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
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
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