### Master theses

with abstracts

in progress

in progress

in progress

in progress

In this thesis the three dimensional constitutive model for reinforced concrete, originally proposed by Grassl and Jirásek (2006), is evaluated by means of finite element analyses of cyclically loaded large scale structures. Two suitable experiments are selected based on the availability of experimental data and on the primary response characteristics, which are sought to be mainly flexural.

The first chosen specimen is a half scale reinforced concrete wall panel tested at the University of Canterbury in New Zealand. The so called "Holden Wall" represents a ductile cast-in-place wall component commonly found in monolithic structural wall systems of building cores all around the world. In a cyclic, yet quasi-static lateral loading scheme, the specimen was brought to full collapse in 19 load cycles. The quasi-static conditions and the simple geometry are favorable features for the first application of the present modeling approach. Monotonic as well es cyclic simulations are conducted in the finite element analysis software Abaqus/Standard, for which well tested implementations of the concrete model but also for the widely used reinforcing steel model by Menegotto and Pinto (1973) are available. The performance of the model is evaluated in global load versus displacement curves from which also energy dissipation characteristics are derived. Visualizations of the simulated concrete damage are presented as well and compared to experimental crack patterns.

A full scale bridge pier, tested on the biggest outdoor shake table in the world at the University of California in San Diego, is chosen for a second numerical investigation. The cantilevered reinforced concrete column represents a single-column bent subjected to base excitation perpendicular to the bridge axis, whereas the bridge's superstructures are idealized through a massive concrete block providing mass inertia. In this dynamic test the specimen is solely exposed to axial weight and base accelerations, thus inertia forces have to be accounted for accurately, which is an additional challenge compared to the previous study. From ten ground motion simulations in the original experiment, five are simulated successfully in Abaqus/Standard. In these three dimensional implicit dynamic analyses, the mentioned concrete model is applied again and its performance is evaluated by means of comprehensive comparison in a global and local fashion. Dynamic characteristics are investigated by modal analyses prior to and after each ground motion simulation.

In these studies, several shortcomings of the used approach are revealed. However, it is also shown that an efficient and computationally affordable application of the finite element method using solid elements is possible and needed improvements to better capture experimental responds are pointed out in this work.

Concrete is a widely used building material. The exact prediction of the strength development of concrete is an advantage in the case of highly utilized structures and if the stripping times are to be kept short. The prediction of the temperature is important for massive structures. Because then self heating affects the curing of the concrete.

In this work three existing modeling approaches for maturing concrete are presented and compared. For this purpose, the governing equations are examined and transformed for comparison. Beside the hydration process, the focus is on the conservation of mass and energy. The theoretical differences are pointed out and theoretical effects and relationships are shown. The main differences are the formulations of the solid phase density and the pore saturation.

A numerical investigation of the differences considered in isolation is performed. Therefore, calculations are carried out at integration point level. A graphic preparation with subsequent interpretation shows that the assumption of a constant density of the solid phase is too simplistic. However, the assumption of a linear relationship between the porosity and the degree of hydration is conﬁrmed. Finally, a new model is presented combining the advantages of the three approaches. With this model three-dimensional simulations are carried out. These simulations together with reference simulations allow to investigate the coupled effects caused by the different approaches.

The realistic representation of the material behavior of concrete in finite element simulations still poses a great challenge. In particular, the regularization of the softening material behavior, which is a requirement for objective results, is the subject of intense research. Damage plasticity models find widespread use for describing the material behavior of concrete. This is due to their ability to describe both inelastic (plastic) deformations and the degradation of elastic properties due to damage.

In the present work, four benchmark examples are analyzed using Abaqus to investigate and compare several damage plasticity models for concrete. These models differ in their formulations and their regularization schemes. It is thereby shown that the regularization of the softening behavior via the specific mode I fracture energy and an element-based characteristic length leads to results that are pathologically dependent on the employed type of finite element. It is further shown that over-nonlocal gradient enhancement of the damage part of one of the employed material models provides a remedy for this deficiency.

Stability problems, which are most likely rooted in the non-associated plastic potential of the plasticity formulations of the employed material models, together with high computational cost, present shortcomings of the models and motivate further research.

Concrete as a building material has a distinctly time-dependent material behaviour. This influences the durability, serviceability and load bearing capacity of concrete structures and is therefore relevant for engineering practice. The time-dependent material behaviour is based on coupled thermal-, hygral-, chemical- and mechanical processes. These can be represented by a multiphase model, within the framework of the theory of porous media. The system is modelled by constitutive relations and balance equations for momentum, enthalpy and mass of all phases. Among the constitutive relationships are multiphase formulations of shrinkage and creep models as well as models for nonlinear material behaviour. In literature the latter has so far been considered for multiphase models by coupling them with damage models. At the Unit of Strength of Materials and Structural Analysis of the University of Innsbruck a program has been developed which allows the coupling of the multiphase model with a damage plasticity model.

This work includes applicability studies and the validation of the implementation on structural level. The reinforced concrete structure used for this purpose is taken from a well-documented test program. In addition, the theoretical foundations of the implementation are comprehensively documented in this thesis for the first time.

The material model is first calibrated with both experimental and literature data. This is the basis for the simulation of the structure. The variation of the ambient temperature and the ambient humidity is considered in the model with convective boundary conditions. The applicability at the structural level is investigated with both an ideal plastic and a damage plasticity formulation.

The calibration based on laboratory tests and literature data provides very satisfying results. However, an application of the coupled damage-plasticity formulation at the structural level is not easily possible. Currently, a solution can only be found for a coarse mesh in case the concrete has sufficient strength at early ages. Such problems do not occur for the multiphase model with ideal plasticity. The simulations show that in the current structural model the temperature curves and thus also the resulting constraining forces cannot be reproduced accurately. Also the predicted crack pattern does not match the one from the experiment, but is similar to calculated crack patterns from literature. One conclusion is that the model needs to take thermal radiation into account for a better representation of the temperature curves. In addition, for a better applicability of the multiphase damage plasticity model a more robust implementation of the balance iteration is needed.

In Austria the majority of bridges were built between 1960 and 2000 and are accordingly already very old. Thus, to sustain the continuously increasing traffic loads the existing bridge structures have to be strengthened. A novel strengthening method by applying a textile-reinforced concrete layer to increase the shear and torsional resistance of existing bridge structures is currently developed in the research project „concreteX” at the Unit of Concrete Structures and Bridge Design at the University

of Innsbruck. Therein, three-point bending tests of plain and textile-reinforced concrete T-beams were carried out in summer 2019, representing the experimental basis for the present thesis.

The aim of the present Master's thesis is to develop a nonlinear finite element model for enabling the prediction of the structural behavior of concrete T-beams strengthened by a textile reinforced concrete layer. For capturing the mechanical behavior of concrete in a realistic manner, a damage- plasticity model is employed, which is available and enhanced at the Unit of Strength of Materials and Structural Analysis at the University of Innsbruck. Initially, a nonlinear finite element model for

replicating the structural behavior of the concrete T-beams in the three-point bending tests is developed, which is subsequently enhanced by considering the textile-reinforced concrete layer. On the basis of parameter studies the numerically predicted mechanical behavior is analyzed and is evaluated by means of comparison with the results from the laboratory tests.

It will be demonstrated that by means of comprehensively calibrated nonlinear finite element models the ultimate loads recorded in the experiments of both, the plain and textile-reinforced concrete T-beams, can be predicted. However, the numerically predicted displacements in the pre-peak regime are underestimated compared to the experimental results, which is attributed to the simplifying model assumptions such as the assumed perfect bond behavior between concrete and

steel reinforcement or textile reinforcement. In the simulations of the textile-reinforced concrete T-beams it will be shown that the textile-reinforcement is the major load-bearing part and that the role of the surrounding concrete lies primarily in the force transmission to the existing concrete part. The presented nonlinear finite element models enable further parameter studies, being particularly important for the prototype development phase, and form a basis for further numerical studies of

textile-reinforced concrete.

The present thesis consists of two main parts. Part one deals with a back analysis of a tunnel advance, which is part of the Brenner Base Tunnel (BBT) project, while the second part deals with experimental investigations on the material behavior of young shotcrete.

Back analysis of a tunnel advance

A drill and blast tunnel advance, which is part of the Brenner Base Tunnel (BBT) project, is simulated by means of a 2D finite element model. Therein, an advanced shotcrete model is used to represent the nonlinear, time-dependent material behavior of the shotcrete lining. Comprehensive geodetic measurement data on the convergences along a distance of 100m is used for the calibration of the numerical model. The numerical results obtained by the calibrated model indicate a good agreement of the measured and predicted deformations. The outcome of the numerical study is a prediction of the arising stresses and the utilization of the shotcrete lining during and after tunnel advance. Due to high loads caused by deformations of the surrounding rock mass immediatly after installation of the securing measures, the first hours and days after placement of the shotcrete lining are of great importance.

Experimental investigations on the material behavior of shotcrete

During preliminary investigations for a currently planned experimental program on shotcrete a method to determine the specific mode I fracture energy is developed. The specific mode I fracture energy is an important material parameter for regularization of the softening behavior in material models in order to obtain nearly mesh-independent results in finite element simulations. Since for numerical simulations of tunnel advance a realistic representation of the material behavior of young shotcrete is of great importance, knowledge on the hydration dependent evolution of the specific mode I fracture energy is required additionally. However, for shotcrete experimental results on this material parameter have not been presented so far, and no information on a proper test setup for determining this parameter is available in the literature. For this reason, a test setup to determine the specific mode I fracture energy of young shotcrete is developed and assessed by means of experimental tests on young concrete and shotcrete specimens. It is shown that by employing the developed procedure the specific mode I fracture energy of shotcrete can be determined successfully already at a young material age.

Beton ist einer der am häufigsten verwendeten Baustoffe. Er wird gerne in Kombination mit Stahl, zu Stahlbeton bzw. Spannbeton, verbaut. Maßgebend für seine Langlebigkeit ist die Widerstandsfähigkeit gegenüber äußeren Einwirkungen. Eine der relevantesten Einwirkungen sind Chloride, welche in gelöster Form in den Betonkörper eintreten und zu einer Korrosion der Stahlbewehrung führen können. ...

Porous materials like soil or concrete commonly contain several different substances so-called phases. In order to make a realistic statement about the behaviour of multi-phase systems under external influences, the properties of the different phases and their mutual interaction has to be taken into account. This consideration is implemented by formulating so-called multi-phase models.

Systems featuring rotationally symmetric properties including the geometry, material as well as the initial and boundary conditions can be reduced to „Pseudo-2D“ problems with regard to the principles of rotational symmetry. This circumstance allows an efficient solution of the problems mentioned before. The result is equivalent to the spatially formulated problem but time and costs are saved in respect of modelling and the duration of the calculation.

Within this thesis, rotationally symmetric finite element formulations for single- and multi-phase systems are derived and subsequently implemented in the FE program mpFEM. The formulation, which builds from single-phase to multi-phase, aims at the effect of the coupled problem on the rotationally symmetric formulation for multi-phase systems. Differences between rotationally symmetric formulations for scalar transport problems and those for structural mechanics problems are highlighted. The impact of the rotationally symmetric formulation on the hygro-mechanical problem is discussed in respect of the deformation depending term of a mass balance. To verify the implemented calculation methods in mpFEM for different single-phase and multi-phase systems the results are compared with analytical and numerical solutions. The results of the comparative calculations show that the implementation of the rotationally symmetric formulations is valid. This approach allows an integration of the rotationally symmetric multi-phase formulation into an existing code with little effort. Hence it is also possible to use this kind of approach for multi-phase models of concrete.

The practical example of the hygro-mechanical multi-phase problem only considers linear-elastic behaviour. The way of the formulation and implementation provides the possibility of using a material law which is more complex. Thereby plastic deformations can also be considered.

Load - bearing capacity and serviceability are major design criteria for the construction of reinforced concrete structures. Both of them need to be maintained over the entire service life of the structure. High carbon dioxide concentrations in the ambient air however can trigger reactions of carbon dioxide with several chemical components of the concrete. This process, called carbonation, starts near the concrete surface and penetrates progressively into the structure. Once the carbonation front reaches the reinforcement bars, it leads to corrosion of the reinforcement steel, causing severe damage of the structure already at an early age.

This work aims at providing a numerical model which allows to predict carbonation - depths already during the design stage for ensuring the desired durability. To this end, the mathematical formulation to describe the complex process of carbonation of concrete, based on the models of Oberbeck and Steffens, is derived. The formulation considers the evolutions of pore humidity and temperature in the concrete, as well as the evolution of the concentration of carbon dioxide in the pores. The resulting system of coupled partial differential equations is restated in its variational form to allow a subsequent discretization based on the finite element method.

A major part of this work is a standalone implementation of this finite element model in Matlab, which allows to solve the coupled system consisting of mass balances and carbonation reaction. For solving even larger problems, the respective element matrices and residuals are also implemented as a user element in the in - house finite element software 'mpFEM' available at the Unit of Strength of Materials and Structural Analysis at Innsbruck University. Simulation results for the evolution of the carbonation front are presented for selected examples. The numerical results show, that in comparison to experimental data, a good estimate of the upper bound of the carbonation depth is obtained. It is found that the carbonation depth is not exclusively affected by the distribution of moisture, temperature and carbon dioxide. It is rather also dependent on the cement content, the quality of the workmanship and the curing conditions, which enter the model indirectly via the model parameters.

The present thesis deals with the modelling of hysteresis in the soil-water characteristic curve, a phenomenon which is observed for processes involving drying and wetting of porous materials like soils and concrete. The soil-water characteristic curve describes the relation between capillary pressure and saturation. Its shape depends on the shapes of the pores as well as on the pore size distribution and is therefore different for different materials.

Three different models are used in order to describe the soil-water characteristic curve. The first one is the equation of van Genuchten. This widely-used model includes no hysteresis, i.e. the same behaviour is assumed for drying and wetting. This model is contrasted with two hysteretic models. The Nuth model uses the formulation of an elasto-plastic constitutive law. The hysteretic effect originates from kinematic hardening, i.e. from a shifting of the elastic range triggered by plastic wetting or drying. The Pedroso model is based on reference curves. Different curves are implemented to represent the drying and wetting path. Their shape is determined by adaption to experimental data. Both hysteretic models are formulated incrementally. The Nuth model exhibits kinks on the drying and wetting path. For the Pedroso model drying as well as wetting paths are smooth.

The implementation of the mathematical models is described. The calibration is carried out on the basis of data for two materials, Del Monte Sand and ordinary concrete. The data for the calibration of the sand is taken from the literature. The measured data used for the calibration of the models for concrete is taken from an experiment to determine the sorption isotherm of ordinary concrete which was conducted at the Unit of Strength of Materials and Structural Analysis. The calibration is more diﬃcult for the more complex models. Nevertheless, a good adaption to the given set of data points is achieved for all models.

All three models are implemented into a multi-phase finite element software. The thesis reviews the basic assumptions and equations for the multi-phase formulation. Results for the desiccation and subsequent watering of a sand column are shown. For this simulation, the parameters obtained from the calibration for the Del Monte Sand are used as input. The hysteretic effect manifests itself in a delay in the watering process. The results are consistent with values from the literature. The comparison of the investigated hysteretic models shows that the Pedroso model is numerically more stable. This behaviour is attributed to the smooth behaviour inherent to its formulation.

As a consequence of the increasing traffic load as well as of the progression of the mean age of bridges, measures of rehabilitation become more and more important. One such measure could be adding a concrete overlay. Therefore, the aim of this master thesis is to provide a better understanding of the material parameters related to shrinkage and parameters for multiphase modeling.

First, a brief introduction to the subject is given. Subsequently, the theoretical foundation is discussed and the concepts of porosity, moisture storage and moisture transport are introduced. Furthermore, the sorption isotherms are defined and the different shrinkage processes are briefly explained.

The composition of the concrete mixture with (compressive) strength class C30/37 is specified as well as the fresh concrete parameters, which are measured during the concreting. In addition to that, the parameters of the hardened concrete, such as Young’s modulus and the compressive strength, are provided for different concrete ages. Additionally the determination of the hygric parameters is presented, with the desorption isotherms as well as the adsorption isotherms being determined on thin concrete slices.

Furthermore, the laboratory tests and the results of the shrinkage tests on thin specimens are described. In the test program the autogenous shrinkage, the pure drying shrinkage and the combined autogenous and drying shrinkage are investigated. The autogenous shrinkage was determined on sealed specimens from the age of one day, whereas the drying shrinkage is measured on two years old specimens, which were therefore completely hydrated. Likewise, the combined autogenous shrinkage and drying shrinkage are determined using specimens from the age of one day, which were simultaneously drying and hydrating. Moreover, the influence of the concrete age on the combined autogenous and drying shrinkage is analysed. Next, the obtained results of the tests are compared to different codes as well as to results of other authors.

In addition, the deformation of young concrete, starting at the age of 5 hours, is observed on prismatic specimens. Simultaneously, the temperature development is measured in the above-mentioned prismatic sample bodies, as well as in a semi-adiabatic experiment using a cubic specimen. All specimens were stored in a climatic chamber at a temperature of (20 ± 1) °C.

Finally, a summary of all the obtained results is provided and a brief outlook is given.

The structural analysis of reinforced concrete parts using the finite element method does not only require an appropriate modelling of the material behaviour of concrete, but also an adequate consideration of the reinforcing steel. In this thesis the modelling of the latter component as embedded reinforcement is examined. This concept is characterised by the superposition of those finite elements that represent concrete and reinforcement. This approach offers a realistic reproduction of the load bearing behaviour and is suited for system level Analysis.

There are different methods of applying the concept of embedded reinforcement. According to comprehensive preliminary investigations that have been carried out within the present thesis, the element-based embedding proves to be advantageous. The distinguishing feature of this method is the partitioning of the reinforcing bars along the boundaries of the elements representing the concrete. The obtained segments are clearly assigned to the concrete elements. This approach requires the calculation of intersection points. This procedure as well as the actual embedding on the level of the element stiffness matrix are explained in the present Thesis.

In order to allow meaningful calculations the concept of embedded reinforcement for two-dimensional problems has been implemented into a capable finite element routine. This software package as well as the material model which was applied to describe the concrete have been continually developed at the Unit of Strength of Materials and Structural Analysis at the University of Innsbruck. By recalculating the tensile tests of reinforced concrete specimens it was possible to examine the consideration of tension stiffening. The calculations show an inaccurate load bearing behaviour if tension stiffening is neglected, whereas a modification of the material model for concrete leads to appropriate results. Furthermore, system level analyses of L-shaped concrete panels under bending were carried out in order to investigate the performance of the concept of embedded reinforcement. Although linear elastic behaviour has been assumed for the reinforcing steel, promising results could be obtained. In addition to a good depiction of the crack formation in the form of concentrated damage zones, the concept of embedded reinforcement allows a detailed examination of the load bearing behaviour of the individual reinforcing bars. The consideration of nonlinear behaviour for the reinforcing steel and the associated reduction of tension stiffening are expected to allow accurate ultimate load calculations.

The subject of this master thesis is the documentation and development of a creep-test bench, which was developed in the years 2013 and 2014 at the Unit for Strength of Materials and Structural Analysis. During this development, three identical test benches have been built up and are currently used in experiments which started in September 2014. The aim of these creep-test benches is to gain measurement data on the creep of concrete over a long time period. For this purpose, a constant stress is applied on two specimens in the test bench. While keeping up this stress, the strain, which is increasing due to creep, is measured regularly. The objectives of this thesis were to specify the requirements, the assembly and documentation of a repeatable adjustment of the test bench. Further on, a sensory system to record all important measurement data has been composed and an application for reading the data has been developed.

Finally, the complete process to prepare, start and monitor an experiment at the test bench has been documented, to give accurate instructions for future test series.

This master thesis deals with the creep and shrinkage behavior of concrete. Results from different experiments will be compared to the results of numerical simulations based on a multi-phase model of concrete.

The basic principles of the multi-phase model will be discussed. This contains descriptions of the theory of porous media, the hygric behaviour of concrete, the hydration process of concrete and the mathematical formulation of concrete creep and shrinkage behaviour. Furthermore, the basic principles of the implementation of a multi-phase model of concrete by means of the FEM is shown.

The larger part of this thesis deals with the comparison of the computed and in different experiments measured strains and relative mass water contents and their interpretation. For the comparison of drying shrinkage strains, results from experiments conducted at the University of Innsbruck, Unit for Strength of Materials and Structural Analysis, were used. Experiments of Bryant and Vadhanavikkit were used for the comparison of creep strains. For all numerical simulations, a good agreement with the experimental results was achieved.

Due to increasing trafﬁc loads and a relatively high mean age of existing concrete bridges, strengthening measures like adding a concrete overlay are becoming more important. The present work deals with monitoring of an existing bridge strengthened by adding a concrete overlay in order to improve the load bearing capacity. Comparison of in-situ-measurements with results of an accompanying lab test shows the effect of environmental inﬂuences on determined measurements.

After a short introduction to the current topic in the ﬁrst chapter as well as a short introduction of the existing concrete bridge in the second chapter, the third chapter introduces the theoretical basics of porosity, moisture storage, moisture transport as well as different types of shrinkage.

At the beginning of the fourth chapter the comprehensive lab test is described and the results are presented. Furthermore, special measuring instruments used on the in-situ-test are explained and the determined in-situ-measurements are described. Afterwards, lab test results are compared with in-situ-measurements as well as with the results calculated according to Euro-code 2 (EN 1992-1-1 [1]).

The ﬁfth chapter gives an outlook on future work. The sixth and last chapter contains a summary of the major ﬁndings of the present work.

There are two different kinds of fastening processes; cast-in-place installations and post-installed installations. The latter has a significantly lower planning effort. Furthermore, one must differentiate between mechanical and chemical systems. While mechanical anchors transfer the applied force into the base material at one point, chemical anchors do this always over the drilling hole's entire area. In the following thesis, the Finite Element Method is used to numerically analyze the time-dependent behaviour of chemical anchors. While the latter is well known for concrete and steel, it still needs to be investigated for chemical mortar systems. The time dependent deformations caused by a constant load, the so-called creep deformations, are defined by compliance functions, where different kinds of formulations are available. For this purpose three different mortar systems are investigated experimentally.

Furthermore, results of long-term experiments for different mortar systems are compared with simulation results. The correspondence between simulation and experiment is good. This means, that the experimentally determined compliance function can be validated. Parameter studies show the significance of several influencing factors, for example, the scatter of experimental data or the interpolation error in the course of determining the compliance function