Numerical Modeling of a Church Nave Wall Subjected to Differential Settlements::Soil-Structure Interaction, Time-Dependence and Sensitivity Analysis

Historic masonry structures are particularly sensitive to differential soil settlements. These settlements may be caused by deformable soil, shallow or inadequate foundation, structural additions in the building and changes in the underground water table due to the large-scale land use change in urban areas. This paper deals with the numerical modeling of a church nave wall subjected to differential settlement caused by a combination of the above factors. The building in question, the church of Saint Jacob in Leuven, has suffered extensive damage caused by centuries-long settlement. A numerical simulation campaign is carried out in order to reproduce and interpret the cracking damage observed in the building. The numerical analyses are based on material and soil property determination, the monitoring of settlement in the church over an extended period of time and soil-structure interaction. A sensitivity study is carried out, focused on the effect of material parameters on the response in terms of settlement magnitude and crack width and extent. Soil consolidation over time is considered through an analytical approach. The numerical results are compared with the in-situ observed damage and with an analytical damage prediction model.The authors acknowledge the funding received by BRAIN.be, Belspo in support of the GEPATAR research project (“GEotechnical and Patrimonial Archives Toolbox for ARchitectural conservation in Belgium” BR/132/A6/Gepatar).Peer ReviewedPostprint (author's final draft

Modelling and Quantification of the Effect of Mineral Additions on the Rheology of Fresh Powder Type Self-Compacting Concrete (Modellering en kwantificering van het effect van minerale vulstoffen op de reologie van vers poeder type zelfverdichtend beton)

Powder type self-compacting concrete (SCC) mixtures are characterised by a higher powder content compared to traditionally vibrated concrete (TC) mixtures in order to increase the viscosity of the concrete mixture and thus achieving a sufficiently high resistance to segregation, while a third generation (polycarboxylate ether based, PCE) superplasticizer is used in order to increase the flowability of the SCC mixture. Besides cement, powder type SCC mixtures mostly incorporate readily available mineral additions like limestone powder, quartz powder, fly ash or silica fume in order to reduce heat generation during cement hydration.The objective of this work is to describe the workability of powder type SCC by means of a rheological approach. In this way, a fundamental description of the concrete flow behaviour during placement is obtained, which is indispensable in case of special concretes (such as SCC) and/or in cases of congested reinforcements.For fresh concrete, two major different rheological approaches can be used, depending on the scale of observation: the suspension approach (local scale) or the continuum/fluid approach (global scale). In this thesis, mainly the global flow behaviour of fresh SCC is treated and a continuum/fluid approach is used in order to describe the concrete flow behaviour.Due to the viscoplastic behaviour of the fresh concrete, it is generally agreed that, as a good first approximation, fresh concrete can be described by a linear flow curve, according to the Bingham model. However, test results on powder type SCC mixtures revealed that a non-linear flow curve (Herschel-Bulkley model) is often needed in order to describe more correctly the shear rate-shear stress relationship.The wide-gap Couette concentric cylinder rheometer used for the experiments, together with the theoretical derivation of the solution of the Couette inverse problem by means of the integration method for both a Bingham and a Herschel-Bulkley fluid are presented in this work.The description of the shear thickening flow behaviour of powder type SCC in terms of shear rate and shear stress can be used as input for the global scale (CFD) simulations of powder type SCC processing operations (e.g. casting, mixing or pumping) and can be considered as a small step into the promising direction of (fresh) concrete flow simulation/prediction tools.To illustrate the importance of predicting the thixotropic behaviour for a given (powder type) SCC mixture, two practical applications, i.e. formwork pressure and distinct-layer casting are discussed.It was found that the Herschel-Bulkley parameters are reliable, absolute rheometry parameters (at least for the shear rate region actually tested). The wide-gap concentric cylinder rheometer provides a reproducible test procedure, from which the parameters and their influencing factors can be derived.Fresh powder type SCC is susceptible to a shear thickening flow behaviour. This is due to its intrinsic mix design philosophy, i.e. the combination of a sufficient amount of small (powder)particles and a low amount of coarse aggregates (where the hydrodynamic forces dominate), which promotes cluster formation.Furthermore, the addition of a PCE superplasticizer will result in a more dispersed state of the smaller (powder)particles, so that a larger amount of these particles is available for shear thickening, while test results also indicated that the molecular design of the PCE superplasticizer has most-likely a non-negligible impact on the shear thickening effect.The intensity of the shear thickening effect can be modified by the nature and fineness of the mineral addition used. It was found that the limestone, quartz and fly ash addition used in this research project respectively increase, unalter and decrease the shear thickening intensity. Increasing the fineness of the limestone addition resulted in a higher shear thickening intensity.Microstructural interpretations of the rheological behaviour are proposed, based on the order-disorder transition theory and the cluster theory, complemented with local mechanical actions caused by the shear effect.nrpages: 364status: publishe

Model Reduction Techniques to Improve the Efficiency of Flexible Multibody Simulations (Ontwikkeling en validatie van modelreductietechnieken voor de efficiënte simulatie van flexibele meerlichamendynamica)

The ever-increasing trend to design machines and processes to befaster, more lightweight, more energy-efficient and more reliablecauses virtual prototyping to gain importance over physicalprototyping. Accurate numerical modeling techniques for flexiblemultibody systems are needed in the different stages of thedesign. Furthermore, numerical models are not only used in thedesign phase; certain applications rely on simulation results ofnumerical models computed in real-time. Real-time targets arecurrently only met for highly simplified multibody models.However, in industry a strong desire exists to extend real-timecapabilities to more advanced models.In model reduction, the evolution of the system state is decomposedin dominant and negligible motion patterns. In the currentstate-of-the-use in flexible multibody modeling mainly body-levelmodel reduction is used. Body-level model reduction refers tomodel reduction applied to the flexibility description ofindividual bodies, i.e. mechanism components. These reduced bodyflexibility models are then incorporated in the model equations ofthe overall system. In case of a multitude of possible loadingpoints on a flexible body, its reduced body flexibility model willbe of significant size, such that time integration of the overallmultibody model becomes expensive. A first goal of this researchis to develop and validate efficient modeling techniques for therepresentation of flexibility in multibody dynamics, especiallytargeting this flaw in the state-of-the-use.A first solution to this problem is interface reduction, in which component interaction is approximated by a limited set of interaction patterns.An alternative interface reduction scheme is proposed and the associated computational hurdles are solved. This offers the user an alternative to model intercomponent interaction, without the numerically introduced artificial stiffness of conventional techniques. In a numerical experiment the effect of this artificial stiffness is illustrated.However, accuracy requirements can impose the use of more detailed body flexibility models. Quite often, many DOFs can be loaded during simulation, but few are loaded simultaneously. The multitude of possibly loaded DOFs imposes an expensive body flexibility description, but at any moment in time only a low-dimensional part of this description contributes to the solution. An innovative methodology is proposed, called Static Modes Switching, which at every time step only includes the strictly needed deformation patterns, so that at every time step an accurate body flexibility description of minimal size is obtained. Considerable simulation speed gains are obtained with an acceptable loss of accuracy.A second goal of this research is to develop and validate system-level model reduction techniques which enable real-time simulation of flexible multibody systems.The presence of both differential and algebraic equations in the model equations, and the number of degrees of freedom needed to accurately represent flexibility prohibit real-time simulation of these systems. Most current model reduction techniques for non-linear systems project the model equations on a set of invariable motion patterns. Only by using configuration-dependent motion patterns, one can transform the model equations from a set of differential-algebraic equations into a set of ordinary differential equations, and achieve a maximal dimension reduction. This is done in Global Modal Parameterization (GMP), for which this research proposes a generalization. Global Modal Parameterization divides the computational load over an expensive preparation phase and a cheap simulation phase. This research focuses on applications where fast online simulation capabilities justify an expensive offline preparation, such as real-time applications.In a first step, modal motion patterns are used. The sources of approximation error of a GMP-description are investigated. The effect of the configuration space discretization coarseness on the different approximation error sources is illustrated. The trade-offs to be defined by the user to control these approximation errors are explained. It was observed that the eigenmodes with eigenfrequencies near or within the frequency range of the excitation should be included in the motion patterns for model reduction. Furthermore, additional motion patterns are required to compensate for the quasi-static contribution of the omitted eigenmodes.Mode veering and mode crossing cause abrupt changes in mode shapes. As a modal GMP approach is based on describing the motion by the contributions of these rapidly changing motion patterns, the degrees of freedom of a GMP-description can vary abruptly for moderate system changes. It is theoretically proven that this even results in singularities for mode veering.Although the individual eigenmodes vary abruptly, the vector space spanned by a pair of veering/crossing modes has limited variability.To exploit this, linear combinations of eigenmodes are proposed to generate smoothly varying motion patterns. This requires an automatic detection of mode veering. A numerical experiment shows that this is unfeasible for systems with multiple parameters defining the dynamics.As a second solution, Krylov subspaces are proposed for the motion patterns of the GMP model reduction. A Krylov subspace also spans the dominant dynamics near a chosen frequency, without singularities due to mode veering.The maximal variability with respect to the system configuration of the first Krylov vector is one order of magnitude lower than the first eigenmode. However, due to the recursive definition and the orthogonalization in the Arnoldi computational process, variability is propagated and amplified through the series of Krylov vectors. By omitting this orthogonalization step, this propagation and amplification of variability vanishes. However, a singularity-free GMP-simulation using Krylov seems to be infeasible.Finally, several future research tracks are proposed.Contents List of symbols xi Contents xix List of Figures xxv List of Tables xxxvii 1 Introduction 1 1.1 The need for numerical simulation of multibody dynamics . . . . . . . . 1 1.2 Optimizing the efficiency of numerical simulations . . . . . . . . . . . . 3 1.3 Modeling of flexible multibody systems . . . . . . . . . . . . . . . . . . 4 1.4 Model reduction of non-linear models . . . . . . . . . . . . . . . . . . . 6 1.5 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.6 Outline and contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.6.1 Body flexibility model reduction . . . . . . . . . . . . . . . . . . 11 1.6.2 System-level model reduction for flexible multibody systems . . . 12 2 Interface reduction of flexible bodies for efficient modeling of body flexibility in multibody dynamics 15 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Condensation of interface DOFs . . . . . . . . . . . . . . . . . . . . . . 19 xix xx CONTENTS 2.3 Computation process in the finite element package . . . . . . . . . . . . 22 2.4 Selecting dependent DOFs . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.1 Mathematical considerations . . . . . . . . . . . . . . . . . . . . 24 2.4.2 Selection of dependent DOFs in practice . . . . . . . . . . . . . . 27 2.5 Numerical example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3 Static Modes Switching for more efficient flexible multibody simulation 35 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.1.1 The floating frame of reference approach in flexible multibody modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.1.2 Body flexibility model reduction . . . . . . . . . . . . . . . . . . 37 3.1.3 Time integration of sets of differential-algebraic equations . . . . 40 3.2 Static Modes Switching . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.3 Numerical Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.3.1 Model description . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.3.2 Effect of the time integration scheme settings . . . . . . . . . . . 49 3.3.3 Validity of the assumptions . . . . . . . . . . . . . . . . . . . . . 50 3.3.4 Approximation errors . . . . . . . . . . . . . . . . . . . . . . . . 51 3.3.5 Simulation time reduction . . . . . . . . . . . . . . . . . . . . . 54 3.3.6 Importance of numerical high-frequency damping . . . . . . . . . 56 3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4 Generalization of Global Modal Parameterization 63 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.2 Original model equations . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.3 Describing instantaneous system change by motion patterns . . . . . . . . 65 4.4 Substitution in original model equations . . . . . . . . . . . . . . . . . . 66 4.5 Mapping inherently satisfies the constraints . . . . . . . . . . . . . . . . 67 CONTENTS xxi 4.6 Left multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.7 Use as a simulation tool . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.8 Redistribution of the computational load . . . . . . . . . . . . . . . . . . 69 4.9 Discretization of the h-space . . . . . . . . . . . . . . . . . . . . . . . . 70 4.10 Choice of motion patterns Y . . . . . . . . . . . . . . . . . . . . . . . . 71 4.11 Exploiting low variability of system dynamics along certain motion patterns 72 4.12 Distinction between low variability and high variability motion patterns . 74 4.13 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5 Approximation errors resulting from a modal GMP description 77 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.2 Global Modal Parametrization . . . . . . . . . . . . . . . . . . . . . . . 80 5.3 Use of GMP for simulation . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.4 Numerical experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6 Mode set requirements for a modal GMP description 99 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.2 Global Modal Parameterization . . . . . . . . . . . . . . . . . . . . . . . 103 6.3 Use of GMP for simulation . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.4 Numerical experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.4.1 Completeness of modal description . . . . . . . . . . . . . . . . 115 6.4.2 Mode veering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 6.4.3 Mode crossing . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 6.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 7 Mode veering/crossing for multidimensional configuration space discretization 133 xxii CONTENTS 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 7.2 Numerical experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.2.1 Model description . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.2.2 Symmetric configurations . . . . . . . . . . . . . . . . . . . . . 136 7.2.3 Slightly asymmetric configurations . . . . . . . . . . . . . . . . 147 7.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 8 Krylov subspaces as GMP vector sets 157 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 8.2 Krylov subspaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 8.2.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 8.2.2 GMP-simulation using a Krylov mode set . . . . . . . . . . . . . 160 8.3 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 8.3.1 Krylov subspaces . . . . . . . . . . . . . . . . . . . . . . . . . . 164 8.3.2 Eigenmodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 8.3.3 Effect on simulation accuracy . . . . . . . . . . . . . . . . . . . 166 8.3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 8.4 Vector variability for multidimensional q-spaces . . . . . . . . . . . . . . 171 8.4.1 Variability of eigenmodes . . . . . . . . . . . . . . . . . . . . . 171 8.4.2 Variability of Krylov vectors . . . . . . . . . . . . . . . . . . . . 172 8.4.3 Effect of the orthogonalization in the Arnoldi computational process174 8.5 GMP-simulation for systems with multiple q-DOFs . . . . . . . . . . . . 175 8.5.1 Model description . . . . . . . . . . . . . . . . . . . . . . . . . 175 8.5.2 GMP-simulation using fixed-q eigenmodes . . . . . . . . . . . . 176 8.5.3 GMP-simulation using Krylov vectors . . . . . . . . . . . . . . . 178 8.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 9 Concluding remarks 193 CONTENTS xxiii 9.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 9.1.1 Improving current state-of-the-art body flexibility model reduction 193 9.1.2 Developing system-level model reduction techniques . . . . . . . 196 9.2 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 9.2.1 Improving current state-of-the-art body flexibility model reduction 200 9.2.2 Developing system-level model reduction techniques . . . . . . . 202 A Additional eigenfrequency difference plots 207 A.1 Difference between successive eigenfrequencies . . . . . . . . . . . . . . 207 B Additional vector variability plots 211 B.1 Variability of rigid body modes . . . . . . . . . . . . . . . . . . . . . . . 211 B.2 Variability of eigenmodes . . . . . . . . . . . . . . . . . . . . . . . . . . 211 B.3 Variability of Krylov modes . . . . . . . . . . . . . . . . . . . . . . . . 212 B.4 Effect of the orthogonalization in the Arnoldi computational process . . . 212 Bibliography 219 Curriculum vitae 227 List of publications 231nrpages: 278status: publishe

Invloed van vulstoffen op hydratatie en eigenschappen van SCC

De in België courante opvattingen betreffende het mengselontwerp van zelfverdichtend beton (SCC) leiden tot het gebruik van grotere hoeveelheden vulstoffen in een zelfverdichtende betonsamenstelling in vergelijking met een traditioneel verdicht betonmengsel (TC). Een belangrijk onderdeel van het fundamenteel onderzoek betreffende SCC spitst zich dan ook toe op de invloed van verschillende types vulstoffen op eigenschappen van het uiteindelijke betonmengsel zoals eigenschappen van het verse mengsel, hydratatie, duurzaamheidsaspecten en tijdsafhankelijke fenomenen.status: publishe

Modal Acceleration to improve the efficiency of flexible multibody simulations

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Interface reduction of flexible bodies for efficient modeling of body flexibility in multibody dynamics

The floating frame of reference techniques is an established technique to incorporate flexibility in multibody models. The model dimension of the body flexibility models can be reduced by model reduction techniques such as Component Mode Synthesis (CMS) or Krylov subspace-based techniques, but the efficiency of these techniques is limited by the number of interface nodes in which the flexible body is or can be loaded. A common solution to this problem is condensing the different nodes of a given interface surface into a single node, which represents the net motion of the interface surface. Commercial finite element packages offer two modeling techniques to condense interface surfaces: rigid multipoint constraints and interpolation multipoint constraints. Rigid multipoint constraints will typically result in stiffness overestimation, whereas interpolation multipoint constraints will lead to an underestimation. Which approximation of both is most suitable depends on the application. However, the default definition of interpolation multipoint constraints does not allow generation of reduced body flexibility models for multibody models. This paper gives a theoretical background of the problem cause, and offers a practical solution. The two modeling techniques result in significantly different approximations of the body flexibility dynamics, as is shown in a numerical example.status: publishe

Properties of self-compacting fibre reinforced concrete

The postcracking behaviour of fibre reinforced concrete is particularly influenced by the fibre distribution and the fibre orientation. One could suppose that in self-compacting fibre reinforced concrete (SCFRC) fibres orient along the flow due to the wall-effect, the flow direction and the velocity profile in the concrete. To investigate the fresh and hardened characteristics (mechanical properties, orientation and distribution of the fibres) of SCFRC and to relate them to those of traditionally vibrated fibre reinforced concrete (TFRC), a research program is set up. The following parameters are investigated: fibre length, concrete flow distance and concrete type (SCFRC and TFRC).status: publishe

Shrinkage, creep and frost resistance of self-compacting concrete

Although already many researches exist about self-compacting concrete (SCC), it is still remarkable to notice that very little fundamental data have been published concerning its durability. This knowledge is, however, of extreme importance for a good and durable construction practice. For that reason, this article outlines laboratory studies concerning durability aspects as shrinkage, creep, salt frost scaling and internal frost resistance of 7 self-compacting concrete mixtures (SCC) and 1 reference, traditionally vibrated, concrete mix (TC1). In concrete science, time-dependent deformation models as the CEB-FIP Model Code 1990 (MC-90) and the Model B3, are well known for their good prediction of shrinkage and creep of normal concrete. In this paper, the possibility of these models to be transposed to the recently new cementitious material as self-compacting concrete is, is investigated. Test results revealed in general higher shrinkage and creep deformations for the SCC mixtures compared with the TC mix. However, while the shrinkage deformations seem to be underestimated by MC-90, the creep and overall behaviour of the SCC mixes seem to be well predicted by the same model. Salt frost scaling tests lead to a higher amount of scaled material due to the imposed freeze-thaw cycles for SCC in comparison with the TC mix, although the ultrasonic measurements indicated that most SCC mixtures suffered less in comparison with the TC mix. On the other hand, ultrasonic measurements executed to determine the internal frost resistance of test specimens not subjected to salt attack showed similar results for all mixtures. A reason for this observation may be found in the test set up.status: publishe

Component Mode Synthesis as an approximation of the frequency response

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The influence of fillers on the properties of self-compacting concrete in fresh and hardened state

This paper represents the results of an investigation of the suitability of different fillers to be used for SCC. An experimental test program has been executed with 12 different SCC mixtures, each mixture containing another type of filler. The other mix parameters (water-to-cement ratio, fine and coarse aggregates content) were the same for all mixtures. Firstly, concrete mixtures were made to examine the influence of the same volume of filler on the mix proportion. Secondly, all mixtures that could not be defined as SCC (according to workability) were adapted. The different mixtures were investigated with respect to workability (slump flow, V-funnel and U-flow), compressive strength, shrinkage, water absorption and freeze-thaw resistance (with and without de-icing salts). Each filler has been characterised by different tests: water demand (beta_p), Blaine, activity index, particle size distribution and microscopic visualisation using a scanning electron microscope (SEM). An effort has been made to link the measured properties of the SCC with the characterising parameters of the fillers.status: publishe