The desire for energy and resource savings brings magnesium alloys as lightweight materials with high specific strength more and more into the focus. Most structural components are subjected to cyclic loading. In the course of computer aided product development, a numerical prediction of the fatigue life under these conditions must be provided. For this reason, the mechanical properties of the considered material must be examined in detail. Wrought magnesium semifinished products, e.g. magnesium sheet metals, typically reveal strong basal textures and thus, the mechanical behavior considerably differs from that of the well-established magnesium die castings. Magnesium sheet metals reveal a distinct difference in the tensile and compressive yield stress, leading to non-symmetric sigmoidal hysteresis loops within the elasto-plastic load range. These unusual hysteresis shapes are caused by cyclic twinning and detwinning. Furthermore, wrought magnesium alloys reveal pseudoelastic behavior, leading to nonlinear unloading curves. Another interesting effect is the formation of local twin bands during compressive loading. Nevertheless, only little information can be found on the numerical fatigue analysis of wrought magnesium alloys up to now. The aim of this thesis is the investigation of the mechanical properties of wrought magnesium alloys and the development of an appropriate fatigue model. For this purpose, twin roll cast AM50 as well as AZ31B sheet metals and extruded ME21 sheet metals were used. Mechanical tests were carried out to present a comprehensive overview of the quasi-static and cyclic material behavior. The microstructure was captured on sheet metals before and after loading to evaluate the correlation between the microstructure, the texture, and the mechanical properties. Stress- and strain-controlled loading ratios and strain-controlled experiments with variable amplitudes were performed. Tests were carried out along and transverse to the manufacturing direction to consider the influence of the anisotropy. Special focus was given to sigmoidal hysteresis loops and their influence on the fatigue life. A detailed numerical description of hysteresis loops is necessary for numerical fatigue analyses. For this, a one-dimensional phenomenological model was developed for elasto-plastic strain-controlled constant and variable amplitude loading. This model consists of a three-component equation, which considers elastic, plastic, and pseudoelastic strain components. Considering different magnesium alloys, good correlation is reached between numerically and experimentally determined hysteresis loops by means of different constant and variable amplitude load-time functions. For a numerical fatigue life analysis, an energy based fatigue parameter has been developed. It is denoted by “combined strain energy density per cycle” and consists of a summation of the plastic strain energy density per cycle and the 25 % weighted tensile elastic strain energy density per cycle. The weighting represents the material specific mean stress sensitivity. Applying the energy based fatigue parameter on modeled hysteresis loops, the fatigue life is predicted adequately for constant and variable amplitude loading including mean strain and mean stress effects. The combined strain energy density per cycle achieves significantly better results in comparison to conventional fatigue models such as the Smith-Watson-Topper model. The developed phenomenological model in combination with the combined strain energy density per cycle is able to carry out numerical fatigue life analyses on magnesium sheet metals.

In geotechnical engineering, the uncertainties such as the variability and uncertainty inherent in the geotechnical properties have caught more and more attentions from researchers and engineers. They have found that a single “Factor of Safety” calculated by traditional deterministic analyses methods can not represent the slope stability exactly. Recently in order to provide a more rational mathematical framework to incorporate different types of uncertainties in the slope stability estimation, reliability analyses and non-deterministic methods, which include probabilistic and non probabilistic (imprecise methods) methods, have been applied widely. In short, the slope non-deterministic analysis is to combine the probabilistic analysis or non probabilistic analysis with the deterministic slope stability analysis. It cannot be regarded as a completely new slope stability analysis method, but just an extension of the slope deterministic analysis. The slope failure probability calculated by slope non-deterministic analysis is a kind of complement of safety factor. Therefore, the accuracy of non deterministic analysis is not only depended on a suitable probabilistic or non probabilistic analysis method selected, but also on a more rigorous deterministic analysis method or geological model adopted. In this thesis, reliability concepts have been reviewed first, and some typical non-deterministic methods, including Monte Carlo Simulation (MCS), First Order Reliability Method (FORM), Point Estimate Method (PEM) and Random Set Theory (RSM), have been described and successfully applied to the slope stability analysis based on a numerical simulation method-Strength Reduction Method (SRM). All of the processes have been performed in a commercial finite difference code FLAC and a distinct element code UDEC. First of all, as the fundamental of slope reliability analysis, the deterministic numerical simulation method has been improved. This method has a higher accuracy than the conventional limit equilibrium methods, because of the reason that the constitutive relationship of soil is considered, and fewer assumptions on boundary conditions of slope model are necessary. However, the construction of slope numerical models, particularly for the large and complicated models has always been very difficult and it has become an obstacle for application of numerical simulation method. In this study, the excellent spatial analysis function of Geographic Information System (GIS) technique has been introduced to help numerical modeling of the slope. In the process of modeling, the topographic map of slope has been gridded using GIS software, and then the GIS data was transformed into FLAC smoothly through the program built-in language FISH. At last, the feasibility and high efficiency of this technique has been illustrated through a case study-Xuecheng slope, and both 2D and 3D models have been investigated. Subsequently, three most widely used probabilistic analyses methods, Monte Carlo Simulation, First Order Reliability Method and Point Estimate Method applied with Strength Reduction Method have been studied. Monte Carlo Simulation which needs to repeat thousands of deterministic analysis is the most accurate probabilistic method. However it is too time consuming for practical applications, especially when it is combined with numerical simulation method. For reducing the computation effort, a simplified Monte Carlo Simulation-Strength Reduction Method (MCS-SRM) has been developed in this study. This method has estimated the probable failure of slope and calculated the mean value of safety factor by means of soil parameters first, and then calculated the variance of safety factor and reliability of slope according to the assumed probability density function of safety factor. Case studies have confirmed that this method can reduce about 4/5 of time compared with traditional MCS-SRM, and maintain almost the same accuracy. First Order Reliability Method is an approximate method which is based on the Taylor\'s series expansion of performance function. The closed form solution of the partial derivatives of the performance function is necessary to calculate the mean and standard deviation of safety factor. However, there is no explicit performance function in numerical simulation method, so the derivative expressions have been replaced with equivalent difference quotients to solve the differential quotients approximately in this study. Point Estimate Method is also an approximate method involved even fewer calculations than FORM. In the present study, it has been integrated with Strength Reduction Method directly. Another important observation referred to the correlation between the soil parameters cohesion and friction angle. Some authors have found a negative correlation between cohesion and friction angle of soil on the basis of experimental data. However, few slope probabilistic studies are found to consider this negative correlation between soil parameters in literatures. In this thesis, the influence of this correlation on slope probability of failure has been investigated based on numerical simulation method. It was found that a negative correlation considered in the cohesion and friction angle of soil can reduce the variability of safety factor and failure probability of slope, thus increasing the reliability of results. Besides inter-correlation of soil parameters, these are always auto-correlated in space, which is described as spatial variability. For the reason that knowledge on this character is rather limited in literature, it is ignored in geotechnical engineering by most researchers and engineers. In this thesis, the random field method has been introduced in slope numerical simulation to simulate the spatial variability structure, and a numerical procedure for a probabilistic slope stability analysis based on Monte Carlo simulation was presented. The soil properties such as cohesion and friction angle were discretized to continuous random fields based on local averaging method. In the case study, both stationary and non-stationary random fields have been investigated, and the influence of spatial variability and averaging domain on the convergence of numerical simulation and probability of failure was studied. In rock medium, the structure faces have very important influence on the slope stability, and the rock material can be modeled as the combination of rigid or deformable blocks with joints in distinct element method. Therefore, much more input parameters like strength of joints are required to input the rock slope model, which increase the uncertainty of the results of numerical model. Furthermore, because of the limitations of the current laboratory and in-site testes, there is always lack of exact values of geotechnical parameters from rock material, even the probability distribution of these variables. Most of time, engineers can only estimate the interval of these variables from the limit testes or the expertise’s experience. In this study, to assess the reliability of the rock slope, a Random Set Distinct Element Method (RS-DEM) has been developed through coupling of Random Set Theory and Distinct Element Method, and applied in a rock slope in Sichuan province China.

Considering the late in-vessel phase of an unlikely core melt down scenario in a light water reactor (LWR) with the formation of a corium pool in the lower head of the reactor pressure vessel (RPV) the possible failure modes of the RPV and the time to failure have to be investigated to assess the possible loadings on the containment. In this work, an integral model was developed to describe the processes in the lower plenum of the RPV. Two principal model domains have to be distinguished: The tem-perature field within the melt and RPV is calculated with a thermodynamic model, while a mechanical model is used for the structural analysis of the vessel wall. In the introducing chapters a description is given of the considered accident scenario and the relevant analytical, experimental, and numerical investigations are discussed which were performed worldwide during the last three decades. Following, the occurring physical phenomena are analysed and the scaling differences are evaluated between the FOREVER-experiments and a prototypical scenario. The thermodynamic and the mechanical model can be coupled recursively to take into account the mutual influence. This approach not only allows to consider the temperature dependence of the material parameters and the thermally induced stress in the mechanical model, it also takes into account the response of the temperature field itself upon the changing vessel geometry. New approaches are applied in this work for the simulation of creep and damage. Using a creep data base, the application of single creep laws could be avoided which is especially advantageous if large temperature, stress, and strain ranges have to be covered. Based on experimental investigations, the creep data base has been developed for an RPV-steel and has been validated against creep tests with different scalings and geometries. It can be stated, that the coupled model is able to exactly describe and predict the vessel deformation in the scaled integral FOREVER-tests. There are uncertainties concerning the time to failure which are related to inexactly known material parameters and boundary conditions. The main results of this work can be summarised as follows: Due to the thermody-namic behaviour of the large melt pool with internal heat sources, the upper third of the lower RPV head is exposed to the highest thermo-mechanical loads. This region is called hot focus. Contrary to that, the pole part of the lower head has a higher strength and therefore relocates almost vertically downwards under the combined thermal, weight and internal pressure load of the RPV. On the one hand, it will be possible by external flooding to retain the corium within the RPV even at increased pressures and even in reactors with high power (as e.g. KONVOI). On the other hand, there is no chance for melt retention in the considered scenario if neither internal nor external flooding of the RPV can be achieved. Two patents have been derived from the gained insights. Both are related to passively working devices for accident mitigation: The first one is a support of the RPV lower head pole part. It reduces the maximum mechanical load in the highly stressed area of the hot focus. In this way, it can prevent failure or at least extend the time to failure of the vessel. The second device implements a passive accident mitigation measure by making use of the downward movement of the lower head. Through this, a valve or a flap can be opened to flood the reactor pit with water from a storage reservoir located at a higher position in the reactor building. With regard to future plant designs it can be stated - differing from former presumptions - that an In-Vessel-Retention (IVR) of a molten core is possible within the reactor pressure vessel even for reactors with higher power. / Für das unwahrscheinliche Szenario eines Kernschmelzunfalls in einem Leichtwasserreaktor mit Bildung eines Schmelzesees in der Bodenkalotte des Reaktordruckbehälters (RDB) ist es notwendig, mögliche Versagensformen des RDB sowie Versagenszeiträume zu ermitteln, um die daraus resultierende mögliche Belastung des Sicherheitsbehälters bestimmen zu können. In dieser Arbeit wird ein integrales Modell entwickelt, das die Vorgänge im unteren Plenum beschreibt. Dabei sind zwei prinzipielle Modellbereiche zu unterscheiden: Das Temperaturfeld in der Schmelze und im RDB wird mit einem thermodynamischen Modell berechnet, während für die Strukturanalyse des RDB ein mechanisches Modell verwendet wird. Zunächst werden das betrachtete Unfallszenario dargestellt und die bisher in den letzten drei Dekaden weltweit durchgeführten wesentlichen analytischen, experimentellen und numerischen Untersuchungen diskutiert. Anschließend werden die auftretenden physikalischen Vorgänge analysiert. Gleichzeitig werden Skalierungsunterschiede zwischen den in dieser Arbeit betrachteten Experimenten der FOREVER-Reihe und einem prototypischen Szenario herausgearbeitet. Das thermodynamische und das mechanische Modell können rekursiv gekoppelt werden, wodurch die wechselseitige Beeinflussung berücksichtigt werden kann. Insbesondere werden damit neben der Temperaturabhängigkeit der Materialparameter und den thermisch induzierten Spannungen im mechanischen Modell auch die Rückwirkungen der Behälterverformung auf das Temperaturfeld selber erfasst. Für die Kriech- und Schädigungssimulation werden in dieser Arbeit neue Verfahren angewendet. Durch die Entwicklung und den Einsatz einer Kriechdatenbasis konnte die bei sehr unterschiedlichen Temperaturen, Spannungen und Dehnungen ungeeignete Verwendung einzelner Kriechgesetze umgangen werden. Aufbauend auf experimentellen Untersuchungen wurde eine Kriechdatenbasis für einen RDB-Stahl entwickelt und an Hand von Kriechversuchen verschiedener Geometrie und Dimension validiert. Als Ergebnis lässt sich festhalten, dass das gekoppelte Modell prinzipiell in der Lage ist, die Behälterdeformation im Falle der skalierten FOREVER-Experimente exakt zu beschreiben bzw. vorherzusagen. Unsicherheiten bezüglich der Versagenszeit resultieren aus nicht exakt bekannten Materialparametern und Randbedingungen. Die wesentlichen Ergebnisse dieser Arbeit lassen sich wie folgt zusammenfassen: Aufgrund des thermodynamischen Verhaltens eines großen Schmelzesees mit inneren Wärmequellen erfolgt die höchste thermomechanische Belastung des RDB im oberen Drittel der Bodenkalotte. Dieser Bereich wird als heißer Fokus bezeichnet. Der untere Bereich der Kalotte weist hingegen eine höhere Festigkeit auf und verlagert sich deswegen bei entsprechender Belastung des RDB im wesentlichen senkrecht nach unten. Bei einer externen Flutung besteht auch bei hohen Innendrücken für einen Reaktor großer Leistung (KONVOI) die Möglichkeit, die Schmelze im RDB zurückzuhalten. Ohne interne oder externe Flutung besteht für das betrachtete Szenario keine Aussicht für eine Schmelzerückhaltung im RDB. Aus den gewonnenen Erkenntnissen wurden zwei Patente abgeleitet. Dabei handelt es sich um passiv wirkende Einrichtungen zur Schadensbegrenzung: Die erste reduziert durch Abstützen des unteren Kalottenzentrums die Maximalspannungen im hochbeanspruchten Bereich des heißen Fokus und kann damit ein Versagen verhindern oder zumindest verzögern. Die zweite Einrichtung ermöglicht die passive Auslösung einer Flutung, indem die Abwärtsbewegung der Kalotte zur Steuerung genutzt wird. Hierdurch kann beispielsweise ein Ventil geöffnet werden, um Wasser aus im Gebäude höher angeordneten Reservoirs in die Reaktorgrube zu leiten. Abweichend von bisherigen Annahmen kann im Hinblick auf die Entwicklung zukünftiger Baulinien festgehalten werden, dass eine Kernschmelzerückhaltung im Reaktordruckbehälter auch für Reaktoren größerer Leistung möglich ist.

In geotechnical engineering, the uncertainties such as the variability and uncertainty inherent in the geotechnical properties have caught more and more attentions from researchers and engineers. They have found that a single “Factor of Safety” calculated by traditional deterministic analyses methods can not represent the slope stability exactly. Recently in order to provide a more rational mathematical framework to incorporate different types of uncertainties in the slope stability estimation, reliability analyses and non-deterministic methods, which include probabilistic and non probabilistic (imprecise methods) methods, have been applied widely. In short, the slope non-deterministic analysis is to combine the probabilistic analysis or non probabilistic analysis with the deterministic slope stability analysis. It cannot be regarded as a completely new slope stability analysis method, but just an extension of the slope deterministic analysis. The slope failure probability calculated by slope non-deterministic analysis is a kind of complement of safety factor. Therefore, the accuracy of non deterministic analysis is not only depended on a suitable probabilistic or non probabilistic analysis method selected, but also on a more rigorous deterministic analysis method or geological model adopted. In this thesis, reliability concepts have been reviewed first, and some typical non-deterministic methods, including Monte Carlo Simulation (MCS), First Order Reliability Method (FORM), Point Estimate Method (PEM) and Random Set Theory (RSM), have been described and successfully applied to the slope stability analysis based on a numerical simulation method-Strength Reduction Method (SRM). All of the processes have been performed in a commercial finite difference code FLAC and a distinct element code UDEC. First of all, as the fundamental of slope reliability analysis, the deterministic numerical simulation method has been improved. This method has a higher accuracy than the conventional limit equilibrium methods, because of the reason that the constitutive relationship of soil is considered, and fewer assumptions on boundary conditions of slope model are necessary. However, the construction of slope numerical models, particularly for the large and complicated models has always been very difficult and it has become an obstacle for application of numerical simulation method. In this study, the excellent spatial analysis function of Geographic Information System (GIS) technique has been introduced to help numerical modeling of the slope. In the process of modeling, the topographic map of slope has been gridded using GIS software, and then the GIS data was transformed into FLAC smoothly through the program built-in language FISH. At last, the feasibility and high efficiency of this technique has been illustrated through a case study-Xuecheng slope, and both 2D and 3D models have been investigated. Subsequently, three most widely used probabilistic analyses methods, Monte Carlo Simulation, First Order Reliability Method and Point Estimate Method applied with Strength Reduction Method have been studied. Monte Carlo Simulation which needs to repeat thousands of deterministic analysis is the most accurate probabilistic method. However it is too time consuming for practical applications, especially when it is combined with numerical simulation method. For reducing the computation effort, a simplified Monte Carlo Simulation-Strength Reduction Method (MCS-SRM) has been developed in this study. This method has estimated the probable failure of slope and calculated the mean value of safety factor by means of soil parameters first, and then calculated the variance of safety factor and reliability of slope according to the assumed probability density function of safety factor. Case studies have confirmed that this method can reduce about 4/5 of time compared with traditional MCS-SRM, and maintain almost the same accuracy. First Order Reliability Method is an approximate method which is based on the Taylor\'s series expansion of performance function. The closed form solution of the partial derivatives of the performance function is necessary to calculate the mean and standard deviation of safety factor. However, there is no explicit performance function in numerical simulation method, so the derivative expressions have been replaced with equivalent difference quotients to solve the differential quotients approximately in this study. Point Estimate Method is also an approximate method involved even fewer calculations than FORM. In the present study, it has been integrated with Strength Reduction Method directly. Another important observation referred to the correlation between the soil parameters cohesion and friction angle. Some authors have found a negative correlation between cohesion and friction angle of soil on the basis of experimental data. However, few slope probabilistic studies are found to consider this negative correlation between soil parameters in literatures. In this thesis, the influence of this correlation on slope probability of failure has been investigated based on numerical simulation method. It was found that a negative correlation considered in the cohesion and friction angle of soil can reduce the variability of safety factor and failure probability of slope, thus increasing the reliability of results. Besides inter-correlation of soil parameters, these are always auto-correlated in space, which is described as spatial variability. For the reason that knowledge on this character is rather limited in literature, it is ignored in geotechnical engineering by most researchers and engineers. In this thesis, the random field method has been introduced in slope numerical simulation to simulate the spatial variability structure, and a numerical procedure for a probabilistic slope stability analysis based on Monte Carlo simulation was presented. The soil properties such as cohesion and friction angle were discretized to continuous random fields based on local averaging method. In the case study, both stationary and non-stationary random fields have been investigated, and the influence of spatial variability and averaging domain on the convergence of numerical simulation and probability of failure was studied. In rock medium, the structure faces have very important influence on the slope stability, and the rock material can be modeled as the combination of rigid or deformable blocks with joints in distinct element method. Therefore, much more input parameters like strength of joints are required to input the rock slope model, which increase the uncertainty of the results of numerical model. Furthermore, because of the limitations of the current laboratory and in-site testes, there is always lack of exact values of geotechnical parameters from rock material, even the probability distribution of these variables. Most of time, engineers can only estimate the interval of these variables from the limit testes or the expertise’s experience. In this study, to assess the reliability of the rock slope, a Random Set Distinct Element Method (RS-DEM) has been developed through coupling of Random Set Theory and Distinct Element Method, and applied in a rock slope in Sichuan province China.

The desire for energy and resource savings brings magnesium alloys as lightweight materials with high specific strength more and more into the focus. Most structural components are subjected to cyclic loading. In the course of computer aided product development, a numerical prediction of the fatigue life under these conditions must be provided. For this reason, the mechanical properties of the considered material must be examined in detail. Wrought magnesium semifinished products, e.g. magnesium sheet metals, typically reveal strong basal textures and thus, the mechanical behavior considerably differs from that of the well-established magnesium die castings. Magnesium sheet metals reveal a distinct difference in the tensile and compressive yield stress, leading to non-symmetric sigmoidal hysteresis loops within the elasto-plastic load range. These unusual hysteresis shapes are caused by cyclic twinning and detwinning. Furthermore, wrought magnesium alloys reveal pseudoelastic behavior, leading to nonlinear unloading curves. Another interesting effect is the formation of local twin bands during compressive loading. Nevertheless, only little information can be found on the numerical fatigue analysis of wrought magnesium alloys up to now. The aim of this thesis is the investigation of the mechanical properties of wrought magnesium alloys and the development of an appropriate fatigue model. For this purpose, twin roll cast AM50 as well as AZ31B sheet metals and extruded ME21 sheet metals were used. Mechanical tests were carried out to present a comprehensive overview of the quasi-static and cyclic material behavior. The microstructure was captured on sheet metals before and after loading to evaluate the correlation between the microstructure, the texture, and the mechanical properties. Stress- and strain-controlled loading ratios and strain-controlled experiments with variable amplitudes were performed. Tests were carried out along and transverse to the manufacturing direction to consider the influence of the anisotropy. Special focus was given to sigmoidal hysteresis loops and their influence on the fatigue life. A detailed numerical description of hysteresis loops is necessary for numerical fatigue analyses. For this, a one-dimensional phenomenological model was developed for elasto-plastic strain-controlled constant and variable amplitude loading. This model consists of a three-component equation, which considers elastic, plastic, and pseudoelastic strain components. Considering different magnesium alloys, good correlation is reached between numerically and experimentally determined hysteresis loops by means of different constant and variable amplitude load-time functions. For a numerical fatigue life analysis, an energy based fatigue parameter has been developed. It is denoted by “combined strain energy density per cycle” and consists of a summation of the plastic strain energy density per cycle and the 25 % weighted tensile elastic strain energy density per cycle. The weighting represents the material specific mean stress sensitivity. Applying the energy based fatigue parameter on modeled hysteresis loops, the fatigue life is predicted adequately for constant and variable amplitude loading including mean strain and mean stress effects. The combined strain energy density per cycle achieves significantly better results in comparison to conventional fatigue models such as the Smith-Watson-Topper model. The developed phenomenological model in combination with the combined strain energy density per cycle is able to carry out numerical fatigue life analyses on magnesium sheet metals.

Considering the late in-vessel phase of an unlikely core melt down scenario in a light water reactor (LWR) with the formation of a corium pool in the lower head of the reactor pressure vessel (RPV) the possible failure modes of the RPV and the time to failure have to be investigated to assess the possible loadings on the containment. In this work, an integral model was developed to describe the processes in the lower plenum of the RPV. Two principal model domains have to be distinguished: The tem-perature field within the melt and RPV is calculated with a thermodynamic model, while a mechanical model is used for the structural analysis of the vessel wall. In the introducing chapters a description is given of the considered accident scenario and the relevant analytical, experimental, and numerical investigations are discussed which were performed worldwide during the last three decades. Following, the occurring physical phenomena are analysed and the scaling differences are evaluated between the FOREVER-experiments and a prototypical scenario. The thermodynamic and the mechanical model can be coupled recursively to take into account the mutual influence. This approach not only allows to consider the temperature dependence of the material parameters and the thermally induced stress in the mechanical model, it also takes into account the response of the temperature field itself upon the changing vessel geometry. New approaches are applied in this work for the simulation of creep and damage. Using a creep data base, the application of single creep laws could be avoided which is especially advantageous if large temperature, stress, and strain ranges have to be covered. Based on experimental investigations, the creep data base has been developed for an RPV-steel and has been validated against creep tests with different scalings and geometries. It can be stated, that the coupled model is able to exactly describe and predict the vessel deformation in the scaled integral FOREVER-tests. There are uncertainties concerning the time to failure which are related to inexactly known material parameters and boundary conditions. The main results of this work can be summarised as follows: Due to the thermody-namic behaviour of the large melt pool with internal heat sources, the upper third of the lower RPV head is exposed to the highest thermo-mechanical loads. This region is called hot focus. Contrary to that, the pole part of the lower head has a higher strength and therefore relocates almost vertically downwards under the combined thermal, weight and internal pressure load of the RPV. On the one hand, it will be possible by external flooding to retain the corium within the RPV even at increased pressures and even in reactors with high power (as e.g. KONVOI). On the other hand, there is no chance for melt retention in the considered scenario if neither internal nor external flooding of the RPV can be achieved. Two patents have been derived from the gained insights. Both are related to passively working devices for accident mitigation: The first one is a support of the RPV lower head pole part. It reduces the maximum mechanical load in the highly stressed area of the hot focus. In this way, it can prevent failure or at least extend the time to failure of the vessel. The second device implements a passive accident mitigation measure by making use of the downward movement of the lower head. Through this, a valve or a flap can be opened to flood the reactor pit with water from a storage reservoir located at a higher position in the reactor building. With regard to future plant designs it can be stated - differing from former presumptions - that an In-Vessel-Retention (IVR) of a molten core is possible within the reactor pressure vessel even for reactors with higher power. / Für das unwahrscheinliche Szenario eines Kernschmelzunfalls in einem Leichtwasserreaktor mit Bildung eines Schmelzesees in der Bodenkalotte des Reaktordruckbehälters (RDB) ist es notwendig, mögliche Versagensformen des RDB sowie Versagenszeiträume zu ermitteln, um die daraus resultierende mögliche Belastung des Sicherheitsbehälters bestimmen zu können. In dieser Arbeit wird ein integrales Modell entwickelt, das die Vorgänge im unteren Plenum beschreibt. Dabei sind zwei prinzipielle Modellbereiche zu unterscheiden: Das Temperaturfeld in der Schmelze und im RDB wird mit einem thermodynamischen Modell berechnet, während für die Strukturanalyse des RDB ein mechanisches Modell verwendet wird. Zunächst werden das betrachtete Unfallszenario dargestellt und die bisher in den letzten drei Dekaden weltweit durchgeführten wesentlichen analytischen, experimentellen und numerischen Untersuchungen diskutiert. Anschließend werden die auftretenden physikalischen Vorgänge analysiert. Gleichzeitig werden Skalierungsunterschiede zwischen den in dieser Arbeit betrachteten Experimenten der FOREVER-Reihe und einem prototypischen Szenario herausgearbeitet. Das thermodynamische und das mechanische Modell können rekursiv gekoppelt werden, wodurch die wechselseitige Beeinflussung berücksichtigt werden kann. Insbesondere werden damit neben der Temperaturabhängigkeit der Materialparameter und den thermisch induzierten Spannungen im mechanischen Modell auch die Rückwirkungen der Behälterverformung auf das Temperaturfeld selber erfasst. Für die Kriech- und Schädigungssimulation werden in dieser Arbeit neue Verfahren angewendet. Durch die Entwicklung und den Einsatz einer Kriechdatenbasis konnte die bei sehr unterschiedlichen Temperaturen, Spannungen und Dehnungen ungeeignete Verwendung einzelner Kriechgesetze umgangen werden. Aufbauend auf experimentellen Untersuchungen wurde eine Kriechdatenbasis für einen RDB-Stahl entwickelt und an Hand von Kriechversuchen verschiedener Geometrie und Dimension validiert. Als Ergebnis lässt sich festhalten, dass das gekoppelte Modell prinzipiell in der Lage ist, die Behälterdeformation im Falle der skalierten FOREVER-Experimente exakt zu beschreiben bzw. vorherzusagen. Unsicherheiten bezüglich der Versagenszeit resultieren aus nicht exakt bekannten Materialparametern und Randbedingungen. Die wesentlichen Ergebnisse dieser Arbeit lassen sich wie folgt zusammenfassen: Aufgrund des thermodynamischen Verhaltens eines großen Schmelzesees mit inneren Wärmequellen erfolgt die höchste thermomechanische Belastung des RDB im oberen Drittel der Bodenkalotte. Dieser Bereich wird als heißer Fokus bezeichnet. Der untere Bereich der Kalotte weist hingegen eine höhere Festigkeit auf und verlagert sich deswegen bei entsprechender Belastung des RDB im wesentlichen senkrecht nach unten. Bei einer externen Flutung besteht auch bei hohen Innendrücken für einen Reaktor großer Leistung (KONVOI) die Möglichkeit, die Schmelze im RDB zurückzuhalten. Ohne interne oder externe Flutung besteht für das betrachtete Szenario keine Aussicht für eine Schmelzerückhaltung im RDB. Aus den gewonnenen Erkenntnissen wurden zwei Patente abgeleitet. Dabei handelt es sich um passiv wirkende Einrichtungen zur Schadensbegrenzung: Die erste reduziert durch Abstützen des unteren Kalottenzentrums die Maximalspannungen im hochbeanspruchten Bereich des heißen Fokus und kann damit ein Versagen verhindern oder zumindest verzögern. Die zweite Einrichtung ermöglicht die passive Auslösung einer Flutung, indem die Abwärtsbewegung der Kalotte zur Steuerung genutzt wird. Hierdurch kann beispielsweise ein Ventil geöffnet werden, um Wasser aus im Gebäude höher angeordneten Reservoirs in die Reaktorgrube zu leiten. Abweichend von bisherigen Annahmen kann im Hinblick auf die Entwicklung zukünftiger Baulinien festgehalten werden, dass eine Kernschmelzerückhaltung im Reaktordruckbehälter auch für Reaktoren größerer Leistung möglich ist.

Geotechnische Problem- und Fragestellungen befassen sich zunehmend mit der komplexen Interaktion unterschiedlicher physikalischer Prozesse. Ein Beispiel sind hydro-mechanische Wechselwirkungen, die in verschiedenen Anwendungsbereichen eine große Rolle spielen (Hydraulic Fracturing, Bewertung von Barriereintegrität, Böschungsanalysen, etc.). Numerische Simulationen helfen dabei, umfangreiche multiphysikalische Vorgänge abzubilden. Zur hinreichend genauen und effizienten Bearbeitung kann es jedoch sein, dass die Anwendung eines einzelnen spezialisierten Softwarepaketes nicht ausreicht und nur Softwarekopplungen Abhilfe schaffen. Die vorliegende Arbeit erweitert die geomechanische Komplexität einer hydro-mechanischen Kopplung auf visko-elasto-plastisches Materialverhalten im Salinar. Betrachtet werden langandauernde und großräumig induzierte Fluidbewegungen in den durch Volumenkonvergenz charakterisierten lösungserfüllten Abbauen in einem generischen Kali- bzw. Steinsalzbergwerk. Zur Bearbeitung der Problemstellung wird eine grundlegende Methode zur Kopplung der numerischen Codes FLAC3D und Ansys Fluent entwickelt, detailliert vorgestellt und verifiziert. Unterschiedliche Modellszenarien in Bezug auf die initiale Fluidverteilung simulieren eindrucksvoll das Strömungsverhalten im generischen Grubenmodell unter Ausbildung eines freien Fluidspiegels oder eines Überdrucks im eingeschlossenen Fluid. Die Ergebnisse werden umfassend analysiert und das Potenzial zu Effizienzsteigerung durch die Softwarekopplung aufgezeigt. / Geotechnical problems and questions are progressively dealing with complex interactions of different physical processes. An example is hydro-mechanical coupling playing an important role in various research topics and applications (e.g. hydraulic fracturing, assessment of barrier integrity and slope analysis). Numerical simulations help to model extensive multi-physical processes. However, for an accurate and efficient processing, using a single specialized numerical code may not be sufficient and solutions can be obtained only with software couplings. The presented work extends the geomechanically complexity of a hydro-mechanical coupling by visco-elasto-plastic material behaviour in salt formations considering long-lasting and large-scale induced fluid flow within solution-filled cavities in a generic potash or rock salt mine, due to volume convergence. For solving this problem, a basic method for coupling the numerical codes FLAC3D and Ansys Fluent is developed, presented, and verified in detail. Different model scenarios in respect to initial fluid saturation are simulating the fluid flow in the generic mine model, depicting either a free fluid surface or an excess pressure in the trapped fluid. The results are analysed, and the potential for the increase of efficiency through the software coupling of FLAC3D and Ansys Fluent is demonstrated.

Groundwater flow modelling provides an important quantitative instrument for addressing issues related to the quantity and quality of groundwater and the connected water resources. Consequently, groundwater flow models have been developed and used ubiquitously in science to deepen the understanding of subsurface processes and their drivers as well as management and planning tools. The present work investigates how numerical models can be linked to field investigations and public databases to quantitatively approach questions in the area of groundwater research. The primary goal is to develop new, efficient ways to overcome limitations of the individual hydrological concepts for solving specific hydrological problems and to increase the understanding of practical applicability of different methods. For this purpose, tailor-made approaches were developed for different study areas covering diverse spatial scales: the hydrology of a small mining lake, the riparian aquifer at the scale of a single meander as well as the aquifer systems of a large-scale river basin in China. The first part of the work deals with the physical and mathematical modelling of water constituents balance in a meromictic mining lake in Lusatia. The capability of using a rather simple mass-balance model based on a sufficient dataset of field data to evaluate lake stratification and lake-groundwater interaction were shown. In the second part, a transient numerical groundwater flow model was developed for the riparian aquifer of a stream meander and was calibrated by three different salt tracer tests. The model was used to proof the reliability of subsurface travel times derived from time series analysis and to give insights in the riparian zone dynamics during changing hydraulic gradients. The third part of the work describes the methodology to conduct risk assessment of groundwater contamination on the large catchment scale of the Songhua River in China. A comprehensive literature study was conducted to get an overview about measurement data on water quality data in China. A three-dimensional numerical flow and mass transport model was applied to access the flow and matter transport dynamics in the aquifer system of a sub-basin considering changing groundwater exploitation scenarios. Consequently, numerical groundwater modelling was combined with processed remote sensing and web mapping service data to overcome field data limitations and to derive groundwater vulnerability, groundwater hazard and groundwater risk maps for the entire Songhua River Basin. Summarizing, this doctoral thesis could develop new methods of combining field measurements, data assimilation and aggregation from various sources and groundwater modelling strategies and successfully apply these methods to find solutions on problems of multiple scales and across water systems. / Die Grundwassermodellierung stellt eine wichtige wissenschaftliche Methode zur quantitativen Analyse von Fragestellungen zum Schutz der Menge und Güte der Grundwasserressourcen sowie der angeschlossenen Wasserkörper dar. Dementsprechend werden Grundwassermodelle sowohl für Planungs- und Bewertungszwecke im Wasserressourcenmanagement als auch zur wissenschaftlichen Erforschung der Prozesse im Untergrund entwickelt und angewendet. Die vorliegende Arbeit untersucht in diesem Rahmen, wie numerische Modelle, Feldmessungen und Daten generiert aus Fernerkundungsdaten und Webplattformen systematisch verknüpft werden können, um Fragestellungen im Bereich der Grundwasserforschung quantitativ zu beantworten. Das Ziel der Arbeit ist es neue effiziente Abläufe zu entwickeln, die die Limitierung der einzelnen Methoden überwinden und diese auf deren Anwendbarkeit für die Lösung spezifischer hydrologischer Probleme zu analysieren. Zu diesem Zweck wurden in dieser Doktorarbeit fallspezifische Lösungen für verschiedene Untersuchungsgebiete entwickelt, die sowohl in der räumlichen Skale als auch in den zu untersuchenden hydrologischen Fragestellungen eine große Diversität aufweisen. Im ersten Teil der Arbeit wurde die Massenbilanz von Wasserinhaltsstoffen in einem meromiktischen Tagebaurestsee im Lausitzer Revier durch physikalische und mathematische Modellierungsmethoden untersucht. Dabei konnte gezeigt werden, dass auf Basis einer gewonnenen mehrjährigen Zeitreihe von Messdaten ein einfaches Massenbilanzmodell in der Lage ist, sowohl Seeschichtungs- als auch Grundwasseraustauschdynamiken quantitativ zu beschreiben. Der zweite Teil der Arbeit umfasst die Entwicklung eines transienten numerischen Grundwassermodells für den quartären Uferaquifer im Bereich eines Flussmäanders der Selke welches anhand von Daten aus mehreren Salztracertests kalibriert wurde. Das Modell wurde dafür verwendet die transienten Verweilzeiten in der gesättigten Zone des Mäanderbogens unter dem Einfluss dynamischer hydraulischer Bedingungen zu untersuchen. Die Ergebnisse wurden im Anschluss mit Verweilzeiten verglichen, die aus der Analyse der zeitlichen Verschiebung von gemessenen elektrischen Leitfähigkeitszeitreihen zwischen Fluss und Grundwassermessstellen gewonnen wurden. Durch dieses kombinierte Verfahren konnten sowohl die Beschränkungen der zeitreihenbasierten Verweilzeitberechnung aufgezeigt als auch ein tieferes Systemverständnis für die Interaktionsdynamiken zwischen Grund- und Flusswasser auf der Mäanderskala gewonnen werden. Der dritte Teil der Arbeit beschreibt die Vorgehensweise für die Bewertung des Grundwasserkontaminationsrisikos im Einzugsgebiet des Songhua Flusses in China. Eine umfassende Literaturstudie wurde durchgeführt, um einen Überblick über die Verfügbarkeit von Messdaten zur Belastung der Wasserressourcen Chinas mit organischen Schadstoffen zu erhalten. Danach wurde für ein Teileinzugsgebiet ein dreidimensionales numerisches Grundwassermodell auf Basis der vorhandenen hydrogeologischen Daten aufgebaut. Dieses wurde dazu verwendet die Änderungen im Stofftransports und den Schadstoffkonzentrationen innerhalb des Aquifersystems unter steigenden Entnahmeraten zu analysieren. Basierend auf diesen Studien wurden auf der Skale des Gesamteinzugsgebiets, um die beschränkte Verfügbarkeit von Felddaten auszugleichen, die Ergebnisse der numerischen Grundwassermodellierung mit Fernerkundungsdaten und Webdatenbanken in einem Indexsystem kombiniert mit dem für die oberflächennahen Aquifere Vulnerabilität, Gefährdungspotential und Verschmutzungsrisiko in einer räumlichen Auflösung von 1 km² bestimmt wurden. Zusammenfassend konnten durch die vorliegende Doktorarbeit neue passgenaue Methoden zur effektiven Kombination von in-situ Messungen, der Datenerhebung und Datenintegration aus vielfältigen Datenquellen sowie numerischen Grundwassermodellierungsstrategien entwickelt und zur Lösung der untersuchten hydrologischer Fragestellen auf den verschiedenen Skalen und über die Grenzen der einzelnen hydrologischen Teilsysteme hinaus erfolgreich angewandt werden.

Groundwater flow modelling provides an important quantitative instrument for addressing issues related to the quantity and quality of groundwater and the connected water resources. Consequently, groundwater flow models have been developed and used ubiquitously in science to deepen the understanding of subsurface processes and their drivers as well as management and planning tools. The present work investigates how numerical models can be linked to field investigations and public databases to quantitatively approach questions in the area of groundwater research. The primary goal is to develop new, efficient ways to overcome limitations of the individual hydrological concepts for solving specific hydrological problems and to increase the understanding of practical applicability of different methods. For this purpose, tailor-made approaches were developed for different study areas covering diverse spatial scales: the hydrology of a small mining lake, the riparian aquifer at the scale of a single meander as well as the aquifer systems of a large-scale river basin in China. The first part of the work deals with the physical and mathematical modelling of water constituents balance in a meromictic mining lake in Lusatia. The capability of using a rather simple mass-balance model based on a sufficient dataset of field data to evaluate lake stratification and lake-groundwater interaction were shown. In the second part, a transient numerical groundwater flow model was developed for the riparian aquifer of a stream meander and was calibrated by three different salt tracer tests. The model was used to proof the reliability of subsurface travel times derived from time series analysis and to give insights in the riparian zone dynamics during changing hydraulic gradients. The third part of the work describes the methodology to conduct risk assessment of groundwater contamination on the large catchment scale of the Songhua River in China. A comprehensive literature study was conducted to get an overview about measurement data on water quality data in China. A three-dimensional numerical flow and mass transport model was applied to access the flow and matter transport dynamics in the aquifer system of a sub-basin considering changing groundwater exploitation scenarios. Consequently, numerical groundwater modelling was combined with processed remote sensing and web mapping service data to overcome field data limitations and to derive groundwater vulnerability, groundwater hazard and groundwater risk maps for the entire Songhua River Basin. Summarizing, this doctoral thesis could develop new methods of combining field measurements, data assimilation and aggregation from various sources and groundwater modelling strategies and successfully apply these methods to find solutions on problems of multiple scales and across water systems. / Die Grundwassermodellierung stellt eine wichtige wissenschaftliche Methode zur quantitativen Analyse von Fragestellungen zum Schutz der Menge und Güte der Grundwasserressourcen sowie der angeschlossenen Wasserkörper dar. Dementsprechend werden Grundwassermodelle sowohl für Planungs- und Bewertungszwecke im Wasserressourcenmanagement als auch zur wissenschaftlichen Erforschung der Prozesse im Untergrund entwickelt und angewendet. Die vorliegende Arbeit untersucht in diesem Rahmen, wie numerische Modelle, Feldmessungen und Daten generiert aus Fernerkundungsdaten und Webplattformen systematisch verknüpft werden können, um Fragestellungen im Bereich der Grundwasserforschung quantitativ zu beantworten. Das Ziel der Arbeit ist es neue effiziente Abläufe zu entwickeln, die die Limitierung der einzelnen Methoden überwinden und diese auf deren Anwendbarkeit für die Lösung spezifischer hydrologischer Probleme zu analysieren. Zu diesem Zweck wurden in dieser Doktorarbeit fallspezifische Lösungen für verschiedene Untersuchungsgebiete entwickelt, die sowohl in der räumlichen Skale als auch in den zu untersuchenden hydrologischen Fragestellungen eine große Diversität aufweisen. Im ersten Teil der Arbeit wurde die Massenbilanz von Wasserinhaltsstoffen in einem meromiktischen Tagebaurestsee im Lausitzer Revier durch physikalische und mathematische Modellierungsmethoden untersucht. Dabei konnte gezeigt werden, dass auf Basis einer gewonnenen mehrjährigen Zeitreihe von Messdaten ein einfaches Massenbilanzmodell in der Lage ist, sowohl Seeschichtungs- als auch Grundwasseraustauschdynamiken quantitativ zu beschreiben. Der zweite Teil der Arbeit umfasst die Entwicklung eines transienten numerischen Grundwassermodells für den quartären Uferaquifer im Bereich eines Flussmäanders der Selke welches anhand von Daten aus mehreren Salztracertests kalibriert wurde. Das Modell wurde dafür verwendet die transienten Verweilzeiten in der gesättigten Zone des Mäanderbogens unter dem Einfluss dynamischer hydraulischer Bedingungen zu untersuchen. Die Ergebnisse wurden im Anschluss mit Verweilzeiten verglichen, die aus der Analyse der zeitlichen Verschiebung von gemessenen elektrischen Leitfähigkeitszeitreihen zwischen Fluss und Grundwassermessstellen gewonnen wurden. Durch dieses kombinierte Verfahren konnten sowohl die Beschränkungen der zeitreihenbasierten Verweilzeitberechnung aufgezeigt als auch ein tieferes Systemverständnis für die Interaktionsdynamiken zwischen Grund- und Flusswasser auf der Mäanderskala gewonnen werden. Der dritte Teil der Arbeit beschreibt die Vorgehensweise für die Bewertung des Grundwasserkontaminationsrisikos im Einzugsgebiet des Songhua Flusses in China. Eine umfassende Literaturstudie wurde durchgeführt, um einen Überblick über die Verfügbarkeit von Messdaten zur Belastung der Wasserressourcen Chinas mit organischen Schadstoffen zu erhalten. Danach wurde für ein Teileinzugsgebiet ein dreidimensionales numerisches Grundwassermodell auf Basis der vorhandenen hydrogeologischen Daten aufgebaut. Dieses wurde dazu verwendet die Änderungen im Stofftransports und den Schadstoffkonzentrationen innerhalb des Aquifersystems unter steigenden Entnahmeraten zu analysieren. Basierend auf diesen Studien wurden auf der Skale des Gesamteinzugsgebiets, um die beschränkte Verfügbarkeit von Felddaten auszugleichen, die Ergebnisse der numerischen Grundwassermodellierung mit Fernerkundungsdaten und Webdatenbanken in einem Indexsystem kombiniert mit dem für die oberflächennahen Aquifere Vulnerabilität, Gefährdungspotential und Verschmutzungsrisiko in einer räumlichen Auflösung von 1 km² bestimmt wurden. Zusammenfassend konnten durch die vorliegende Doktorarbeit neue passgenaue Methoden zur effektiven Kombination von in-situ Messungen, der Datenerhebung und Datenintegration aus vielfältigen Datenquellen sowie numerischen Grundwassermodellierungsstrategien entwickelt und zur Lösung der untersuchten hydrologischer Fragestellen auf den verschiedenen Skalen und über die Grenzen der einzelnen hydrologischen Teilsysteme hinaus erfolgreich angewandt werden.

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