Exploring topology and shape optimisation techniques in underground excavations

摘要

Topology optimisation techniques help designers to nd the best layout of structural members. When followed by shape and sizing optimisation, these techniques result in far greater savings than shape and sizing optimisation alone. During the last three decades extensive research has been carried out in the topology optimisation area. Consequently topology optimisation techniques have been considerably improved and successfully applied to a range of physical problems. These techniques are now regarded as invaluable tools in mechanical, aerostructural and structural design. In spite of great potential in geomechanical problems, however, the application of topology optimisation techniques in this field has not been studied thoroughly. This thesis explores the state-of-the-art topology and shape optimisation methods in excavation design. The main problems of concern in this thesis are to find the optimum shape of an underground opening and to optimise the reinforcement distribution around it. To tackle these problems, new formulations for some topology optimisation techniques are proposed in this thesis to match the requirements in excavation problems. Although linear elastic material models have limited applications in excavation design, these models are used in the first part of this thesis to introduce the proposed optimisation technique and to verify it. Simultaneous shape and reinforcement optimisation is considered as well. Using the proposed optimisation techniques, it is shown that the computational effort needed for this mixed optimisation problem is almost the same as the effort required to solve each of shape or reinforcement optimisation problems alone. In the next part of this thesis, reinforcement optimisation of tunnels in massive rocks is addressed where the behaviour of the rock mass is in uenced by few major discontinuities. Although discontinuities exist in the majority of rock masses, due to its complexities, optimising the excavations in these types of rocks has not been considered by any other researcher before. A method for reinforcement optimisation of tunnels in such rock masses is proposed in this thesis and its capability is demonstrated by means of numerical examples. Lastly, shape optimisation of excavations in elasto-plastic soil is addressed. In this problem the excavation sequence is also taken into account. A stressbased parameter is dened to evaluate the efficiency of the soil elements assuming Mohr-Coulomb material model. Some examples are solved to illustrate and verify the application of the proposed technique. Being one of the first theses on the topic, this work concentrates on the theoretical background and the possibility of applying topology optimisation techniques in excavation designs. It has been demonstrated that a properly tailored topology optimisation technique can be applied to find both the optimum shape and the optimum reinforcement design of openings. Optimising the excavations in various types of grounds including elastic homogeneous rock masses, massive rocks, and elasto-plastic soil and rock media have been considered. Different objective functions, namely, mean compliance, oor heave, and tunnel convergence have been selected and successfully minimised using the proposed techniques. The results obtained in this thesis illustrate that the proposed topology optimisation techniques are very useful for improving excavation designs.