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Hydraulic fracturing has attracted a tremendous amount of attention due to its abundant applications, such as magma-driven dykes, fracturing of oil and gas reservoirs, heat production from geothermal reservoirs, ice melt, and fault reactivation in mining. Therefore, the development of fracture propagation models is of great significance to provide more effective technical tools for the dynamic simulation of fracture formation and propagation. Hydraulic fracturing involves a complex process due to the strong coupling between the fluid and solid rock. The finite element method (FEM) is a traditional method for solving the fracture propagation problem. FEM has the advantage of being robust and flexible. However, special treatment is required when dealing with complex fracture problems such as fracture intersection and branching because of discontinuities across fracture surfaces. Instead of seeking to approximate partial differential equations in a conventional framework, the peridynamic approach (PD) uses spatial integral equations that overcome the limitations of defining partial derivatives at discontinuities, which makes it quite suitable for solving complex fracture problems. Therefore, it is of great importance to combine the advantages of both FEM and PD to develop a more robust and flexible fracture propagation model. The main contribution of the thesis is to study fracture propagation problems in fully saturated porous media based on both FEM and PD. Three fracture models based on FEM, PD, hybrid FEM and PD are developed to simulate and explore more "realistic" fracture propagation processes. The main research work of the thesis contains the following four parts. First, comprehensive reviews of the fracture propagation literature, crack branching and PD theory are given. The fracture propagation review includes a review of the fracture propagation process, fracture models and various numerical methods for predicting fracture propagation. The review of crack branching provides a state-of-the-art review of crack branching, including experimental observations, physics, fracture models and associated numerical methods. The latest advances and existing issues of crack branching are discussed. The review of PD theory provides a review of theoretical aspects of PD and related applica-tions of PD in different fields, especially in the field of fracture mechanics. The challenges and new prospects for the development of PD are discussed. Then, a fully implicit, FEM-based fracture model using zero thickness cohesive interface elements is developed. The rock formation is considered as a fully saturated porous medium. The fracture surface is deemed to be permeable, the fracturing fluid is treated as an impressible Newtonian fluid, and the cohesive zone model is employed for the fracture propagation criterion. After verifying the model, the stepwise phenomenon, which has been observed in the field and experiments and reported recently in the numerical modelling literature, is investigated with the model. Then, an explicit PD approach for simulating fracture propagation in saturated porous media is developed. A staggered method is adopted to solve the coupled system. The solid deformation equation is solved for the displacement field, and the fluid flow equation is solved for the pressure field with PD. After verification via benchmark examples, including a 1D consolidation problem and a 2D fluid-filled crack propagation problem, a series of tests are conducted to study the fracture propagation phenomena in porous media, including the crack branching phenomenon and the stepwise phenomenon. Effects of pore pressure in fracture propagation branching are investigated, and the stepwise phenomenon is successfully reproduced. All the examples presented demonstrate the capability of the approach in solving fracture propagation problems in saturated porous media. Finally, a fully coupled hybrid FEM-PD approach for simulating fracture propagation in saturated porous media is presented. Considering the ability of PD in solving discontinuous problems, the area where cracks can potentially occur is discretised by PD and the crack-free area is discretised by FEM. The solid deformation and fracture propagation are captured by PD and FEM, while the fluid flow in both the reservoir and fracture is simulated with FEM. The whole process is solved in a monolithic way with an implicit scheme. The approach demonstrates the capability of modelling complex dynamic crack propagation via benchmark examples. The branching phenomenon is then investigated with the proposed approach. In conclusion, complex crack patterns are prone to form with faster loading rate, more brittle and impermeable media, and with lower energy release rate.

This research deals with Chinoiserie architecture in Germany during the eighteenth century and the early nineteenth century. The purpose of this research is not to describe the developmental process of this style in detail but to explore two different scopes of conducting historical research for historic architecture-a micro approach and a macro approach. The former approach focuses on individual buildings and describes their history by integrating written records and archaeological evidence, particularly the wood elements in the old structure. The latter approach takes a higher perspective and looks at the formation of the style, especially demonstrating the social dynamics that supported the movement of the ideas and objects. Taking the Chinese Tower in Donaustauf as an example, the first part of this work investigates the history of the Chinoiserie building with the help of two archaeological investigation techniques- wood anatomy and dendrochronology. It investigates its technical/design details and explains its construction history. The second part of this work seeks the reasons that Chinoiserie chose these design elements by examining its social context. Several studies by previous scholars have demonstrated the important role of the nobility in the diffusion of this pseudo-Chinese fashion. Using the methods of social network analysis, three factors are examined that may have influenced the choice of paradigms among the patrons of the buildings: iii geographical adjacency, personal contact, and kinship. The statistical results of the Quadratic Assignment Procedure (QAP) indicate that patrons' usage of paradigms is considerably correlated with their kinship, which improves our understanding of the significance of the genealogical relationship in influencing the taste in design and construction and the reception of foreign cultures. iv