Christian Duenser

Isogeometric Boundary Element Method for the Simulation in Tunneling

Isogeometric finite element methods and more recently boundary element methods have been successfully applied to problems in mechanical engineering and have led to an increased accuracy and a reduction in simulation effort. Isogeometric boundary element methods have great potential for the simulation of problems in geomechanics, especially tunneling because an infinite domain can be considered without truncation. In this paper we discuss the implementation of the method in the research software BEFE++. Based on an example of a spherical excavation we show that a significant reduction in the number of parameters for describing the excavation boundary as well as an improved quality of the results can be obtained.

New Developments of the Boundary Element Method for Underground Constructions

AbstractIn this paper, an innovative modeling approach is presented for the simulation of underground construction with the emphasis on tunneling. The boundary element method (BEM) is used, and the theoretical background is discussed first. This is followed by test examples, where the results are compared with results from available software, showing the efficiency and accuracy of the new method. Finally, a practical example considering nonlinear material, sequential excavation, and installation of ground support is presented.

MODELLING THE PROCESS OF SEQUENTIAL EXCAVATION WITH THE BOUNDARY ELEMENT METHOD

The Boundary Element Method (BEM) is ideally suited for the simulation of underground constructions like tunnels or caverns. Such structures are modelled with the BEM inside an infinite or semi-infinite domain. As the radiation condition is fulfilled by the BEM no truncation of the domain is necessary. Only the surface of the structure (e.g. tunnel) has to be discretised by boundary elements (BE). An accurate simulation of the tunnelling process has to consider the sequential excavation where parts of the rock mass are excavated at different time and location. This special constructional condition has a direct influence onto the simulation model. In this work different methods are presented which consider the sequential excavation. The first method is the discretisation of the problem by multiple BE regions (MRBEM). Each region, which will be excavated during the excavation process, is discretised by a separate finite BE region. These regions are embedded inside an infinite region which represent the infinite extend of the domain. Thus, a system of BE regions arise which have to be coupled at their common interfaces. Two coupling strategies, the Boundary Element Tearing and Interconnecting Method (BETI) and the method of Interface Coupling (IC) will be presented to solve the sequential tunnel excavation. The second method uses only a single BE region (SRBEM) for every step of excavation. For each load step the geometry/mesh has to be updated. Thus, the mesh of the previous load step will be extended by the surface of the new excavation volume of the current load step. Beside the geometry update an essential part of this method is an accurate evaluation of the excavation loading. The excavation loads for each excavation step are tractions applied at the part of the boundary surface just generated by the geometry update. These tractions depend on all previous load steps and will be evaluated by a calculation of internal results in the interior of the single region. The internal results can be either stresses or displacements. In this work the modelling strategies of the MRBEM and SRBEM approach will be presented. On a realistic tunnel example the accuracy of the results for the mentioned methods will be shown as well as the performance of the calculations.