Traffic-induced building vibrations in Montréal - National Research ...

Hunaidi and Tremblay 749Fig. 9. Vertical response and coherence functions obtained with thedrop weight device in summer and spring for the ground in front ofbuilding at site 9.measurements in summer and fall. Site response functions obtainedwith the drop weight device were used as an additionalsource of information on the effect of the frost layer and variationin ground water table level.Frozen soil samples were obtained at a depth of about 0.6to 0.8 m in front of the building at the time of winter tests.Dynamic shear moduli and damping ratios of the soil sampleswhile frozen and after they were allowed to thaw were determinedfrom resonant column tests (Al-Hunaidi et al. 1996b).Fall versus winter vibration levelsVibration levels and ratios obtained during the fall and winterare listed in Tables 7 and 8, respectively. Vibration levelsmeasured in winter were about one half those measured in thefall. This is in agreement with the results reported by Sutherland(1950) for similar vibration measurements in Winnipeg.Ratios of vibrations measured by Sutherland (1950) were generallyhigher than those found in this study. This is believed tobe due to the depth of the frost layer during Sutherland’s measurementsbeing 0.9 m, compared with 1.1 m in this study, and(or) due to the dominant frequency at the site of Sutherland’smeasurements in Winnipeg being about 7.5 Hz, comparedwith 13 Hz in this study.Vertical response and coherence functions obtained withten load impacts using the drop weight device during summerand winter are shown in Fig. 7 for the ground measurementlocations. The coherence is close to 1 over the frequency rangethat is of interest regarding traffic vibrations, i.e., 8–20 Hz,thus indicating a high signal-to-noise ratio. In this frequencyrange, it can be seen that the response function obtained insummer is higher than that obtained in the winter. This is consistentwith the results obtained using the test bus. For frequencieshigher than about 40 Hz, however, the response functionobtained in winter has higher magnitudes than that obtained inthe summer. This seems to corroborate the observation mentionedearlier that subway-induced building vibrations inToronto are higher in winter than in summer, as the dominantfrequency of these vibrations is between 40 and 50 Hz.Results of resonant column tests on frozen and unfrozensoil samples taken at the site used in this study show that thestiffness of soil samples while frozen is about 30–50 times thestiffness after they were allowed to thaw. In addition, thedamping ratio obtained with frozen samples was roughly twotimes that obtained with thawed samples. Apparently the increasein stiffness and damping of the top part of the soil ledto smaller vibrations (i.e., smaller dynamic deformations) forfrequencies up to 30 Hz. On the other hand, the increase instiffness of the top frozen part of the soil has led to a majorshift for the dominant frequency in the site response.Finally, it was observed that the range of predominantfrequencies of vibrations measured in the fall was widerthan the frequency range of vibrations measured in thewinter, i.e., the former had higher levels at higher frequencies(e.g., 20–30 Hz). This can be seen, for example,from the narrow-band spectra shown in Fig. 8. The followingmay provide the reason. Attenuation of vibrations in soils, dueto material damping only, along the direction of wave propagation,can be expressed as follows (Richart et al. 1970):[1] A 2 = A 1 exp[–α(r 2 – r 1 )]where A 1 and A 2 are vibration amplitudes at distances r 1 and r 2from the vibration source, respectively; α is the coefficient ofattenuation which is related to the soil damping ratio and frequencyof vibration by[2] α= 2πfDcwhere f is frequency, D is damping ratio, and c is wave propagationvelocity. Because of the exponent in the above attenuationrelationship, a higher damping ratio in winter will lead togreater attenuation at high frequencies than at low ones.Spring versus fall vibration levelsVibration levels and ratios obtained during the spring and fallare listed in Tables 7 and 9, respectively. Vibration levelsmeasured during the thaw period in spring were only slightlyhigher than those measured in the fall. The highest ratio of 1.33occurred in the second storey.The increase in vibration levels in the spring is not as highas expected, considering that more vibration complaints areusually made during this season. Possibly, the water table levelat the time of vibration measurements made in the spring wasnot as high as usual during the snow thaw period. On the otherhand, it might be speculated that the higher number ofcomplaints in the spring is in fact due to the significantly lowervibration levels during winter. The “quiet” winter period mightbe leading to a loss of familiarity with vibration and subsequentlyleading to a decrease in tolerance as vibration levelsincrease again in the spring.Vertical response and coherence functions obtained withthe drop weight device in summer and spring are shown inFig. 9 for the ground measurement locations. The coherence© 1997 NRC Canada