each drift level, and at each building component, and included the plastic deformation capacity of the columns, flexural residual strength of the columns, and shear capacity of the beams. Those modifications were later applied to the Perform-3D model of the actual building in an attempt to assess its actual performance under seismic loading. This study presents the findings of the two biaxial tests conducted on two building subassemblies and reveals that the test specimens sustained damages beyond the Collapse Prevention and Life-Safety limits of ASCE 41-13. The specimens did not lose their gravity load-carrying capacity during the test (even after exceeding 2.5% lateral drift ratio), which also provided for a higher Expected Seismic Level Performance per UCSPR, performance rating III (seismic safety policy compliant). Finally, this study provides a holistic overview on the proposed retrofit program that includes downtime and repair costs in case of a major ground shaking, utilizing the FEMA P-58, Seismic Performance Assessment of Buildings, Methodology which was developed by the Applied Technology Council (ATC) and funded by FEMA. (ATC, 2020) This study includes building assessments per the Seismic Performance Prediction Program (SP3), including analyses per the governing standards, as well as analyses per the experimental test observations. Downtime and repair cost are of great importance to the public while not directly considered in ASCE 41-13 and other local building documents. Hence, the SP3 Risk Model Engine, was used to calculate the mean loss and time to regain function. Implementation of test data in the SP3 analysis input showed not only the retrofit program enhanced building performance in terms of life safety of the occupants, but it also showed lower expected loss, as well as significantly lower downtime in comparison to prescriptive retrofit methods.

A study was conducted to develop a modeling approach that integrates flexure and shear interaction under cyclic loading conditions to obtain reliable predictions of inelastic responses of reinforced concrete (RC) structural walls. The proposed modeling approach incorporates cyclic RC panel constitutive behavior based on an interpretation of the fixed-strut-angle approach into a two-dimensional fiber-based macroscopic model. Coupling of axial and shear responses under cyclic loading is achieved at the fiber (panel) level, which further allows coupling of flexural and shear responses at the element level.

The sensitivity of model results to various modeling parameters (e.g., material constitutive parameters and modeling parameters), wall configuration parameters (e.g., aspect ratio, boundary and web reinforcement ratios), and response parameters (levels of wall axial load and shear) was investigated to demonstrate the ability of the model to predict the behavior or RC walls for a broad range of conditions. The proposed analytical model was validated and calibrated against experimental results obtained from six large-scale, heavily instrumented, cantilever structural wall specimens characterized with different aspect ratios (1.5, 2.0 and 3.0), axial load levels (0.0025 A_{gf'c, 0.07 Agf'c and 0.10 Agf'c) and wall shear stress levels (between approximately 4 and 8 √("f'c" ) psi) tested under combined constant axial load and reversed cyclic lateral loading applied at the top of the wall.}

Comparisons of experimental and analytical model results for moderately slender RC walls (aspect ratio 1.5 and 2.0) revealed that the model successfully captures experimentally observed interaction between nonlinear shear and flexural deformations under cyclic loading and predicts lateral strength and stiffness that is within 10% of experimentally measured values. In addition, the magnitudes and relative contributions of shear and flexural deformations along the wall height were predicted closely at low and moderate drift levels, whereas at drift levels larger than 2.0%, model results were within 25% of experimentally measured deformation components. As well, localized nonlinear responses such as vertical tensile and compressive strains and wall rotations at the wall base were well predicted by the model. The model results were less accurate for the slender (aspect ratio 3.0) RC wall specimen in terms of relative contributions of shear and flexural deformations and magnitudes of compressive strains.

Demonstrated model sensitivity to parameters of the implemented RC panel behavior suggested the need for calibration of these parameters for reliable predictions of nonlinear wall behavior. Given the limited model calibration performed in this study, additional work is needed, particularly for slender RC walls where preliminary results were less accurate. Finally, the implementation of the model into a publicly available computational platform is required to enable more detailed system level studies and future model development.

Structural seismic resilience society has been grown rapidly in the past three decades. Extensive probabilistic techniques have been developed to address uncertainties from ground motions and building systems to reduce structural damage, economic loss and social impact of buildings subjected to seismic hazards where seismic structural responses are essential and often are retrieved through Nonlinear Response History Analysis. This process is largely limited by accuracy of model and computational effort. An alternative data-driven framework is proposed to reconstruct structure responses through machine learning techniques from limited available sources which may potentially benefit for “real-time” interpolating monitoring data to enable rapid damage assessment and reducing computational effort for regional seismic hazard assessment. It also provides statistical insight to understand uncertainties of seismic building responses from both structural and earthquake engineering perspective.

Along the west coast of the United States, reinforced concrete core wall systems are commonly selected as seismic force resisting systems for tall buildings. During strong ground shaking, core wall systems are intended to dissipate energy by yielding of coupling beams, followed by flexural yielding at the wall base. Although the wall behavior is governed by flexure, the wall design is often governed by shear, as the walls experience high shear demands, usually up to the ACI318-11 code limiting shear stress of 8∙√(f'c ) psi over a significant wall height. The high shear demands are due to a lack of redundancy in tall buildings, as the wall lengths are limited to the perimeter of the elevator core.

Design of tall buildings is typically conducted using performance-based design procedures recommended by Los Angeles Tall Buildings Structural Design Council (LATBSDC, 2014) or Pacific Earthquake Engineering Research Center Tall Buildings Initiative (PEER TBI, 2010). Provisions in these two documents recommend shear design per acceptance criterion Fuc ≤ κi ϕ Fn,e, where Fuc is 1.5 times the mean shear demand resulting from a suite of ground motions, Fn,e is the nominal strength computed from expected material properties, κi is the risk reduction factor based on risk categories, and ϕ is the uncertainty in Fn,e. The 1.5 factor applied to the mean shear demand is referred to as the demand factor, γ. Although shear failure can be fatal due to its sudden and brittle nature, the reliability of this shear design acceptance criterion has not yet been thoroughly researched.

To assess seismic reliability of structural wall shear design acceptance criterion, dispersion in structural responses, specifically for shear demands, must be quantified. Dispersion in structural responses (referred to as engineering demand parameters, EDPs) primarily results from three sources, namely, record-to-record (RTR) variability, modeling and/or model parameter uncertainties, and design uncertainties. To study how these uncertainties contribute to dispersion in tall building EDPs, eleven input random variables (expected to be the most relevant) were selected. Specifically, uncertainties in scaled ground motions, unconfined and confined concrete compressive strengths, reinforcing steel yield strength, shear modulus, coupling beam strength, seismic mass, dead and live gravity loads, damping, and shear wall design variations were considered. A series of 20 and 30-story nonlinear models for reinforced-concrete core wall systems were built and Monte Carlo simulations were utilized to assign values for random variables and to perform nonlinear response history analyses. Analyses were performed at five seismic hazard levels corresponding to return periods of 25, 43, 475, 2495, and 4975 years, until an adequate convergence in dispersion measure was reached. Selected EDPs (base shear, roof drifts, coupling beam rotations, and structural wall boundary element axial strains) were evaluated and statistical parameters were quantified. Results show that dispersion in EDPs was the largest for coupling beam rotations and shear wall axial strains. Total dispersion, measured in coefficient of variation, ranged between 0.15 and 0.85, considering all EDPs at all five hazard levels. The relative contributions from RTR variability and model parameter/design uncertainties accounted for 72-98% and 2-28% of the total dispersion, respectively. Fitted probability distributions were either normal or lognormal for all EDPs and using correlated random variables for model parameter uncertainties resulted in changes in dispersion of -6% to 5% compared with using independent random variables.

Using the measured dispersion values, the current recommendations in Los Angeles Tall Buildings Structural Design Council (LATBSDC, 2014) were reviewed for shear design of structural walls in tall reinforced-concrete core wall buildings (Fuc ≤ κi ϕFn,e). Both closed-form solutions using full distribution methods and Monte Carlo simulation results were used to assess reliability of the current shear design acceptance criterion. Statistical parameters were established for shear demand by using measured dispersion values from nonlinear response history analyses of tall reinforced-concrete core wall buildings, and experimental test results from shear-controlled walls were used to establish statistical parameters for shear capacity. A range of reliability results were computed for various shear demand and capacity statistical parameters. The current shear design acceptance criterion using γ=1.5 and ϕ=1.0 resulted in 94.2% reliability for structural walls with f’c < 8ksi and 96.5% reliability for structural walls with f’c ≥ 8ksi. Minimum values for the demand factor, γ, are tabulated for various risk categories defined per ASCE7-10.

Results suggest that the use of ϕ=1.0, along with appropriate expected material properties, produce an acceptable probability of failure. Per Pacific Earthquake Engineering Center Tall Buildings Initiative (PEER TBI, 2010), the recommended use of ϕ=0.75 appears excessively conservative. However, due to a lack of experimental tests on possible shear strength degradation in walls that yield in flexure, limitations on curvature ductility or plastic rotation demands are recommended in the plastic hinge regions. Moreover, since this study is based on variations of results from two prototype tall core wall buildings; to reduce the potential conservatism in the current guidelines, a comprehensive reliability study including a larger population of tall buildings is further needed to calibrate γ and ϕ factors.

The level of structural damage and the associated economic impact caused by recent earthquakes worldwide have spurred an increased interest in high performance seismic resisting systems that can sustain severe earthquakes with minimal damage. A particularly efficient high performance wall system consists of precast concrete panels vertically post-tensioned to the foundation with unbonded post-tensioning steel. The system relies on the vertical unbonded post-tensioning steel for flexural strength and re-centering, while mild bonded steel bars provide energy dissipation and additional flexural strength. Under lateral loading, the traditional plastic hinge mechanism, associated with structural damage and the potential for large residual deformation, is replaced by a controlled rocking mechanism at the wall-to-foundation interface that allows the system to undergo large nonlinear displacements with minimal damage and minor residual deformations.

This thesis presents experimental results from a dynamic test on a full-scale, four-story precast concrete building that utilized unbonded post-tensioned (UPT) walls in one principal direction of response and bonded post-tensioned concrete frames in the orthogonal direction. The building was subjected to simultaneous three-dimensional shaking using recorded ground motions from the 1995 Kobe earthquake. The excellent performance of the test building in the wall direction of response, exhibiting minimal damage and no residual deformations, confirms that UPT walls are a viable alternative to conventional reinforced concrete (RC) structural walls. In addition to providing experimental evidence of seismic performance of UPT walls incorporated into a building system, the tests provided valuable insight into issues typically not addressed in component-level experimental studies, such as the role of the floor diaphragm, influence of component interactions, and contributions of three-dimensional responses and torsion. As evidenced by the E-Defense test building, these effects need to be considered to obtain realistic estimates of lateral resistance and displacement demands.

The tests also provided a wealth of data against which design methodologies and analytical models for UPT systems can be benchmarked. Based on a detailed assessment of the E-Defense UPT walls in accordance with ACI ITG-5.2 (2009), and the performance of the UPT walls in the tests, design implications were identified and some revisions to ACI ITG-5.2 were suggested. Finally, an analytical model of the building in the wall direction was developed. Experimental results in this direction were used to assess the ability of the model to capture the dynamic responses and interactions of unbonded post-tensioned structural systems. Correlations between analytical and experimental results were satisfactory for a range of global and local responses, and key aspects of the interaction between components such as framing action and beam elongation effects were adequately reflected in the model.

Reinforced concrete structural (shear) walls are commonly used as lateral load resisting systems in high seismic zones because they provide significant lateral strength, stiffness, and deformation capacity. Understanding the response and behavior of shear walls is essential to achieve more economical and reliable designs, especially as performance-based design approaches for new buildings have become more common. Results of a case study of 42-story RC dual system building, designed using code-prescriptive and two different performance-based design approaches, are presented to assess expected performance. Median values and dispersion of the response quantities are, in general, well-below acceptable limits and the overall behavior of the three building designs are expected to be quite similar. However, the ability to define shear failure and collapse proved difficult and provided motivation to conduct additional studies.

For both design of new buildings and evaluation/rehabilitation of existing structural wall buildings, an accurate assessment of median (expected) and dispersion of wall shear strength and deformation capacity are needed. A wall test database (124 specimens) was assembled to investigate the influence of various parameters on wall shear strength and deformation capacity, and to recommend alternative relations for strength and deformation capacity depending on expected wall behavior. Test results indicated that ACI 318-11 underestimates the shear strength of the shear-controlled walls. Mean curvature ductility ratios were obtained as about 3 and 7 for shear- and flexure-controlled walls, respectively. The new relations will allow improved damage and failure assessment of buildings utilizing structural walls for lateral load resistance.

Failure assessment of RC shear walls also was conducted for the 15-story Alto Rio building which collapsed in the 2010 Chile earthquake. Possible reasons for collapse were identified using post-earthquake observed damage, structural drawings, and nonlinear static and dynamic response analyses. Analysis results indicate that collapse was likely influenced by various factors, including compression failure at the web boundary of T-shaped walls on the east side of the building, large shear demands at the filled-in corridor walls at the first level, and tensile fracture and splice failures at the west side of the building.

Nonlinear modeling and analysis of the four-story RC building that was tested on E-Defense shaking table (2010) was investigated to assess current modeling approaches and assumptions, and to identify issues that require additional study. Including concrete tension strength, stiffness degradation, and strength degradation significantly improved the correlation between the analytical and test results.

Strong wind events are the major factor governing the structural design of many tall buildings in regions with low-to-moderate seismic hazard; however, unlike seismic design, where performance-based design of tall buildings has become common in regions impacted by strong shaking, wind design is still based on linear elastic response under ASCE 7 strength-level demands. Application of performance-based wind design, where modest nonlinear responses are allowed in ductile elements at prescribed locations, has been hampered in part by the lack of experimental data on the performance of key elements subjected to wind loading protocols. For tall concrete buildings subjected to strong wind, allowing modest nonlinearity in coupling beams is an attractive option; therefore, four 2/3-scale reinforced concrete coupling beams were tested under a simulated windstorm loading protocol, which consists of a large number of elastic load cycles and a dozen mildly-inelastic displacement cycles. The test parameters included aspect ratio, presence of floor slab, level of detailing (seismic versus standard), and loading protocol (wind versus seismic). The test results indicate that rotational ductility demands of 1.5 can be achieved with only small residual crack widths (less than 1/16 in.; 1.6 mm) and no concrete spalling or bar buckling, indicating that allowing modest inelastic responses in strong wind may be a viable approach.

Reinforced concrete (RC) moment frames and shear walls are amongst the most widely used lateral force resisting systems in regions of high seismicity in the US and around the world. Hence, understanding and accurately capturing the behavior of buildings with these lateral systems via nonlinear computer modeling is of great importance for design engineers. In 2018, a 10-story, full-scale, RC building utilizing these lateral systems was tested on the E-Defense shake table. This test provides a unique opportunity to analyze the response of a thoroughly instrumented building with special moment frames and special structural walls that are generally compliant with ASCE 7-16 and ACI 318-19 design requirements. Furthermore, it allows for the experimental verification of common nonlinear computer modeling techniques for these lateral systems. The direction of this research is to accurately capture the nonlinear global and local behavior of the 10-story test specimen subjected to ground shaking using a sophisticated non-linear computer model. Although this experimental test does present some difficulties, specifically the effect of the sliding-base foundation, validation studies demonstrate that the nonlinear model can accurately predict overall building behavior when subjected to ground excitation. This thesis outlines the experimental program of the shake table test and the nonlinear modeling approach used to best capture the response of the building.