Dynamic effect of metro-induced vibration on the rammed earth base of the Bell Tower
- Jinxing Lai^{1},
- Fangyuan Niu^{1},
- Ke Wang^{1, 2}Email author,
- Jianxun Chen^{1},
- Junling Qiu^{1}Email author,
- Haobo Fan^{1} and
- Zhinan Hu^{3}
Received: 3 March 2016
Accepted: 20 June 2016
Published: 30 June 2016
Abstract
Xi’an Bell Tower (the Bell Tower) is a state-level ancient relic in China. The vibration caused by metro will exert adverse effect on the Bell Tower. This paper aims at presenting 3D-FEM models to predict the peak period velocity (PPV) of rammed earth base when the metro passing through the Bell Tower. The calculation results are compared with those of field test. Both results were found to be in good agreement. Furthermore, the results indicated that the effect of shock absorption measures is significant. The shock absorption tracks can obviously decrease the vibration of the Bell Tower, and the maximum decrease of PPV of the rammed earth base is 78.91 %. The proposed prediction has the potential to be developed as a decision and management tool for the evaluation of the risk associated with the influence of vibration caused by metro on buildings in urban areas.
Keywords
Metro vibration The Bell Tower FEM Tunnel Peak particle velocity (PPV)Background
As one of four ancient capitals in the world, Xi’an was once the capital for 13 dynasties in Chinese history. The Bell Tower, as a city landmark, is a precious ancient building with a history of over 600 years, but its durability has been gradually weakened for the long history. Xian is now enjoying a boom in metro construction, which will unavoidably cause vibration for the Bell Tower. In the other word, even the tiniest vibrations may lead to fatigue failure for the Bell Tower since the continuous vibration.
In 1970s to 1990s, some researches analyzed the deformation and failure rules of the ancient structures under the vibration according to field tests (Mata 1971; Rueker 1982; Ellis 1987; Clemente and Rinaldis 1998). At the same tine, some researches on prevention of ancient buildings against transportation vibration are made by some European and American experts (Lang 1971; Dawn and Stanworth 1979; Kurzweil 1979). In addition, some new methods, such as artificial neural networks and numerical simulations, are used to address the vibration features of buildings under seismic wave (Degrande and De Roeck 1998; Degrande and Lombaert 2001; Lombaert et al. 2006; Real et al. 2015; Real 2014; Lai et al. 2014, 2015a, 2016b; Ye et al. 2014; Li et al. 2013; Han and Jia 2015; Han et al. 2014). In recent years, some scholars studied the structural and mechanical characteristics under the vibration energy. For example, Dr. Jia Yingxun et al. studied the influence of vibration of Beijing Metro Lines 6 and 8 on ancient buildings (Luo et al. 2015; Yu and Fang 2006; Jia et al. 2009; Xie 2008). Research results indicated that the dynamic response of ancient building structure caused by train vibration changed along with the change of horizontal and vertical distances. On the other hand, to better understand and preserve ancient ruins against train-induced vibrations, vibration measurements and FE analysis were conducted on the Hangu Pass, Luoyang, China, located adjacent to the Longhai railway line (Ye et al. 2015), and the results showed that the set isolation trench can protect the ancient ruin against environmental vibration. In order to ensure the safety and stability of subway tunnel in the practical operation of demolition blasting of the viaduct, Zhao et al. (2015) put forward composite protective structures of steel-rubber tires and makes safety checking calculation of the subway tunnel on the basis of composite protective measures by numerical simulation, and the composite protection system was further optimized.
The influence of metro vibration on REB of the Bell Tower was studied in this paper which will provide valuable experience for protecting similar ancient cultural relics. In order to make an evaluation on the stability of the Bell tower, the field investigation was conducted in the paper firstly that can provide soil parameters for finite element model of the Bell Tower and get the soil layer structure and engineering characteristics. What is more, here we summarized a lot of vibration safety standards of buildings, and got the most suitable vibration safety standards for the Bell Tower. Thirdly, 3D-FEM models are made to simulate the working conditions including with or without shock absorption tracks and different train speeds. Finally, the calculation results are compared with field tests for verifying the correctness in the paper.
Overview of the Bell Tower
Vibration safety standards
Summary of vibration guide values for structure damage
Vibration standard | Evaluating index | Evaluation object | Evaluation value (mm/s) |
---|---|---|---|
ISO 4866:2010 (ISO 2010) | PPV | Ancient architecture | 2.5 |
Germany DIN4150-3:1999 (Germany 1999) | PPV | Ancient architecture | 3–10 |
UK BS7385-2 (UK 1993) | PPV | Ancient architecture | 7.5 |
Switzerland 6.10SN640312:1992 (Swiss 1992) | PPV | Old and poorly maintained buildings | 2 |
Portugal (Meng 2009) | PPV | Ancient architecture | 2.5 |
Japan (Cao 2006) | PPV | Ancient architecture | 5 |
China GB10070-88 (China 2003) | PPV | Ancient architecture (cracking and weathering) | 1.8–3.0 |
China GB/T50452:2008 (China 2008) | PPV | Ancient architecture | 3–5 |
State Administration of Cultural Heritage (Meng 2009) | PPV | The Bell Tower and the City Wall | 0.15–0.2 |
Numerical analysis
Research content
Six combinations
Condition | Track type | Metro combination | Train amount |
---|---|---|---|
1 | Conventional track | 2# + 6# | 4 |
2 | Conventional track | 2# + 2# | 2 |
3 | Conventional track | 6# + 6# | 2 |
4 | Shock absorption track | 2# + 6# | 4 |
5 | Shock absorption track | 2# + 2# | 2 |
6 | Shock absorption track | 6# + 6# | 2 |
Numerical model
Numerical model soil parameters
Parameter | Unit | Fill | Q^{3} | Q^{4} | Silty clay |
---|---|---|---|---|---|
Height (H) | (m) | 8 | 3.5 | 8 | 40 |
Soil Young modulus (E) | (MPa) | 110 | 403 | 495 | 622 |
Poisson’s ratio (ν) | (–) | 0.175 | 0.163 | 0.160 | 0.158 |
Cohesion (C) | (kPa) | 24.3 | 25.3 | 37.5 | 35.5 |
Angle of internal friction (φ) | (°) | 12 | 12.5 | 20.2 | 25.2 |
Soil unit weight (γ) | (kg/m^{3}) | 17.8 | 20.4 | 20.2 | 20.6 |
Unit parameters
Unit | ρ (g/cm^{3}) | E (Gpa) | ν | C (Kpa) | Φ (°) |
---|---|---|---|---|---|
Jet grouting piles | 2.3 | 39 | 0.29 | – | – |
REB | 1.67 | 3 | 0.3 | 48 | 35 |
Tunnel lining | 2.5 | 40 | 0.29 | – | – |
Track | 2.4 | 46 | 0.3 | – | – |
The time period and time increment size
According to different sampling frequency, the time period and time increment size of the environmental vibration problem are studied in many Literatures (Ma et al. 2016; Lai et al. 2016a, b, c). The research results show that when the minimal time period of the model is 50 times as much as the time increment size, the error of the calculation results can not be considered. The ground time-period of the Bell Tower is 0.29–0.4 s, so when the time increment size is 0.005 s, the computational accuracy meets the requirements.
Dynamic analysis equation
Boundary conditions
Train load
Numerical results
A number of numerical simulations have been carried out to investigate the effects of metro vibration to the Bell Tower: (1) the distribution of PPV in REB; (2) the laws of P PV in different condition; (3) the effect of the shock absorption tracks.
The PPV of the REB
PPV of each condition
PPV of each condition
Condition | 1 | 4 | 2 | 5 | 3 | 6 |
---|---|---|---|---|---|---|
20 | D | D | A | A | A | C |
40 | C | D | D | A | B | B |
60 | C | C | C | C | A | A |
80 | D | D | D | D | B | A |
Distribution laws of PPV
Effect of the shock absorption measures
Condition 1 versus condition 4
Point | A (mm/s) | B (mm/s) | C (mm/s) | D (mm/s) |
---|---|---|---|---|
Condition 1 | 0.634 | 0.584 | 0.655 | 0.753 |
Condition 4 | 0.172 | 0.165 | 0.175 | 0.199 |
R (%) | 72.87 | 71.75 | 73.28 | 73.57 |
Condition 2 versus condition 5
Point | A (mm/s) | B (mm/s) | C (mm/s) | D (mm/s) |
---|---|---|---|---|
Condition 2 | 0.455 | 0.455 | 0.488 | 0.479 |
Condition 5 | 0.117 | 0.108 | 0.122 | 0.136 |
R (%) | 74.29 | 76.92 | 75 | 71.61 |
Condition 3 versus condition 6
Point | A (mm/s) | B (mm/s) | C (mm/s) | D (mm/s) |
---|---|---|---|---|
Condition 3 | 0.445 | 0.479 | 0.388 | 0.372 |
Condition 6 | 0.109 | 0.101 | 0.093 | 0.106 |
R (%) | 75.51 | 78.91 | 76.04 | 71.51 |
When there were no shock absorption measures, the PPV of the REB was 0.372–0.753 mm/s, beyond the standard value of 0.15–0.2 mm/s. In conditions 4–6 with shock absorption tracks, the PPV of the REB was 0.093–0.199 mm/s, which decreased to the allowable value range. When compared with the condition 1, the PPV of four points in condition 4 reduces by 71.75–73.57 %. Compared with condition 2, the PPV of four points in condition 5 reduces by 71.61–76.92 %. Compared with the condition 3, the PPV of four points in condition 6 reduces 71.51–78.91 %. Thus, the application of shock absorption tracks can largely weaken the influence of vibration on the Bell Tower.
On-site monitoring
On-site versus calculation results
Point | On-site (mm/s) | Model (mm/s) |
---|---|---|
A | 0.125 | 0.117 |
B | 0.133 | 0.108 |
C | 0.148 | 0.122 |
D | 0.153 | 0.136 |
Conclusions
- 1.
The vibration velocity of the REB does not increase monotonically with the increase of the train velocity; however, it is related to the train quantity, track category and running mode of train.
- 2.
When shock absorption tracks are not adopted, the PPV of the REB beyond the safety standard, which has the potential to induce severe damage to the Bell Tower. However, the PPV of the Bell Tower decreases greatly when vibration reduction track is adopted, and the PPV does not exceed the allowable maximum value, and the maximum decreases are 78.91 %. The whole predicted that the application of shock absorption tracks can weaken the influence of vibration on the Bell Tower to a great extent.
- 3.
After the verification on calculation result for the model in this article through on-site monitor, it is discovered that the model can quantitatively reflect the actual vibration response of the Bell Tower. Therefore, we will investigate the settlement of REB and the PPV of the wooden structure caused by vibration for the Bell Tower in the following study.
Declarations
Authors’ contributions
JXL established the analytical approach. FYN and KW performed the numerical analysis and wrote the manuscript. JXC, JLQ, HBF and ZNH compared the calculation results. All the authors read and approved the final manuscript.
Acknowledgements
This work is financially supported by the Special Fund for Basic Scientific Research of Central Colleges of Chang’an University (Grant No. 310821165011), the Integrated Innovation Project of Shaanxi Provincial Science and Technology Department (Grant No. 2015KTZDGY01-05-02) and the Brainstorm Project on Social Development of Shaanxi Provincial Science and Technology Department (Grant No. 2016SF-412).
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
- BS7385-2 (1993) Evaluation and measurement for vibration in buildings—part 1. In: Guide for measurement of vibrations and evaluation of their effects on buildingsGoogle Scholar
- Cao YM (2006) Vibration of high-rise buildings induced by running trains. Eng Mech 23(3):162–167Google Scholar
- Chen RC (2008) Study on effects on Bell Tower due to train-induced vibrations on metro in Xi’an. Ph.D. Thesis, Beijing Jiaotong UniversityGoogle Scholar
- Clemente P, Rinaldis D (1998) Protection of a monumental building against traffic induced vibrations. Soil Dyn Earthq Eng 17(5):289–296View ArticleGoogle Scholar
- Dawn TM, Stanworth CG (1979) Ground vibration from passing trains. J Sound Vib 66(2):355–362View ArticleGoogle Scholar
- Degrande G, De Roeck G (1998) Wave propagation in layered dry, saturated and unsaturated pore elastic media. Solid Struct 35(34–35):4753–4778View ArticleGoogle Scholar
- Degrande G, Lombaert G (2001) An efficient formulation of Krylov’s prediction model for train induced vibrations based on the dynamic reciprocity theorem. J Acoust Soc Am 110(3):1379–1390View ArticleGoogle Scholar
- DIN4150-3 (1999) Structural vibration Part3. In: Effect of vibration on structuresGoogle Scholar
- Ellis P (1987) Effect of traffic vibration on historic buildings. Sci Total Environ 59:37–45View ArticleGoogle Scholar
- GB/50894 (2003) Code for design of environment protection for machinery industry. China Machine Press, BeijingGoogle Scholar
- GB/T50452 (2008) Technical specification for protection of historic buildings against man-made vibration. China Machine Press, BeijingGoogle Scholar
- Han XH, Jia WL (2015) Study on the effect and mechanism of aerodynamic measures for the vortex-induced vibration of separate pairs of box girders in cable-stayed bridges. Shock Vib. doi:https://doi.org/10.1155/2015/792957 Google Scholar
- Han WS, Yuan SJ, Ma L (2014) Vibration of vehicle-bridge coupling system with measured correlated road surface roughness. Struct Eng Mech. doi:https://doi.org/10.12989/sem.2014.51.2.315 Google Scholar
- ISO 4866 (2010) Mechanical vibration and shock-vibration of fixed structures-guidelines for the measurement of vibrations and evaluation of their effects on structuresGoogle Scholar
- Jia YX, Guo M, Liu WN et al (2009) Dynamic effect of train induced vibration on historic buildings. J Beijing Jiaotong Univ 33(1):118–122Google Scholar
- Kurzweil G (1979) Ground borne noise and vibration from underground rail systems. J Sound Vib 66(3):363–370View ArticleGoogle Scholar
- Lai HP, Wang SY, Xie YL (2014) Experimental research on temperature field and structure performance under different lining water contents in road tunnel fire. Tunn Undergr Space Technol 43:327–335View ArticleGoogle Scholar
- Lai JX, Fan HB, Chen JX et al (2015a) Blasting vibration monitoring of under crossing railway tunnel using wireless sensor network. Int J Distrib Sens Netw, Article ID 703980, 7 pages. doi:https://doi.org/10.1155/2015/703980
- Lai JX, Qiu JL, Chen JX et al (2015b) New technology and experimental study on snow-melting heated pavement system in tunnel portal. Adv Mater Sci Eng, Article ID 706536, 11 pages. doi:https://doi.org/10.1155/2015/706536
- Lai JX, Mao S, Qiu JL et al (2016a) Investigation progresses and applications of fractional derivative model in geotechnical engineering. Math Probl Eng, Article ID 9183296, 15 pages. doi:https://doi.org/10.1155/2016/9183296
- Lai JX, Qiu JL, Feng ZH et al (2016b) Prediction of soil deformation in tunnelling using artificial neural networks. Comput Intell Neurosci, Article ID 6708183, 16 pages. doi:https://doi.org/10.1155/2016/6708183
- Lai JX, Wang KY, Qiu JL et al (2016c) Vibration response characteristics of the cross tunnel structure. Shock Vib, Article ID 9524206, 11 pages. http://www.hindawi.com/journals/sv/aip/9524206/. Accessed 28 June 2016
- Lang J (1971) Result of measurements on the control of structure-borne noise from subways. In: Seventh international congress on acoustics, Budapest, pp 421–424Google Scholar
- Li JC, Li HB, Ma GW et al (2013) Assessment of underground tunnel stability to adjacent tunnel explosion. Tunn Undergr Space Technol 35:227–234View ArticleGoogle Scholar
- Lombaert G, Degrande G, Kogut J (2006) The experimental validation of a numerical model for the prediction of railway induced vibrations. J Sound Vib 297(3–5):512–535View ArticleGoogle Scholar
- Luo G, Chen JX, Zhou XJ (2015) Effects of various factors on the VIV-induced fatigue damage in the cable of submerged floating tunnel. Pol Marit Res 4(88):76–83Google Scholar
- Ma M, Liu W, Qian CY, Deng GH, Li YD (2016) Study of the train-induced vibration Impact on a historic Bell Tower above two spatially overlapping metro lines. Soil Dyn Earthq Eng 81:58–74View ArticleGoogle Scholar
- Mata M (1971) Effects on buildings of vibrations caused by traffic. Build Sci 6:221–246View ArticleGoogle Scholar
- Meng ZB (2009) Analysis and assessment of the vibration responds traffic-induced of Xi’an Bell Tower, Ph.D. Thesis, Xi’an University of Architecture and TechnologyGoogle Scholar
- MIDAS Co. Ltd. MIDAS/NX manual. http://manual.midasuser.com/encommon/GTS%20NX/250/GTX.htm
- Real J (2014) Computational considerations of 3-D finite element method models of railway vibration prediction in ballasted tracks. J Vibroeng 16(4):1709–1722Google Scholar
- Real T, Zamorano C, Ribes F (2015) Train-induced vibration prediction in tunnels using 2D and 3D FEM models in time domain. Tunn Undergr Space Technol 49:376–383View ArticleGoogle Scholar
- Rueker W (1982) Dynamic behavior of rigid foundations of arbitrary shape on a half-space. Earthq Eng Struct Dyn 66(5):674–690Google Scholar
- Swiss Association of Standards (1992) Effects of vibration on construction, SN 640312, CH8008, ZurichGoogle Scholar
- Xie DW (2008) Evaluation report of vibration influence to historic and sensitive buildings along Beijing Subway Line8, Ph.D. Thesis, Beijing Jiaotong UniversityGoogle Scholar
- Ye F, Gou CF, Sun HD et al (2014) Model test study on effective ratio of segment transverse bending rigidity of shield tunnel. Tunn Undergr Space Technol 41:193–205View ArticleGoogle Scholar
- Ye M, Cao BX, Ren YP et al (2015) Field measurement, analysis and protection for the vibration of an ancient ruin induced by railway. J Vibroeng 17(4):2049–2065 Google Scholar
- Yu MH, Fang DP (2006) Advances in structural mechanics of Chinese ancient architectures. Adv Mech 36(1):43–64Google Scholar
- Zhao HB, Long Y, Ji C et al (2015) Study on the dynamic response of subway tunnel by viaduct collapsing vibration and the protective measures of reducing vibration. J Vibroeng 17(5):2433–2443Google Scholar