Rob Long, Peter Cawley and Mike Lowe Press PGDN when arrow appears Acoustic wave propagation in...

Rob Long, Peter Cawley and Mike Lowe

Press PGDNwhen arrow appears

Acoustic wave propagation in Acoustic wave propagation in buried iron water pipes buried iron water pipes

WITE ProgrammeWITE Programme

Work reported in this presentation

1. Predict wave propagation characteristics in water pipes

2. Validate predictions using tests on buried water mains in streets.

Presentation Content

1: IntroductionMotivation for research

2: Predictions2:1 Dispersion curves for guided waves in water pipes2:2 Mode shapes of fundamental modes2:3 Phase velocity dispersion of fundamental modes2:4 Effect of pipe bore variation on velocity dispersion2:5 Effect of soil properties on mode attenuation2:6 Effect of joints and fittings on mode attenuation

3: Validations 3:1 Experimental technique 3:2 Mode phase velocity measurement 3:3 Mode attenuation measurement 3:4 Soil property measurement 3:5 Experimental results

4: Summary

Leakage from water pipes is a major issue concerning all water companies

Leaking pipes should be located

And Repaired

However many leaks are not so obvious from the surface

Introduction

Motivation for research

One method is to locate leaks by acoustic signal analysis

Acoustic noise that arises from the leak propagates through the system

Accelerometers are mounted typically on valve stems to record the signals

Data recorded results in two signalsThese two signals are cross correlated

so as to obtain a time delay tt

V . t d d

Z

2d = z - (V .t )

The distance to the leak d from one monitoring pointis then formulated by assuming that the leak noise propagates at a non dispersive (ie does not vary with frequency) velocity V

How reasonable is it to assume that leak noise propagates non dispersively ?

If we are considering sound propagation in bulk materials that have no boundaries then it would be a reasonable

assumption

For sound propagation in structures such as pipes reflection and refraction of waves at the boundaries sets up a series

guided waves.

In the case of leak noise the vibrations recorded by the accelerometers are dominated by a guided wave that

predominantly propagates in the water contained within the pipe

With guided waves we need to look at the dispersive characteristics

We use the Disperse software developed by the NDT Group Imperial College to obtain dispersion curve numerical solutions

Lets solve dispersion curves for a water filled 250mm bore 10mm wall thickness cast iron pipe surrounded by a vacuum

The solution shown plots the phase velocity of each mode as a function of frequency

Modes in red are axially symmetric modes whilethose in blue are non axially symmetric modes

Predictions

Dispersion curves for guided waves in water pipes

Let us now examine the mode shapes ofthree modes that exist at low frequenciesWe will first look at the characteristics of the so called L(0,1) fundamental longitudinal modeThe Mode Shape window shows radial displacements and axial displacements in the water and iron layers for the given mode at the given frequency.

0- +

water

iron

For L(0,1) at near zero frequency the radial displacements are insignificant in both the water and iron layers. While axial displacements predominantly occur in the pipe wall.Watch the animation of the mode displacements for L(0,1) at near zero frequency. Notice the displacements are axially symmetric, predominantly occur in the pipe wall and the motion is purely extensional/longitudinal.

0- +

Next we will look at the characteristics of the so called F(1,1) fundamental Flexural mode at near zero frequency.Notice the axial displacements for F(1,1) are insignificant.While the radial displacements dominate in both the water and iron layer

water

iron 0- +

water

iron

Watch the animation of the mode displacements for F(1,1) at near zero frequency. Notice the motion of the mode behaves as if bending/flexural.Finally we will look at the 1 mode shapesThe axial displacements occur predominantly in the water in the pipeThe radial displacements are insignificant in the water and iron layersWatch the animation of the mode displacements for 1 at near zero frequency. Notice the displacements are axially symmetric, predominantly occur in the water and the motion is purely extensional/longitudinal.

Mode shapes of fundamental modes

Let us now examine the dispersion characteristics of the three modes that exist at low frequenciesThe fastest mode shown is the so called L(0,1) mode.L for longitudinal- mode displacements at low frequencies predominantly longitudinal0 for zero phase change over the circumference ie axially symmetric1 for the first Longitudinal mode that appears

L(0,1)

Notice how the phase velocity of the L(0,1) mode varies with frequency (dispersion).For 10 inch pipe the L(0,1) mode is particularly dispersive about 4kHz to 6kHz.

0kHz Vph 4048m/s2kHz Vph 4031m/s4kHz Vph 3900m/s6kHz Vph 1950m/s8kHz Vph 1650m/s

Next the so called F(1,1) mode. F for flexural- since mode displacements at low frequencies are as if the pipe is being flexed1 for one phase change over the circumference ie non axially symmetric1 for the first Flexural mode that appears

F(1,1)


For 10 inch pipe the phase velocity of the F(1,1) mode is dispersive particularly about 0kHz to 2kHz.


1

Finally the alpha 1 mode. It is the low frequency asymptote of the 1 mode that corresponds to velocity that leak location techniques assume leak noise to propagate at.

For 10inch pipe the 1 mode is particularly dispersive about 2kHz to 4kHz

Phase velocity dispersion of fundamental modes

Frequency kHz

Pha

se V

eloc

ity

m/m

s

0

1

2

3

4

0 2 4 6 8 10

Let us compare dispersion curves for different bore pipes.First the dispersion curves for a 6 inch bore pipe showing

the L(0,1), F(1,1) and 1 modes

Followed by the curves for a 10 inch bore pipeThen those for a 24 inch bore pipeFollowed finally by those for a 36 inch bore pipeNotice that the effect of an increase in bore size shifts the dispersion curves to the left for

L(0,1) 1 and F(1,1)

For a given ratio of pipe-wall thickness to pipe bore size we can plot one set of curves as a function of Frequency-radius product for all pipe sizes.

L(0,1)

F(1,1)

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1 1.2

Frequency-radius (MHz-mm)

Pha

se V

eloc

ity

(m/m

s)

Effect of pipe bore variation on velocity dispersion

Up to now we have considered the wave propagation only for a pipe surrounded by a vacuum

Now we need to look at the effect of embedding the pipe in a surrounding medium

L(0,1)

F(1,1)

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1 1.2


Pha

se V

eloc

ity (

m/m

s)Dispersion Curves shown

Coloured curves for water filled pipe surrounded by water (w-p-w)Black dotted curves for water filled pipe surrounded by a vacuum (w-p-v)

For w-p-w system L(0,1) Phase velocity dispersion is very similar to w-p-v at lower frequencies

then follows higher order Longitudinal modes at higher frequencies

For w-p-w system a phase velocity is very similar to w-p-v at lower frequencies F(1,1) phase velocity is slower than w-p-v due to the surrounding medium

Now we will consider the effects of surrounding the pipe with soil.Typical soils are either saturated such as a clay slurryor unsaturated such as unconsolidated sand or clay

Both types of soil will be characterised by density and the bulk longitudinal CL and shear CS velocities in the soil

If the phase velocity of a mode is above CL or CS in the soilthen the mode will couple to leaking longitudinal or shear waves in the soil

These leaking waves carry away energy into the soil leading to mode attenuation

First we will plot attenuation due to leakage for a pipe surrounded by saturated soil where=1000kg/m3, CL =1500m/s and CS varies from

0

10

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40

50

60

70

0 0.2 0.4 0.6 0.8 1 1.2

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0 0.2 0.4 0.6 0.8 1 1.2

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0 0.2 0.4 0.6 0.8 1 1.2

0

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70

0 0.2 0.4 0.6 0.8 1 1.2Frequency-radius (MHz-mm)

Atte

nu

atio

n (

dB

-mm

/m)


Atte

nu

atio

n (

dB

-mm

/m)


Atte

nu

atio

n (

dB

-mm

/m)

25m/s25 to 50m/s25 to 75m/s25 to 100m/s

mode F(1,1) mode L(0,1) mode

For saturated soil All modes couple to leaking shear waves in the soil.

Only L(0,1) couples to leaking longitudinal waves in the soil.

Attenuation due to leakage increases for all modes with increasing bulk shear velocity in the soil

Of the three modes the mode is less attenuated at low frequencies such that it would be expected to become the

dominate mode in received signals for long propagation distances

mode

Effect of soil properties on mode attenuation

Next we will plot attenuation due to leakage for a pipe surrounded by unsaturated soil where=1900kg/m3, CS =100m/s and CL varies from 250m/s250 to 500m/s250 to 750m/s250 to 1000m/s

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8 1 1.2

0

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300

0 0.2 0.4 0.6 0.8 1 1.2

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0

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300

0 0.2 0.4 0.6 0.8 1 1.2

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0 0.2 0.4 0.6 0.8 1 1.2

0

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300

0 0.2 0.4 0.6 0.8 1 1.2

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8 1 1.2Frequency-radius (MHz-mm)

Atte

nu

atio

n (

dB

-mm

/m)


Atte

nu

atio

n (

dB

-mm

/m)


Atte

nu

atio

n (

dB

-mm

/m)

mode F(1,1) mode L(0,1) mode mode

Again of the three modes the mode is less attenuated at low frequencies such that it would be expected to become the

dominate mode in received signals for long propagation distances

soilpipewater

In practice a water main will have fittings such as

JointJointJointJoint

r

Branch

a

joints every few metres that connect individual lengths

and tees where pipes of bore r branch off to another pipe of bore a

As a mode encounters such fittingsattenuation will occur due to scattering

and will be a function of wavelength and hence frequency.

First we look at mode propagation across a joint.We consider a solid metal to metal contact joint and

a soft joint where the joint is filled with sealant or rust.

The water borne mode suffers little attenuation for either joint whereas attenuation of the pipe-wall borne L(0,1) mode is

significant particularly for the soft joint

Next we look at mode propagation passed a branch withratios of branch bore a over pipe bore r of 0.125 to 1.

A branch acts as a high pass filter particularly when the branching is large.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5

Frequency-radius (MHz mm)

Tra

nsm

issi

on C

oeff

icie

nt.

, soft joint

L(0,1) soft joint

L(0,1) metal-metal

, metal-metal

Frequency-radius (MHz mm)

Tran

smis

sion

Coe

ffic

ient

.

a/r=1

a/r=0.5

a/r=0.25

a/r=0.125

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5

Effect of joints and fittings on mode attenuation

Alnwick(Northumberland Water)

Greenwich(Thames Water)

Imperial College

Guildford(Thames Water)

Experiments were performed on buried water pipes at various sites in the UK

to measure mode phase velocity and attenuation

Pipes of various bore sizes buried in different soils were chosen for the measurements

At a given site pits were dug to get access to the full circumference of the pipe

in 3 locations

At one location an automatic tapper device was mounted on the pipe surface

to input low frequencies vibrations

At 2 other locations 4 off accelerometers were mounted equi-spaced around the circumference to

monitor propagating signals

Tap on pipe

to excite LF modesMonitor sound with4 off accelerometers

Monitor sound with4 off accelerometers

Joint

Path length Z

Measurements were conducted for a pipe buried in soil

and for a pipe surrounded by aggregate

for a pipe surrounded by air

Excavation

soil

pipewater

Validations

Experimental technique

Received signal at location a and b are windowedThe FFTs of each signal is computed

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1

time ms

ampl

itude

Location a(t)

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1

time ms

ampl

itude

Location b(t)

The Phase spectrum is then computed

0

10

20

30

40

0 50 100 150 200

Frequency kHz

Mod

ulus FFT A*()

0

10

20

30

40

0 50 100 150 200

Frequency kHz

Mod

ulus

FFT B()

0

2

4

6

0 50 100 150 200

Frequency kHz

Phas

e ra

dian

s

Phase spectrum

The Phase spectrum is unwrapped

0

50

100

150

200

250

0 50 100 150 200

Frequency kHz

Unw

rapp

ed p

hase

radi

ansUnwrap ()

0

2000

4000

6000

0 50 100 150 200

Frequency kHz

Velo

city

m/s Phase velocity

Group velocity

zv ph

grv

The Phase velocity Vph is computed from which the group velocity Vgr can be obtained

Mode phase velocity Measurement

Mode attenuation Measurement

We also need to evaluate the acoustic properties of the soil that surrounds the pipe

We use the pipe material and measured pipe dimensions to produce predictions which

we will compare to experimental results

At each site the material of the pipe was noted

Pipe wall thickness was measured by the pulse-echo technique

As was the pipe circumference

Soil property measurement

We need a technique to evaluate the acoustic properties of near surface unconsolidated material

Testing something like dry sand would be somewhat challenging

Whereas wet sand would be a bit more manageable

We use a technique that infers the bulk velocity in the soil from the attenuation characteristics of a mode

that propagates down a bar embedded in the soil

Piezo electric element

Backing

Axial excitement

We take a steel bar about 1m long with a piezo electric element bonded at one endAn electrical pulse is applied across the

piezo electric element resulting in an axial excitementin the bar

This mechanical pulse propagates down the bar

Is reflected off the other endis received at the piezo electric element where an electrical

signal is produced and saved

soil Bar

The bar is then embedded in the soil up to a length L

L

Signal for bar in air

The pulse again propagates down the barInto the embedded portion where it attenuates due to leakage

Is reflected, attenuates in the embedded portion again

And is received at the element

Signal for embedded bar

Attenuation = [20 log (R soil/Rair)]/2L

The attenuation characteristics of the mode are then obtained by dividing the FFT of the signal for a bar in soil by

that for a bar in air

0

3

6

9

12

15

0 0.05 0.1 0.15 0.2 0.25

0

3

6

9

12

15

0 0.05 0.1 0.15 0.2 0.25

0

3

6

9

12

15

0 0.05 0.1 0.15 0.2 0.25

0

3

6

9

12

15

0 0.05 0.1 0.15 0.2 0.25

0

3

6

9

12

15

0 0.05 0.1 0.15 0.2 0.25

0

3

6

9

12

15

0 0.05 0.1 0.15 0.2 0.25

The measured attenuation is then plotted

A series of predicted dispersion curves are solved for soils with different values of CL and CS in the soil

The predicted dispersion curve that best matches the measured attenuation infers the soil properties

0

3

6

9

12

15

0 0.05 0.1 0.15 0.2 0.25

Frequency (MHz)

Atte

nuat

ion

(dB

/m)

Goals

To verify predicted alpha mode phase velocity for a pipe surrounded by soil, air and aggregate

To verify predicted alpha mode attenuation for a buried pipe

Site location in Guildford UKTests conducted over 3 days in June 2002

A number of tests have been carried out on various water mains at sites in the UK. Presented are results from

Pipe detailsPath Length 15mDuctile Iron6 inch bore6.5mm wall thickness

Measured soil PropertiesDensity 1900kg/m3

CL soil 900m/sCS soil 80m/s

0

6

12

18

24

30

0 0.1 0.2 0.3

0

6

12

18

24

30

0 0.1 0.2 0.3

Frequency (MHz)

Att

en

ua

tion

(d

B/m

)

Experimental Result

1150

1200

1250

1300

1350

0 1 2 3 4 5 6

1150

1200

1250

1300

1350

0 1 2 3 4 5 6

1150

1200

1250

1300

1350

0 1 2 3 4 5 6

1150

1200

1250

1300

1350

0 1 2 3 4 5 6

1150

1200

1250

1300

1350

0 1 2 3 4 5 6

Verification of mode phase velocity

Frequency (kHz)

Pha

se V

eloc

ity (

m/s

)

Predicted dispersion curves for pipe surrounded by air and clay

Experimental dispersion curves for pipe surrounded by air clay

and aggregate

Predicted dispersion verified

Verification of mode attenuation due to leakage

Predicted dispersion curves for pipe surrounded by air and aggregate

Experimental dispersion curves for pipe surrounded by air and aggregate

0

0.1

0.2

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0 0.5 1 1.5 2 2.5 3

0

0.1

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0

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0 0.5 1 1.5 2 2.5 3

Predicted dispersion verified

Frequency (kHz)

Atte

nuat

ion

(dB

/m)

Identified what modes propagate over short and long path lengths on different pipe diameters

Introduced new technique for measuring bulk velocities in near surface soils

Verified predicted dispersion curves

Main project achievements covered in this presentation

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Rob Long, Peter Cawley and Mike Lowe Press PGDN when arrow appears Acoustic wave propagation in...

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