VIBRATION ANALYSIS OF UNDERGROUND TUNNEL AT HIGH-TECH FACILITY JUAN NEGREIRA MONTERO Structural Master’s Dissertation Mechanics Denna sida skall vara tom! Department of Construction Sciences Structural Mechanics ISRN LUTVDG/TVSM--10/5170--SE (1-80) ISSN 0281-6679 VIBRATION ANALYSIS OF UNDERGROUND TUNNEL AT HIGH-TECH FACILITY Master’s Dissertation by JUAN NEGREIRA MONTERO Supervisor Kent Persson, PhD, Div. of Structural Mechanics Examiner: Delphine Bard, Associate Professor, Div. of Structural Mechanics Copyright © 2010 by Structural Mechanics, LTH, Sweden. Printed by Wallin & Dalholm Digital AB, Lund, Sweden, August, 2010 (Pl). For information, address: Division of Structural Mechanics, LTH, Lund University, Box 118, SE-221 00 Lund, Sweden. Homepage: http://www.byggmek.lth.se Denna sida skall vara tom! Contents 1 Introduction 9 1.1 Max Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 MAX IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 Synchrotron Light . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Linac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 Objective and Method . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.5 Disposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 Structural Dynamics. Vibration Theory 15 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Single-Degree-of-Freedom (SDOF) Systems . . . . . . . . . . . . . . . 16 2.3 Multi-Degree-of-Freedom (MDOF) Systems . . . . . . . . . . . . . . . 17 2.4 Modal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4.1 Natural Frequencies . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.2 Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4.3 Vibration Modes . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.5 Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.5.1 Damping Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.6 RMS Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.7 Wave Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3 Materials 27 3.1 Boulder Clay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4 Finite Element Method (FEM) 29 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.2 Isoparametric Finite Elements . . . . . . . . . . . . . . . . . . . . . . 29 4.3 Finite Element Formulation of 3D-Elasticity . . . . . . . . . . . . . . 31 5 FE Model 35 5.1 Software: Abaqus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.3 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.3.1 Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3 4 CONTENTS 5.3.2 Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.4 Simplified Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.5 Chosen Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5.5.1 Linac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.5.2 Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.5.3 Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.5.4 Road . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 5.6 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5.7 Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 6 Modelling Results 47 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 6.2 Evaluation Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 6.3 Harmonic Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 6.3.1 Parameter Study . . . . . . . . . . . . . . . . . . . . . . . . . 47 6.3.2 Dynamic Component of a Bus Load on an Even Road . . . . . 51 6.4 Transient Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 6.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 6.4.2 Road Irregularity: Pulse Load . . . . . . . . . . . . . . . . . . 56 6.4.3 Walking Load . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 6.5 Pillars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 7 Discussion 65 8 Suggestions for Further Work 67 A Appendix 69 A.1 Figures Steady-State Analyses . . . . . . . . . . . . . . . . . . . . . . 69 A.2 Figures Transient Analyses . . . . . . . . . . . . . . . . . . . . . . . . 81 B Appendix 83 B.1 Damping Ratio: Matlab code . . . . . . . . . . . . . . . . . . . . . . 83 B.2 RMS: Matlab code . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Preface This master thesis was carried out at the Division of Structural Mechanics at LTH, Lund University, from November 2009 to May 2010. First of all I would like to thank my supervisor PhD Kent Persson, for his contin- uous support, encouragement and patience. My most grateful appreciation as well to Dr. Sc. Delphine Bard for her great assistance, always motivating and helping me throughout the coarse of this work. A special thank to the staff of the Division of Structural Mechanics, the Max-Lab staff and the fellow students I shared office with for interesting and helpful discussions during meetings and coffee breaks. I would also like to express my deepest gratitude and love to my parents Juan and Mariluz for their infinite patience, support and understanding throughout all my life. Nothing would be as it is without them. Finally, Iwould like tothankall therestof my familyandfriends backhome(special mention to Alberto Trillo, the one always there) and all the people I met during this unforgettable year in Sweden. Juan Negreira Montero Lund, in May 2010. 5 Denna sida skall vara tom! Abstract Max-lab is a national laboratory operated jointly by the Swedish Research Council and Lund University. Nowadays, the Max project consist of three facilities (three storage rings): MAX I, MAX II, MAX III and one electron pre-accelerator called Max Injector. A new storage ring is needed due to improved nanotechnology. MAX IV is planned to be the next generation Swedish synchrotron radiation fa- cility. The main source at MAX IV will be a 3-GeV ring with state-of-the-art low emittance for the production of soft and hard x-rays as well as an expansion into the free electron laser field [13]. In this master thesis, the vibration levels at the Linac will be analysed. Linac stands for "Linear accelerator" and its function is to accelerate the electron beam until it has almost reached the speed of light and then shoot it into the ring where it can begin to spin around producing synchroton light. The Linac as well as the bridge over it will be mostly built on concrete, while the soil will be mainly constituted by boulder clay. Since this construction will be used for high precision measurements, it will be asked to have very strict technical conditions where only very low vibration levels will be allowed. The technical condition states that only an RMS value of 100 nm during 1 second will be permitted in the vertical direction. Realistic finite element models of the Linac underground tunnel will be stablished in order to analyse the influence of the surrounding vibration sources on the MAX IV Lab’s underground tunnel. To achieve this purpose both steady-state and transient analysis were performed: 1. In the first case, a parameter study was made by varying material properties and checking its influence on the model. Thus, the damping ratio and the den- sity of the soil and the modulus of elasticity and the thickness of the concrete floor were varied. This was done by carrying out a frequency sweep. Likewise and since a bridge for bus traffic is supposed to be built over the Linac, a simulation of the dynamic component of a bus load was performed by means of a frequency sweep as well. 2. For the transient loads, two realistic types of loading were simulated. On one hand, anirregularityontheroadwasassumedandontheotherhandawalking load was also performed. 7 8 CONTENTS All the parts in the model were meshed with solid isoparametric hexaedra elements. They are essentially constant strain elements with first-order linear interpolation. They are 8 node brick elements with no rotations, hence having only three degrees of freedom (translations) on each node. The model has a total number of 135919 nodes and 107530 elements, making a total of 407757 degrees of freedom. In most of the cases studied, the requirement was not fulfilled, so some solutions were tried out. Thus, the addition of pillars under the bridge was checked out. After all the simulations carried out, it can be concluded that the soil has a great influence on the response of the structure. Attention should be paid to its proper- ties due to the lack of data existant right now. Properties could even be determined through field measurements. Besides, the conditions of the road crossing over the bridge should periodically be checked. The analysis results indicate that the technical requirements may be reached for a bus running on smooth asphalt. However, small irregularities on the road at the bridge will create vibration levels that are too high and the quality of the measurements at the MAX IV will be affected. Since the probability of not always having a smooth road is rather high, especially during the winter, it is recommended that the bridge is avoided and that the road will be relocated to not crossing the Linac. Likewise and looking at the simulations of the walking load, it can be concluded that worrying levels of vibrations can be caused by groups of people walking close to the beamline.