The Influence of Healed Intrablock Rockmass Structure on the Behaviour of Deep Excavations in Complex Rockmasses

Conventional rockmass characterization and analysis methods for geotechnical assessment in mining, civil tunnelling, and other excavations consider only the intact rock properties and the discrete fractures that are present and form blocks within rockmasses. Field logging and classification protocols are based on historically useful but highly simplified design techniques, including direct empirical design and empirical strength assessment for simplified ground reaction and support analysis. As modern underground excavations go deeper and enter into more high stress environments with complex excavation geometries and associated stress paths, healed structures within initially intact rock blocks such as sedimentary nodule boundaries and hydrothermal veins, veinlets and stockwork (termed intrablock structure) are having an increasing influence on rockmass behaviour and should be included in modern geotechnical design. Due to the reliance on geotechnical classification methods which predate computer aided analysis, these complexities are ignored in conventional design. Given the comparatively complex, sophisticated and powerful numerical simulation and analysis techniques now practically available to the geotechnical engineer, this research is driven by the need for enhanced characterization of intrablock structure for application to numerical methods. Intrablock structure governs stress-driven behaviour at depth, gravity driven disintegration for large shallow spans, and controls ultimate fragmentation. This research addresses the characterization of intrablock structure and the understanding of its behaviour at laboratory testing and excavation scales, and presents new methodologies and tools to incorporate intrablock structure into geotechnical design practice. A new field characterization tool, the Composite Geological Strength Index, is used for outcrop or excavation face evaluation and provides direct input to continuum numerical models with implicit rockmass structure. A brittle overbreak estimation tool for complex rockmasses is developed using field observations. New methods to evaluate geometrical and mechanical properties of intrablock structure are developed. Finally, laboratory direct shear testing protocols for interblock structure are critically evaluated and extended to intrablock structure for the purpose of determining input parameters for numerical models with explicit structure.

New Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming

Process systems design, operation and synthesis problems under uncertainty can readily be formulated as two-stage stochastic mixed-integer linear and nonlinear (nonconvex) programming (MILP and MINLP) problems. These problems, with a scenario based formulation, lead to large-scale MILPs/MINLPs that are well structured. The first part of the thesis proposes a new finitely convergent cross decomposition method (CD), where Benders decomposition (BD) and Dantzig-Wolfe decomposition (DWD) are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. A variant of CD, which includes multiple columns per iteration of DW restricted master problem and multiple cuts per iteration of BD relaxed master problem, called multicolumn-multicut CD is then developed to improve solution time. Finally, an extended cross decomposition method (ECD) for solving two-stage stochastic programs with risk constraints is proposed. In this approach, a CD approach at the first level and DWD at a second level is used to solve the original problem to optimality. ECD has a computational advantage over a bilevel decomposition strategy or solving the monolith problem using an MILP solver. The second part of the thesis develops a joint decomposition approach combining Lagrangian decomposition (LD) and generalized Benders decomposition (GBD), to efficiently solve stochastic mixed-integer nonlinear nonconvex programming problems to global optimality, without the need for explicit branch and bound search. In this approach, LD subproblems and GBD subproblems are systematically solved in a single framework. The relaxed master problem obtained from the reformulation of the original problem, is solved only when necessary. A convexification of the relaxed master problem and a domain reduction procedure are integrated into the decomposition framework to improve solution efficiency. Using case studies taken from renewable resource and fossil-fuel based application in process systems engineering, it can be seen that these novel decomposition approaches have significant benefit over classical decomposition methods and state-of-the-art MILP/MINLP global optimization solvers.