(PHD, 2016)

Abstract:

FRAME3D, a program for the nonlinear seismic analysis of steel structures, has previously been used to study the collapse mechanisms of steel buildings up to 20 stories tall. The present thesis is inspired by the need to conduct similar analysis for much taller structures. It improves FRAME3D in two primary ways.

First, FRAME3D is revised to address specific nonlinear situations involving large displacement/rotation increments, the backup-subdivide algorithm, element failure, and extremely narrow joint hysteresis. The revisions result in superior convergence capabilities when modeling earthquake-induced collapse. The material model of a steel fiber is also modified to allow for post-rupture compressive strength.

Second, a parallel FRAME3D (PFRAME3D) is developed. The serial code is optimized and then parallelized. A distributed-memory divide-and-conquer approach is used for both the global direct solver and element-state updates. The result is an implicit finite-element hybrid-parallel program that takes advantage of the narrow-band nature of very tall buildings and uses nearest-neighbor-only communication patterns.

Using three structures of varied sized, PFRAME3D is shown to compute reproducible results that agree with that of the optimized 1-core version (displacement time-history response root-mean-squared errors are ~〖10〗^(-5) m) with much less wall time (e.g., a dynamic time-history collapse simulation of a 60-story building is computed in 5.69 hrs with 128 cores—a speedup of 14.7 vs. the optimized 1-core version). The maximum speedups attained are shown to increase with building height (as the total number of cores used also increases), and the parallel framework can be expected to be suitable for buildings taller than the ones presented here.

PFRAME3D is used to analyze a hypothetical 60-story steel moment-frame tube building (fundamental period of 6.16 sec) designed according to the 1994 Uniform Building Code. Dynamic pushover and time-history analyses are conducted. Multi-story shear-band collapse mechanisms are observed around mid-height of the building. The use of closely-spaced columns and deep beams is found to contribute to the building’s “somewhat brittle” behavior (ductility ratio ~2.0). Overall building strength is observed to be sensitive to whether a model is fracture-capable.

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(PHD, 2015)

Abstract: Toppling analysis of a precariously balanced rock (PBR) can provide insights into the nature of ground motion that has not occurred at that location in the past and, by extension, realistic constraints on peak ground motions for use in engineering design. Earlier approaches have targeted simplistic 2-D models of the rock or modeled the rock-pedestal contact using spring-damper assemblies that require re-calibration for each rock. These analyses also assume that the rock does not slide on the pedestal. Here, a method to model PBRs in three dimensions is presented. The 3-D model is created from a point cloud of the rock, the pedestal, and their interface, obtained using Terrestrial Laser Scanning (TLS). The dynamic response of the model under earthquake excitation is simulated using a rigid body dynamics algorithm. The veracity of this approach is demonstrated by comparisons against data from shake table experiments. Fragility maps for toppling probability of the Echo Cliff PBR and the Pacifico PBR as a function of various ground motion parameters, rock-pedestal interface friction coefficient, and excitation direction are presented. The seismic hazard at these PBR locations is estimated using these maps. Additionally, these maps are used to assess whether the synthetic ground motions at these locations resulting from scenario earthquakes on the San Andreas Fault are realistic (toppling would indicate that the ground motions are unrealistically high).

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(PHD, 2014)

Abstract:

In the 1994 M_{w} 6.7 Northridge and 1995 M_{w} 6.9 Kobe earthquakes,
steel moment-frame buildings were exposed to an unexpected flaw. The commonly utilized
welded unreinforced flange, bolted web connections
were observed to experience brittle fractures in a number of buildings, even at
low levels of seismic demand. A majority of these buildings have not been retrofitted
and may be susceptible to structural collapse in a major earthquake.

This dissertation presents a case study of retrofitting a 20-story pre-Northridge steel moment-frame building. Twelve retrofit schemes are developed that present some range in degree of intervention. Three retrofitting techniques are considered: upgrading the brittle beam-to-column moment resisting connections, and implementing either conventional or buckling-restrained brace elements within the existing moment-frame bays. The retrofit schemes include some that are designed to the basic safety objective of ASCE-41 Seismic Rehabilitation of Existing Buildings.

Detailed finite element models of the base line building and the retrofit schemes are constructed. The models include considerations of brittle beam-to-column moment resisting connection fractures, column splice fractures, column baseplate fractures, accidental contributions from ``simple’’ non-moment resisting beam-to-column connections to the lateral force-resisting system, and composite actions of beams with the overlying floor system. In addition, foundation interaction is included through nonlinear translational springs underneath basement columns.

To investigate the effectiveness of the retrofit schemes, the building models are analyzed under ground motions from three large magnitude simulated earthquakes that cause intense shaking in the greater Los Angeles metropolitan area, and under recorded ground motions from actual earthquakes. It is found that retrofit schemes that convert the existing moment-frames into braced-frames by implementing either conventional or buckling-restrained braces are effective in limiting structural damage and mitigating structural collapse. In the three simulated earthquakes, a 20% chance of simulated collapse is realized at PGV of around 0.6 m/s for the base line model, but at PGV of around 1.8 m/s for some of the retrofit schemes. However, conventional braces are observed to deteriorate rapidly. Hence, if a braced-frame that employs conventional braces survives a large earthquake, it is questionable how much service the braces provide in potential aftershocks.

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(PHD, 2012)

Abstract:

For the last few decades, we have obtained tremendous insight into underlying microscopic mechanisms of degrading quasi-brittle materials from persistent and near-saintly efforts in laboratories, and at the same time we have seen unprecedented evolution in computational technology such as massively parallel computers. Thus, time is ripe to embark on a novel approach to settle unanswered questions, especially for the earthquake engineering community, by harmoniously combining the microphysics mechanisms with advanced parallel computing technology.

To begin with, it should be stressed that we placed a great deal of emphasis on preserving clear meaning and physical counterparts of all the microscopic material models proposed herein, since it is directly tied to the belief that by doing so, the more physical mechanisms we incorporate, the better prediction we can obtain.

We departed from reviewing representative microscopic analysis methodologies, selecting out “fixed-type” multidirectional smeared crack model as the base framework for nonlinear quasi-brittle materials, since it is widely believed to best retain the physical nature of actual cracks. Microscopic stress functions are proposed by integrating well-received existing models to update normal stresses on the crack surfaces (three orthogonal surfaces are allowed to initiate herein) under cyclic loading.

Unlike the normal stress update, special attention had to be paid to the shear stress update on the crack surfaces, due primarily to the well-known pathological nature of the fixed-type smeared crack model–spurious large stress transfer over the open crack under nonproportional loading. In hopes of exploiting physical mechanism to resolve this deleterious nature of the fixed crack model, a tribology-inspired three-dimensional (3d) interlocking mechanism has been proposed. Following the main trend of tribology (i.e., the science and engineering of interacting surfaces), we introduced the base fabric of solid particle-soft matrix to explain realistic interlocking over rough crack surfaces, and the adopted Gaussian distribution feeds random particle sizes to the entire domain. Validation against a well-documented rough crack experiment reveals promising accuracy of the proposed 3d interlocking model.

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A consumed energy-based damage model has been proposed for the weak correlation between the normal and shear stresses on the crack surfaces, and also for describing the nature of irrecoverable damage. Since the evaluation of the consumed energy is directly linked to the microscopic deformation, which can be efficiently tracked on the crack surfaces, the proposed damage model is believed to provide a more physical interpretation than existing damage mechanics, which fundamentally stem from mathematical derivation with few physical counterparts.

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Another novel point of the present work lies in the topological transition-based “smart” steel bar model, notably with evolving compressive buckling length. We presented a systematic framework of information flow between the key ingredients of composite materials (i.e., steel bar and its surrounding concrete elements). The smart steel model suggested can incorporate smooth transition during reversal loading, tensile rupture, early buckling after reversal from excessive tensile loading, and even compressive buckling. Especially, the buckling length is made to evolve according to the damage states of the surrounding elements of each bar, while all other dominant models leave the length unchanged.

What lies behind all the aforementioned novel attempts is, of course, the problem-optimized parallel platform. In fact, the parallel computing in our field has been restricted to monotonic shock or blast loading with explicit algorithm which is characteristically feasible to be parallelized. In the present study, efficient parallelization strategies for the highly demanding implicit nonlinear finite element analysis (FEA) program for real-scale reinforced concrete (RC) structures under cyclic loading are proposed. Quantitative comparison of state-of-the-art parallel strategies, in terms of factorization, had been carried out, leading to the problem-optimized solver, which is successfully embracing the penalty method and banded nature. Particularly, the penalty method employed imparts considerable smoothness to the global response, which yields a practical superiority of the parallel triangular system solver over other advanced solvers such as parallel preconditioned conjugate gradient method. Other salient issues on parallelization are also addressed.

The parallel platform established offers unprecedented access to simulations of real-scale structures, giving new understanding about the physics-based mechanisms adopted and probabilistic randomness at the entire system level. Particularly, the platform enables bold simulations of real-scale RC structures exposed to cyclic loading–H-shaped wall system and 4-story T-shaped wall system. The simulations show the desired capability of accurate prediction of global force-displacement responses, postpeak softening behavior, and compressive buckling of longitudinal steel bars. It is fascinating to see that intrinsic randomness of the 3d interlocking model appears to cause “localized” damage of the real-scale structures, which is consistent with reported observations in different fields such as granular media.

Equipped with accuracy, stability and scalability as demonstrated so far, the parallel platform is believed to serve as a fertile ground for the introducing of further physical mechanisms into various research fields as well as the earthquake engineering community. In the near future, it can be further expanded to run in concert with reliable FEA programs such as FRAME3d or OPENSEES. Following the central notion of “multiscale” analysis technique, actual infrastructures exposed to extreme natural hazard can be successfully tackled by this next generation analysis tool–the harmonious union of the parallel platform and a general FEA program. At the same time, any type of experiments can be easily conducted by this “virtual laboratory.”

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(PHD, 2009)

Abstract:

In order to develop seismic codes that can effectively mitigate damage to wood-frame construction under seismic activity, the dynamic characteristics of wood-frame buildings must be well understood. Funding of full-scale structure experimental tests can be costly and may not be a true replica of real life scenarios. Therefore, data interpretation projects focusing on dynamic behavior of low-rise wooden shearwall buildings under large seismic motions have become increasingly important. Procedures include determining the modal parameters and extracting hysteretic characteristics from the available records. The results help extend the understanding of wood-frame structures and update building codes. Furthermore, the amount of information extracted can help evaluate the effectiveness of the current instrumentation program.

This work focuses on the seismic records from wood-frame structures during the 2004 Parkfield Earthquake. Studies involve verifying the amplitude dependence of modal parameters and retrieving pinching hysteresis curves that are common in wood-frame structures. Modal parameters are identified with a robust routine called MODE-ID. Equivalent viscous damping estimates in wood-frame buildings can range from 5% - 10% in largely linear behavior and 10% - 20% in significant nonlinear behavior. The discrepancies of damping estimates reported in the past are a result of inappropriate comparisons without understanding 1) the degree of nonlinear response and 2) the system identification methods used for the studies. By studying the hysteretic curves, insights can be obtained to reveal and to resolve the damping estimate discrepancies. Since displacement time histories of structures are not typically measured, the hysteretic curves are extracted from acceleration time histories. The proposed process accounts for inherent double integration errors and phase delay through filtering. It is still being debated that if the double integration can provide meaningful structural relative displacement time histories. In a laboratory setting with unilateral ground motion, the extraction process provides accurate hysteretic curves. However, this dissertation demonstrates that if the building experiences bi-directional ground motions, the nonlinear behavior of the diaphragm tampers with this process.

The results from modal identification and hysteresis curves serve as a basis for creating numerical models. Direct and gradient search methods were used for model updating. Bayesian updating and model selection provided the best results for dealing with hysteretic structural models. This probabilistic framework demonstrates potential benefits in a seamless integration with a seismic database. The selected hysteretic model showed great resemblance to the measured responses and had evidence of pinching hysteresis. Insights on the structure’s deformations and dissipation of energy can be inferred from the model.

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(PHD, 2008)

Abstract: A plasticity model to predict the behavior of confined concrete is developed. The model is designed to implicitly account for the increase in strength and ductility due to confining a concrete member. The concrete model is implemented into a finite element (FE) model. By implicitly including the change in the strength and ductility in the material model, the confining material can be explicitly included in the FE model. Any confining material can be considered, and the effects on the concrete of failure in the confinement material can be modeled. Test data from a wide variety of different concretes utilizing different confinement methods are used to estimate the model parameters. This allows the FE model to capture the generalized behavior of concrete under multiaxial loading. The FE model is used to predict the results of tests on reinforced concrete members confined by steel hoops and fiber reinforced polymer (FRP) jackets. Loading includes pure axial load and axial load-moment combinations. Variability in the test data makes the model predictions difficult to compare but, overall, the FE model is able to capture the effects of confinement on concrete. Finally, the FE model is used to compare the performance of steel hoop to FRP confined sections, and of square to circular cross sections. As expected, circular sections are better able to engage the confining material, leading to higher strengths. However, higher strains are seen in the confining material for the circular sections. This leads to failure at lower axial strain levels in the case of the FRP confined sections. Significant differences are seen in the behavior of FRP confined members and steel hoop confined members. Failure in the FRP members is always determined by rupture in the composite jacket. As a result, the FRP members continue to take load up to failure. In contrast, the steel hoop confined sections exhibit extensive strain softening before failure. This comparison illustrates the usefulness of the concrete model as a tool for designers. Overall, the concrete model provides a flexible and powerful method to predict the performance of confined concrete.

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(PHD, 2005)

Abstract:

Spatially uniform ground motion is an assumption that has often been made for structural analysis of arch dams. However, it has been recognized for many years that the ground motion in a canyon during an earthquake is amplified at the top of the canyon relative to the base. Pacoima Dam has been strongly shaken by the 1971 San Fernando earthquake and the 1994 Northridge earthquake. The acceleration records from both of these events demonstrate the spatial nonuniformity of the ground motion, but the amount and quality of the data made it difficult to study in detail. An opportunity to do so arose on January 13, 2001, when a relatively small magnitude 4.3 earthquake was recorded by an upgraded accelerometer array at Pacoima Dam.

Frequency-dependent topographic amplification is apparent at locations along both abutments at 80% height of the dam relative to the base. Also, the ground motion is delayed at the abutment locations compared to the base. The delays are consistent with seismic waves traveling upward along the canyon, and the waves appear to be dispersive since the delays are frequency-dependent. Both of these effects are quantified in this thesis by several approaches that involve varying degrees of approximation. A method for generating nonuniform ground motion from a single 3-component ground motion specified for one location in the canyon, e.g., at the base, is developed using transfer functions that quantify the amplification and phase delay. The method is demonstrated for the 2001 earthquake and the Northridge earthquake with several variations in the transfer functions.

The 2001 earthquake records were also used for system identification. These results do not agree with results from a forced vibration experiment, which indicate a stiffer system. The earthquake must induce nonlinear vibrations, even though the excitation is quite small. This observation has implications for applications of structural health monitoring.

The generated nonuniform ground motions are supplied as input to a finite element model. The results indicate that the method for generating nonuniform input produces ground motion that yields reasonable modeled responses, but there is some evidence that the time delays may be larger for stronger ground motion. Comparisons of the responses from ground motions generated with various implementations of amplification and time delays were made. For modeling purposes, accuracy of the amplification appears to be more important than the delays, which can be dealt with using a simpler approximation. The nonuniform input produces a response that is substantially different than the response produced by uniform input. The major difference is that while the pseudostatic response is a rigid body motion for uniform input, it causes deformation of the dam, mostly close to the abutments, for nonuniform input. In order to refine the proposed method for generating nonuniform ground motion, more data is required from Pacoima Dam and other structures with instrumentation coverage along the abutments.

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(PHD, 2004)

Abstract:

Strong ground motion from a nearby fault has frequency content in the same range as the natural frequencies of tall buildings. This may have serious repercussions and is the topic of this dissertation.Buildings are designed per building code standards. But, are the code provisions adequate? Strong motion from large earthquakes has been recorded only in recent times in the near-source region. Have the current codes used this information to update tall structure design guidelines? Considerable damage has been observed in tall buildings from the Northridge, Kobe, Turkey, and Taiwan earthquakes. How will tall buildings designed per the latest code regulations perform if they were to be shaken by any of these earthquakes? This thesis attempts to answer these questions.

Tall buildings by their nature are computationally intensive to analyze. They consist of thousands of degrees of freedom and when subjected to strong ground motion from a nearby source, exhibit inelastic response. Modeling this inelastic response requires an iterative approach that is computationally expensive. Furthermore, a large class of buildings, classified as irregular, exhibits complex behavior that can be studied only when the structures are modeled in their entirety. To this end, a three-dimensional analysis program, FRAME3D, has been developed incorporating two special beam-column elements – the plastic hinge element and the elastofiber element that can model beams and columns in buildings accurately and efficiently, a beam-column joint element that can model inelastic joint deformation, and 4-noded elastic plane-stress elements to model floor slabs acting as diaphragms forcing the lateral force resisting frames in a building to act as one unit. The program is capable of performing time-history analyses of buildings in their entirety.

Six 19-story irregular steel moment frame buildings (with buildings 2A and 3A being variants of buildings 2 and 3, respectively) have been designed per the latest code (Uniform Building Code, 1997). Two of these buildings have reentrant corners and the other two have torsional irregularity. Their strength and ductility are assessed by performing pushover analyses on them. To assess their performance under strong shaking, FRAME3D models of these buildings are subjected to near-source strong motion records from the Iran earthquake (Mw = 7.3, Tabas Station) of 1978, the Northridge earthquake (Mw = 6.7, Sylmar Station) of 1994 and the Kobe earthquake (Mw = 6.9, Takatori Station) of 1995. None of the buildings collapsed under these strong events in the computer analyses. However, when compared against the acceptable limits for various performance levels in FEMA 356 document, the damage in terms of plastic deformation at the ends of beams and columns and at joints would render the buildings inadequate in terms f life safety in quite a few cases and would even indicate possible collapse in a couple of cases. Thus, in these terms, the code falls short of achieving its life safety objective, and the near-source factors introduced in the code in 1997 in recognition of the special features of near-source ground motion seem to be inadequate.

The ductility demand, in terms of plastic rotation at the ends of beams and columns and in joints, on these buildings during this class of earthquakes is up to 6% of a radian, which is far greater than a typical limiting plastic rotation of 3% associated with fracture and consequent failure of large wide-flanged steel sections during experiments. Thus, if strength degradation due to fractures, local buckling, etc., were to be included in the analysis, then the results would likely to be worse, as far as the ability of these buildings to withstand these earthquakes without collapse is concerned.

Due to damage localization, the peak drifts observed in the structure far exceeded the inelastic drift limit in the code of 0.02 (in some cases up to 3 times). This points to serious non-structural damage to facades, interior dry wall, etc. Furthermore, large roof permanent offsets after the events indicate significant post-earthquake repair requiring considerable disruption and building closure.

Column yielding was minimal thus validating the strong-column weak-beam criterion in the code. Redundancy factors used to assess the redundancy in the system need to take into account the case of torsionally sensitive structures where frames in both principal directions are simultaneously activated. Stress concentration was not observed at the reentrant corners in L-shaped buildings.

Finally, the data catalogued in this work could be useful for future code development and tall structure design guidelines.

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(PHD, 2003)

Abstract: A database of dynamic characteristics of woodframe buildings was developed through analysis of recorded earthquake response and by forced vibration and shake-table testing. Modal identification was performed on eight sets of strong-motion records obtained from five buildings, and forced vibration tests were performed on five other buildings. The periods identified were sensitive to the amplitude of shaking, due to the reduction in lateral stiffness at stronger shaking levels. The equivalent viscous damping ratios were usually more than 10% of critical during earthquake shaking. A regression analysis was performed on the earthquake and forced vibration test data to obtain a simple, but reasonably accurate, period formula for woodframe buildings at low drift levels (less than 0.1%). Data obtained from the UC San Diego and UC Berkeley full-scale shake-table tests illustrate the shift in periods due to increasing shaking amplitude. Forced vibration tests of the UC Berkeley 3-story building before and after the shake-table tests showed how the periods and modeshapes shift due to damage. A simple analytical model of masses and springs was used to model the UC Berkeley test structure. The effects of diaphragm stiffness and mass distribution assumptions were evaluated and found to have a significant effect on the model torsional response. This model was used to find the equivalent wall stiffnesses giving frequency-response curves that best-fit the experimental data. These spring values were used to quantify the stiffness loss resulting from severe shaking of the structure, and the observed damage corresponded to stiffness losses of over 75%. The correlation between stiffness loss and damage to woodframe buildings has potential structural health monitoring implications.

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(PHD, 2000)

Abstract:

This thesis discusses simulations of earthquake ground motions using prescribed ruptures and dynamic failure. Introducing sliding degrees of freedom led to an innovative technique for numerical modeling of earthquake sources. This technique allows efficient implementation of both prescribed ruptures and dynamic failure on an arbitrarily oriented fault surface. Off the fault surface the solution of the three-dimensional, dynamic elasticity equation uses well known finite-element techniques. We employ parallel processing to efficiently compute the ground motions in domains containing millions of degrees of freedom.

Using prescribed ruptures we study the sensitivity of long-period near-source ground motions to five earthquake source parameters for hypothetical events on a strike-slip fault (M_{w} 7.0 to 7.1) and a thrust fault (M_{w} 6.6 to 7.0). The directivity of the ruptures creates large displacement and
velocity pulses in the ground motions in the forward direction. We found a good match between the severity of the shaking and the shape of the near-source factor from the 1997 Uniform Building Code for strike-slip faults and thrust faults with surface rupture. However, for blind thrust faults the peak displacement and velocities occur up-dip from the region with the peak near-source factor. We assert that a simple modification to the formulation of the near-source factor improves the match between the severity of the ground motion and the shape of the near-source factor.

For simulations with dynamic failure on a strike-slip fault or a thrust fault, we examine what constraints must be imposed on the coefficient of friction to produce realistic ruptures under the application of reasonable shear and normal stress distributions with depth. We found that variation of the coefficient of friction with the shear modulus and the depth produces realistic rupture behavior in both homogeneous and layered half-spaces. Furthermore, we observed a dependence of the rupture speed on the direction of propagation and fluctuations in the rupture speed and slip rate as the rupture encountered changes in the stress field. Including such behavior in prescribed ruptures would yield more realistic ground motions.

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(PHD, 1999)

Abstract:

The Northridge earthquake of January 17, 1994, highlighted the two previously known problems of premature fracturing of connections and the damaging capabilities of near-source ground motion pulses. Large ground motions had not been experienced in a city with tall steel moment-frame buildings before. Some steel buildings exhibited fracture of welded connections or other types of structural degradation.

A sophisticated three-dimensional nonlinear inelastic program is developed that can accurately model many nonlinear properties commonly ignored or approximated in other programs. The program can assess and predict severely inelastic response of steel buildings due to strong ground motions, including collapse.

Three-dimensional fiber and segment discretization of elements is presented in this work. This element and its two-dimensional counterpart are capable of modeling various geometric and material nonlinearities such as moment amplification, spread of plasticity and connection fracture. In addition to introducing a three-dimensional element discretization, this work presents three-dimensional constraints that limit the number of equations required to solve various three-dimensional problems consisting of intersecting planar frames.

Two buildings damaged in the Northridge earthquake are investigated to verify the ability of the program to match the level of response and the extent and location of damage measured. The program is used to predict response of larger near-source ground motions using the properties determined from the matched response.

A third building is studied to assess three-dimensional effects on a realistic irregular building in the inelastic range of response considering earthquake directivity. Damage levels are observed to be significantly affected by directivity and torsional response.

Several strong recorded ground motions clearly exceed code-based levels. Properly designed buildings can have drifts exceeding code specified levels due to these ground motions. The strongest ground motions caused collapse if fracture was included in the model. Near-source ground displacement pulses can cause columns to yield prior to weaker-designed beams. Damage in tall buildings correlates better with peak-to-peak displacements than with peak-to-peak accelerations.

Dynamic response of tall buildings shows that higher mode response can cause more damage than first mode response. Leaking of energy between modes in conjunction with damage can cause torsional behavior that is not anticipated.

Various response parameters are used for all three buildings to determine what correlations can be made for inelastic building response. Damage levels can be dramatically different based on the inelastic model used. Damage does not correlate well with several common response parameters.

Realistic modeling of material properties and structural behavior is of great value for understanding the performance of tall buildings due to earthquake excitations.

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(PHD, 1997)

Abstract:

This thesis consists of three parts. Chapter 2 deals with the dynamic buckling behavior of steel braces under cyclic axial end displacement. Braces under such a loading condition belong to a class of “acceleration magnifying” structural components, in which a small motion at the loading points can cause large internal acceleration and inertia. This member-level inertia is frequently ignored in current studies of braces and braced structures. This chapter shows that, under certain conditions, the inclusion of the member-level inertia can lead to brace behavior fundamentally different from that predicted by the quasi-static method. This result is to have significance in the correct use of the quasi-static, pseudo-dynamic and static condensation methods in the simulation of braces or braced structures under dynamic loading. The strain magnitude and distribution in the braces are also studied in this chapter.

Chapter 3 examines the effect of column uplift on the earthquake response of braced steel frames and explores the feasibility of flexible column-base anchoring. It is found that fully anchored braced-bay columns can induce extremely large internal forces in the braced-bay members and their connections, thus increasing the risk of failures observed in recent earthquakes. Flexible braced-bay column anchoring can significantly reduce the braced bay member force, but at the same time also introduces large story drift and column uplift. The pounding of an uplifting column with its support can result in very high compressive axial force.

Chapter 4 conducts a comparative study on the effectiveness of a proposed non-buckling bracing system and several conventional bracing systems. The non-buckling bracing system eliminates buckling and thus can be composed of small individual braces distributed widely in a structure to reduce bracing force concentration and increase redundancy. The elimination of buckling results in a significantly more effective bracing system compared with the conventional bracing systems. Among the conventional bracing systems, bracing configurations and end conditions for the bracing members affect the effectiveness.

The studies in Chapter 3 and Chapter 4 also indicate that code-designed conventionally braced steel frames can experience unacceptably severe response under the strong ground motions recorded during the recent Northridge and Kobe earthquakes.

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(PHD, 1995)

Abstract:

Base isolation is a recently applied technology for building structures in the United States. To date, the three base-isolated buildings considered in this study have been subjected to earthquakes of varying magnitudes and epicentral distances. The records obtained from these instrumented buildings demonstrate low levels of excitation and small structural responses. In all cases, the maximum relative displacement of the roof to the foundation is less than 3 cm. However, an increasing quantity of near-source strong-motion records produces large spectral displacements of up to approximately 50-55 cm in the 2 to 2.5 sec period range for 15% damping. This suggests that long-period structures such as base-isolated structures would be vulnerable to these near-source ground motions.

The current study contains two major parts. Part One consists of the identification and analysis of three existing base-isolated buildings in Southern California. The identification and analysis utilize the recorded motions of these structures from past earthquakes. System identification is useful for understanding the extent to which the structures enter the nonlinear realm and how much their properties change.

Models are constructed assuming completely elastic three-dimensional superstructures, with idealized bi-linear hysteretic elements for the isolating bearings. The properties used in the bearing models were taken from tests of the actual bearings before installation. The models were then verified by comparing their responses computed using the various recorded foundation ground motions, with the recorded responses of the actual structures. The models were adjusted to minimize the error of several response quantities.

Part Two contains computer simulations for the three structural models developed in Part One subjected to large-amplitude near-source ground motions. These structural models were subjected to two classes of ground motions. The first is a sampling of near-source recorded motion from past moderate-to-large earthquakes. The second is a group of synthetic near-source motions generated for a hypothetical M 7.0 earthquake. In some cases, the lateral response of the models exceeds the isolation gap, indicating that the displacement barrier would be impacted.

In order to further study base-isolated buildings when the isolation bearings undergo large displacements, a typical base-isolated building (TBIB) model is used and the computer program 2D-BUMP is developed. This program includes the effects of a fully nonlinear superstructure, nonlinear springs acting as displacement barriers which engage at specified distances, and a tri-linear model for the elastomeric bearings. Using this model, several conclusions are drawn regarding the probable areal extent of damaging near-source ground motions from the M 7.0 event, as well as the behavior of base-isolated structures due to these near-source long-period ground motions.

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(PHD, 1995)

Abstract:

Motion of a block on flat ground under the influence of gravity is studied.

A general model is introduced for the free motion of a rectangular, rigid block on a continuous, perfectly elastic foundation. The model includes friction forces between the block and foundation and allows for sliding, rocking and flight of the block. Solutions are obtained through numerical integration. A three parameter study is carried out, namely as a function of aspect ratio, r, coefficient of friction, µ and non-dimensional stiffness, k_, for various initial conditions.

Dominant types of response are identified and the stability of the block against overturning and its tendency to fly are studied. For initial conditions with sufficient energy, critical curves are found in the (k_, r) parameter space which define a transition between a flight and no flight region. For initial conditions with sufficient energy there also exists a critical curve in the same parameter space which separates a region of overturning from a region where the block does not overturn.

Chaos is found in the flight region of the (k_,r) parameter space for sufficiently high r. Poincare maps and Liapunov exponents are computed to document the existence of chaos.

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(PHD, 1992)

Abstract:

The nonlinear response of steel planar moment-resisting frames during strong earthquakes poses a strong need for accurately modelling inelastic behaviour and large displacements. This thesis attempts to provide realistic and efficient analytical tools to aid this study.

Two large-displacement small-strain beam-column models are employed to include material and geometric nonlinearities. The first model assumes lumped plasticity, and discretises an element into segments. Axial force-Bending Moment strength interaction and flexural bowing are considered. Ten characteristic segment states are identified. An efficient numerical scheme is suggested to solve the nonlinear governing equations. This model only approximately represents the strength and stiffness of beam-columns.

A comprehensive finite element beam-column model is developed to more accurately model the strength and stiffness. A beam-column is discretised into segments, and further, each segment into one-dimensional fibres. A uniaxial cyclic constitutive law valid under arbitrary transient loading is proposed for structural steel. This physically motivated law incorporates the initial yield plateau, and provides explicit expressions for stress in terms of strain throughout the hysteretic path. This law is used to control the hysteretic loading of fibres.

A simple semi-empirical model is employed to analytically describe the highly nonlinear hysteretic behaviour of flexible joint panel zones in steel planar frames. Some modelling assumptions that may be made in frame analyses are evaluated. Numerical study of a building frame with flexible joints indicates that its collapse is sensitive to the joint panel zone design in addition to the ground motion.

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(PHD, 1989)

Abstract:

Standard earthquake analyses of civil engineering structures use uniform ground motions even though considerable variations in both amplitude and phase can occur along the foundation interface for long-span bridges and large dams. The objective of this thesis is to quantify the effect that these nonuniformities have on the structural response.

The nonuniform, free-field motions of the foundation interface are assumed to be caused by incident plane body waves. The medium in which these waves travel is a linear, elastic half-space containing a canyon of uniform cross section in which the structure is placed. The solutions for the free-field motions that are due to incident SH, P and SV waves are calculated using the boundary element method.

An analysis of Pacoima (arch) dam located near Los Angeles, California, is performed for both uniform and nonuniform excitations. The important effect of nonuniformities in the free-field motions, sometimes leading to a decrease in the dam response and sometimes to an increase, is quantified.

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(PHD, 1989)

Abstract:

The nonlinear seismic response of concrete gravity dams is investigated experimentally through the use of small-scale models. Of primary interest is crack formation, crack opening and closing, and sliding along crack planes. Also of concern is the stability of the structure after cracking. Three small-scale models (length scale - 115) of a single monolith of Pine Flat Dam are tested to determine the extent of such behavior and its effect on structural stability. The models are constructed of one polymer-based and two plaster-based materials developed for these experiments. The plaster-based materials fulfill the strength, stiffness, and density requirements established by the laws of similitude, while the polymer-based material fulfills only the stiffness and density requirements and is used only in the lower part of the dam where cracking is not expected. The excitation is a modified version of the N00E component of the 1940 Imperial Valley earthquake, applied to each model’s base in the stream direction through a vibration table with high-frequency capability. Tests are performed with and without water in the reservoir. The response of each earthquake test is presented in the form of acceleration and displacement time histories, Fourier spectra, and frames taken from high-speed films of the model’s response. The results of the experiments indicate that the neck region of a concrete gravity dam is most susceptible to cracking, although crack profiles can differ as a result of variations in excitation, material properties, and construction techniques. These results also indicate alternate design techniques which could improve the seismic stability of a cracked gravity dam.

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(PHD, 1989)

Abstract:

The earthquake response of concrete gravity dam systems is investigated with emphasis on the nonlinear behavior associated with tensile concrete cracking and water cavitation. A single dam-monolith is considered and is assumed to respond independently as a two-dimensional system under plane stress conditions. The two-dimensional assumption is also extended to model the compressible water body impounded upstream of the dam. Standard displacement-based finite element techniques are used to spatially discretize the field equations and produce a single symmetric matrix equation for the dam-water system. Energy dissipation in the reservoir, through radiation in the infinite upstream direction and absorption at the bottom, is approximately accounted for, and a set of numerical examples is presented to demonstrate the accuracy of the present formulation in modeling the linear earthquake response of infinite reservoirs. An approximate procedure to account for dam-foundation interaction is incorporated based on the response of a rigid plate attached to a three-dimensional viscoelastic half-space.

Water cavitation is modeled by a smeared approach which uses a bilinear pressure-strain relation. It is shown that the water response becomes dominated by spurious high frequency oscillations upon closure of cavitated regions, and improved results can be obtained by using some stiffness-proportional damping in the water reservoir. As demonstrated in an example analysis of Pine Flat Dam (linear dam), cavitation occurs in the upper part of the reservoir along the dam face, unlike other investigations which show cavitated regions at considerable distances from the dam, and both the tensile pressure cutoffs and compressive impacts have a minor effect on the dam response.

Tensile cracks are incorporated using the smeared crack approach, and sliding along closed cracks is allowed. Coupling effects inherent in the finite element formulation are explained, and their influence on open and closed cracks is investigated. Propagation of cracks is monitored in an interactive environment which uses an equivalent strength criterion and allows for user input; remeshing is avoided. The algorithm adopted here produces narrow cracks, unlike many other investigations which show large zones of cracking. An extensive numerical study of Pine Flat Dam demonstrates some interesting features of the nonlinear response of the system, identifies potential failure mechanisms, and reveals a number of difficulties that the analysis encounters. Although no instability of the dam occurs, the numerical difficulties will have to be overcome before definite conclusions regarding stability can be made. It is shown that cracking reduces the hydrodynamic pressures in the reservoir and, hence, reduces water cavitation.

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(PHD, 1988)

Abstract:

Forced vibration field tests and finite element studies have been conducted on Morrow Point (arch) Dam in order to investigate dynamic dam-water interaction and water compressibility. Design of the data acquisition system incorporates several special features to retrieve both amplitude and phase of the response in a low signal to noise environment. These features contributed to the success of the experimental program which, for the first time, produced field evidence of water compressibility; this effect seems to play a significant role only in the symmetric response of Morrow Point Dam in the frequency range examined. In the accompanying analysis, frequency response curves for measured accelerations and water pressures as well as their resonating shapes are compared to predictions from the current state-of-the-art finite element model for which water compressibility is both included and neglected. Calibration of the numerical model employs the antisymmetric response data since they are only slightly affected by water compressibility, and, after calibration, good agreement to the data is obtained whether or not water compressibility is included. In the effort to reproduce the symmetric response data, on which water compressibility has a significant influence, the calibrated model shows better correlation when water compressibility is included, but the agreement is still inadequate. Similar results occur using data obtained previously by others at a low water level. A successful isolation of the fundamental water resonance from the experimental data shows significantly different features from those of the numerical water model, indicating possible inaccuracy in the assumed geometry and/or boundary conditions for the reservoir. However, the investigation does suggest possible directions in which the numerical model can be improved.

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(PHD, 1988)

Abstract:

A nonlinear finite element procedure for arch dams is described in which the gradual opening and closing of vertical contraction joints and predetermined horizontal cracking planes are considered. A special joint element approximately represents the deformations due to plane sections not remaining plane at each open joint and allows a single shell element discretization in the thickness direction to be used for the dam. Compressive and sliding nonlinearities are not included. Finite element treatments are also used for the water, assumed incompressible, and for the foundation rock, assumed massless, with all degrees of freedom (dof) off the dam condensed out. For efficiency in the computations, the condensed water and foundation matrices are localized in a way which maintains good accuracy. The response of Pacoima Dam to the 1971 San Fernando ground motion recorded on a ridge over one abutment and scaled by two-thirds is computed first for water at the intermediate level that existed during the 1971 earthquake and then for full reservoir. In the first analysis, the dam exhibits pronounced opening and separation of the contraction joints, allowing violation of the no-slip assumption. The presence of a full reservoir greatly increases the dam response, enough to bring some of the assumptions of the analysis into question. Reducing the ground motion scale to 0.44 with full reservoir drops the response back to a reasonable level, but the contraction joint separations remain.

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(PHD, 1988)

Abstract:

A multigrid algorithm is described that can be used to obtain the finite element solution of linear elastic solid mechanics problems. The method is applied to some simple two and three dimensional problems to evaluate its strengths and weaknesses. The usefulness of the method is demonstrated by solving some large three dimensional problems of practical interest.

When conditions of near incompressibility are encountered, the multigrid method performs poorly due to a combination of a reduction in the smoothing effect of the Gauss-Seidel relaxation method and coarse mesh locking. These problems can be partially cured by using the Jacobi preconditioned conjugate gradient method to smooth the error, and assembling the coarse mesh stiffness matrices using a reduced integration scheme.

It is also found that the bending behavior of the linear brick and quadrilateral elements used in this thesis slow the convergence of the multigrid method. This effect also causes nonuniform meshes to yield computation times that are not proportional to the problem size; however, the linear dependence can be recovered by increasing the refinement of the finite element meshes. It is demonstrated that reduced integration techniques become less effective in relieving the stiffness of the coarse mesh for nonuniform meshes as the problem size is increased. The solution of a well-conditioned three dimensional test problem shows that the multigrid algorithm requires far less computational effort than a direct method, and that its performance is comparable to that of the Jacobi preconditioned conjugate gradient method.

The usefulness of the multigrid method is demonstrated by applying it to the finite element solution of two solid mechanics problems of engineering interest: the elastostatic state near a three dimensional edge crack, and the relationship between the average offset and the stress drop for two and three dimensional faults in a half-space. The features of the solution to these problems are extensively discussed. It is found that the multigrid method is faster than the Jacobi preconditioned conjugate gradient method when applied to these practical problems.

The investigations described in this thesis reveal some interesting features of the performance of the multigrid method when it is applied to the finite element solution of solid mechanics problems. In particular, the storage requirements of the method are linearly proportional to the problem size. The constant of proportionality depends only on the dimension of the problem. The solution times of the multigrid method are found to be linearly proportional to the problem size if uniform meshes are used. However, this is not true for most of the problems that are solved with nonuniform meshes. The constant of proportionality in the relationship between the problem size and the solution time depends on the particular problem under consideration.

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