Effect of ground borne vibrations on underground pipelines

Transcription

1 Effect of ground borne vibrations on underground pipelines N.. Thusyanthan, S. L. D. Chin & S. P. G. Madabhushi Department of Engineering, University of Cambridge, United Kingdom. Proceedings of the nternational Conference on Physical Modelling in Geotechnics 26, Hong Kong. Vibrations produced on the ground surface by engineering construction processes can damage underground structures. At present, there is little knowledge on the level of surface vibrations that could result in such damage. This paper presents experimental investigation on small scale model pipes buried in dry sand and instrumented with an array of miniature accelerometers. Experiments were conducted in a geotechnical centrifuge up to 4g. mpulse and harmonic surface loadings were generated by dropping a standard mass and by using an electric eccentric mass motor respectively. t was found that different pipe materials absorb different amounts of energy. A relationship between the ratio of energy transferred and the impedance mismatch ratio between the pipes and the soil has been proposed. 1 NTRODUCTON Construction activities such as blasting, pile driving, dynamic compaction and traffic loading such as train and vehicle loading generate vibrations to varying degrees (Hope & Hiller, 2; Kin & Lee, 2). The vibrations are transmitted through the ground in the form of stress waves. When these waves encounter an underground structure such as a pipeline, part of the wave is reflected and part of it is transmitted into the structure. The cyclic nature of these vibrations will induce changes in stress levels in the pipes. This in turn may lead to fatigue related damage such as crack propagation. Therefore it is important to understand the magnitude of vibrations transmitted into an underground pipeline. At present there is little knowledge on the level of surface vibrations that could cause damage to underground pipelines. Guidance on the levels of groundborne vibration that may cause damage to buildings is given mainly in two British Standards, BS 5228 and BS Both of these give guidance on the peak particle velocity () above which cosmetic damage could occur in buildings. British Standards have very little reference to underground structures. BS 7385 states: Structures below ground are known to sustain higher levels of vibration and are very resistant to damage unless in very poor condition. BS 5228 gives threshold values for underground services: a maximum of 3 mm/s for transient and 15 mm/s for continuous vibrations. The standard fails to state the basis on which these levels were obtained, or the frequencies at which these limits apply with regard to underground structures. n order to analyse vibration related problems thoroughly, many factors such as the vibration source characteristics, site characteristics, propagation of body waves and response of the structure need to be considered. t is therefore important to gain an understanding of how ground borne vibrations are transmitted into underground pipelines. This paper discusses findings based on the behaviour of two different model pipes made of brass and concrete under impulse and harmonic surface loading at 1g and at varying g-levels up to 1g in a geotechnical centrifuge (Schofield, 198). This study is a continuation of research presented by Thusyanthan and Madabhushi (23). 2 EXPERMENTAL TECHNQUES OVERVEW The propagation of waves in the vicinity of underground pipelines was studied using both impulse and harmonic surface loads placed in an 85mm tub filled with dry sand. Miniature accelerometers buried at different locations were used to measure the vibration levels in the sand and model tunnels. All measurements were logged using DASYLab (Data Acquisition System Laboratory) onto a computer. The experimental apparatus is shown in Figure 1.

2 3 SOURCES OF VBRATONS 3.1 mpulse load A 1kg standard mass was dropped onto the base plate from a height of 6mm to simulate an impulse load. Peak particle acceleration = 2πf (1) where f = frequency; = component peak particle velocity (). 4 MODEL PREPARATON AND SOL TYPE The soil used was dry Hostun sand with a specific gravity of 2.65 and a critical friction angle of 32 o. All models were prepared by pluviating the sand through air with the aid of a hopper to ensure similar void ratio and uniformly distributed packing. A sand voids ratio of.75, which corresponds to a mediumdense state, was used in the experiments. 5 MODEL PPES AND EXPERMENTAL SETUP Figure 1. Experimental setup for centrifuge experiments Figure 2. Vibratory motor attached to base plate, with accelerometers 3.2 Vibrating Load A 5Hz electric eccentric mass a.c. motor was used to simulate a harmonic load as shown in Figure 2. The motor was attached to the same plate as was used in the impulse load. Accelerometers were also attached to the plate to measure the input horizontal and vertical accelerations. The base plate experiences a peak particle acceleration of 3g and can be approximated by a sinusoidal wave. Hence the component peak particle velocity can be estimated by equation 1 to be 93.7 mm/s. Two model pipes made of concrete and brass were used. Both pipes had the same outer dimensions of length 32mm and outer diameter 55 mm. The brass and concrete pipe had a mass of.72 kg and.67 kg corresponding to a density of 75 kg/m 3 and 1977 kg/m 3 respectively. Ordinary Portland cement and builder s sand was used at a cement/sand ratio of 1:4 for the concrete pipe. Two accelerometers were fastened at right angles in the middle of each pipe to measure the vibration of the pipe walls. Experiments on plaster of Paris model pipes were also conducted in a similar manner to the brass and concrete pipes. However, results obtained from this set of experiments will not be described due to space constraints. The cross section of the experimental setup for the 1g experiments are shown in Figure 3. Twelve accelerometers were used in the 1g experiments. Six accelerometers were placed horizontally to measure the horizontal acceleration while the other 6 were placed vertically at mirror locations. Two sets of experiments, A and B were carried out to measure the accelerations in the model pipes. Figure 4 shows the experimental setup for the centrifuge experiments (set C). 2 accelerometers were used to measure both vertical and horizontal components of acceleration simultaneously. Centrifuge experiments were conducted at 1g, 1.1g, 2.g and 4.1g respectively. At 4.1g, the corresponding prototype would have a pipe diameter of 22 mm buried at a depth of 492 mm below ground level. These dimensions are representative of typical pipelines buried in the field. Figure 5 shows the plan section of the model during the set C experiments.

3 6 DATA ACQUSTON AND FLTERNG All acceleration signals were recorded using DA- SYLab software at a sampling frequency of 5 khz. Post processing of the data was done in MATLAB. Any zero error in the signals were corrected and then filtered to eliminate high frequency noise. The acceleration signals were filtered using an 8 th order low pass Butterworth filter with a cutoff frequency of 5Hz. 7 RESULTS FROM 1G EXPERMENTS Figure 3. Cross-sectional view of the models used in the 1g experiment. Figure 4. Cross-sectional view of the model used in the centrifuge experiment. Figure 5. Plan section of Experiment C Figure 6 shows the horizontal and vertical acceleration in the brass and concrete pipes under harmonic loading. The concrete pipe experiences higher peak accelerations compared to the brass pipe. This shows that concrete absorbs a larger proportion of the vibrations compared to brass. Velocity-time profiles of the signals were obtained by integrating the acceleration signal using a MATLAB routine and passing the signal through a low pass Butterworth filter to eliminate any zero error. The peak particle velocity was then taken as half the peak-to-peak velocity amplitude. Table 1 summarises the vertical of the brass and concrete pipes under harmonic loading. The mean of the ratio of vertical in brass to that in concrete is.93 (standard deviation.12). This implies that the vertical in the concrete pipe is 7% higher than that in the brass tunnel. Table 1. Vertical peak particle velocity of model pipes under vibratory loading Test nput Brass Concrete Ppv Brass/Concrete mm/s mm/s mm/s AV AV AV AV AV AV BV BV BV BV BV BV The relative amount of energy transferred into the pipes can be quantified by the ratio of the vertical peak particle velocity in the brass model pipe to that in the concrete pipe which is.93. The energy transferred into the pipes is proportional to the square of the peak particle velocity in the model tunnel and can be obtained by Equation 2. Energy transferred into brass model pipe 2.93 Energy transferred into concrete model pipe = (2) = 87%

4 The brass model pipe absorbs only 87% of the energy absorbed by the concrete model pipe. The impedance mismatch appears to be the main parameter which determines the amount of vibration energy transferred into the model pipe. Table 2 shows the impedance mismatch of several media. An expression relating the impedance mismatch ratio to the square of the ratio was proposed by Thusyanthan & Madabhushi (23) as T b s s n = Brass T 2 (3) where T, s and b are the impedances of the pipe, sand and brass respectively. Brass is used as the control experiment and T refers to any other material. Figure 7 shows the above relationship plotted for the concrete pipe. Also shown is the data point for plastic from Thusyanthan & Madabhushi (21) and plaster of paris from present experiment. A best fit line corresponding to n=.1 in Equation 3 appears to agree well with experimental results. Figure 7 can be used to predict the energy transferred into a material T at shallow depths (low soil stresses). Table 2. mpedance of several media Material Density, Young s Modulus, Velocity of pressure mpedance, = V p E wave, V p kg/m 3 GPa m/s kg/m 2 s 1 3 Sand Brass Concrete Plaster Plastic Energy transferred to Brass / Energy transferred to pipe Concrete Plastic Plaster n=.1 Plastic (.21,.71) Plaster (.6,.76) Concrete (.19,.87) mpedance mismatch of pipe / 1 mpedance mismatch of Brass Figure 7. Ratio of energy transferred vs ratio of impedance mismatch 8 RESULTS FROM CENTRFUGE EXPERMENTS 8.1 Variation of peak particle velocity with g-level Table 3 shows the vertical of brass and concrete at different g-levels. At all g-levels, the concrete pipe experienced a higher peak particle velocity than the brass pipe. However the ratio of vertical in brass to that of concrete reduces with increasing g- level as evident in Figure 8. PPV ratios from the 1g experiments are also plotted on the same figure. At 1g, the spread of the vertical ratio is quite large. The spread of the data narrows at higher g-levels. This is because at higher stress levels in the sand, there is more consistent coupling between the model pipes and the surrounding soil. As the g-level increases, the vertical ratio decreases until it finally bottoms out at about 4g. A best-fit line through the mean of all the data points can be modeled by Equation 4. 1 PPV Brass PPV Concrete where g is the g-level..58 = g (4) Figure 6. Accelerations in model pipes under vibratory loading There is insufficient data to conclude what the actual ratio is at high g s since the source motor stopped operating above 4g. This is evident from Figure 9, which shows the variation of the vertical input of the motor with g-level. However the data gives a vertical ratio of brass to concrete of.44 at 4g. f we assume that the rate of decrease in the ratio levels out at higher g s, this implies that the final vertical in the concrete pipe is approximately 27% higher than in the brass pipe. The ratio of energy transferred into the brass pipe to the concrete pipe can then be calculated as per Equation 2 to be 19% at 4g. This value is 4.6 times lower than the value of 87% obtained from the 1g experiments. This implies that under higher stresses,

5 much more energy is absorbed by the concrete pipe than the brass pipe. Table 3. Vertical peak particle velocity in model pipes Test set g- level nput Brass Concrete Ppv Brass/Concrete mm/s mm/s mm/s C C C Wavelet analysis The peak particle velocity experienced by the pipes indicates the amount of energy transferred into the structure but does not provide the frequencies at which this energy is transferred. Wavelet analysis (Newland, 1993a,b&c, 1995) shows both the frequency content of the signal and time duration of its occurrence. Wavelet analysis of the vertical acceleration signals in brass, concrete and the vibrating source was carried out using a MATLAB routine. Results show that the energy distribution in brass is very different from that of concrete and may not necessarily occur at the same frequencies as the source frequencies (Fig.1). Figure 1 shows the results of this analysis at 2g during steady state harmonic loading. The input energy has peaks at the first 5 harmonics of the input frequency of 5Hz. However, the brass pipe selectively absorbs the most energy at 3 Hz, 15 Hz, 18Hz and 4 Hz while the concrete pipe absorbs the most energy at 5Hz and 2 Hz. PPV Brass / PPV Concrete C1 C3 B C g-level / g A Trendline brass / concrete = g (-.58) (R =.98) Figure 8. Vertical ratio of brass to concrete vs g-level nput PPV (mm/s) C1 C2 C g-level / g Figure 9. Vertical input of source motor vs g-level 9 CONCLUSON The material of the pipe plays an important role in deciding the amount of vibrations transferred into the pipe. Under both impulse and vibratory loading at 1g, the concrete pipe experiences a higher level of vibration compared to the brass tunnel. The mean vertical peak particle velocity ratio of brass to concrete was shown experimentally to be.93. Hence the ratio of energy transferred into the concrete pipe compared to brass which is proportional to the square of the peak particle velocity was.87. The higher the impedance mismatch between the pipe and the sand, the lower the energy transferred into the pipe. As the g-level increases, the vertical ratio of brass to concrete shows a decreasing trend. Under vibratory loading at 4g, the ratio decreases to.44. This means that the concrete pipe now absorbs nearly five times as much energy as a brass pipe. Wavelet analysis indicates that the energyfrequency distribution is different for different pipe materials. Under vibratory loading at 2g, vibrations transmitted into the brass pipe at higher frequencies than those transmitted into the concrete pipe. At the start of the load application, most of the energy in the brass pipe is in the 14Hz to 18Hz range which changes to include a concentration around 5Hz as the vibration progresses. The concrete pipe has most of its energy at 5Hz throughout the load application. The results shown provide preliminary design guidance for estimating the level of vibrations transmitted into buried pipelines from ground-borne vi-

6 brations. However, the conclusions reached need to be validated by further centrifuge experiments, possibly carried out at higher g-levels than were achieved in this set of experiments. REFERENCES British Standard BS , Part 4, Noise and vibration control on construction and open sites. Code of practice for basic information and procedures for noise and vibration control. Britisch Stardard BS , Part 2, Evaluation and measurement for vibration in buildings, Guide to damage levels from groundborne vibration. DASYLab (Data Acquisition System Laboratory), DASYTEC USA, 11 Eaton Road, PO Box 748, Amherst, NH , USA ( Hope, V.S. & Hiller, D.M. 2, The prediction of groundborne vibration from percussive piling, Canadian Geotechnical Journal, Vol-37, pp Kim, D.S. & Lee J.S. 2, Propagation and attenuation characteristics of various ground vibrations, Soil Dynamics and Earthquake Engineering 19, Newland, D.E. 1993a. An introduction to random vibrations, Spectral and wavelet analysis, Addision-Wesley. Newland, D.E., 1993b, Wavelet analysis of vibrations. Part1:Theory, Part : Wavelet maps, Cambridge University Engineering Department, Technical Report C- MECH/TR54. Newland, D.E., Harmonic wavelet analysis, harmonic and musical wavelets, 1993c, Cambridge University Engineering Department, Technical Report C-MECH/TR51. Newland, D.E., 1995, Signal analysis by the wavelet method, Cambridge University Engineering Department, Technical Report, C-MECH/TR65. Schofield, A.N Cambridge geotechnical centrifuge operations, Geotechnique, Vol.25., No.4, pp Thusyanthan, N.. & Madabhushi, S.P.G. 23. Experimental study of vibrations in underground structures, Proceedings of the nstitution of Civil Engineers, Geotechnical Engineering 156, April 23 ssue GE2. pp Thusyanthan, N Construction process induced vibrations on underground structures, Cambridge University MEng Report. Figure 1. Wavelet plot of steady state harmonic loading vertical acceleration signals in: (a) source input: (b) brass pipe: (c) concrete pipe