AXISYMMETRIC MODES THAT PROPAGATE IN BURIED IRON
WATER PIPES
R. Long, M.J.S. Lowe and P. Cawley
NDT Group, Department of Mechanical Engineering, Imperial College, Exhibition
Road, London. SW7 2BX, UK.
ABSTRACT. Research is being conducted at Imperial College to investigate the characteristics of
acoustic wave propagation in buried iron water mains. The dispersive mode shapes and mode
attenuation due to leakage have been investigated to predict what axisymmetric modes will
propagate over any significant distance at low frequencies. Experiments have been conducted on
buried water mains at three test sites in the UK to ascertain what modes propagate and to verify
dispersion predictions.
INTRODUCTION
Earlier investigations, reported in previous proceedings by Long et al [1, 2], found
that the dominant mode that propagates over significant distances in buried iron water
mains is a mode which at low frequencies is characterized by predominantly axial waterborne displacements. The established method of locating leaks by acoustic signal analysis
[3] assumes that leak noise propagates as a single non-dispersive mode at a velocity
related to the low frequency asymptote of this dispersive water-borne mode. In addition
to this mode, this paper explores two other, less well known, axisymmetric modes whose
existence depends on the acoustic properties of the outer medium that surrounds a pipe.
The predicted characteristics of these modes are presented; the likelihood of them
propagating over any significant distance in a buried water pipe is discussed, followed by
an experimental validation using measurements on water mains in urban areas of the UK.
POSSIBLE AXISYMMETRIC MODES THAT PROPAGATE IN BURIED
WATER MAINS
Predictions of the nature of actual wave propagation in buried water filled pipes
were obtained using the Disperse software [4]. For a buried pipe the characteristics
depend on the geometry of the system and on the acoustic properties of the different
media. The phase velocity dispersion curve predictions shown as dashed lines in Fig. 1
for a vacuum filled pipe surrounded by a vacuum (v-p-v) are well known. The
fundamental axi-symmetric mode conventionally labeled L(0,l) in accordance with, for
example, Silk and Bainton [5], exists at low frequencies. For a pipe filled with water but
surrounded by a vacuum (w-p-v), dispersion curves are shown as solid lines in Fig. 1. The
L(0,l) mode is similar to that predicted for the v-p-v and now an extra mode is introduced
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
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which is labeled, similar to Aristegui et al [6], as al. The axi-symmetric al mode at low
frequencies has predominantly axial, water-borne displacements. The lower horizontal
dotted line in Fig. 1 represents the low frequency asymptote of the al mode (V), which
corresponds with the assumed non dispersive leak noise velocity V derived for example
by Pinnington and Briscoe [7]. The vertical line in Fig. 1 at 2.5kHz represents the upper
frequency limit reached for reception of signals with significant signal to noise ratio in
the experimental results shown in this paper. Fig. 2a and 2b show the power normalised
mode shapes of the L(0,l) and al modes respectively at 2.5kHz. Axial displacements for
the L(0,l) mode occur predominantly in the pipe wall. Attenuation of L(0,l) results
partially from scattering as the wave encounters joints and fittings as it propagates along
the pipe, and also from leakage of energy when the pipe is surrounded by soil. Leakage of
energy occurs when the phase velocity of the guided wave is greater than the bulk
velocity of the soil, and this is the case for L(0,l) for all realistic soil properties. For the
al mode, axial displacements occur predominantly in the water filling the pipe.
0
10
2.5kHz
15
25
Frequency (kHz)
FIGURE 1. Phase velocity dispersion curves for axi symmetric modes in 10 inch bore cast iron pipe (wall
thickness = 16mm). Dashed lines are vacuum-pipe-vacuum (v-p-v) and solid lines are water-pipe-vacuum
system (w-p-v).
Radial
A.xial 160
P
140 " 1
<£
120 "
S
100 "
•3
*
Vacuum
Pipe
Water
80 '
60 "
1
40
20 '
' 1
-2.0
-1.0
0.0
Displacement
(a)
l.O
2.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
Displacement
FIGURE 2. Axial and radial mode shapes obtained from dispersion curve shown in Fig J at 2.5kHz for, (a)
1202
Dispersion curve predictions for a water filled pipe surrounded by soil (w-p-s)
were investigated where for simplification the soil was assumed not to support shear.
Material properties used for the predictions are given in Table 1. Phase velocity
dispersion curve predictions where the bulk longitudinal velocity in the soil is less than
the low frequency asymptote of the al mode (c^sou <V) are shown in Fig 3. As for w-p-v
the al mode appears and it has been found to exist for all values of CL soli- At low
frequencies the L(0,l) mode follows the path of the curve for w-p-v and then in the
frequency region where a maximum in attenuation occurs it jumps over to follow the path
of the L(0,2) mode. At higher frequencies the L(0,l) curve for the w-p-v system is
followed by a mode labeled as a2. For this soil model at low frequencies the a2 mode
phase velocity tends to zero velocity and is characterized by high attenuation in this
region so it is considered practically not to propagate at low frequencies. For CLsoii < V an
additional, less familiar, mode appears in the dispersion curve solution in Fig. 3 which is
labeled as a3. At low and high frequencies its phase velocity asymptotes to CLSOIIThe mode shapes of the propagating modes in Fig 3 at 2.5kHz are shown in Fig.
4. For the al mode, displacements again occur predominantly in the water in the pipe.
Oscillating displacements in the outer medium confirm that for this soil model al is
leaky. Loss of energy due to leakage will be the primary means by which the al mode
attenuates. The mode shape for a3 reveals that the displacements decay away
exponentially with distance from the pipe wall similar to a Sholte mode in a fluid loaded
plate. Here the wave in the pipe bore tows along a wave in the outer medium. For modes
where the phase velocity falls below the bulk velocity CL of the surrounding medium,
then Snell's Law implies that energy will not leak out into the soil in the form of bulk
waves. Therefore the a3 mode is always non leaky. The a3 characteristics are thus
governed by the properties of the surrounding medium. This is evident in Fig. 3 where at
low frequencies the phase velocity asymptotes to CLsoii. Attenuation of the a3 mode will
thus be governed by the loss characteristics in the surrounding soil.
6.0
1
2.0 -
0.0
2.5kHz
10
Frequency (kHz)
15
20
25
FIGURE 3. Phase velocity dispersion curves for axi symmetric modes in 10 inch bore cast iron pipe (wall
thickness = 16mm). Dashed lines are water-pipe-vacuum (w-p-v) and solid lines are water-pipe-soil system
(w-p-s) where C Ls oii < VNDLN- For clarity, higher order modes are not shown.
1203
idial
-4.0
-3.0
-2.0
-1.0
0.0 1.0 2.0 3.0 4.0 5.0
Displacement
-10.0
-5.0
0.0
Displacement
FIGURE 4. Axial and radial mode shapes obtained from dispersion curve shown in Fig 3 at 2.5kHz for, (a)
al,(b)o3.
TABLE 1. Material properties used for dispersion curve predictions
Material
CL (m/s)
Density p ( g/cm )
Cs (m/s)
water
1.0
1480
0
Ductile iron pipe
7.1
5500
3050
Cast iron pipe
7.1
4500
2500
C L s o i l <V
1.0
900
0
C Lsoil >V
1.0
1750
0
For soil acoustic properties of CL water > CLSOU > ^ me L(0,l) mode shows similar
characteristics to that for the c^soii < V soil model shown in Fig 3. The al mode will exist
but not the a3 mode since CL soii > V. The phase velocity of the a2 mode will still tend
towards zero velocity and this is the case whenever CL S0ii < CL water.
Phase velocity dispersion curve predictions for CLSOII > CL water are shown in Fig. 5.
The al mode appears but the a3 mode does not exist. Whereas before the a2 mode
tended towards zero velocity at low frequencies, this mode now asymptotes to CLSOU- The
mode shapes of the propagating modes at 2.5kHz are shown in Fig. 6. The mode shape
for al does not alter significantly for this different soil model except that now the al
mode is non-leaky. The mode shape for a2 exhibits similarities to the Scholte type a3
mode in that displacements decay away exponentially in the soil. The characteristics are
governed by the properties of the surrounding medium such that at low frequencies the
phase velocity asymptotes to CLsoii as evident in Fig. 5. When the a2 mode does propagate
at low frequencies it is always non-leaky and attenuation will be governed by the loss
characteristics in the surrounding soil. Additionally, greater displacements occur in the
pipe wall for the a2 mode, compared to the al mode, and so attenuation due to scattering
for the a2 mode becomes an issue.
1204
10
Frequency (kHz)
2.5kHz
15
20
25
FIGURE 5. Phase velocity dispersion curves for axi symmetric modes in 10 inch bore cast iron pipe (wall
thickness = 16mm). Dashed lines are water-pipe-vacuum (w-p-v) and solid lines are water-pipe-soil system
(w-p-s) where C Lsoi i > CLwater. For clarity, higher order modes are not shown.
-2.0
-1.0 0.0
1.0 2.0 3.0
Displacement
-2.0 -1.0 0.0
1.0 2.0 3.0
Displacement
4.0
5.0
FIGURE 6. Axial and radial mode shapes obtained from dispersion curve shown in Fig 5 at 2.5kHz for, (a)
al,(t>)o2.
Soil properties by
Guided wave
attenuation method
Tap on pipe
to excite LF modes
Dig pits
x)se pipe
Monitor sound with
Accelerometers
4 offequi spaced
F
\
FIGURE 7. Experimental technique for measurement of dispersion in buried water pipes
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EXPERIMENTAL INVESTIGATION
Experiments have been conducted on buried water mains at three sites in the UK
to verify dispersion predictions. Fig. 7 shows a schematic of the experimental technique.
At each site three pits were dug so as to get localized access to the full circumference of
the buried pipe. At one location a tapper device was mounted on the pipe to excite low
frequency (LF) vibrations in the pipe wall. The propagating signal was received at two
other locations where four accelerometers were mounted around the pipe circumference.
The averaged signals at each accelerometer were summed together to help eliminate any
unwanted anti symmetric vibrations. The phase velocity was then calculated in the
manner given by Long et al [1]. To enable attenuation measurements to be made, at one
site a 12m long trench was excavated between the measurement pits, allowing received
signal amplitudes to be compared between a pipe surrounded by soil and by air.
Measurements were made before the trench between the pits was dug, with the trench
open, and with it back-filled with crushed concrete. For dispersion curve predictions, the
soil properties were evaluated using the guided wave attenuation method described by
Long et al [2], wall thickness was determined by the ultrasonic pulse echo technique, and
the pipe outer circumference was measured directly.
COMPARISON BETWEEN EXPERIMENTAL AND PREDICTED DISPERSION
CURVES
The soil acoustic properties that were measured at each site are given in Table 2.
A time trace for the signal received at site 1 is shown in Fig. 8, where the distance
between the monitoring locations was z =9.9m. Phase velocities are given for the relevant
modes at the center frequency. The earliest arrival is the L(0,l) mode, which was not
normally noticeable in results for propagation distances over 10m. Both the al and a3
modes are evident. The velocity of the a3 mode was found to coincide with the value of
C L soil which was measured as 900m/s. At this site, tests were also conducted over a
longer propagation distance by tapping on a valve stem and receiving on another 175m
away. The time trace obtained is shown in Fig 9 where again the al mode is dominant
and the a3 mode is still evident. Fig. 10 shows the time trace for a signal received at site
2 where z =21.6m. Both the al and a3 modes are evident and CL soil for this site was
measured as 350m/s. Fig. 11 shows the time trace for the signal received at site 3 where z
=16.5m where only the al mode is evident. At this site CL soil was measured as 1900m/s
and it had been hoped that the a2 mode would be evident in the received signal.
However, much like the L(0,l) mode, the a2 mode is predicted to suffer attenuation due
to scattering at the pipe joints. Fig. 12 shows predicted versus experimentally obtained al
attenuation at site 1. For a pipe surrounded by clay the experimental results shown as
solid lines verify the predictions shown as dashed lines. The soil around the pipe was then
replaced with crushed concrete. As expected the al mode attenuation for the pipe
surrounded by such unconsolidated material is less than when surrounded by clay. It was
not possible to measure the acoustic properties of the crushed concrete in the vicinity of
the pipe so the dashed line is a dispersion curve has been fitted to the data which is
indicative of a material with CL soil =250m/s.
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TABLE 2. Soil material properties measured at test sites.
CL soil (m/s )
Test site
Density p ( g/cm3)
Cs soil (m/s)
1
1.95
900
80
2
2.10
350
72
3
1.95
1900
84
3 1
ccl
(1298m/s)
al
(1294m/s)
2 -
cc3
(922m/s)
1
.-3 o
Time( ms)
-3
J
Time( ms)
FIGURE 8. Time trace for a signal received on 6 FIGURE 9. Time trace for a signal received on 6
inch bore ductile iron pipe (wall thickness = 8mm) at inch bore ductile iron pipe (wall thickness = 8mm) at
site 1 where z=9.9m.
site 1 where z= 175m.
al
(1290m/s)
Time(ms)
'3
Time (ms)
FIGURE 10. Time trace for a signal received on 6 FIGURE 11. Time trace for a signal received on 14
inch bore ductile iron pipe (wall thickness =8mm) at inch bore cast iron pipe (wall thickness = 19mm) at
site 2 where z= 21.6m.
site 3 where z= 16.5m.
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0.8 - Predicted attenuation for
measured soil properties
0.7 - CL=900m/s Cs=80m/s p=l .7g/cm3
x-s
°'6
/
/>
~
4
Experimental results for
pipe surrounded by
crushed concrete
s
« 0.5 - Experimental results for
3-
o 0.4 -
pipe surrounded by
,
.
clay soil
"^^^^ / j
0.3
Fitted dispersion curve
indicative of material
with CL=250m/s
0.2 ~
0.1 -
0.5
1.5
2
Frequency (kHz)
2.5
3.5
FIGURE 12. Predicted and experimental attenuation dispersion, for 6 inch ductile iron pipe surrounded by
soil and crushed concrete where z= 15m.
CONCLUSIONS
The established acoustic leak location technique assumes that leak noise
propagates as a single, non-dispersive mode in buried water pipes. By contrast, the
predicted dispersion curves suggest that a number of modes may propagate with
significant dispersion. Experimentally the dominant mode identified for all path lengths
was the dispersive, water-borne ocl mode. Since the established technique does not allow
for dispersion, location errors are likely to be obtained. These will be most significant in
large diameter pipes where dispersion is more severe at the frequencies measured. The
oc3 mode has been identified in results for pipes surrounded by soils that support its
propagation for propagation distances up to 175m. The oc2 mode has not been identified
in experimental results. The predicted attenuation of the ocl mode for a pipe surrounded
by soil has been verified.
REFERENCES
1. R. Long, K. Vine, M.J.S. Lowe and P. Cawley, in Review of the progress in QNDE,
Vol. 20, eds. D. O. Thompson, and D. E. Chimenti, American Institute of Physics,
New York, 2001, p. 1202.
2. R. Long, K. Vine, M.J.S. Lowe and P. Cawley, in Review of the progress in QNDE,
Vol. 21, op. cit. (2002), p.1310.
3. H. V. Fuchs, and R. Riehle, Applied Acoustics, 33, 1 (1991).
4. M. J. S. Lowe, IEEE Tram. UFFC, 42, 525 (1995).
5. M. Silk and K. Bainton, Ultrasonics, 17(1), 11 (1979).
6. C. Aristegui, P. Cawley and M. Lowe, in Review of the progress in QNDE, Vol. 18,
op. cit. (1999), p. 159.
7. R. J. Pinnington and A. R. Briscoe, /. Sound and Vib., 173(4), 503 (1994).
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