Exploring topology and shape optimisation techniques in underground excavations

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

Tunnel reinforcement optimisation for nonlinear material

In this paper, topology optimization is applied in optimizing tunnel reinforcement. Nonlinear behavior of geotechnical material is considered to illustrate the practical material behavior under working condition. The adjoint method is used to derive the nonlinear sensitivities. A revised bi-directional evolutionary optimization (BESO) is used to maximize the structural stiffness of reinforced tunnel with a prescribed volume of reinforcement. The developed BESO method is illustrated in a simple example of tunnel reinforcement design to verify the proposed approach

Study of truss bolt system for highly stressed rock mass using finite element modelling techniques

Instability of underground excavations causes many problems, it affects safe working environment, reduces recovery of minerals and increases costs of mining operations. Following excavation in rock, a new stress distribution will be produced around the opening. It is known that after a distance from opening boundary, a stable rock arch will be formed regardless of the shape of the opening

Computational algorithms for generating efficient and innovative load-carrying structures

The evolutionary structural optimization (ESO) method is based on the simple concept of gradually removing underutilized material and at the same time adding efficient material to the structure. As a result, the resulting structural shape evolves towards an optimum. This paper presents the latest developments of ESO method in generating efficient and innovative structures, including optimal design of bridges, optimization of periodic structures, optimal design of a structure with multiple materials and shape and reinforcement optimization of undergroudn tunnels

Using BESO method to optimize the shape and reinforcement of underground openings

In excavation design, optimizing the reinforcement and finding the optimal shape ofthe opening are two significant challenges. Both ofthese problems can be viewed as searching for the optimum distribution of material in the design domain. In structural design, topology optimization techniques have been successfully used to deal with such problems. One ofthese techniques, known as bi-directional evolutionary structural optimization (BESO), is employed here to improve the shape and reinforcement designs of underground openings. The BESO algorithm is extended to simultaneously optimize the shape of the opening and the topology of the reinforcement. The capability of the proposed approach is illustrated via numerical examples

Shape optimization of underground excavation using ESO method

In underground excavations, the shape of the opening is of main concern due to its impact on the stress distribution around the opening. However, because of the complex and non-linear behaviour of soil only a few works have dealt with this problem. In this paper an evolutionary structure optimization (ESO) procedure is used for optimizing the shape of underground excavations in a cohesive frictional material obeying Mohr-Coulomb material model. The presented examples show the capability of ESO method in tackling such problems

Improving rockbolt design in tunnels using topology optimization

© 2015 American Society of Civil Engineers. Finding an optimum reinforcement layout for underground excavation can result in a safer and more economical design, and is therefore highly desirable. Some works in the literature have applied topology optimization in tunnel reinforcement design in which reinforced rock is modeled as homogenized isotropic material. Optimization results, therefore, do not clearly show reinforcement distributions, leading to difficulties in explaining the final outcomes. To overcome this deficiency, a more sophisticated modeling technique in which reinforcements are explicitly modeled as truss elements embedded in rock mass media is used. An optimization algorithm extending the solid isotropic material with penalization method is introduced to seek for an optimal bolt layout. To obtain the stiffest structure with a given amount of reinforced material, external work along the opening is selected as the objective function with a constraint on the volume of reinforcement. The presented technique does not depend on material models used for rock and reinforcements and can be applied to any material model. Nonlinear material behavior of rock and reinforcement is considered in this work. Through solving some typical examples, the proposed approach is proved to enhance the conventional reinforcement design and provide clear and practical reinforcement layouts

Applying bi-directional evolutionary structural optimisation method for tunnel reinforcement design considering nonlinear material behaviour

In the empirical methods for reinforcement design of underground excavations, an even distribution of rock bolts is generally recommended. This work proves that this design is not necessarily optimal and shows how the state-of-the-art reinforcement design could be improved through topology optimisation techniques. The Bidirectional Evolutionary Structural Optimisation (BESO) method has been extended to consider nonlinear material behaviour. An elastic perfectly-plastic Mohr-Coulomb model is utilised for both original rock and reinforced rock. External work along the tunnel wall is considered as the objective function. Various in situ stress conditions with different horizontal stress ratios and different geostatic stress magnitudes are investigated through several examples. The outcomes show that the proposed approach is capable of improving tunnel reinforcement design. Also, significant difference in optimal reinforcement distribution for the cases of linear and nonlinear analysis results proves the importance of the influence of realistic nonlinear material properties on the final outcome