Linear Collider Collaboration Tech Notes

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1 LCC-0123 Rev. 3 August 2003 Rev. June 2004 Linear Collider Collaboration Tech Notes Design Guideline Summary Based on the GEOVISION Report of Stanford Linear Accelerator Tunnel Vibration Measurements Parsons Pasadena, CA For Stanford Linear Accelerator Center Stanford University Stanford, CA Abstract: This summary report is provided in order to suggest how the measurement data from the GEOVision report might be used by SLAC for their proposed Next Linear Collider facility. See the referenced report Stanford Linear Accelerator Tunnel Vibration Measurements, Conducted at MTA Universal Subway Station, North Hollywood, California, by GEOVision dated July 28, The following discussions are an attempt to determine an upper bound methodology that can be used for design purposes. The data in the GEOVision report remains as a source of actual measurements and can always be used directly. However, it is very evident that there are many different phenomena influencing the transmission of the vibratory waves through the concrete tunnels and the rock materials. This report will suggest some upper bound curves that can be used for design and also discuss some of the possible reasons for the variability in the measured data. In general the most important cause of the variability in the data is the result of the multiple paths that the vibratory waves travel. That is, the waves can travel longitudinally in the tunnels either as compression waves or beam bending waves. The vibrations in the tunnel can travel around the circumference of the tunnels as well. It is possible that the vibrations travel out of the tunnel into the surrounding rock material and then re-enter the tunnels at some greater distance. This summary report is divided into three sections. These sections are: Transmissibility From Tunnel A To Tunnel B; Transmissibility Along Tunnel A; and Transmissibility From Ground Surface To Tunnel A.

2 DESIGN GUIDELINE SUMMARY Based On The GEOVISION REPORT OF MTA UNIVERSAL SUBWAY STATION, NORTH HOLLYWOOD, CALIFORNIA TUNNEL VIBRATION MEASUREMENTS Revision 3 By Parsons Pasadena, California May 5, 2004

3 INTRODUCTION This summary report is provided in order to suggest how the measurement data from the GEOVision report might be used by SLAC for their proposed Next Linear Collider facility. See the referenced report Stanford Linear Accelerator Tunnel Vibration Measurements, Conducted at MTA Universal Subway Station, North Hollywood, California, by GEOVision dated July 28, The following discussions are an attempt to determine an upper bound methodology that can be used for design purposes. The data in the GEOVision report remains as a source of actual measurements and can always be used directly. However, it is very evident that there are many different phenomena influencing the transmission of the vibratory waves through the concrete tunnels and the rock materials. This report will suggest some upper bound curves that can be used for design and also discuss some of the possible reasons for the variability in the measured data. In general the most important cause of the variability in the data is the result of the multiple paths that the vibratory waves travel. That is, the waves can travel longitudinally in the tunnels either as compression waves or beam bending waves. The vibrations in the tunnel can travel around the circumference of the tunnels as well. It is possible that the vibrations travel out of the tunnel into the surrounding rock material and then re-enter the tunnels at some greater distance. This summary report is divided into three sections. These sections are: TRANSMISSIBILITY FROM TUNNEL A TO TUNNEL B; TRANSMISSIBILITY ALONG TUNNEL A; and TRANSMISSIBILITY FROM GROUND SURFACE TO TUNNEL A. The most unique data obtained by GEOVision in these measurements is contained in the first section describing the results of the vibration transmissions from Tunnel A to the adjacent Tunnel B. The tunnels are separated by 39 feet, centerline to centerline. The tunnels are concrete lined and are approximately 20 feet in diameter. The tunnels are approximately 90 feet below the surface of the ground to the elevation of the track bed in the tunnels, and the depth below ground increases considerably along the tunnel measurement locations. Special thanks are given to Dr. Robert Nigbor, Professor at the University of Southern California, and Fred Asiri and Andrei Seryi at Stanford/SLAC for their assistance in preparing and reviewing this report. 2

4 TRANSMISSIBILITY FROM TUNNEL A TO TUNNEL B From Test 4 in the GEOVision report, a simple enveloping curve fit of the transmissibility curves shown in Figure 10 of the GEOVision report results in the following upper bounds to the measured data for transmission from tunnel A to tunnel B at 0 feet, 100 feet, and 300 feet along tunnel B from the source in tunnel A. These straight-line limits are shown in the following graph: Attenuation (Response in Tunnel B/Source in Tunnel A) FIG10-REV-2.PDW 0 Feet 100 Feet 300 Feet Frequency (Hz) The following equations can be used to describe these upper bounds for the attenuation functions in terms of the frequency, f, in Hz. Note, T AB00 refers to the attenuation between the source in tunnel A and the measurement in tunnel B, directly across from the source in tunnel A; T AB100 refers to the attenuation between the source in tunnel A and the measurement in tunnel B, 100 feet along tunnel B from the source in tunnel A; T AB300 refers to the attenuation between the source in tunnel A and the measurement in tunnel B, 300 feet along tunnel B from the source in tunnel A. T AB00 = exp[-(1.527x10-2 )( f )] T AB100 = exp[-(3.258x10-2 )( f ) 0.696] T AB300 = exp[-(3.586x10-2 )( f ) 2.580] 3

5 For reference, Figure 10 from the GEOVision report is reprinted in the following graph: Reprint of Figure 10, from the GEOVision Report, Revision 4 The straight-line curves in the semi-log plots are essentially upper bounds of the measured attenuation data. The straight-line curves are plotted from 10 Hz to 120 Hz since the data is not reliable below 3 Hz and there is considerable scatter in the data between 3 Hz and 10 Hz. It is also interesting to note that the attenuation in Tunnel A at 48 feet is similar to the attenuation in Tunnel B at 0 feet (actually 39 feet apart, centerline to centerline). Also the attenuation at 95 feet in tunnel A is similar to the attenuation at 100 feet in tunnel B. This indicates that the two tunnels are experiencing similar vibration levels at similar distances from the vibratory source. These comparisons also give an indication to the variability that might be expected. An alternative to using the straight-line curves for estimating the transmissibility between the two tunnels would be to use the GEOVision plots directly. This may be more representative in the frequency range from 3 Hz to 25 Hz. In this frequency range there is a tendency for the attenuation to decrease with decreasing frequency for the tunnel B transmissibility at 0 feet. This phenomenon may be related to the difficulty in transmitting and developing very long wavelength vibrations near the vibration source. It is expected that the shear wave velocity of the ground is about 3,000 to 4,000 feet per second and the shear wave velocity of concrete is expected to be similar. Thus at 3 Hz 4

6 the wavelength would be 1000 feet and at 30 Hz the wavelength would be 100 feet. Since the tunnels are only 39 feet apart, it is not surprising that long wavelengths cannot be represented by simple transmissibility curves. Effect of Changes in Shear Wave Velocity The following discussion attempts to formulate an intuitive prediction for the effect of changing the shear wave velocity of the rock in which the tunnels may be located. The equations proposed in this discussion require further analytical investigation and/or testing to validate their accuracy, but they represent a first step in developing an insight into the possible effect of the change of rock properties associated with different tunnel sites. Note that the relationship between frequency, wave velocity, and wavelength is: f = Vs/L Where f = Frequency (Hz); Vs = Shear Wave Velocity (Feet/Second); L = Wave Length (Feet) Although no tunnel vibrations were measured using different shear wave velocity media in these tests, it is likely that longer wavelength conditions produced by higher shear wave velocities would be similar to shifting the frequency so that the effective wavelength was maintained. L 1 = L 2, Vs 1 /f 1 = Vs 2 /f 2, or f 1 =f 2 [Vs 1 /Vs 2 ] Thus the straight-line curves in the semi-log plots might become as follows, where Vs 2 and f 2 represent the new site conditions relative to the 3000 feet/second shear wave velocity of the MTA tunnel rock: T B00 = exp[-(1.527x10-2 )(3000/Vs)( f )] T B100 = exp[-(3.258x10-2 )(3000/Vs)( f ) 0.696] T B300 = exp[-(3.586x10-2 )(3000/Vs)( f ) 2.580] 5

7 A comparison of the transmissibility functions is made in the following figure for Vs equal to 3000 feet/second and Vs = 6000 feet/second. Attenuation (Response in Tunnel B/Source in Tunnel A) FIG10A-REV-2.PDW 0 Feet 100 Feet 300 Feet Frequency (Hz) One would expect that higher shear wave velocities would result in flatter transmissibility (decreased slope) functions as shown in the above figure, but it is uncertain whether this effect is as dramatic as is estimated in the proposed equations. Further analysis and/or testing is needed to determine whether this intuitive solution to the effect of variations of shear wave velocity are correct. 6

8 Mobility Function Estimate The mobility function for Test 4 could not be plotted since the transducer on the hammer mechanism failed. However, the mobility function at the 20-foot location for Test 3 should be essentially identical to the mobility function for the 17-foot location in Test 4. From Test 3 in the GEOVision report, a simple curve fit of the mobility curve as shown in Figure 9 of the GEOVision report results in the following upper bounds to the data for the mobility function at 20 feet from the vibration source. This straight-line limit is shown in the following graph: FIG-9-REV-1.PDW Mobility [Velocity/Force - (cm/sec)/n] Feet From Source Frequency (Hz) The following equation can be used to describe the upper bound of the straight-line mobility curve shown above. The mobility function 20 feet from the source in tunnel A is denoted as M AA00 refers to the mobility function of the source in tunnel A and the measurement 20 feet away in tunnel A. M AA00 = exp[+(2.682x10-2 )( f ) ] The mobility plots for Test 3 are reprinted from the GEOVision report in the following graph: 7

9 Reprint of Figure 9, from the GEOVision Report, Revision 4 Therefore, the above graphs could be used to determine the transmission from vibratory sources in adjacent tunnels. The first step would be to determine the source vibration velocity from the mobility curve at a given force and frequency at the 20 feet from the source. Then the transmission of vibrations from the source tunnel to the adjacent tunnel would be determined using the transmissibility graph at the given frequency. Note that it is assumed that the data measured from the frequency content of an impulsive hammer test is applicable to steady-state vibratory sources. This assumption may require further verification. 8

10 TRANSMISSIBILITY ALONG TUNNEL A From Test 3 in the GEOVision report, a simple enveloping curve fit of the transmissibility curves shown in Figure 8 of the GEOVision report results in the following upper bounds to the data for transmission from the source in tunnel A to the instrumentation at various locations along tunnel A. These straight-line limits are shown in the following graph: Attenuation (Response in Tunnel A/Source in Tunnel A) FIG-8-REV-1.PDW 100 Feet 200 Feet 300 Feet 500 Feet Frequency (Hz) The following equations can be used to describe these upper bounds for the attenuation functions in terms of the frequency, f, in Hz. Note, T AA100 refers to the attenuation between the source in tunnel A and the measurement 100 feet along tunnel A; T AA200 refers to the attenuation between the source in tunnel A and the measurement 200 feet along tunnel A; T AA300 refers to the attenuation between the source in tunnel A and the measurement 300 feet along tunnel A; T AA500 refers to the attenuation between the source in tunnel A and the measurement 500 feet along tunnel A; T AA100 = exp[-(2.054x10-2 )( f ) 0.656] T AA200 = exp[-(3.664x10-2 )( f ) 1.230] T AA300 = exp[-(3.170x10-2 )( f ) 2.538] T AA500 = exp[-(2.754x10-2 )( f ) 3.520] 9

11 For reference, Figure 8 from the GEOVision report is reprinted in the following graph: Reprint of Figure 8, from the GEOVision Report, Revision 4 The straight-line curves in the semi-log plots are essentially upper bounds of the measured attenuation data. The straight-line curves are plotted from 10 Hz to 120 Hz since the data is not reliable below 3 Hz and there is considerable variability in the plots between 3 Hz and 10 Hz. An alternative to using the straight-line curves for estimating the transmissibility along the tunnels would be to use the GEOVision plots directly. This may be more representative in the frequency range from 3 Hz to 10 Hz 10

12 Mobility Function From Test 3 in the GEOVision report, a simple curve fit of the mobility curve as shown in Figure 9 of the GEOVision report results in the following upper bounds to the data for the mobility at 20 feet. This straight-line limit is shown in the following graph: FIG-9-REV-1.PDW Mobility [Velocity/Force - (cm/sec)/n] Feet From Source Frequency (Hz) The following equation can be used to describe the upper bound of the straight-line mobility curve shown above. The mobility function 20 feet from the source in tunnel A is denoted as M AA00 refers to the mobility function of the source in tunnel A and the measurement 20 feet away in tunnel A. M AA00 = exp[+(2.682x10-2 )( f ) ] 11

The mobility plots for Test 3 are reprinted from Figure 9 in the GEOVision report in the following graph: Reprint of Figure 9, from the GEOVision Report Therefore, the above graphs could be used to

13 The mobility plots for Test 3 are reprinted from Figure 9 in the GEOVision report in the following graph: Reprint of Figure 9, from the GEOVision Report Therefore, the above graphs could be used to determine the transmission from vibratory sources in the same tunnel. The first step would be to determine the source vibration velocity from the mobility curve at a given force and frequency. Then the transmission of vibrations from the source to locations along the tunnel would be determined using the transmissibility graph at the given frequency. Note that it is assumed that the data measured from the frequency content of an impulsive hammer test is applicable to steady-state vibratory sources. This assumption may require further verification. 12

14 TRANSMISSIBILITY FROM GROUND SURFACE TO TUNNEL A From Test 2 in the GEOVision report, a simple enveloping curve fit of the transmissibility curves shown in Figure 6 of the GEOVision report results in the following upper bounds to the data for transmission from the source at the ground surface to the instrumentation at various locations along tunnel A. These straight-line limits are shown in the following graph: Attenuation (Response in Tunnel Surface) FIG6.PDW 0 Feet 100 Feet 200 Feet Frequency (Hz) The following equations can be used to describe these upper bounds for the attenuation functions in terms of the frequency, f, in Hz. Note, T SA00 refers to the attenuation between the source at the surface and the measurement 0 feet in tunnel A, directly under the source; T SA100 refers to the attenuation between the source at the surface and the measurement 100 feet along tunnel A; T SA300 refers to the attenuation between the source at the surface and the measurement 200 feet along tunnel A; T SA00 = exp[-(4.567x10-2 )( f ) 2.120] T SA100 = exp[-(4.674x10-2 )( f ) 2.813] T SA200 = exp[-(5.757x10-2 )( f ) 3.101] 13

15 For reference, Figure 6 from the GEOVision report is reprinted in the following graph: Mobility Function Reprint of Figure 6, from the GEOVision Report From Test 2 in the GEOVision report, a simple curve fit of the mobility curve could not be made due to the extreme curvature in the measured mobility curve. It is likely that the extreme curvature of the mobility curve at the surface (20 feet from the source) is due to the soft soil layers near the surface of the ground. Thus it is recommended that the rather smooth, but curved, measured mobility curve be used to determine the surface ground motions without attempting to smooth or bound the measured data. 14

16 Reprint of Figure 7, from the GEOVision Report Therefore, the above graphs could be used to determine the transmission from vibratory sources at the surface to the tunnel. The first step would be to determine the source vibration velocity from the measured mobility curve, 20 feet from the source, at a given force and frequency. Then the transmission of vibrations from the source to locations along the tunnel would be determined using the transmissibility graph at the given frequency. Note that it is assumed that the data measured from the frequency content of an impulsive hammer test is applicable to steady-state vibratory sources. This assumption may require further verification. 15

17 APPENDIX FULL SIZE PLOTS OF FIGURES 16

18 Attenuation (Response in Tunnel B/Source in Tunnel A) FIG10-REV-2.PDW 0 Feet 100 Feet 300 Feet Frequency (Hz) 17

19 Attenuation (Response in Tunnel B/Source in Tunnel A) FIG10A-REV-2.PDW 0 Feet 100 Feet 300 Feet Frequency (Hz) 18

20 19

21 FIG-9-REV-1.PDW Mobility [Velocity/Force - (cm/sec)/n] Feet From Source Frequency (Hz) 20

22 21

23 Attenuation (Response in Tunnel A/Source in Tunnel A) FIG-8-REV-1.PDW 100 Feet 200 Feet 300 Feet 500 Feet Frequency (Hz) 22

24 23

25 Attenuation (Response in Tunnel Surface) FIG6.PDW 0 Feet 100 Feet 200 Feet Frequency (Hz)

26 25

27 26

An Overview of Ground Motion and Vibration Studies

An Overview of Ground Motion and Vibration Studies 1 Acknowledgements SLAC Accelerator Physics: Andrei Seryi, Fredric Le Pimpec SLAC Conventional Facility: Clay Corvin, Javier Sevilla, Jerry Aarons Colin