Time-dependency of Rocks and Implications Associated with Tunnelling

The formulation of a geotechnical model and the associated prediction of the mechanical behaviour is a challenge engineers need to overcome in order to optimize tunnel design and meet project requirements. Special challenges arise in cases where rocks and rockmasses are susceptible to time-effects and time-dependent processes govern. Progressive rockmass deformation and instability, time-dependent overloading of support and delayed failures are commonly the result of time-dependent phenomena. The research work presented in this thesis serves as an attempt to provide more insight into the time-dependent behaviour of rocks. Emphasis is given on investigating and analyzing creep deformation and time-dependent stress relaxation phenomenon at the laboratory scale and in-depth analyses are presented. This thesis further develops the understanding of these phenomena and practical yet scientific tools for estimating and predicting the long-term strength and the maximum stress relaxation of rock materials are proposed. The identification of the existence of three distinct behavioural stages during stress relaxation is presented and discussed. The main observations associated with time-dependent behaviour are employed in numerical analyses and applied at the tunnel scale. A new approach for simulating and capturing the time-dependent behaviour coupled with the tunnel advancement effect is also developed and analyzed. Guidance is provided to increase the understanding of the support-rockmass interaction and the main implications and significance of time-dependent behaviour associated with rock tunnelling are discussed. The work presented in this thesis advances the scientific understanding of time-dependent rock and rockmass behaviour, increases the awareness of how such phenomena are captured numerically, and lays out a framework for dealing with such deformations when predicting tunnel deformations. Practical aspects of this thesis are also presented, which will increase their usage in the associated industries and close the gap between the scientific and industry communities.

Distributed Extremum-Seeking Control with Applications to High-Altitude Balloons

The real-time optimization of large-scale systems is a difficult problem due to the need for complex models involving uncertain parameters and the high computational cost of solving such problems by a decentralized approach. Extremum-seeking control (ESC) is a model-free real-time optimization technique which can estimate unknown parameters and can optimize nonlinear time-varying systems using only a measurement of the cost function to be minimized. In this thesis, we develop a distributed version of extremum-seeking control which allows large-scale systems to be optimized without models and with minimal computing power. First, we develop a continuous-time distributed extremum-seeking controller. It has three main components: consensus, parameter estimation, and optimization. The consensus provides each local controller with an estimate of the cost to be minimized, allowing them to coordinate their actions. Using this cost estimate, parameters for a local input-output model are estimated, and the cost is minimized by following a gradient descent based on the estimate of the gradient. Next, a similar distributed extremum-seeking controller is developed in discrete-time. Finally, we consider an interesting application of distributed ESC: formation control of high-altitude balloons for high-speed wireless internet. These balloons must be steered into a favourable formation where they are spread out over the Earth and provide coverage to the entire planet. Distributed ESC is applied to this problem, and is shown to be effective for a system of 1200 ballons subjected to realistic wind currents. The approach does not require a wind model and uses a cost function based on a Voronoi partition of the sphere. Distributed ESC is able to steer balloons from a few initial launch sites into a formation which provides coverage to the entire Earth and can maintain a similar formation as the balloons move with the wind around the Earth.