### Abstract

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.

Original language | English |
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Title of host publication | ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering |

Publisher | National Technical University of Athens |

Pages | 3168-3180 |

Number of pages | 13 |

Volume | 2 |

ISBN (Electronic) | 9786188284401 |

Publication status | Published - 2016 |

Event | 7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016 - Crete, Greece Duration: 5 Jun 2016 → 10 Jun 2016 |

### Conference

Conference | 7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016 |
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Country | Greece |

City | Crete |

Period | 5/06/16 → 10/06/16 |

### Fingerprint

### Keywords

- BEM
- BETI
- DDM
- Sequential excavation

### ASJC Scopus subject areas

- Artificial Intelligence
- Applied Mathematics

### Cite this

*ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering*(Vol. 2, pp. 3168-3180). National Technical University of Athens .

**Modelling the process of sequential excavation with the boundary element method.** / Duenser, C.; Beer, G.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

*ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering.*vol. 2, National Technical University of Athens , pp. 3168-3180, 7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016, Crete, Greece, 5/06/16.

}

TY - GEN

T1 - Modelling the process of sequential excavation with the boundary element method

AU - Duenser, C.

AU - Beer, G.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - BEM

KW - BETI

KW - DDM

KW - Sequential excavation

UR - http://www.scopus.com/inward/record.url?scp=84995377854&partnerID=8YFLogxK

M3 - Conference contribution

VL - 2

SP - 3168

EP - 3180

BT - ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering

PB - National Technical University of Athens

ER -