# Doctoral Theses

in progress

in progress

in progress

Performance-based earthquake engineering (PBEE) is a framework that provides the tools to assess structures under seismic actions in order to quantify the seismic risk (i.e., seismic damage, loss, downtime and casualties expressed through the probability or frequency of occurrence in a time frame). The need to communicate seismic risk and to compare it with other sources of risk is essential for informed decisions to be taken and reduce the economical and societal impact. Even though the PBEE framework has been introduced more than two decades and it is widely appreciated, engineering practice is not able to employ it extensively because of the increased resources required in terms of computation time and expertise. In particular, the processes of ground motion (GM) selection and nonlinear response history analysis (NLRHA) are notably challenging because of the involved computational cost and complex formulation. Moreover, if amplitude scaling is also employed, then the integrity of the results is questioned under the notion that bias is introduced. The advances in these three areas proposed in this work are supposed to reduce their hardships and promote PBEE in engineering practice.

A GM record selection scheme typically ensures that the input excitation to be used in NLRHA is appropriate in terms of spectral compatibility, hazard and intensity measure (IM) consistency, seismological and site-specific criteria (with respect to corresponding targets). Simultaneously, it is expected that it performs in a computationally efficient manner. A GM selection scheme utilizing genetic algorithms is proposed here, able to select multi-component GM and satisfying simultaneously all the typically required selection objectives of earthquake engineering applications while ensuring increased ef- ficiency. Multi-objective optimization is performed, claimed to be superior in delivering robust results that account for spectral compatibility in first and second order statistics (i.e., mean and standard deviation) in a wide range of spectral values, while satisfying seismological and site-specific criteria. A unique contribution of the proposed scheme is the ability to include probability distribution targets in specific ordinates of the spectrum, on top of the mean and standard deviation. This delivers more refined ground motion sets that can be used to reduce the number of GM required in NLRHA. Additionally, a novel benchmarking process to assess the efficiency of GM record selection methodologies is introduced. Instead of assessing the resulting quality in spectral compatibility, it is claimed that GM selection efficiency should be investigated in providing GM sets that are globally-optimal solutions to the optimization problem. Through this benchmarking algorithm, the proposed methodology appears to be impeccable in extracting the best possible GM sets.

The application of amplitude scaling of GM is controversially discussed in earthquake engineering. In this study, bias is questioned in determining an engineering demand parameter (EDP) as a result of NLRHA when using scaled rather than unscaled GM that have the same level of intensity as described through IM. To this end, 10 planar steel- frame building models are analyzed ranging from low- to high-rise. The EDP of interest is the maximum interstory drift ratio (MIDR) and the structural responses range from linear to collapse. For an in-depth investigation of the research question, a vast number of more than 17,000 recorded GM are collected from the NGA-West2 database. Performing incremental dynamic analyses in all structural models subjected to all GM resulted in approximately 3.4 million NLRHA thus creating a rich database of structural responses. The importance of well-known IM is discussed and by considering them together with newly-introduced spectra describing the sustained vibration amplitude, the introduction of bias is examined from different points of view. Firstly, simple and intuitive statistical methods are employed, then machine learning techniques, and finally the GM selection approach proposed in this work is applied. In the numerous investigations, no bias could be detected under the inherent uncertainty of the calculations. The results indicate that scaled records can be safely used in NLRHA to assess the seismic structural behaviour if spectral and scenario compatibility are ensured and it is verified that the sustained amplitude is also consistent.

To circumvent the state-of-the-art NLRHA and reduce the computation time, simplified procedures have long been pursued. To this end, this study investigates artificial neural networks (NN) as prediction models to bypass the NLRHA and quickly and reliably determine the MIDR of building structures. First, the possible designs of such prediction models are discussed in terms of their scope, implementation and corresponding database. The database of structural responses mentioned above is utilized again for this investigation. Based on this database, a designated prediction model is developed for each building, capable of predicting the outcome of NLRHA under a GM excitation that is not included in the database. In addition to the ten building-specific (i.e., record- to-record) prediction models, another one is developed that can predict the outcome of NLRHA for a building and GM excitation, both of which are not included in the database. These investigations indicate that NN is an excellent tool to capture the record-to-record uncertainty and reliably predict MIDR ranging from linear responses to the collapse limit state without resorting to the tedious NLRHA. It is shown that in addition to record-to- record predictions, building-to-building predictions are also feasible if the database used to create the prediction models consists of building structures that are comparable to the building of interest.

Since cross-laminated timber (CLT) has been introduced 30 years ago, the application of timber construction has been constantly expanding from single-story buildings to multi-story buildings in residential housing but also in industrial construction. CLT is commonly composed of an uneven number of three, five or seven glued timber layers and used in typical structural engineering applications as floor and wall elements. The individual layers consist of wooden boards, which are placed side by side, and adjacent layers are arranged at an angle, typically perpendicular to each other. Compared to reinforced concrete buildings, timber construction has a high stiffness-to-weight ratio, which allows to build comparatively lightweight structures. Consequently, timber structures are more prone to vibration, and therefore, the design is generally based on serviceability criteria. Advances in timber construction, such as a recently developed star-shaped steel connector that allows to build wide span point-supported CLT slabs without joists, amplify the problem of undesirable vibrations in ways that they may affect the structural integrity of building components. Therefore, one of the aims of this doctoral thesis is to contribute to the understanding of the dynamic behavior of various timber structures, especially timber floors with different boundary conditions made of CLT panels, in-situ and under laboratory conditions, using the methods of system identification and model updating. In order for these methods to be applicable to the investigated timber structures, they need to be adapted, modified and improved, which is another aim of this doctoral thesis.

First, a pilot study on CLT beams is presented, where it is investigated to which extend structural health monitoring can be applied to CLT structures. To compare the undamaged and damaged states, the modal parameters, i.e. natural frequencies and mode shapes, of the test specimens are used as damage indicators. These parameters are estimated with the developed experimental modal analysis routine that is further extended for application on different CLT structures. Additionally, the modal parameters are the basis for a model updating procedure in which the input parameters of a numerical model are varied until the numerical and experimental results coincide. By performing the experimental modal analysis and model updating in a controlled environment, limitations of the applied procedures are revealed and possible requirements are carried out before testing large-scale test objects.

The second test object investigated in this doctoral thesis is a large-scale point-supported CLT slab, for which a two-day test campaign in form of an experimental modal analysis was carried out. The dynamic response of the structure was recorded at 651 measurement points distributed over the slab surface. The dense grid was chosen to capture possible local affects in the identified mode shapes due to the point-supports realized with a novel star-shaped steel connector. As a result of this long measurement time, the structure cannot be assumed time invariant since it was exposed to environmental effects, which contradicts with one criterion in modal analysis. Consequently, complex modes are identified during the evaluation of the measured data. However, in this doctoral thesis an approach is presented to minimize the imaginary parts of the mode shape vector components by performing a piecewise central axis rotation. Additionally, to extend the findings of the study on this particular test object, model updating is performed to identify the uncertain elastic parameters and support flexibilities for a finite element model, and subsequently, various parametric studies are performed.

The point-supported CLT slab could only be investigated in its raw state, i.e. without floor construction. However, in timber engineering, the dynamic performance of a floor needs to be assessed including floor construction. Since information on the evolution of the dynamic properties of timber floors during different construction states is sparse, a CLT floor with floor construction, i.e. elastic bonded fill, footfall sound insulation and screed, and drywall ceiling is examined continuously during the construction phase. Performing system identification in the different construction states, the shaker, which was used to excite the structure in the experimental modal analysis, is identified as disturbance factor. Therefore, in this doctoral thesis, a two-step model updating approach is presented, in which the shaker is considered in the finite element models as a spring-mass system. After calibrating the different numerical models for each investigated state, the shaker model is omitted in the coupled finite element models, and subsequently, the modal properties of the timber floor are computed numerically. Additionally, it is shown that a superficial finite element model of the timber floor, as used in engineering practice, underestimates the natural frequencies of the structure considerably, which underlines the importance of the presented model updating procedure.

One method to predict the dynamic response of structures is by performing deterministic model updating on a finite element model. The result is a point-estimate of the uncertain input parameters, however, no uncertainty in the experimental data or the input parameters is considered. Therefore, in this doctoral thesis, a stochastic model updating procedure using Bayesian inference is adopted. To perform Bayesian model updating it is necessary to formulate a measure of fit, where commonly the modal parameters of a structure are used, resulting in a modal measure of fit. However, it is shown that using the modal measure of fit for structures with free-free boundary conditions, the outcomes are ambiguous when both the mass and the stiffness properties of the test object are unknown. For this reason, a novel formulation of the measure of fit using cross-signature correlations is proposed. This alternative approach is then verified on a numerical CLT panel and simulated experimental data, and subsequently, the algorithm is used on real test data.

Despite the fact that in the last decades the knowledge of earthquake induced forces has increased, the assessment of the vertical acceleration demand is still an open issue. Commonly in earthquake engineering it is assumed that buildings under seismic impact behave rigidly in vertical direction. Some studies in the last few years, however, have indicated that the vertical acceleration response increases with the height of a seismically excited regular structure and should not be neglected.

The scope of this thesis is the quantification of vertical peak floor acceleration demands at column lines and along the length of beams of elastic and inelastic moment-resisting regular steel frames subjected to recorded and simulated ground motions. These demands correlate with the maximum strength demands on rigid nonstructural components attached to a frame structure. Nonstructural components have a major impact on the seismic risk. Since it is commonly assumed that buildings behave flexibly in the horizontal direction and rigidly in the vertical direction, the assessment of vertical acceleration demands is typically not considered. Therefore, in this dissertation time history analyses are conducted on regular steel frame structures that are excited with the horizontal and vertical component of ground motions simultaneously to assess the acceleration response in both directions.

The results of this dissertation show that vertical peak floor accelerations of regular steel frames can be up to five times larger than the vertical peak ground acceleration. In contrast, the horizontal peak floor acceleration predictions are only up to three times larger than the horizontal peak ground acceleration for the numerical models used in this study. The most significant amplifications estimated in the vertical direction are found at the center of the girders and the exterior column lines of the considered three bay frame structures. Further investigations on modified steel frames indicate that the story-wise mass distribution has an influence on the vertical acceleration demand. In contrast, the response in the vertical and horizontal direction is only slightly affected by an increase in the flexural stiffness of the beams.

Another scope of this doctoral thesis is the impact of different ground motion sets on the vertical acceleration demand. Thus, the time history analyses were conducted with four different ground motion sets, three recorded ground motion sets and one simulated ground motion set. The results show that all considered ground motion sets yield similar acceleration demands, i.e. also the simulated ground motion set can capture the seismic demands adequately for the investigated steel frame in horizontal as well as in vertical direction.

Finally, this dissertation is concerned with the modeling of different energy dissipation mechanisms for the numerical prediction of the vertical acceleration demand in the considered regular frame structures. One of these issues discussed is the consideration of viscous damping in the structural model. As is shown, well-established Rayleigh-damping may highly overestimate the damping of vertical modes, resulting in much too low vertical acceleration response predictions. The result of a model study provides an appropriate damping modeling strategy that leads to reasonable predictions of both horizontal and vertical frame acceleration demands. Another open question addressed is the effect of inelastic material behavior on the vertical acceleration demand on the considered regular structures. The results of a shell model of a frame structure exposed to high intensity ground motion excitation indicate that inelastic material behavior has virtually no impact on the vertical acceleration demand, while the structural inelasticity leaves the horizontal response significantly smaller compared to the elastic demand. This leads to the conclusion that common frame models, which represent the inelastic horizontal response, but behave purely elastic in vertical direction, are suitable for the computation of the acceleration response.

The detailed consideration of the dynamic response characteristics of railway bridges has become an increasingly important design issue of railway bridges in recent years due to the encouraged expansion and construction of high-speed lines. Bridges located on high-speed railway lines can be vulnerable to resonant excitation when crossed by high-speed trains. In a state of resonance, the bridge is excited to excessive structural vibrations, leading to ballast instability, impaired rail quality, and an increased risk of train derailment. These aspects demand a detailed assessment of the reliability of railway bridges for high-speed trains, for which in this doctoral thesis stochastic methods based on a fully stochastic approach are used in the reliability evaluation process. For the reliability assessment, suitable mechanical models are required to determine the structural responses accurately and efficiently. Semi-analytical bridge models allow for an efficient evaluation of the structural responses of the bridge-train interaction problem and also of the soil-structure-vehicle interaction problem.

In this doctoral thesis the performance and computational efficiency of various stochastic simulation methods for a stochastic based reliability assessment of railway bridges subjected to high-speed trains are evaluated and contrasted. Depending on the degree of sophistication, application of crude Monte Carlo simulation to a realistic mechanical model of the uncertain bridge-train interacting dynamical system can be prohibitively expensive. Thus, three alternative stochastic methods, i.e. line sampling, subset simulation, and asymptotic sampling, are tested on two example problems. These examples represent two classes of bridges with random properties characterized by significant different dynamic response behavior. While in the one class of bridges distinctive resonance peaks govern the dynamic peak response, the random response amplification of the second group of bridges is primarily induced by track irregularities. Main sources of uncertainty, i.e. damping, track irregularities, and the environmental impact are taken into account. The studies are conducted on a simplified mechanical model, composed of a plane beam representing the bridge and a planar mass-spring-damper system representing the train. In this approach that considers explicitly dynamic bridge-train interaction, random irregularity profiles describe the effect of track irregularities. This modeling strategy captures the fundamental characteristics of dynamic bridge-train interaction, and thus, facilitates the desired assessment of the stochastic methods with reasonable computational effort. It is shown that both line sampling and subset simulation reduce significantly the computational expense for the first class of bridges, while maintaining the accuracy of the predicted bridge reliability. To ensure accuracy and efficiency, these methods need to be modified when applied to systems where track irregularities dominate the random response. For the latter class of bridges, subset simulation proved to be a suitable method for assessing the reliability of this dynamic interacting system when appropriately modified.

Next, in this doctoral thesis, several more sophisticated measures of the probability of failure of the bridge-train interaction problem are proposed, considering the peak acceleration as a function of the speed in a certain interval and the distribution of the actual train speed. The peak bridge deck acceleration, which is commonly the governing response quantity for dynamic bridge design and failure, depends strongly on the type of train and the train speed. Since in many cases the critical speeds related to response maxima are below the design speed and failure, and during operation the speed varies up to the design speed, the assessment of the probability of failure is not straightforward. These measures are tested on the two considered test bridges. It is shown that in certain speed intervals the predicted probability of failure strongly depends on the underlying measure of the probability of failure. In the first example bridge, whose response is governed by a pronounced resonance peak, exceedance of the serviceability limit state is predicted by all measures at virtually the same speed. The second example problem, where track irregularities lead to considerable response amplifications, only some of the measures predict failure.

The subsequent chapter presents a formalism to efficiently determine the dynamic responses of high-speed railway bridges taking into account both bridge-train interaction as well as soil-structure interaction effects. A viscoelastically supported Euler-Bernoulli beam with general end conditions, which is crossed by a mass-spring-damper system, is utilized as a simplified model of the high-speed railway bridge and the high-speed train, respectively. Due to its viscoelastic supports, the bridge model is non-classically damped. Complex modal analysis provides the complex mode shapes and the complex modal equations of motion of the bridge model to which inherent structural damping is added modally. Based on a dynamic substructuring technique, the beam subsystem in modal state space representation is coupled with the interacting degrees of freedom of the mass-spring-damper system by applying a generalized corresponding assumption, which implies equal displacement of the bridge model and the wheels of the mass-spring-damper system at the contact points. Special attention is paid to the appropriate formulation of the mass-spring-damper system's arrival and departure conditions on the bridge model. In an application example, the dynamic response of a viscoelastically supported bridge model with a lumped mass at both ends crossed by a mass-spring-damper system is analyzed. In particular, the effect of the speed and various parameters of the viscoelastic bearings on the maximum acceleration of the bridge model is examined. The results of the coupled beam-mass-spring-damper system show on the one hand the significant influence of the subsoil on the structural responses and on the other hand by a comparison with the results of a less expensive approach, where the train is represented simplified by its static axle loads, how important explicit consideration of the interaction between the beam and the mass-spring-damper system is for accurate prediction of system behavior.

Soil compaction is a fundamental and critical construction phase of a wide variety of engineering structures, since the quality of fills in foundation work of hall and industrial facilities, soil replacements, dam and base layers in road, railway and airport construction depends on the built-in material and in particular on the realization of earthwork. Dynamic roller compaction has become the common method for proper near-surface compaction to prevent future damage of constructions connected to layered earth structures, failure of long-term pavement performances and increasing maintenance costs. While a static roller uses only its weight to compact filled layers, a dynamic roller enhances the efficiency of subsurface compaction through dynamic excitation of the drum.

Depending on the drum excitation, two basic types of dynamic rollers do exist, i.e. vibratory rollers and oscillation rollers. In a vibrating drum a single unbalance mass, which is attached concentrically to the drum axis, generates a rapidly alternating upward-downward motion of the drum. The subgrade is compacted by the dynamic pressure applied by the drum. The drum of an oscillation roller, as considered in the present thesis, is equipped with two offset eccentric masses, which rotate synchronously in the same direction. The resulting alternating high-frequency forward-backward motion of the drum (oscillatory drum motion) is superposed with the translational roller motion (moving drum under the static axle load). Due to the frictional contact between drum and subsoil mainly dynamic shear forces are transmitted to the soil, which in turn increase the subgrade density, also known as shear force compaction.

The lack of real-time compaction information may lead to both under- and overcompaction and, moreover, to an increased wear of the drum of oscillation rollers. Thus, instant compaction control is of particular importance. A high-leveled quality management requires continuous control of the soil compaction in the entire compacted area, which can be achieved only by work-integrated methods. Roller vibration monitoring has been used for over 40 years during soil compaction to provide what is referred to as Continuous Compaction Control (CCC). CCC has become the standard technology for assessing work-integrated and continuously the achieved compaction by vibratory rollers. For oscillation rollers, however, until recently no mature CCC system did exist, although initial approaches to a CCC system were already proposed almost four decades ago. The recently developed CCC technique has neither been verified by analytical nor by numerical studies. The present doctoral thesis therefore aims to fill this gap by pursuing two modelling strategies, lumped parameter modeling and Finite Element modeling.

The proposed lumped parameter model of the interacting oscillation roller-subsoil system facilitates the response simulation of an oscillation drum with the least numerical effort. The compaction process itself is not captured, but different degrees of compaction are considered by varying the soil stiffness. The roller is represented by the oscillation drum and its viscoelastic connection to the roller frame. In the chosen modeling strategy, the curvature of the soil surface below the drum is prescribed. In this way, also the vertical drum acceleration can be computed. The discrete viscoelastic subsoil model consists of a vertical and a horizontal Kelvin-Voigt element. Contact between drum and soil surface is described by means of dry friction according to Coulomb's law. As such, the stick-slip motion of the drum can be simulated. The highly nonlinear equations of motion of this three degrees-of-freedom model are derived separately for the stick and the slip phase of the motion. A detailed response study of one selected roller type shows that this model captures the fundamental response characteristics of the drum-subsoil interaction system observed in the field. The results of a comprehensive parametric study based on four different oscillation rollers essentially confirm the compaction indicator for the considered oscillation rollers in a wide range of soil stiffness. The found application limits of this value are clearly influenced by the device parameters and the operating oscillation frequency.

The presented Finite Element model allows for the first time the numerical prediction of both the dynamic response acceleration and the compaction effect of an oscillation roller during near-surface compaction of non-cohesive soils. In the developed plane-strain model, the intergranular strain enhanced hypoplastic constitutive model captures the nonlinear behavior of the soil below the drum. A “protective foil” is applied to the soil surface to ensure the numerical stability of the model solved with the Finite Element software suite ABAQUS/Standard. The derived stresses, strains, and change of the void ratio in the subsoil representative for the compaction effect as well as the dynamic response of the drum center are analyzed in detail. In addition, computed dynamic stress components in the soil and drum accelerations are compared with data recorded in field tests. It is shown that the developed model qualitatively and partially also quantitatively predicts the fundamental response characteristics of the interacting oscillation-subsoil system observed in field tests. The outcomes of a comprehensive sensitivity study confirm that the quantities derived from the drum response are basically suitable as indicators for CCC with oscillation rollers. Moreover, the results impressively demonstrate that the roller speed has a significant effect on both drum response and achievable soil compaction.

This doctoral thesis deals with numerical modeling of Deep Vibratory Compaction, used to compact non-cohesive granular soils in deep regions. Inside the vibrator an unbalanced mass excentric with respect to the (vertical) axis of symmetry is mounted, which applies by rotation the centrifugal force into the soil. The vibrator is connected via extension tubes to a crane. During application, at first the vibrator is embedded in the soil at the desired depth into the soil. Subsequently, supported by water jetting, the centrifugal force compacts the soil progressively from the bottom to the free surface. As state of the art, online compaction control is based on the electric current consumption of the imbalance engine. Up to now, however, the relationship between electricity and soil compaction has not been verified. In fact, the efficiency of soil compaction depends on the machine operator. The aim of this work is to model Deep Vibratory Compaction numerically, in an effort to select the relevant physical properties of soil compaction and subsequently to develop a simplified mechanical model.

Numerical modelling of Deep Vibratory Compaction considering all nonlinear properties of the soil and vibrator-soil-interaction is complex. In this doctoral thesis some physical properties of this problem are investigated. These numerical studies are based on different numerical discretization strategies and variations of the excitation frequency of the unbalanced mass rotation. The contact condition between vibrator and soil and the influence of the compaction degree on the system response are studied. The soil is assumed to be linear elastic with adapted material parameters in the sense of a current state simulation. Based on the outcomes of these numerical studies it can be conduced that the contact behaviour of the soil is a non-sensitive property. Assuming rigid bound between vibrator and soil, methods of linear algebra can be used to describe the vibrator-soil-interaction system. For vibro excitation the most relevant mode shapes were computed, which mainly describe shear deformations of the soil. In addition, modal analysis can reduce the number of degrees of freedom without significant loss of accuracy of the results. Progressive soil compaction is described by a priori defined compacted sections to show their influence on the vibrator amplitudes. In order to provide a measure of soil compaction, the equations of motion of a simplified mechanical model of the vibrator-soil-interaction system are solved for the soil parameters. These parameters are determined using numerically generated data of a more complex numerical model. With this method, the value of the Young´s modulus, specified in the numerical simulations, could be identified up to a constant offset from inverting of the simplified mechanical model.

In the early days of earthquake engineering less attention has been paid to building contents, often referred to as nonstructural components (NSCs). In the last two decades, however, the potential seismic risk associated with NSCs has been recognized, separated into life safety and economic loss.

It is reasonable to distinguish NSCs with respect to their response behavior. Displacement sensitive (drift sensitive) NSCs such as claddings or partition walls are mounted multiply at different slabs of the load-bearing structure, and thus, are damaged if the inter-story drift ratio exceeds a certain amount. In contrast, NSCs such as boilers or medical equipment are attached at a single wall or a single slab only. The equivalent seismic force is proportional to the total acceleration of the center of mass of the NSC. Thus, these NSCs are denoted as acceleration sensitive.

During the design process usually the seismic behavior of NSCs cannot be considered by the structural engineer. Moreover, relocating an NSC in a facility may lead to amplified responses, and subsequently, to higher damage probabilities. Hence, efficient and sufficiently accurate methods are required to estimate the maximum absolute (peak) responses of NSCs. This dissertation focuses on the probabilistic seismic assessment of peak floor acceleration (PFA) demands. Research effort during the last decade has shown that damage of acceleration sensitive NSCs is well correlated with the PFA demand of the attachment point. Thus, the strategy of this research is to estimate PFA demands of the load-bearing structure in order to draw conclusions of the seismic response behavior of NSCs.

In the first part of this dissertation a stochastic ground motion selection procedure is introduced to identify quickly record sets consistent with the site specific hazard. The selection is based on an optimization procedure such that the first moment and the second central moment of the spectral acceleration of the record set matches a target spectrum and a target dispersion in a certain period (or frequency) range. Information of the structure such as the fundamental period is explicitly not required. Once a record set is found, it can be used for a broad class of buildings at the specified location. This is an enormous benefit compared to common ground motion selection algorithms.

Generic structural models tuned to fundamental properties of real buildings are developed in an effort to the study the seismic PFA demand. The generic formulation of these structures allows sensitivity analyses, and thus, global conclusions for a class of building types such as moment-resisting frames or structural walls can be drawn. The novelty of the presented generic buildings is its extension to spatial structures and the explicit consideration of vertical PFA demands as a consequence of the vertical component of the ground motion. Additionally, the response behavior to multi-directional earthquake input can be studied yielding new insights for seismic assessment of acceleration sensitive nonstructural components.

Nonlinear response history analysis of various steel-, concrete-, and wall structures is conducted, which, nowadays, provides the closest approximation of real structural behavior in a seismic event. Based on an inelastic single-degree-of-freedom system the concept of acceleration ductility is introduced, which is consistent to the definition of the well known displacement ductility. The concept of acceleration ductility can be used to assess in a simplified manner the PFA demand of inelastic multi-story structures. The PFA demands obtained from response history analysis of multi-story structures are consistent with observations of other research groups. It is shown that application of simplified methods provided in building codes may lead to non-conservative estimations of PFA demands, particularly in the vertical direction.

Nonlinear response history analysis methods are, however, computationally expensive and can only be conducted by an experienced seismic engineer. To avoid this effort, response spectrum analyses based on various modal combination rules are widely accepted in research and professional engineering. If correctly applied, a wealth of information can be exploited with minimum computational effort. In this dissertation a response spectrum method for estimation of elastic PFA demands is rigorously derived. Application to various planar and spatial structures shows the superiority of this method compared to approaches available in literature. Additionally, various simplifications of this method are presented and subsequently evaluated.

The assessment of collapse-induced earthquake casualties requires the collapse fragility of a building, which is a relationship that defines the probability of structural collapse with respect to the ground motion intensity. The prediction of this quantity for regular, Moment Resisting Frame (MRF) structures vulnerable to the PDelta effect and cyclic deterioration based on a simplified assessment methodology is the main objective of this dissertation. In the first step the parameter range in terms of fundamental structural properties is revealed, where global sidesway collapse is in general governed by PDelta only, and where cyclic deterioration in combination with PDelta has a significant impact on the sidesway collapse capacity. Additionally, an “optimal” Intensity Measure (IM) that results in a low inherent Record-To-Record (RTR) depended variability of collapse capacity of the considered types of structures is identified, composed of the geometric mean of spectral pseudo accelerations in a certain period range.

The simplified collapse assessment methodology is based on an equivalent Single-Degree- Of-Freedom (equivalent SDOF) system. Since a previously developed equivalent SDOF model incorporates only the PDelta effect, nonlinear quasi-static cyclic tests in combination with subsequent optimization analyzes are used to identify cyclic deterioration parameters for the equivalent SDOF systems in terms of empirical relations. For these equivalent SDOF models the collapse fragility is obtained from series of Incremental Dynamic Analyses (IDAs) and compared to the “reference” values of the corresponding Multi-Degree-Of- Freedom (MDOF) systems. In an effort to reveal the parameter range of the applicability of the equivalent SDOF model the outcomes of the simplified collapse fragility assessment with respect to the underlying IM is evaluated, and in further consequence an “optimal” IM for the simplified assessment of the “equivalent” collapse fragility is defined. Based on these outcomes, a simplified methodology for the quick and accurate assessment of the sidesway collapse fragility of regular, MRF structures is presented. The proposed methodology relies on an empirically derived, analytical description of the collapse fragility of the equivalent SDOF systems as a function of characteristic structural properties and does not require time-demanding nonlinear dynamic analyses on the frame structure. The accuracy is tested by comparison of the predicted values with the actual collapse fragilities of the corresponding MDOF system. For instance, the relative error of the approximation of the median collapse capacity is for a certain class of structures less than 20 %, and for 75 percent of those structures less than 10 %.

Due to the development and construction of new high-speed lines there is a high demand for reliable design and assessment of railway bridge constructions crossed by trains with high speed. Excessive vibrations of railway bridges lead to amplified deformations, stresses and accelerations of the structure and must be limited to prevent derailment and structural failure. Additional complexity of this reliability problem is caused by uncertainties that influence the resistance and the load level of the structure, such as material dispersion, irregular rail surfaces or local ballast settlements, undetermined and unpredictable energy dissipation mechanisms, and the environmental impact on the dynamic behavior of the bridge.

In contrast to the standard engineering design assessment based on partial safety factors, in this dissertation a probabilistic approach is used to quantify structural reliability of railway bridges, which are dynamically excited by crossing trains. Random variables describe the inherent uncertainties of the problem, and the compliance of performance criteria is checked by probabilistic numerical simulations, yielding estimates of the probability of failure of the train-bridge interaction system for assessing reliability.

A sophisticated numerical model is developed for the dynamic assessment of railway bridge structures, capable of taking into account vehicle-bridge interaction and track irregularities. By applying a substructure approach, which couples bridge and train models, different degrees of idealization can be implemented for the individual parts of the problem. For the mechanical description of the bridge structure simple beam models, and plane and three-dimensional finite element models are utilized. The crossing train is either idealized by concentrated forces at the train axles or by a multi-body system. The influence and validity of different degrees of sophistication of the numerical model on the resonance prediction is evaluated for deterministic example structures. The environmental impact on the bridge structure from seasonal changing temperatures and frost in subsoil and ballast is taken into account within a stochastic description. Based on these models in a probabilistic analysis the probability of failure due to acceleration thresholds is evaluated with simulation methods. Additionally to Monte Carlo simulations with crude direct and Latin Hypercube samples also more elaborated methods such as line sampling and subset simulation are applied to the reliability problem.

On a case study object the outcomes of the probabilistic assessment are compared to the standardized engineering design concept for dynamically loaded railway bridges based on European and Austrian building codes. Monte Carlo simulations provide a view on the scatter of the dynamic response and its variability. It is found that track irregularities significantly affect the variance and magnitude of the peak acceleration response. Although being conservative, a good agreement of the results of code based and stochastic analysis is found, leading to the conclusion that the applicable codes provide reasonable design rules.

This dissertation aims to provide a better understanding of seismic sidesway collapse of highly inelastic basic structure vulnerable to the destabilizing effect of gravity loads (i.e., the P-delta effect), and to enhance the prediction of their seismic collapse capacity with simple measures.

A major part of this dissertation is devoted to the quantification of the collapse capacity uncertainty of P-delta vulnerable single-degree-of-freedom (SDOF) systems. In particular, the reduction of record-to-record variability (RTR) of the collapse capacity is addressed through an appropriate choice of the intensity measure (IM) of the earthquake excitation. It is proposed to utilize an IM based on the averaged spectral pseudo-acceleration in a certain period interval. Furthermore, a relative IM is introduced that takes into account the structural parameters of the SDOF system affected by P-delta. That is, the 5% spectral pseudo-acceleration is read at the at the period of vibration of the system in the presence of gravity loads, and further normalized by base shear coefficient of the P-delta affected system. Through a parametric study it is shown that both IMs reduce significantly the RTR dispersion of the seismic collapse capacity compared to the widely used benchmark IM, i.e., the spectral pseudo-acceleration at the system period without considering P-delta.

The effect of uncertainty of the main characteristic parameter responsible for seismic induced global collapse, i.e. a post-yield negative stiffness ratio, on the median and the dispersion of the collapse capacity is quantified. The outcomes of the first-order-second-moment method are verified by results of the latin hypercube sampling (LHS) technique. Subsequently, the total uncertainty composed of the parameter uncertainty and the RTR variability is assessed with two approaches, using the square-root-sum-of-squares superposition rule, or alternatively, two-dimensional LHS. The latter approach allows the simultaneous consideration of both sources of uncertainty with the same computational demand compared to simulations considering the RTR variability only. It is shown that the parameter dispersion of the collapse capacity can be of the same order as the RTR variability. The inclusion of epistemic uncertainties flattens the fragility curves, and larger probabilities of collapse are predicted for small intensity values.

The impact of the characteristic structural parameters and various IMs on the collapse capacity and its RTR variability of P-delta sensitive multi-degree-of-freedom systems is studied. It is confirmed that the negative global post-yield stiffness ratio is the dominant parameter for collapse of P-delta vulnerable and non-deteriorating systems. The choice of an “average” IM that considers also higher mode effects results in the smallest dispersion for the considered generic moment resisting frames. Thus, it can be concluded that an equivalent SDOF system cannot reflect directly the collapse capacity dispersion of a multi-story building.

Design collapse capacity spectra and fragility curves with reduced RTR dispersion based on the proposed “average” IM, refined collapse capacity spectra and fragility curves based on a conventional IM, and analytical parameter dispersion collapse capacity spectra are provided through multiple regression analysis, aiming to enhance the simplified assessment of P-delta vulnerable systems within the general framework of the collapse capacity spectrum methodology.

In the dissertation, the vibration energy distribution in structural acceleration responses is investigated, and a novel two-step damage identification procedure based on this quantity is introduced. Many existing damage identification methods rely on a mechanical model of the considered structure. The advantage of the proposed procedure is that it avoids this restriction as far as possible. In the first step – damage detection: Is there a damage? – no modal parameters are required, because it is completely based on the vibration energy / vibration characteristics of response measurements. The normalized cumulative power spectral density (NCPSD) is defined as the damage sensitive feature. Its dissimilarity in an undamaged reference state and in the actual structural state is expressed by a so-called NCPSD damage index that is defined in this dissertation. This flexible quantity can be computed for individual structural nodes, averaged over the whole structure, or also statistically evaluated in long-term monitoring, since the evaluation is completely automatable. Variation of temperature and excitation can be taken into account. Only for the second step – damage localization: Where is the damage? – it was found that identified mode shape data is necessary for successfully locating the damage, based on two defined mode shape damage indexes. The proposed two-step damage identification procedure has been tested on several models simulated on the computer and on three real structures. It is shown that the NCPSD damage index is suitable to indicate most of the imposed structural modifications, representing damage, despite the unknown nature of the ambient excitation. In a simulated long-term monitoring project, the statistical characteristics of the NCPSD damage index indicate damage successfully.

Diese Arbeit befasst sich mit der numerischen Simulation des Struktur- und Stabilitätsverhaltens von Schalen. Dies beinhaltet die theoretische Aufbereitung und numerische Umsetzung eines finiten Schalenelements für geometrische und materielle Nichtlinearität sowie die Darstellung und Bewertung numerischer Lösungsalgorithmen zur Bestimmung des Beulverhaltens ausgesteifter Schalenstrukturen im Rahmen der Finite-Elemente Methode. Nach Aufbereitung der kontinuumsmechanischen Grundlagen wird durch räumliche Reduktion eine geometrisch exakte Schalentheorie abgeleitet. Neben glatten Schalen sollen auch Schalenverschneidungen berücksichtigt werden. Unter Annahme der Reissner-Mindlin Hypothese erfolgt daher die kinematische Beschreibung des inextensiblen Direktors durch den orthogonalen Rotationstensors. Zur Gewinnung einer singulär-freien Parametrisierung wird dieser innerhalb eines Lastinkrements durch den Rotationsvektor dargestellt. Nach jeder erfolgreichen Gleichgewichtsiteration erfolgt eine Aktualisierung des Rotationstensors durch Quaternionen. Die variationelle Basis für die Elementformulierung bildet das Hu-Washizu Funktional mit den drei unabhängigen Feldern der Verschiebungen, Verzerrungen und Spannungen. Die Diskretisierung der Referenzfläche erfolgt durch ein vierknotiges Element. Parasitäre transversale Gleitungen werden durch Anwendung des ANS-Konzepts eliminiert. Die Interpolation der Verzerrungen wird in zwei Teile aufgespaltet: der erste Teil ist ident mit der Interpolation der Spannungen, und im zweiten Teil sind in Analogie zum EAS-Konzept die Interpolationsansätze orthogonal zu den Spannungen. Dadurch können Dickenverzerrungen der Schale berücksichtigt werden und vollständige dreidimensionale Materialmodelle ohne zusätzliche Modifikationen verwendet werden. Die hier gewählte Interpolation der unabhängigen Felder gewährleistet, dass die Steifigkeitsmatrix den vollen Rang besitzt. Das Stabilitätsverhalten einer Schale soll aus vollständig ermittelten Last-Verschiebungskurven erkennbar sein. In dieser Arbeit werden sogenannte direkte Verfahren zur Bestimmung von (vorwiegend) Verzweigungspunkten eingesetzt. Die Grundidee dieser Verfahren ist die Erweiterung der Gleichgewichtsbedingungen um Funktionen, die den Stabilitätspunkt beschreiben. Um die Singularität der Jacobi Matrix des erweiterten Gleichungssystem zu vermeiden, wird eine Modifikation der Gleichgewichtbedingungen vorgeschlagen. Mit branch-switching Algorithmen, die große Ähnlichkeit zu Pfadverfolgungsalgorithmen aufweisen, wird das anfängliche Nachbeulverhalten berechnet. Zum Abschluss wird die nichtlineare Strukturantwort von ausgewählten Schalenbeispielen berechnet.

Despite the fact that increased research efforts in the last decade have led to a greater understanding of seismic induced global structural collapse, assessment of seismic collapse is still a challenging and in general computer-demanding task. In particular in an early stage of the design process, the benefits of a detailed determination of the collapse capacity are relatively small compared to the required computational efforts. Thus, it is desirable to have simplified procedures available for a simple and fast to apply but sufficiently accurate assessment of the seismic collapse capacity.

In this thesis such a simplified methodology is proposed aiming at prediction of the seismic collapse capacity of planar moment-resisting frame structures with enelastic non-degrading component behavior, which are vulnerable to the destabilizing effect of gravity loads.

The methodology is based on the transformation of the multi-degree-of-freedom system into an equivalent single-degree-of-freedom system. Its parameters are derived from global pushover curves with and without consideration of gravity loads. Subsequently, the collapse capacity is assessed using so-called collapse capacity spectra. In the spectra the non-dimensional median collapse capacity of a single-degree-of-freedom system is presented as a function ot the elastic structural period and the negative post-yield stiffness. In this thesis these spectra are derived from extensive time history analysis and subsequent applicatioon on nonlinear regression analyses. Consideration of the transformation coefficient yields to the assessment of the collapse capacity of the equivalent single-degree-of-freedom system, which is assumed to be a reasonable estimate of the actual median collapse capacity. Since the essential part of the methodology are collapse capacity spectra, the methodology is referred to as "collapse capacity spectra methodology".

The proposed collapse assessment methodology is applied and tested on a large number of planar moment-resisting frame structures. Moreover, its limitations are discussed.

Reliability of existing buildings is a major issue of a comprehensive seismic hazard assessment. Particularly in urban areas with a huge amount of historic buildings the evaluation and assessment of those buildings is indispensable. In the city centre of Vienna so-called Gründerzeithäuser, structures, which were erected within the building phase between 1840 and 1918, represent the predominant type of building. Mostly, these structures have been retained unchanged without considerable structural improvement for decades, but nevertheless are typically still used as residential buildings. Especially the lack of information and scientific investigations about the material properties, the detailed construction and the dynamic behavior of those buildings has led to many discussions about their vulnerability under seismic loading.

It is therefore the main intent of the Doctoral Thesis to carry out a comprehensive assessment and evaluation methodology based on visual inspections for the considered historic buildings in Vienna in order to obtain a realistic estimation of the damage potential under seismic loading of this particular building type. According to existing assessments an efficient method was developed to assess and evaluate a large amount of buildings within an adequate period. The essential information for the development of the method was made available from historic documents as well as from current scientific research results. Hence the evaluation and assessment method for Gründerzeithäuser in Vienna consists of various parameters to describe the actual condition of the structure and the damage potential of the building in case of an earthquake event. After the evaluation and assessment of a certain structure, the building will be classified in order to estimate the possible damages due to an earthquake. In an application of the evaluation and assessment methodology a large amount of Gründerzeithäuser in the 20th district of Vienna was investigated. Subsequent to the classification of the buildings a seismic hazard map of the reviewed area was plotted to identify local damages due to a local earthquake event.

In a further part of the Doctoral Thesis basic information about the dynamic system of the considered historic buildings in Vienna was obtained by means of in-situ investigations in order to derive scientific findings on the dynamic behavior under seismic loading of these structures. One of the biggest advantages of experimental investigations on existing buildings is the recording of the actual condition of a structure. In particular the most interesting parameters of the present historic buildings are the modifications of the dynamic behavior during structural changes. These modifications can be favorably identified by comparison of the structural behavior with and without certain changes.

During a further investigation of the test object Spittelbreitengasse the contribution of non-structural elements on the dynamic behavior of the building could be identified. Especially the influence of partition walls and wooden floors on the global stiffness of the building could be verified. In addition the experimental results were checked by means of a numerical model of the structures. The conclusions therefore provide important technical expertise for the seismic vulnerability assessment of the Gründerzeithäuser in Vienna.

This thesis deals with the numerical modeling of historic brick masonry in the framework of

Finite Element (FE-) simulations. Based on experimental investigations on bricks, mortar, and

small scale masonry specimens, adequate material models and parameters for the constituents

are determined. Therefore, a material model for concrete available in the utilized FE program

is choosen. Since for the simulation of larger structures only a smeared modeling of masonry

is reasonable, such a macromodel is implemented in the framework of multi-surface plasticity

theory. The model is able to capture the hardening and softening behaviour as well as the

essential failure modes of masonry, taking into account in-plane behaviour only. Parameters of

the model are derived via homogenization, because corresponding experimental investigations

on the historic masonry considered are difficult to carry out. Two- and threedimensional unit

cells are used for the homogenization, taking into account the actual geometry and material

behaviour of historic brick masonry. Finally, numerical investigations on a historic building

concering its behaviour in case of an earthquake are conducted using the capacity spectrum

method.