Analytic Element Models for Groundwater Flow and Linear Elasticity in Fractured Rocks

Sammanfattning: There is an increasing demand for using deep underground space at various scales, such as small-scale geothermal wells and large-scale projects like tunnels or nuclear waste disposal. The deep underground space in fractured rock is a heterogeneous and challenging medium. Fractures have a significant impact on both the groundwater flow and the mechanical behavior. This thesis aims to develop analytic element models that capture the behavior of fractured rock for both groundwater flow and linear elasticity at different scales. Because these models are analytic in their formulation, they can model with machine precision and investigate behavior near singular points.For groundwater flow, the thesis deals with two approaches to capture the groundwater flow behavior in fractured rock: a continuum approach and a discrete fracture network approach. The continuum approach considers the impact of fractures by varying the hydraulic conductivity based on depth. This method allows for efficient modeling while still capturing the depth-dependent behavior accurately. The discrete approach, in turn, implements the fractures directly by embedding them in the continuum. Unlike previous models, this model implements intersection without the need for approximations. The discrete model also demonstrates how fractures with discontinuous transmissivity are connected to model a heterogeneous fracture network.For linear elasticity, the fractures and tunnels are modeled discretely in a plane strain continuum as analytic elements. These elements possess degrees of freedom, and no theoretical limitation exists on the number of elements. The execution of a model with 10,000 fractures effectively demonstrates the speed and accuracy of this method. Integrating seepage forces into the linear elastic model has improved the correlation between groundwater flow and linear elasticity. This enhancement allows for a more precise analysis of the impact of seepage forces near singular points. The solution's analytic formulation allows for the investigation of the behavior of the seepage force as a continuous function.To conclude, a comparison between the analytic element model and a range of numerical methods reveals a strong agreement, with a mean error of less than 0.32%. The results demonstrate that the developed models are highly accurate and valuable tools for modeling fractured rocks.