Vibration mitigation for metro line on soft clay

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1 Bergen, Norway BNAM May - Vibration mitigation for metro line on soft clay Karin Norén-Cosgriff and Christian Madshus Norwegian Geotechnical Institute (NGI), Sognsveien 7, 7, NO-86 Oslo, Norway, Arild Brekke Brekke & Strand Akustikk AS, Postboks 4, Hoff NO-8 OSLO, Norway, Soft clay ground conditions regularly lead to annoying vibration in buildings along railed traffic lines. This paper will present results from an actual case where an excising metro line is upgraded to modern standard. Prediction based on empirical models concluded that countermeasures would be needed to avoid unacceptable indoor low frequency vibration in neighbouring communities. Norwegian vibration acceptance criteria are formulated in a national standard which is based on extensive sociological investigations on human reaction to vibration in everyday living situations. Lime-cement pillars under the track were found to be the most beneficial countermeasure under the present conditions and would substantially reduce vibration in the low frequency range. Such pillars also have the geotechnical side benefit of preventing settlements. However, introducing lime-cement pillars which constitutes a much stiffer element than the clay may have the disadvantage of increasing the higher frequency audible ground borne or structure borne noise level. The paper will describe how dynamic finite element analyses is used to find an optimum solution based on a combination of lime cement pillars and under-ballast mats to meet acceptance criteria for both low frequency whole body vibration and audible structure borne noise. Introduction Trains and trams generate vibrations as they pass over local variations along their track. These vibrations propagate from the track through sleepers, ballast and foundation to the ground and are subsequently transmitted to the structure of nearby buildings. The low frequency part of the vibrations can be felt by occupants as whole body vibrations and shaking of the building structure and the more high frequency vibrations can be radiated from the building surfaces as audible structure borne noise. As part of the planning work for upgrading the existing metro line Kolsåsbanen to modern standard, calculations of low frequency vibrations and structure borne noise were performed. The calculations showed low frequency vibration velocity levels higher than the limit value for parts of the section under consideration. A solution with lime cement column soil stabilization beneath track was therefore suggested. However, experience gained from other sites where lime cement column stabilization has been introduced show that this low frequency vibration countermeasure may give rise to higher structure borne noise levels. Since structure borne noise is of as much concern as low frequency vibrations for nearby buildings, the project wished to combine measures against low frequency vibrations, lime cement column stabilization, with measures against structure borne noise based on subballast mats. Since there is limited experience with such combinations it was decided to perform a dynamic FE-analysis to verify the effect of the solution. Another uncertain factor which needed to be verified is how lime cement column stabilization works when the distance from track foundation to bedrock is short, e.g. typically m, as is the case for part of Kolsåsbanen.

2 Vibration limit value in Norway Norwegian vibration acceptance criteria from land based transport are formulated in a national standard NS 876 []. The standard gives limits of acceptable vibration velocity in four classes where class C corresponds to the recommended limit value for vibration in new residential buildings and in connection with the planning and building of new or upgraded transport infrastructure. The recommended limit for Class C is v w,95 =. mm/s where v w,95 is the statistical maximum weighted vibration value, i.e. the vibration value that 5 % of the train passages are expected to exceed. Frequency weighting is performed according to ISO 84 []. Description of the calculation model The analysis was performed using the FE-program Comsol Multiphysics. Characteristics of materials have been derived from geotechnical site investigations performed by the geotechnical consultant of the project and laboratory tests of typical filling materials performed in an earlier project by NGI for the Norwegian Rail Administration. The FE-model is -dimensional, describing a track cross-section representing a typical m thick segment of the track. In a -D model the vibrations will not decline with distance as much as in reality. However, since the aim of the study was to compare different vibration mitigation measures and not to determine absolute vibration values use of a -D model was found to be adequate. The model length is 58 m with the tracks centered in the middle of the model. The calculations have been performed in the frequency domain. The element type is quadratic (second order) Lagrange elements with a maximum element size of.4 m for frequencies up to Hz and.5 m for frequencies from to 6 Hz. With typical shear wave velocities in the clay between 8- m/s this is considered to be appropriate. The models have transmitting boundaries in order to allow the vibration energy to spread out of the model and prevent it from reflecting back from the boundaries.. Geometry The following rail, foundation mitigation solution has been modeled as the basic case, listed from above top of rail and downwards: -Unsprung mass of wheel shaft -Rail -Sleeper -.5 m ballast -.85 m subballast mat -. m gravel -.6 m XPS -. m gravel -. m quarry dust with lime cement columns -. m dry crust with lime cement columns - m silty clay with lime cement columns -6. m quick clay with lime cement columns -/5/8 m quick clay -Bedrock The lime cement columns have a typical shear strength of 65 kpa, a diameter of 6 mm and centre to centre distance of.5 m. Calculations have been performed for the following models:. Basic model as described above, see Figure. The lime cement columns have a row distance of. m in the track longitudinal direction.. Reference solution. As the basis model but without lime cement columns.. As the basis model but without subballast mats. 4. As the basis model but with varying configuration and length of the lime cement columns (6 m and m), see Figure. The long lime cement columns overlap in the track longitudinal direction. 5. As model 4 but without subballast mats.

3 Figure. Basic model. Figure. Model 4.. Material parameters Sub-surface surveys with sample taking has been performed in two positions along the section in question. Material parameters to the model have been derived from survey results and laboratory tests. Material parameters used in the models are shown in Tabel. Tabel. Material parameters Material E mod ) (MPa) ν ρ (kg/m ) η = /Q Rail 5E.8 49 (kg/m). Concrete sleeper 5E.. Ballast 5-8 ).5 5. ) Subballast mat. ). 9. Gravel/ quarry dust -9 ) ) XPS. 8. Dry crust Silty clay 8-66 ) Quick clay 8-8 ) Lime cement column in clay.. ) Varies with depth from surface, related to shear strength. ) Based on experience from laboratory tests performed for Norwegian Rail Administration. ) Corresponds to k dyn =.5 N/mm and a subballast mat thickness of 85 mm.

4 . Load from mass of wheel shaft The load of the unsprung mass of the wheel shaft has been introduced in the models as increased rail density for one of the two tracks. As mentioned before the -D model does assume a m thick cross section in the track longitudinal direction. Therefore this segment has been given an additional load by the mass of two wheel shafts and this mass has been distributed over the two rails..4 Excitation of model by a dynamic force The model has been excited by a vertical dynamic unity force over the entire frequency range of interest. The force has been applied synchronously on both rails of one of the tracks at the mid frequencies of the /-octave frequency bands from. to 6 Hz. 4 Calculation results The results are shown as amplitudes of normalized vertical vibration velocity. In order to reduce the influences of local phenomena, which can be essential in the dry crust especially for the higher frequencies, we have from the FEM output determined the average value over the depth of the dry crust and also the average value over a 6 m long section along the surface with its closest point at m distance from centre line between the two tracks. This has been done in order to give a realistic picture of the vibrations a building foundation close to the line will be exposed to. The results for all frequencies are shown in Figure - Figure 5. The plots to the left compare the various mitigation measures shown as the ratio between calculated vibration velocity for the model describing the mitigation measure in question and calculated vibration velocity with the reference model (model nr ). A ratio equal to. corresponds to no effect of the mitigation measure. A ratio higher than. corresponds to increased vibration levels as result of the mitigation measure, i.e. a negative effect. The plots to the right presents calculated vertical normalized vibration velocity at the different frequencies as the models are excited by a unity force over the entire analyzed frequency range. The values are not comparable to vibration values seen during a real train pass by since all frequencies have been excited with an equal unity force in the FE-model. What the figures show is at which frequencies the ground response (including mitigation measures) to excitation from trains is highest. The vibration velocity has been further normalized by dividing the results for all models with the highest vibration velocity for the reference model (model )..5.5 Kolsåsbanen..5 m from ground to bedrock KC m, subballast mats/reference KC /6m, subballast mats/reference Normalized vertical vibration velocity.5.5 Kolsåsbanen..5 m from ground to bedrock KC m, subballast mats KC /6m, subballast mats Reference Figure. Case with.5 meter from track foundation to bedrock. Comparison of lime cement column stabilization (denoted KC in the figure legends) with the reference solution without mitigation measures. Dashed lines shows model, dotted lines model 4 and solid lines model (reference model).

5 .5.5 Kolsåsbanen. 6 m from ground to bedrock. KC m, subballast mats/reference KC /6m, subballast mats/reference Normalized vertical vibration velocity.5.5 Kolsåsbanen. 6 m from ground to bedrock. KC m, subballast mats KC /6m, subballast mats Reference Figure 4. Case with 6 meter from track foundation to bedrock. Comparison of lime cement column stabilization (denoted KC in the figure legends) with the reference solution without mitigation measures. Dashed lines show model, dotted lines model 4 and solid lines model..5.5 Kolsåsbanen. 9 m from ground to bedrock. KC m, subballast mats/reference KC /6m, subballast mats/reference Normalized vertical vibration velocity.5.5 Kolsåsbanen. 9 m from ground to bedrock. KC m, subballast mats KC /6m, subballast mats Reference Figure 5. Case with 9 meter from track foundation to bedrock. Comparison of lime cement column stabilization (denoted KC in the figure legends) with the reference solution without mitigation measures. Dashed lines show model, dotted lines model 4 and solid lines model. 5 Comments to results and conclusions Vibration measurements performed along Kolsåsbanen before the upgrading work started shows that most vibration velocity spectra has a first peak in the frequency range between 8 and Hz, see Figure 6.

6 Kolsåsbanen. Results from measurement in buildings at different distances from centre line between tracks Vibration velocity [mm/s] - - 9m distance 6m distance 6m distance 6m distance m distance Figure 6. Measured vibration velocity in nearby buildings before upgrading Kolsåsbanen. The performed FEM calculations show that lime column stabilization shifts the first resonance of the ground to a higher frequency. For the longer distances from track foundation to bedrock (6 m and 9 m) this is not of concern since the resonance frequency will still be below 5 Hz and hence not in the region for major vibration energy from the passing trains, see Figure 6. For the situation where the distance from track foundation to bedrock is short (.5 m) the calculations show that the first resonance is shifted from about 4-5 Hz to 8 Hz and hence into the frequency region of excitation from trains. However, the calculations do also show that by varying the configuration and length of the lime cement columns the frequency range where the vibrations are amplified can be reduced. Further, the FEM calculations show that subballast mats will reduce the vibrations at higher frequencies which can cause structure borne noise. Note however that use of subballast mats will introduce a new peak in the vibration spectra caused by the resonance of the composed system: mass of track and ballast on the spring that the subballast mats constitute. This peak can be seen around Hz in Figure 7 below. The calculations do also show that by varying configuration and length of the lime cement columns this peak can be reduced, see Figure -Figure 5. Kolsåsbanen..5 m from ground to bedrock Kolsåsbanen..5 m from ground to bedrock KC m, subballast mats/reference KC m/reference KC /6m, subballast mats/reference KC /6m/Reference Figure 7. Comparison of solution with lime cement columns and subballast mats (dashed line), lime cement columns without subballast mats (dotted line) and the reference solution (model ). Figure to the left show situation with m long lime cement columns and the figure to the right situation with varying length and configuration of columns.

7 Acknowledgments We thank the project organization at Dr Ing Aas Jakobsen and the client KTP for founding the study and giving permission to publish results. References [] NS 876.E Vibration and shock Measurement of vibration in buildings from landbased transport and guidance to evaluation of its effects on human beings. [] ISO 84 Human response to vibration -- Measuring instrumentation.

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