Die Analyse des wissenschaftlich-technischen Standes zeigt, dass die gegenwärtige mineralogisch-petrographische Gesteinscharakterisierung in vielen Fällen nur eine verbale Gefügebeschreibung erlaubt. In der Aufbereitungstechnik ist diese Verfahrensweise jedoch nicht ausreichend. Hier ist eine quantitative Charakterisierung der Gesteine erforderlich. Deshalb bestand die Aufgabe darin, eine neue mathematisch-petrographische Methode zur Charakterisierung der unterschiedlichen Gesteinseigenschaften zu entwickeln. Im Ergebnis der neuen mathematisch-petrographischen Methode wurde festgestellt, dass die verbale Beschreibung der Gesteinsstruktur und -textur durch quantitative Gesteinskennwerte ersetzt werden kann. Mit Hilfe der quantitativen Gesteinskennwerte kann eine Prognostizierung relevanter Produkt- bzw. Systemkenngrößen ohne zerkleinerungstechnische Untersuchungen vorgenommen werden. Die Gesteinskenngrößen erlauben eine Einschätzung des Gesteins hinsichtlich Brechbarkeit und Produktkornform einerseits sowie Verschleiß und erforderlichem Energieaufwand andererseits und stellen somit eine wichtige Grundlage für die Auswahl und den Betrieb der Maschinen und Anlagen der Naturstein-Industrie dar.

Die Analyse des wissenschaftlich-technischen Standes zeigt, dass die gegenwärtige mineralogisch-petrographische Gesteinscharakterisierung in vielen Fällen nur eine verbale Gefügebeschreibung erlaubt. In der Aufbereitungstechnik ist diese Verfahrensweise jedoch nicht ausreichend. Hier ist eine quantitative Charakterisierung der Gesteine erforderlich. Deshalb bestand die Aufgabe darin, eine neue mathematisch-petrographische Methode zur Charakterisierung der unterschiedlichen Gesteinseigenschaften zu entwickeln. Im Ergebnis der neuen mathematisch-petrographischen Methode wurde festgestellt, dass die verbale Beschreibung der Gesteinsstruktur und -textur durch quantitative Gesteinskennwerte ersetzt werden kann. Mit Hilfe der quantitativen Gesteinskennwerte kann eine Prognostizierung relevanter Produkt- bzw. Systemkenngrößen ohne zerkleinerungstechnische Untersuchungen vorgenommen werden. Die Gesteinskenngrößen erlauben eine Einschätzung des Gesteins hinsichtlich Brechbarkeit und Produktkornform einerseits sowie Verschleiß und erforderlichem Energieaufwand andererseits und stellen somit eine wichtige Grundlage für die Auswahl und den Betrieb der Maschinen und Anlagen der Naturstein-Industrie dar.

The time-independent and -dependent damage characteristics of brittle rocks inside the pre-failure range have been investigated using numerical simulations and lab testing. Grain-based discrete element models have been developed to simulate both, time-independent and -dependent damage evolution leading to ultimate failure of sandstone and granite, respectively. The models take into account elastic grain and elasto-plastic contact deformation, inter- and intra-granular fracturing and lifetime prediction on the basis of subcritical crack growth. The time-independent mechanical behavior of Coconino sandstone and Lac du Bonnet granite during uniaxial compression tests, Brazilian splitting tests and fracture toughness tests was simulated. Triaxial compression tests and fracture toughness tests for Kirchberg II granite and fracture patterns tests for Eibenstock II granite were carried out in laboratory to perform time-independent damage and failure criterion analysis. The corresponding simulations showed reasonable damage phenomena compared with experimental results. Damage indices were deduced and were applied for different time-independent simulations. Based on calibrations of the time-independent damage simulations of selected brittle rocks, Charles equation and Hillig-Charles equation, which are generally used to describe subcritical crack growth, were implemented into the numerical code to simulate time-dependent damage. One-edged crack growth in Coconino sandstone specimen due to stress corrosion has been analyzed theoretically and numerically. Uniaxial compressive creep tests for Lac du Bonnet granite were simulated and time-dependent behavior in terms of the damage process during primary, secondary and tertiary creep until final failure characterized by macroscopic fracturing was discussed in detail. Subsequent to this, the time-dependent Mode-I crack growth tests and uniaxial compressive creep tests for Kirchberg II granite were carried out and the corresponding simulations were performed. Simulation results are in good agreement with experimental observations. In addition, damage indices and time-dependent fracture development were monitored and illustrated. The developed approach was applied to two potential practical applications: the damage analysis of a sandstone landscape arch and a tunnel. Finally, the results are summarized and recommendations for future work are proposed.

The time-independent and -dependent damage characteristics of brittle rocks inside the pre-failure range have been investigated using numerical simulations and lab testing. Grain-based discrete element models have been developed to simulate both, time-independent and -dependent damage evolution leading to ultimate failure of sandstone and granite, respectively. The models take into account elastic grain and elasto-plastic contact deformation, inter- and intra-granular fracturing and lifetime prediction on the basis of subcritical crack growth. The time-independent mechanical behavior of Coconino sandstone and Lac du Bonnet granite during uniaxial compression tests, Brazilian splitting tests and fracture toughness tests was simulated. Triaxial compression tests and fracture toughness tests for Kirchberg II granite and fracture patterns tests for Eibenstock II granite were carried out in laboratory to perform time-independent damage and failure criterion analysis. The corresponding simulations showed reasonable damage phenomena compared with experimental results. Damage indices were deduced and were applied for different time-independent simulations. Based on calibrations of the time-independent damage simulations of selected brittle rocks, Charles equation and Hillig-Charles equation, which are generally used to describe subcritical crack growth, were implemented into the numerical code to simulate time-dependent damage. One-edged crack growth in Coconino sandstone specimen due to stress corrosion has been analyzed theoretically and numerically. Uniaxial compressive creep tests for Lac du Bonnet granite were simulated and time-dependent behavior in terms of the damage process during primary, secondary and tertiary creep until final failure characterized by macroscopic fracturing was discussed in detail. Subsequent to this, the time-dependent Mode-I crack growth tests and uniaxial compressive creep tests for Kirchberg II granite were carried out and the corresponding simulations were performed. Simulation results are in good agreement with experimental observations. In addition, damage indices and time-dependent fracture development were monitored and illustrated. The developed approach was applied to two potential practical applications: the damage analysis of a sandstone landscape arch and a tunnel. Finally, the results are summarized and recommendations for future work are proposed.:1 Introduction 2 State of the art 3 Time-independent damage analysis 4 Time-dependent damage analysis 5 Applications of numerical models . 6 Conclusions and outlook References

The field of geosciences, including geophysics, plays a crucial role in addressing society's pressing concerns related to energy demand, climate change, resource preservation, and environmental protection. Reactive systems encountered in this context are characterized by intricate interactions among various phases, environmental conditions, physical and chemical processes. Achieving a comprehensive understanding of these processes and quantitatively evaluating reactive systems necessitates a holistic scientific approach. This approach encompasses efficient categorization of reactive systems, the development of appropriate experimental and computational tools, and the collection and dissemination of relevant data. In this context, this thesis contributes to geophysics and petrophysics with a focus on reactive systems. It presents and interprets laboratory datasets that address various complex aspects of rock behavior, including the presence of graphite, resulting anisotropy, and the challenging petrophysical characteristics of carbonate rocks. This compilation of research results provides a multifaceted perspective on the complex nature of rocks, including their mineralogical, physical, and chemical properties. It thus contributes to a deeper comprehension of electrical rock properties and their practical utility. Upon examining carbonate rocks and the response of graphitic schist to CO$_\mathrm{2}$ under reservoir conditions, it becomes clear that the impact of increased reactivity in a system on geophysical parameters varies depending on the specific characteristics of the rocks and systems under investigation. Consequently, geophysical methods aiming at a quantitative assessment of reactive systems must exhibit robustness and efficiency in order to be effectively applied in a site- and system-specific manner. Expanding on this foundation, computational methods have been developed to aid in the quantitative analysis of reactive processes in laboratory experiments. These methods also serve as tools for gaining insights into the origin of rock properties and the impact of microstructure variation. Furthermore, inversion techniques are introduced in conjunction with custom-designed experiments within the field of petrophysics. The resultant software tool is made publicly accessible. The research further delves into the exploration of how physical properties of rocks are influenced by their microstructure, as well as how the stochastic nature of pore space geometry can introduce variability and uncertainty in rock physics data. This investigation was carried out through microstructure modeling and finite element simulations. Leveraging these tailored computational techniques allowed for a comprehensive understanding of laboratory data, facilitating robust generalizations and contextualization for field applications and site-specific integrated interpretation. To illustrate the application in a complex natural reactive system, a field study focusing on coastal fumarolic vents in volcanic terrain was carried out and is presented. The challenges, prospects and visualization strategies for integrating simulation or inversion results from different methods are examined. Effective evaluation of complex sites requires open access to existing knowledge, including laboratory datasets. Consequently, this work documents and provides openly accessible examples of complex multi-method laboratory datasets to facilitate better understanding, re-evaluation and application in the field. Finally, the handling of multi-reactive systems in field applications is discussed. It involves the integration of three-dimensional subsurface models with petrophysical insights related to multi-reactive systems. These models are calibrated using additional complementary data from surface or borehole sources. This integrated approach enables a quantitative assessment of site-specific multi-reactive systems.