Missing:
Reducing railway induced ground-borne vibration by using trenches and buried soft barriers J. Jiang1, M. G. R. Toward1, A. Dijckmans2, D. J. Thompson1, G. Degrande2, G. Lombaert2 and J. Ryue3 1
Institute of Sound and Vibration Research University of Southampton, Southampton, SO17 1BJ, UK 2 KU Leuven, Department of Civil Engineering, Kasteelpark Arenberg 40, 3001 Leuven, Belgium 3
School of Naval Architecture and Ocean Engineering, University of Ulsan, Ulsan, 680-749, Korea
Summary To reduce railway induced low frequency vibration, two mitigation measures open trenches and buried soft wall barriers, have been studied in this paper by using coupled finite element-boundary element models. These models were developed at KU Leuven and ISVR, and have been cross-validated within the EU FP7 project RIVAS (Railway Induced Vibration Abatement Solutions). Variations in the width, depth, location of trench and properties of soft barrier material are considered under various soil conditions. Results show that in all ground conditions, the notional rectangular open trench performs better than the other constructions. The width of an open trench has little influence on its performance, whereas increasing the width of a filled trench reduces the stiffness of the material, improving the performance of the trench. Likewise, fill materials with lower Young’s modulus give higher insertion losses.
1
Introduction
Train-induced vibration can be a source of annoyance for line-side residents. For surface railways this vibration often has its highest amplitudes below 30 Hz. Most mitigation methods, such as resilient track systems, are effective at ‘high’ frequencies (typically above around 40 Hz). Open trenches and buried barriers, applied in the transmission path [1], are among the few mitigation methods that have the potential to reduce vibration at lower frequencies. For soil considered as a homogeneous half-space, an open rectangular trench with a depth greater than about one Rayleigh wavelength can lead to a ~12 dB reduction [2], while in-filled trenches are less effective than open trenches.
2
In practice, most sites cannot be simplified as homogeneous half-spaces, and often a relatively thin (and soft) upper layer of soil is present. Increased propagation can occur within this upper layer at frequencies where surface waves are effectively constrained. Analyses show that trenches in layered soils may be expected to have a greater effect than at homogeneous sites [3-6]. In practice, a deep (> 2m) rectangular open trench would be unfeasible to construct and maintain, and therefore trenches filled with soft material, lined by a retaining wall structure, or having sloping sides have been proposed [6]. The present study is part of the EU funded project RIVAS [7]. Here, results are presented of a parametric study of the effectiveness of open and soft-filled trenches for different soil conditions. In Sect. 2 the methodology used in this study is briefly introduced. In Sects. 3 and 4, parametric studies of open trenches and buried soft barriers are presented respectively. Conclusions are given in Sect.5.
2
Methodology
The geometry of a railway line with a trench adjacent to it is two-dimensional but the loading due to a train introduces a dependence on the third (longitudinal) dimension. So-called 2.5D numerical simulations have been carried out by project partners ISVR and KU Leuven using two different models [8, 9]. In these models, the profile of the track, ground and trench are modelled in 2D using a combination of finite elements and boundary elements (e.g. Fig. 1). By assuming homogeneity of the geometry and material properties in the track direction, the response along this third dimension is formulated in terms of the wavenumber. A Fourier transform is used to recover the three-dimensional response. This method is computationally more efficient than a full 3D approach. -9
Mobility [m/s/N]
2.5
32m
2 1.5 1 0.5 0
Fig. 1. Example sketch of track, soil layers and trench used in 2.5D model.
x 10
0
50 Frequency [Hz]
100
Fig. 2. Vertical insertion loss at 32 m from a vertical point force. KU Leuven results (solid lines) and ISVR results (circles).
Initially, independent analysis was conducted, by both project partners, for three benchmark cases with typical soil conditions: (i) a homogeneous half space, (ii) a soft upper layer over a stiffer soil (e.g. Fig. 1), and (iii) a stiffer upper layer over a softer sub-layer. In each case, transfer mobility and insertion loss were considered
3
for a single trench type. Fig. 2 shows results of one of the benchmark cases. In this case, a point force is applied directly on the soil at the centre of a homogeneous half-space with a rectangular open trench between the force and receiver locations. The track structure was not included in this case. The open trench is 0.5 m wide, 11.75 m deep and 5.6 m away from the force. The homogeneous half-space has a shear velocity Cs = 250 m/s, a Young’s modulus E = 3.61 x 108 Pa, a Poisson’s ratio ν = 0.485 and a density ρ = 1945 kg/m³. Both partners used boundary elements to simulate this case, although different approaches were used. KU Leuven use Green’s functions for a half-space, including layers if necessary, whereas ISVR use a full space Green’s function but need to mesh the ground surface to sufficient distance. Calculations were performed in the frequency range from 1 to 100 Hz, with every 1 Hz for KUL and every 5 Hz for ISVR. Vertical transfer mobility at 32 m from the point force is shown in Fig.2. At all frequencies, the results agree reasonably well. Subsequent to the benchmarking, ISVR undertook a parametric study aimed at investigating the effectiveness of open trenches and buried soft barriers (trench filled with soft material).
3
Open trench
Calculations are presented here for an open trench. A two-layer ground was considered. The upper layer has a shear velocity Cs = 150 m/s, a Young’s modulus E = 1.07 x 108 Pa, a Poisson’s ratio ν = 0.33 and a density ρ = 1800 kg/m³. The underlying half-space has a shear velocity Cs = 600 m/s, a Young’s modulus E = 1.92 x 109 Pa, a Poisson’s ratio ν = 0.33 and a density ρ = 2000 kg/m³. The depth of the trench is kept fixed at 6 m (unless otherwise stated). A line force is placed on top of upper layer. The parameters varied are the width of the trench, w, the distance from the force point, d, and the depth of the upper layer of soil, h1. 3.1 Width of trench Fig. 3 shows the insertion losses at 32 m away from the force for five different widths of open trench: 0.25, 0.75, 1.25, 2.25 and 3.25 m. In each case the nearest edge of the trench is 3 m away from the force point. From these results it is clear that the width of the open trench does not have much influence on the insertion loss. 3.2 Trench location Next, the location of the trench is varied. Four locations are studied: 1, 3, 5 and 7 m away from the force point. Fig. 4 shows the insertion losses at the same positions as before. From these results it is clear that the location of the trench also has little influence on the insertion loss. Although there are some differences, these do not appear systematic. Therefore, a fixed location, 3 m away from the force, was used in the remainder of the study to reduce the number of variables and associated computational cost.
4
Fig.3. Insertion loss for an open trench of different widths obtained at 32 m away from the force. Trench is 3 m away from the force, ground with h1 = 3 m.
Fig.4. Insertion loss for an open trench at different distances from the force point obtained at 32 m away from the force. Trench is 6 m deep, ground with h1 = 3 m.
3.3 Ground properties To investigate the influence of ground condition, five different cases are considered, with upper layer depths of 0, 3, 6, 9 and ∞ m. Fig. 5 shows the insertion losses obtained at 32 m away from the force using an open trench which is 6 m deep, 0.25 m wide and 3 m away from the force. As seen in Fig. 5, the 6 m deep open trench has no effect below 8 Hz for any of the grounds considered. For the stiff homogeneous half-space there is no benefit below 30 Hz. In this case the criterion that the depth should be at least 0.6 times the Rayleigh wavelength [1, 2] is only met above 60 Hz; in this frequency region an attenuation of over 10 dB is found. For the soft homogeneous half-space the criterion relating to the Rayleigh wavelength is met at about 15 Hz and the attenuation is greater than 10 dB for frequencies above this, increasing to around 30 dB by 30 Hz. For the layered ground with h1 = 9 m, the trench (6m deep) does not cut the upper layer completely. The insertion loss resembles that of the half-space of soft material although with a reduced performance at higher frequencies. For the layered ground with h1 = 6 m, the trench does cut the upper layer completely. Here, the insertion loss rises sharply between 10 and 20 Hz, which is the region where surface waves become localised in the upper layer. Consequently, between 10 and 30 Hz the benefit of the trench is greater than for the half-space of soft material. For a layered ground with h1 = 3 m, the 6 m deep trench cuts the upper layer and penetrates the underlying stiffer soil by a further 3 m. Here, the benefit of the trench increases sharply between 20 and 30 Hz which, again, is the range where waves start to propagate within the upper layer. In order to investigate this further, a case is considered for the ground with layer depth h1 = 3 m where the trench depth is reduced to 3 m, the same as the depth of upper layer. Results are shown in Fig. 6. For this case, for frequencies up to 40 Hz, a similar insertion loss is achieved as with the 6 m deep trench. At higher frequencies the deeper trench has some additional benefit. However, it
5
seems that for this soil there is little benefit in taking the trench any deeper than the upper surface layer into the stiffer soil.
Fig.5. Effect of ground condition on the insertion loss of an open trench obtained at 32 m away from the force. Trench is 3 m away from the force with 0.25 m width.
4
Fig.6. Effect of trench depth for a 3 m deep soil layer of an open trench obtained at 32 m away from the force. Trench is 3 m away from the force with 0.25 m width.
Buried soft barrier
4.1 Initial results In practice an open trench of depth 6 m will not be stable. One method to ensure its stability is to fill the trench with a relatively soft material, although this should be sufficiently stiff to sustain the confining pressure in the soil. In this section various notional materials are considered, as listed in Table 1. In Table 1, A1 and B1 are materials originally proposed in the project for use in a field test. To investigate further the influence of the material properties, the original properties given for A1 were varied by changing either the shear wave velocity or the Young’s modulus by a factor of 2. Table 1. Properties of fill materials
Material A
B
1 2 3 4 5 1
Shear wave speed (m/s) 330 330 330 150 600 50
Density (kg/m3) 80 40 160 387.2 24.2 133.4
Poisson’s ratio 0.3065 0.3065 0.3065 0.6035 0.3065 0.4999
Damping ratio 0.025 0.025 0.025 0.025 0.025 0
Young’s modulus (MPa) 22.76 11.38 45.53 22.76 22.76 1
Some results are shown in Fig. 7. This shows the insertion loss at 32 m away from the force for a 0.25 m wide, 6 m deep trench located 3 m away from the force point, and the upper layer depth h1=3m here. The performance of two fill materials (A1 and B1) and the open trench are compared. From the figure it can be seen that an open trench gives the best attenuation. Both materials have a much lower performance, with an attenuation limited to about 5-10 dB. Material B1 performs better than material A1, which is stiffer (see Table 1).
6
To illustrate the results further, Fig. 8 shows the results for each material in a single graph with the lines corresponding to the different ground types. From this it can be seen that the material A1 is not effective below 40 Hz for any ground, while material B1 is effective from 10 Hz for the soft homogeneous soil and the soil with 6 m or 9 m deep upper layer.
Fig.7. Insertion loss of trenches filled with different materials obtained at 32 m away from the force. Trench is 3 m away from the force point with 0.25 m width and 6 m depth. h1=3 m.
Fig.8. Insertion loss of trenches filled with different materials obtained at 32 m away from the force. Trench is 3 m away from the force point with 0.25 m width and 6 m depth.
4.2 Material variants Results are shown in Fig. 9 for the different variants of material group A as identified in Table 1. From this it appears that varying the Young’s modulus (Fig. 9a) has more effect than varying the shear wave speed (Fig. 9b), with a lower Young’s modulus being more beneficial. An ideal material therefore has a low Young’s modulus, although in practice the value that is achievable is limited by the ability of a material to sustain the confining pressure in the ground.
Fig.9. Insertion loss of trenches filled with material group A. Trench is 3 m away from the force point with 0.25 m width and 6 m depth; response is obtained at 32 m away from the force. h1=3 m.
Fig.10. Effect of trench width on insertion loss of using martial B1 to fill a trench 6 m deep 3 m away from the force. h1=3 m.
7
Fig. 10 shows the results of changing the width of the trench for the case of material B1 and h1=3 m. As seen from the figure, a wider trench gives a higher insertion loss at high frequencies when such soft materials are used, although the width does not affect the frequency at which attenuation commences. 4.3 Effect on train vibration To show the effect on train vibration, Fig. 11 shows an example of a predicted RMS velocity spectrum at 32 m during a train pass-by, obtained using the TGV model [10]. By applying the insertion losses from the previous sections as corrections to the predicted vibration spectra, estimates are given of the response for the open trench and trenches filled with materials A1 and B1. The vibration with no mitigation can be seen to rise sharply at about 10 Hz for this ground due to the layering. While the hypothetical open trench can reduce the level of vibration effectively, the more practical solutions have a modest but still significant effect. The improvement achieved commences at a frequency just above the first rise in vibration associated with the upper layer.
Fig.11. One-third octave band RMS spectra of vertical free field velocity for the ground with h1=6 m at 32 m from track. The trenches are 6 m deep and 3 m away from the force.
5
Conclusion
Mitigation applied in the transmission path as considered here is one of the few measures that has potential to reduce vibration at lower frequencies. Overall, under all ground conditions investigated in this paper, the notional rectangular open trench performs better than the other constructions. The width of an open trench has little influence on the performance, whereas increasing the width of a filled trench reduces the stiffness of the in-fill, improving the performance of the trench. Likewise, fill materials with lower Young’s modulus give higher insertion losses. The distance of the trench from the track is of secondary importance. It is also shown that when the soft soil layer is 6 m deep, a 6 m deep filled trench could provide benefit from around 10 Hz. At these low frequencies, trenches have the potential to provide significant mitigation of vibration. Field tests are proposed to confirm these conclusions.
8
Acknowledgments The research leading to these results has received funding from the European Union Seventh Framework Programme under grant agreement number 265754, project RIVAS (Railway Induced Vibration Abatement Solutions) [7].
References [1] Richart, F.E., Hall, J.R. and Woods, R.D.: Vibrations of soils and foundations, Prentice Hall, 1970. [2] Beskos, D.E., Daskupta, B., Vardoulakis, I.G.: Vibration isolation using open or in filled trenches, Journal of Computational Mechanics 1(1), 43-63 (1986). [3] May, T., Bolt, B.A.: The effectiveness of trenches in reducing seismic motion. Earthquake Engineering and Structural Dynamics, 10(2), 195-210, (1982). [4] Hung, H.H., Yang, Y.B. and Chang, D.W.: Wave barriers for the reduction of train-induced vibrations in soils. Journal of Geotechnical and Geo-environmental Eng., 130(12), 1283-1291 (2004). [5] Garcia-Bennett, A., Jones, C.J.C. and Thompson, D.J.: A numerical investigation of railway ground vibration mitigation using a trench in a layered soil. IWRN10, 2010, Nagahama (Japan). [6] Jones, C.J.C., Thompson, D.J. and Andreu-Medina, J.I.: Initial theoretical study of reducing surface-propagating vibration from trains using earthworks close to the track, EURODYN, 2011, Leuven (Belgium). [7] http://www.rivas-project.eu [8] Nilsson, C.-M. and Jones, C.J.C.: Theory manual for WANDS 2.1, ISVR Technical Memorandum No. 975. University of Southampton, 2007. [9] Lombaert, G., Degrande, G. and Clouteau, D.: Numerical modelling of free field traffic induced vibrations. Soil Dynamics and Earthquake Engineering, 19(7), 473–488 (2000). [10] Sheng, X., Jones, C.J.C. and Thompson, D.J.: TGV - A computer program for train-induced ground vibration. ISVR Technical Memorandum No. 878, University of Southampton, December 2001.
