1

Ultrasonic Isolation of Buried Pipes 1

Eli Leinov*, Michael JS Lowe and Peter Cawley 2

NDE Group, Department of Mechanical Engineering, Imperial College, London SW7 2AZ, 3

UK. 4

* Corresponding author: Tel. +44 207 594 7227 e.leinov@imperial.ac.uk 5

6

Abstract 7

Long-range guided wave testing (GWT) is used routinely for the monitoring and detection of 8

corrosion defects in above ground pipelines. The GWT test range in buried, coated pipelines 9

is greatly reduced compared to above ground configurations due to energy leakage into the 10

embedding soil. In this paper, the effect of pipe coatings on the guided wave attenuation is 11

investigated with the aim of increasing test ranges for buried pipelines. The attenuation of the 12

T(0,1) and L(0,2) guided wave modes is measured using a full-scale experimental apparatus 13

in a fusion-bonded epoxy (FBE)-coated 8” pipe, buried in loose and compacted sand. Tests 14

are performed over a frequency range typically used in GWT of 10-35 kHz and compared 15

with model predictions. It is shown that the application of a low impedance coating between 16

the FBE layer and the sand effectively decouples the influence of the sand on the ultrasound 17

leakage from the buried pipe. Ultrasonic isolation of a buried pipe is demonstrated by coating 18

the pipe with a Polyethylene (PE)-foam layer that has a smaller impedance than both the pipe 19

and sand, and has the ability to withstand the overburden load from the sand. The measured 20

attenuation in the buried PE-foam-FBE-coated pipe is found to be substantially reduced, in 21

the range of 0.3-1.2 dBm-1 for loose and compacted sand conditions, compared to measured 22

attenuation of 1.7-4.7 dBm-1 in the buried FBE-coated pipe without the PE-foam. The 23

2

acoustic properties of the PE-foam are measured independently using ultrasonic 24

interferometry and incorporated into model predictions of guided wave propagation in buried 25

coated pipe. Good agreement is found between the experimental measurements and model 26

predictions. The attenuation exhibits periodic peaks in the frequency domain corresponding 27

to the through-thickness resonance frequencies of the coating layer. The large reduction in 28

guided wave attenuation for PE-coated pipes would lead to greatly increased GWT test 29

ranges; such coatings would be attractive for new pipeline installations. 30

31

32

33

Keywords: Guided wave testing; Buried pipes; Coated pipes; Sand; Ultrasonic isolation. 34

35

3

1. Introduction 36

The abundance of pipelines worldwide requires the use of inspection technologies to facilitate 37

integrity management for early detection of corrosion and possible leakage locations. Elastic 38

wave propagation along cylindrical shells has received comprehensive treatment in the 39

literature [e.g. 1-5] and has been utilised successfully in non-destructive evaluation for the 40

inspection of pipelines [6-11]. The long-range guided wave testing (GWT) method has been 41

routinely used for over a decade in the petrochemical, energy and nuclear industries [12-15]. 42

GWT offers rapid screening of pipework for the detection and monitoring of corrosion 43

defects from a single transducer position. The method typically employs torsional (T(0,1)) or 44

longitudinal (L(0,2)) wave modes in frequencies below 100 kHz. Waves are excited and 45

received either using a transducer ring comprising an array of dry-coupled piezoelectric 46

elements equally spaced around the circumference of the pipe [10, 16-20] or magnetostrictive 47

sensors [e.g. 21-22]. The method is commonly applied to bare- or thinly epoxy-painted pipes 48

in above-ground configurations, where a single transducer ring location provides coverage of 49

several tens of metres [e.g. 12]. However, for pipes buried in soil test ranges are drastically 50

reduced [15, 23]. Typically for modern pipeline engineering practices, coating materials, e.g. 51

fusion-bonded epoxy (FBE), coal-tar-enamel and high-density polyethylene (HDPE), are 52

either factory- or field-applied to pipes that are buried in the ground in order to provide 53

insulation from harsh environments and protection from corrosion. The guided wave 54

attenuation in coated or embedded waveguides is due to leakage of energy radiating out into 55

the embedding material, and damping by energy-absorbing materials of the waveguide 56

system, resulting in a severe reduction of the test range. The extent of leakage depends on the 57

material properties of both the pipe and the embedding material. For structures coated with 58

materials having internal damping, e.g. bitumen, the attenuation is also related to the fraction 59

4

of energy in the mode of interest that is carried in the coating layer and generally increases 60

with frequency. 61

Wave propagation in multi-layered systems has been described in the literature in the context 62

of geophysics and acoustics [e.g. 24-26]. Matrix techniques [e.g. 27 and references therein] 63

have been used for embedded and coated waveguides to yield dispersion curves and through-64

thickness wave mode-shapes for certain regular geometries, i.e. flat plate and cylindrical 65

structures. These were used to evaluate the guided wave mode properties, including 66

attenuation and sensitivity to target defect morphologies [27-28]. Leaky cylindrical 67

waveguides embedded in infinite media were studied in several configurations, including 68

steel bars embedded in cement grout [29], rock bolts embedded in rock strata [30], 69

reinforcing bars and anchor bolts embedded in concrete [31], steel bars embedded in soil 70

[32], and wires in epoxy resin [33-34]. Wave propagation in attenuative viscoelastic materials 71

was treated rigorously for plastic plates [35-36], elastic plates coated with viscoelastic 72

materials [37-39], and elastic hollow cylinders coated with viscoelastic material externally 73

[40] and internally [41]. Finite-element modeling and semi-analytical finite-element 74

formulations were utilised to address coated pipes [42-45] and coated pipes buried in soil [46-75

47], as well as the general case of arbitrary section waveguides embedded in solid media 76

[48]. Only limited measurements of the torsional guided wave attenuation in buried pipes 77

have ever been reported in the literature [49]. Recently, Leinov et al. [23, 50] studied 78

systematically guided wave propagation in a bare steel pipe buried in sand under a variety of 79

experimental conditions and examined the nature of the attenuation of the modes, which is 80

primarily due to leakage of energy. 81

Buried pipelines are currently accessed for GWT by digging a pit to expose the pipe at the 82

location where a transducer ring is to be attached (Figure 1). A very large fraction of the costs 83

involved in GWT of such buried-pipe systems is in gaining access to attach the transducer 84

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ring and re-covering the pipeline after the inspection. Hence, maximizing the distance over 85

which the guided waves can propagate and defects can be detected from a single access 86

location is essential and has substantial economic implications. 87

In the present study, we investigate guided wave propagation in buried FBE-coated pipe 88

using a full-scale experimental apparatus and model simulations. Measurements of torsional 89

and longitudinal guided wave mode attenuation are compared to an earlier investigation 90

performed by the authors on bare pipe buried in sand [23]. We aim to investigate the effect of 91

the pipe coating on the guided wave attenuation and to determine whether a pipe coating can 92

be used to increase the test range in buried pipelines. Ultrasonic isolation of a buried pipe is 93

demonstrated by utilising a low impedance coating material which effectively decouples the 94

influence of the sand on the ultrasound leakage from the buried pipe. The acoustic properties 95

of the coating material are evaluated independently using ultrasonic interferometry. The 96

nature of the attenuation behaviour is examined, providing understanding of the phenomena 97

of generic value to cases of coated or embedded multilayer waveguides. 98

This paper is organised as follows. The theoretical model of guided wave propagation in 99

embedded and coated cylindrical shells is discussed in section 2.1 and the acoustic properties 100

of soils are reviewed in section 2.2. The experimental apparatus and measurement method are 101

described in section 3. The experimental and model results are reported and discussed in 102

section 4 and the conclusion are provided in section 5. 103

104

2. Background 105

2.1 Guided wave modelling 106

6

The propagation of a stress wave in an isotropic elastic medium is governed by Navier’s 107

equation of motion: 108

𝜇∇2𝒖 + (𝜆 + 𝜇)∇(∇ ∙ 𝒖) = 𝜌 𝜕2𝒖 𝜕𝑡2⁄ (1) 109

where 𝒖 is the displacement vector field, 𝜆 and 𝜇 are the Lamé constants for the material, and 110

𝜌 the density. Using Helmholtz’s decomposition the displacement vector in Eq. (1) is 111

replaced by a combination of the gradient of a scalar potential field, 𝜙, and the curl of a 112

vector potential field, 𝝍: 113

𝒖 = ∇𝜙 + ∇ × 𝝍 (2) 114

Substituting Eq. (2) into Eq. (1), along with ∇ ∙ 𝝍 = 0, yields the standard wave equations 115

describing longitudinal and shear propagation, respectively: 116

𝑐𝐿2∇2𝜙 = 𝜕2𝜙 𝜕𝑡2⁄ (3) 117

𝑐𝑆2∇2𝝍 = 𝜕2𝝍 𝜕𝑡2⁄ (4) 118

where 𝐶𝐿 = �(𝜆 + 2𝜇) 𝜌⁄ and 𝐶𝑆 = �𝜇 𝜌⁄ are the longitudinal and shear velocities. The 119

solutions of Equations (3-4) along with relevant boundary conditions represent all elastic 120

wave modes propagating in a structure. Considering an infinitely long homogeneous hollow 121

cylinder with its axis along the z-coordinate of a cylindrical system (𝑟, 𝜃, 𝑧) and assuming 122

harmonic wave propagation, it follows that Bessel functions of the first and second kind have 123

to be introduced into the scalar potential and into the three components of the vector potential 124

in order to satisfy Equations (3-4). The components of the displacement field are then 125

obtained in terms of the potentials from Equation (2). Boundary conditions of zero traction 126

need to be satisfied on both the external and inner surfaces of the hollow cylinder. Thus, there 127

are three equations for each of the stress components (𝜏𝑟𝑟; 𝜏𝑟𝑟; 𝜏𝑟𝑟) expressing the boundary 128

7

conditions on each of the two free surfaces, resulting in six unknown constants in total. 129

Setting the determinant of these six equations to zero yields the dispersion relation which can 130

only be solved using numerical techniques (see [1-2, 11, 27, 40, 51-52]). Three classes of 131

propagating wave modes are recognised in the solutions, namely, longitudinal axially 132

symmetric, torsional axially symmetric and flexural non-axially symmetric [e.g. 7]. 133

A system comprising a hollow cylindrical waveguide coated with a finite number of 134

cylindrical layers can be analysed using the same formalism of Equations (1-4), considering 135

different acoustic properties for each layer and additional boundary conditions to include the 136

additional boundary surfaces. For an infinite embedding medium, the exterior surface of the 137

waveguide is no longer a free surface and the boundary conditions change to allow radiating 138

waves from the waveguide out into the embedding material. The leakage of energy from the 139

waveguide results in attenuation of the guided wave modes. The acoustic properties of the 140

coating and embedding layers dictate the attenuation regime. For a pipe embedded in an 141

elastic medium having a lower acoustic impedance the attenuation is governed only by 142

leakage of energy. However, for attenuative viscoelastic materials, e.g. coal-tar-enamel [49], 143

HDPE [35] and bitumen [36, 40, 42-46], dissipation of energy also occurs due to internal 144

losses. The hysteretic nature of damping is taken into account under linear viscoelasticity 145

assumption by modifying the Lamé constants into the following operators: 146

𝜆 → 𝜆 + 𝜆�

𝜔𝜕𝜕𝜕

; 𝜇 → 𝜇 + 𝜇�𝜔

𝜕𝜕𝜕

(5) 147

where �̃� and 𝜇� represent the viscoelastic material constants and 𝜔 the frequency. The 148

equation of motion (Equation (1)) is modified accordingly, resulting in definition of 149

velocities which include complex parts: 150

𝐶𝐿′ = �𝜆+2𝜇−𝑖�𝜆�+2𝜇��𝜌

; 𝐶𝑆′ = �𝜇−𝑖𝜇�𝜌

(6) 151

8

The real parts of 𝐶𝐿′ and 𝐶𝑆′ are the longitudinal and shear velocities for a material without 152

damping. The bulk wave phase velocities are obtained from: 153

𝐶𝐿,𝑆 = 𝜔|𝑅𝑅(𝒌)| (7) 154

The formal solutions of the resulting wave equations are identical to those of the elastic case 155

(Equation (2)), except the harmonic wave formulation has to involve a complex wavenumber 156

vector, 𝒌 = 𝒌𝑅𝑅 + 𝑖𝒌𝐼𝐼. Waves propagate in the direction of the real wavenumber vector 157

𝒌𝑅𝑅, and the attenuation with propagation distance is described by the imaginary 158

wavenumber 𝒌𝐼𝐼. The angle between the relative orientation of the real and imaginary 159

wavenumber vectors dictates the attenuation regime. The acoustic properties of a viscoelastic 160

material are defined by considering a case where the real and the imaginary parts of 𝒌 are 161

parallel. The frequency dependent complex velocities are related to the acoustic properties 162

according to [27, 36]: 163

𝐶𝐿,𝑆′ = 𝐶𝐿,𝑆

1+𝑖𝛼𝐿,𝑆2𝜋

(8) 164

where 𝛼𝐿,𝑆 are the bulk attenuation in nepers per wavelength and corresponds to the ratio of 165

the imaginary wavenumber to the real wavenumber moduli. The attenuation per wavelength 166

is considered constant for all frequencies, and therefore the attenuation per unit distance 167

increases linearly with frequency [27]. For an elastic coating material 𝒌𝐼𝐼 is normal to 𝒌𝑅𝑅 168

and leakage occurs when the phase velocity in the inner cylindrical shell is larger than that in 169

the coating layer. When the phase velocity in the coating layer is larger than that in the inner 170

cylindrical shell the guided wave becomes non-leaky. 171

The guided wave attenuation exhibits periodic peaks and troughs in the frequency domain 172

which are related to the through-thickness resonance frequencies of the viscoelastic layer [37-173

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38]. In turn, the shear cutoff frequencies of interest in this study depend on the thickness and 174

bulk shear velocity of the coating layer and can be approximated as [41]: 175

𝑓𝑟𝑅𝑟,𝑛 ≅𝐶𝑆4ℎ

(2𝑛 − 1); 𝑛 = 1,2, … (9) 176

where ℎ is the thickness of the coating layer. 177

In this study, we investigate wave propagation in a coated pipe embedded in sand. In 178

particular, we are interested in the zero-order torsional (T(0,1)) and longitudinal (L(0,2)) 179

modes. The displacement field associated with these axially symmetric modes propagating 180

along the axial direction in the embedded-coated-pipe system are analysed using the 181

formalism of Equations (1-8), considering different material properties of each of the layers 182

and modifying the boundary conditions. Specifically, continuity of displacements and stresses 183

is imposed at the interfaces between the pipe and the coating and between the coating and the 184

soil. The resulting characteristic dispersion relation is solved using the Disperse modelling 185

software [27-28]. 186

The Disperse software was used to predict the attenuation as a function of frequency for 187

different sand and coating acoustic properties to match the conditions covered in this study. 188

Figure 2 presents an example of dispersion curves of the zero-order modes for a Schedule-40, 189

8 inch pipe with and without FBE-coating embedded in soil with representative acoustic 190

properties. The group velocities are presented in Figure 2a and the corresponding attenuation 191

of the modes is presented in Figure 2b. The T(0,1) mode is non-dispersive for all frequencies, 192

while the L(0,2) mode is essentially non-dispersive over the ~20-100kHz range. The 193

attenuation values of the modes in the coated-embedded-pipe are slightly higher than the 194

bare-embedded pipe for low frequencies and increase with frequency. The attenuation values 195

depend on the bulk velocities of the embedding medium and will vary for different acoustic 196

properties of the soil. 197

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2.2 Acoustic properties of soils 198

The acoustic properties of the embedding soil dictate the amount of energy leakage from the 199

wave modes guided along the pipe, and hence have a major role in the guided wave 200

inspection range obtained in practice. Wave velocities and attenuation depend on the wave 201

parameters, e.g. frequency, wavelength and mode of propagation, and on the material 202

acoustic parameters. The acoustic parameters are linked to a range of geophysical properties, 203

e.g. grain density and diameter, porosity, degree of saturation, skeleton stiffness and bulk and 204

shear moduli. Materials with internal spatial scales such as soils, i.e. consisting of grains, 205

clusters and layers, are inherently dispersive [53]. Hence, bulk velocities in porous and 206

particulate media are generally reported in the literature for low frequency applications within 207

the framework of exploration seismology, earthquake engineering and structural stability. 208

Measurement techniques and measured values of velocity and attenuation in shallow near 209

surface unconsolidated soils reported in the literature were recently reviewed and summarised 210

in a preceding paper [23 and references therein]. Leinov et al. [23] extracted the shear 211

velocity of sand for a range of conditions from full-scale GWT experiments on a buried bare 212

pipe. 213

The model used in this study treats the embedding sand as an elastic solid. The Biot theory 214

[54-56] predicts the propagation of two compressional (dilatation) waves and a shear 215

(rotational) wave in a fluid-saturated porous medium. However, in the infinite frame-rigidity 216

limit of the Biot theory, the pore fluid viscosity is negligible and the two compressional 217

waves become decoupled. The rigid-frame limit was found to be appropriate to the study of 218

acoustic wave propagation within air-filled natural rock samples [e.g. 57] as well as granular 219

media such as sand [e.g. 58]. At the low strains common to guided wave propagation, 220

frictional loss, arising from inter-particle displacement and leading to slippage in the sand, is 221

not expected to be significant. 222

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223

3. Guided wave tests setup 224

A full-scale laboratory apparatus was used to allow well-controlled experimental conditions 225

for the measurement of ultrasound attenuation in the coated-pipe buried in sand. A detailed 226

description of the full-scale apparatus was provided in a preceding paper [23]. Here we 227

provide a short description of the significant features and the experimental set-up, followed 228

by a description of the measurement technique. 229

3.1 Full-scale experiments 230

The buried coated-pipe experimental apparatus consisted of a 6-meter long, 8 inch carbon 231

steel pipe (schedule-40, 9mm wall thickness), FBE-coated (Resicoat R4 AkzoNoble, 0.25mm 232

nominal thickness) embedded for 3-meters of its length in a rectangular container of 0.76m x 233

0.76m inner cross-section (Figure 3a-b). The container was constructed from 40mm-thick 234

plywood plates, reinforced with a system of inter-connected rectangular section steel beams 235

to support the load from the sand and was fitted with a tank-liner to contain the embedding 236

sand. The pipe was fitted to the container at the entry and exit positions through circular 237

openings in the corresponding wooden faces of the container, forming a 20mm gap around 238

the pipe from the opening edge, in order to allow the pipe to settle in the sand without making 239

contact with the openings in the wooden faces. A rectangular inflatable air-bladder (3m x 240

0.76m x 0.1m, Polyurethane fabric) was fitted between the sand surface and the container 241

covering plate in order to allow the application of different overburden pressure loads on the 242

sand corresponding to different depth conditions. The air-bladder was connected in-line with 243

an air compressor, needle valve regulator and air pressure gauge. Figure 3c presents a 244

photograph of the operating apparatus. Well-graded, dry clean sand (sand grain density of 245

2600 kgm-3) was used as the embedding medium. This type of sand is used as a structural 246

12

backfill material and complies with standardised practices for pipeline installation. The 247

particle size distribution of the sand was determined using a laboratory sieving test (See 248

[23]). 249

Ultrasonic guided waves were generated in the pipe using commercial transducer rings 250

(Guided Ultrasonics Ltd) and signals were transmitted and collected using the Wavemaker 251

G4 instrument (Guided Ultrasonics Ltd). The transducer ring consists of dry-coupled 252

piezoelectric transducer elements which are clamped to the pipe surface using an air-253

inflatable sleeve. Two independent transducer rings were attached in turn along the exposed 254

length of the pipe for the torsional (T(0,1)) and longitudinal (L(0,2)) modes. 255

Guided wave attenuation was measured in two different sets of sand conditions: loose and 256

compacted. The loose sand case was formed by pouring dry loose sand from bulk bags to 257

backfill the container up to a height of 0.76m (Figure 3b) and the compacted sand case was 258

obtained by application of overburden pressure up to 1bar on the sand, an equivalent to ca. 259

6m depth of dry sand with uniform density. The sand bulk densities associated with the cases 260

are presented in Table 1. The bulk densities were determined from measurement of the net 261

weight of sand used to fill the container and the volume it occupied in the container. A 262

detailed description of the set-up procedures of the loose and compacted sand conditions is 263

provided in [23], where similar conditions were undertaken to investigate buried bare pipe. 264

3.2 Measurement technique 265

The L(0,2) and T(0,1) guided wave modes were excited and recorded in separate independent 266

tests for each experimental condition using two different transducer rings. The transducer 267

rings were attached near the entrance to the container. Received raw signals obtained from 268

the transducer rings were applied with a Hilbert envelope in order to determine the 269

amplitudes of the reflections peaks; signals were converted to the frequency domain via 270

13

Fourier transform. Two different central frequencies, 16.5 kHz and 23.5 kHz, were used for 271

each mode to allow overlap of the frequencies in the range covered. 272

The attenuation characteristic was obtained from the ratio of the signal amplitudes measured 273

from the pipe end reflections: 274

𝛼 = −20𝑙𝑙𝑙10(𝐴1 𝐴0⁄ )2𝐿

(10) 275

where L is the length of the pipe embedded in sand, A0 is the reference reflection amplitude 276

and A1 is the measurement amplitude. The reference reflection signal is received echo from 277

the free end and the measurement signal is received echo from the pipe-end beyond the 278

buried section. The attenuation of both modes in air was found to be less than 0.1dBm-1 in 279

reference tests; hence the attenuation of the modes in the pipe section exposed to air is 280

considered to be negligible. 281

To interpret the data, a series of dispersion curves were produced for a coated steel pipe 282

embedded in an infinite layer of sand with a variety of possible values of acoustic parameters 283

using the Disperse modelling software [27-28]. The acoustic properties of the sand were 284

extracted from the best fit to the experiments. The use of two different modes for each 285

experimental condition provides a verification of the model predictions with a high degree of 286

confidence. 287

288

4. Results 289

4.1 Buried FBE-coated pipe 290

Results obtained from typical guided wave tests are shown in Figures 4a,b for the FBE-291

coated pipe buried in loose sand and in compacted sand (overburden pressure of 1 bar 292

14

applied), respectively. The mode of excitation was T(0,1) at a central frequency of 23.5 kHz. 293

The results are displayed as the amplitude of the Hilbert envelope of the recorded signal on a 294

logarithmic scale as a function of distance from the transducer ring position. Reflections from 295

both pipe-end locations are clearly evident, with the reflection from the free end of the pipe to 296

the left of the transducer ring location and the reflection from the pipe end past the embedded 297

section to the right of the transducer ring location. The attenuation is inferred from the 298

amplitudes of these reflections using Equation 10. Two reverberations from the two pipe ends 299

are also evident in the loose sand case (Figure 4a). The increase in the attenuation of the 300

signal is noticeable in the compacted sand case (Figure 4b), where the reflection from the 301

embedded pipe-end is much smaller than its counterpart in the loose sand case and the 302

reverberation from the pipe end past the embedded part cannot be distinguished from the 303

noise floor. 304

Figure 5 presents the attenuation measurements of the T(0,1) and L(0,2) modes as a function 305

of frequency in the FBE-coated pipe for the loose sand (no applied pressure) and compacted 306

sand (1 bar applied pressure) cases. The measured attenuation in a particular sand condition 307

at a particular frequency is the average of the values obtained from at least two different tests 308

performed at these conditions and from different excitation central frequencies; error bars 309

represent the variation between measurements at a certain frequency. The Disperse software 310

was used to predict the attenuation as a function of frequency for a variety of sand acoustic 311

velocities and the estimated density values (Table 1). Figure 5 presents the simulation best 312

fits to the measured attenuation in each mode for both sand cases. Also presented are 313

measurements and simulation fits reported in Leinov et al. [23] for bare steel pipe embedded 314

in similar conditions. The best fit curve is determined from the simultaneous fit to both the 315

torsional and longitudinal modes measured attenuation. Initially, the lower and higher 316

attenuation values of the torsional mode (Figure 5a and 5c) are fitted to find the range of 317

15

shear velocity values, then a single value of shear velocity within this range is found to match 318

the longitudinal mode measured attenuation (Figure 5b and 5d). The extracted best fit values 319

of the shear velocity are 93 ms-1 and 131 ms-1 for the loose and compacted sand cases, 320

respectively. The measured attenuation and the resulting shear velocity values are similar to 321

values obtained for bare pipe tests under similar loose and compacted sand conditions [23], 322

albeit the values in the FBE-coated pipe cases are slightly higher. However, the sand density 323

values for the FBE-coated pipe cases (Table 1) were higher than those reported in [23] for 324

both loose and compacted sand. The difference in sand density, resulting from variation in 325

sand packing between experiments, was 2 percent in the loose sand case and less than 1 326

percent in the compacted sand case. Hence, the FBE-coating does not cause a large increase 327

in the guided wave attenuation in buried pipes for the range of frequencies used. 328

The compaction of the sand significantly increases the attenuation of both modes. The 329

attenuation of the torsional mode is larger than the attenuation of the longitudinal mode for 330

both loose and compacted sand cases. These trends are similar to those found in [23]. 331

4.2 Ultrasonic isolation of buried pipe 332

The density and shear velocity of the coating layer and the embedding sand dictate the 333

attenuation of the guided wave modes. The impedance of the embedding sand promotes 334

guided wave energy leakage and results in high attenuation values. It is possible to achieve 335

ultrasonic isolation of a buried pipe by introducing a coating layer of smaller impedance than 336

both pipe and sand. Figure 6 presents the effect of the coating impedance on the attenuation 337

of the T(0,1) mode for a coated-pipe buried in compacted sand. The attenuation is presented 338

as a function of the non-dimensional frequency, 339

𝑓′ = 𝑓 ∙ 𝑑 𝐶𝑆,𝐶𝑙𝐶𝜕.⁄ (11) 340

16

where 𝑓 is the frequency, 𝑑 is the coating-layer thickness and 𝐶𝑆,𝐶𝑙𝐶𝜕. is the shear velocity in 341

the coating layer. When the impedance of the coating layer equals the impedance of the sand, 342

the attenuation of the torsional mode is non-dispersive, yielding a constant attenuation value. 343

As the impedance of the coating layer decreases from that of the sand impedance, the 344

torsional mode attenuation decreases with a minimum when the coating layer thickness is a 345

quarter wavelength; as the impedance of the coating layer increases from that of the sand, the 346

attenuation increases with a maximum at the same layer thickness. The minimum and 347

maximum values are a function of the shear velocity of the coating layer; the absolute 348

frequency at which these values are obtained is determined by the actual coating layer 349

thickness since it always occurs at a non-dimensional frequency of 0.25. 350

Ultrasonic isolation of the buried FBE-coated pipe was realised experimentally by the 351

application of a Polyethylene (PE)-foam layer (85 kgm-3, 19 mm thickness, Plastazote HD80, 352

Zotefoams) around the buried section of the pipe. PE-foam was selected due to its low 353

density and its rigidity, allowing it to withstand the load experienced by the sand backfill and 354

applied overburden pressure. The PE-foam was applied to the pipe with an epoxy spray 355

adhesive (HS-300, Ambersil) and was secured with a set of cable-ties (Figure 3d). 356

A set of guided wave measurements was performed on the FBE-PE-foam-coated pipe in air, 357

supported by wooden mounts, using both T(0,1) and L(0,2) modes. Figure 7 presents the 358

guided wave mode attenuation as a function of frequency, compared with reference tests 359

performed on bare and FBE-coated pipes in air. The attenuation of both modes in the bare 360

and FBE-coated pipes was found to be less than 0.1 dBm-1 and is considered negligible. The 361

attenuation in the FBE-PE-foam-coated pipe exhibits larger values for both modes. 362

The acoustic properties of the PE-foam coating were estimated using an ultrasonic 363

interferometry technique. Simonetti and Cawley [59] have developed a technique for the 364

17

measurement of the shear properties of viscoelastic materials, enabling measurements to be 365

performed on highly attenuating materials and at low frequencies. The technique is based on 366

measurement of the transmission and reflection coefficient spectra of the zero-order torsional 367

guided wave mode passing through a cylindrical sample of the viscoelastic material clamped 368

between two cylindrical steel rods (Figure 8a). The measurement of signals is performed by 369

two pairs of piezoelectric transducers placed at the free ends of the rod-specimen-rod system. 370

Tests were performed using 5 mm-dia. steel rods and ultrasonic signal excitation at 90 kHz 371

central frequency on several cylindrical specimens of PE-foam, 5 mm-dia. and different 372

lengths in the range of 2-32 mm. Initially, calibration procedures included measurement of a 373

reference pulse-echo response of one of the steel rods, without a specimen in place. 374

Subsequently, a specimen was positioned between the two rods under axial compressional 375

loading and measurements of pulse-echo and pitch-catch in the rod-specimen-rod system 376

were performed. The transmission and reflection coefficient spectra exhibit maxima and 377

minima which occur approximately at the resonance frequencies of the free viscoelastic 378

cylinder. Therefore, the shear velocity can be obtained by measuring the frequency interval 379

between two consecutive maxima or minima. The shear velocity and shear damping are 380

derived by best fitting the analytical expression of the reflection and transmission coefficients 381

[59] to the experimental spectra. 382

It was found that signal transmission was only measurable in specimens shorter than 2.5 mm, 383

demonstrating that the PE-foam is highly attenuative. Figure 8b-d presents the raw 384

measurement signals of reflection and transmission. Figure 8b shows the first reflected echo 385

from the free end of a steel rod and Figure 8c shows the reflected echo from the same rod 386

when a 2.5 mm long PE-foam specimen is clamped between the two rods. Figures 8b and 8c 387

are very similar, indicating that the reflection coefficient is very little affected by the presence 388

of the PE-foam. The signal transmitted through the second rod is shown in Figure 8d. The 389

18

measured transmission coefficient, obtained from the measured transmission through the PE-390

foam and the air-reference reflection signals, and the calculated best fit are presented in 391

Figure 8e. The best fit was obtained by a least-squares procedure on the analytical expression 392

of the transmission coefficient (Eq. 7 in [59]), yielding values of 312 ms-1 for the shear 393

velocity and 0.48 Np wavelength-1 for the shear attenuation. For comparison, reported values 394

of shear attenuation in HDPE are 0.29 (±10%) Np wavelength-1 [e.g. 35]; the porous nature of 395

the PE-foam medium is expected to increase the attenuation compared with the HDPE. 396

4.3 Buried FBE-PE-foam-coated pipe 397

Next, tests were performed on the FBE-PE-foam-coated pipe buried in sand in the full-scale 398

apparatus (Figure 3d). Typical guided wave tests, using the T(0,1) mode at a central 399

frequency of 23.5 kHz, for loose and compacted sand conditions are presented in Figures 400

4c,d, respectively. Reflections from both pipe-end locations are clearly evident. The 401

amplitude of the pipe-end reflection past the embedded section, appearing as the first 402

reflection to the right of the ring position, is larger in the FBE-PE-foam-coated pipe 403

compared with the FBE-coated pipe for both the loose sand (Figures 4c,a) and compacted 404

sand (Figures 4d,b) cases. The pipe-end reflection amplitudes obtained in the FBE-PE-foam-405

coated pipe cases are very similar, indicating the sand compaction has a minor effect on the 406

results. 407

Figure 9 presents the attenuation measurements of the T(0,1) and L(0,2) modes in the 408

frequency domain for the FBE-PE-foam-coated pipe buried in sand. Measurements were 409

performed for three sand conditions: loose sand (no applied pressure), intermediate 410

compacted sand (0.5 bar applied) and compacted sand (1 bar applied pressure). Also 411

presented in Figure 9 are measurements from the buried FBE-coated pipe and the 412

corresponding Disperse simulation fits (see Figure 5). A substantial decrease in attenuation is 413

19

clearly evident for both guided wave modes in the FBE-PE-foam-coated pipe. The 414

attenuation is found to be smaller than 1 dBm-1 for the T(0,1)-mode and smaller than 0.5 415

dBm-1 for the L(0,2)-mode. The attenuation measured in the compacted sand case was only 416

slightly larger than the loose sand, up to 0.3 dBm-1 for the T(0,1)-mode and up to 0.1 dBm-1 417

for the L(0,2)-mode. The compacted sand conditions were kept for over three months for 418

monitoring purposes, with periodic measurements performed. The attenuation values for both 419

modes remained within 0.1 dBm-1 of the initially measured values. The estimated values of 420

sand density for the loose and compacted cases for this pipe configuration were less than 1 421

percent different compared to those in the FBE-coated pipe configuration (Table 1). 422

The guided wave propagation in a buried FBE-PE-foam-coated pipe system was simulated 423

with the Disperse software using the material properties given in Table 1. Figure 10 presents 424

the effect of internal damping of the PE-foam layer on the attenuation of the modes in the 425

frequency domain. The peaks occur at three frequency values within the range of 10-40 kHz, 426

16.6, 24.8 and 33.2 kHz, which correspond to the through-thickness resonance frequencies of 427

the PE-foam layer and depend on the ratio of the shear velocity to thickness of the layer 428

(Equation 9). The troughs occur at frequency values equal to midway between two 429

consecutive through-thickness resonance frequencies of the layer. Strong frequency 430

dependence is evident. As the internal damping in the PE-foam layer increases, the difference 431

between the peaks and the troughs decreases. This behaviour is expected since material 432

absorption depresses the through-thickness resonance phenomenon [37]. 433

The amplitude spectra of the two end reflections for the torsional mode in the FBE-PE-foam-434

coated pipe buried in compacted sand case were computed via Fourier analysis and the 435

attenuation spectrum was computed from Equation (10); this is shown in Figure 11 along 436

with the corresponding simulation from Disperse. The measured curve was obtained from a 437

superposition of measurements performed at the different central frequencies. These 438

20

correspond to higher spectral resolution of the measurements presented in Fig. 9a (notice the 439

different ordinate scale). The simulation curve was calculated using the measured acoustic 440

properties of the PE-foam. The measured and predicted curves are qualitatively very similar 441

with peaks occurring at similar frequencies. The attenuation values at the peaks are somewhat 442

different and this is probably due to inaccuracies in the measurement of the PE-foam 443

attenuation which was difficult in such a low impedance, high attenuation material. The 444

Disperse prediction for a pipe surrounded by an infinite layer of PE-foam is also shown in 445

Figure 11. Since the infinite layer has no through-thickness resonances, this is a constant 446

value and the experimental curve is tending towards this value at higher frequencies as the 447

resonances are heavily attenuated. This indicates that the pipe is increasingly decoupled from 448

the sand; effectively, minimisation of the influence of the sand on the attenuation behaviour 449

was accomplished. 450

451

5. Conclusions 452

The attenuation of the T(0,1) and L(0,2) guided wave modes has been studied in a FBE-453

coated pipe buried in loose and compacted sand conditions over the frequency range 454

commonly used in GWT of 10-35 kHz. The attenuation of the guided wave modes in buried 455

pipes is largely due to energy leakage into the embedding sand. The thin FBE pipe coating 456

was found to slightly increase the attenuation of the modes compared to buried bare pipe. The 457

large values of attenuation measured for both guided wave modes dictate a significant 458

reduction of GWT test ranges for buried pipes compared with above-ground pipes. The 459

feasibility of ultrasonic isolation of the buried FBE-coated pipe using an additional coating 460

layer has been investigated. Ultrasonic isolation has been demonstrated by the application of 461

a PE-foam coating layer between the FBE-coated pipe and the sand. A PE-foam coating layer 462

21

was selected since its impedance is smaller than that of both pipe and sand, and due to its 463

ability to withstand the load from the sand and the applied overburden pressure. The 464

measured guided wave attenuation values in the buried PE-foam-FBE-coated pipe were 465

found to be substantially smaller than those measured in the buried FBE-coated pipe for both 466

loose and compacted sand conditions. The measured attenuation was found to be 0.5-1.2 467

dBm-1 for the T(0,1) mode and 0.3-0.5 dBm-1 for the L(0,2) mode in the pipe buried with the 468

PE-foam coating, compared to 2.8-4.7 dBm-1 for the T(0,1) mode and 1.7-2.8 dBm-1 for the 469

L(0,2) mode in the pipe buried without the PE-foam coating. 470

The shear velocity and attenuation in the PE-foam were measured independently using an 471

ultrasonic interferometry technique. The measured values were used to model the attenuation 472

behaviour of the modes in the buried FBE-PE-foam-coated pipe, good agreement being found 473

between the experimental measurements and model predictions. The torsional mode 474

attenuation showed periodic peaks in the frequency domain which correspond to the through-475

thickness resonance frequencies of the PE-foam coating layer and depend on the ratio of the 476

shear velocity to thickness of the layer. The attenuation peak values depend on the 477

attenuation in the coating layer, and decrease with increasing coating layer attenuation. 478

The large reduction in guided wave attenuation of the ultrasonically isolated buried pipe due 479

to the low impedance coating yields a substantial increase of guided wave inspection range. 480

The guided wave attenuation measurements can be used to estimate the inspection pipe-481

length for a pipe buried in sand. Given minimum signal to coherent noise ratio of 40 dB 482

generated by a GWT instrument (see [12]), propagation distances for the torsional mode in a 483

buried pipe without ultrasonic isolation would be limited to ~10m, corresponding to a test 484

range in a pulse-echo configuration of ~5m; however, for an ultrasonically isolated pipe the 485

torsional mode pulse-echo test range would increase to ~15-30 m. 486

22

487

488

Acknowledgments 489

The authors gratefully acknowledge support from the UK Engineering and Physical Sciences 490

Research Council (EPSRC) in this work, under research grant EP/J01284X/1 and the UK 491

Research Centre in Nondestructive Evaluation (RCNDE). This work was carried out in 492

collaboration with BP Exploration Operating Company Ltd, EDF Energy, EDF R&D and 493

Shell Global Solutions International BV. 494

The authors would like to thank Dr. David Alleyne, Dr. Brian Pavlakovic and Dr. Thomas 495

Vogt at Guided Ultrasonics Ltd for the loan of equipment and advice. The authors would also 496

like to thank Mr. Leslie Clark and Mr. Bob Hewitt at the Structures Laboratory, Dept. of 497

Civil and Environmental Engineering, Imperial College, for the excellent technical support. 498

E.L. would like to thank Mr. Tim Karaiskos for his help with the ultrasonic interferometry 499

measurements. 500

23

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668

669

31

Figure captions 670

Figure 1. Schematic of a coated pipe buried in soil. An access pit is excavated in order to 671

perform guided wave inspection, where a guided wave transducer ring is attached to the pipe. 672

(Online version in colour) 673

Figure 2. Dispersion curves of the zero-order guided wave modes of interest in this study: (a) 674

group velocity, and (b) attenuation. Solid lines: 8” carbon steel pipe (Schedule 40, 9 mm 675

wall thickness, ρSteel=7932 kgm-3; CL,Steel=5960 ms-1; CS,Steel=3260 ms-1), coated with fusion-676

bonded epoxy (0.3 mm thickness, ρFBE=1170 kgm-3; CL,FBE=2610 ms-1; CS,FBE=1100 ms-1) 677

and embedded in sand (ρSand=1620 kgm-3; CL,Sand=500 ms-1; CS,Sand=120 ms-1); and dashed 678

lines: 8” carbon steel pipe without coating embedded in sand (properties of the pipe and sand 679

are identical to properties in coated case). (Online version in colour) 680

Figure 3. Full-scale experimental apparatus: (a) Side view drawing, (b) front view drawing, 681

(c) photograph of the operating apparatus with the FBE-coated pipe embedded in sand in the 682

container, the transducer ring attached to the pipe and the data acquisition system, (d) 683

photograph of the FBE-coated pipe with additional layer of PE-foam coating being embedded 684

in sand; sand is poured from a bulk bag. (Online version in colour) 685

Figure 4. Typical experimental results from the coated buried pipe tests: amplitudes (in 686

arbitrary units) as a function of distance from the transducer ring, located adjacent to the 687

container entrance, using T(0,1) mode at central frequency of 23.5 kHz. FBE-coated pipe in 688

(a) loose sand, and (b) compacted sand (1bar applied pressure); and FBE-coated pipe (same 689

as used in (a-b)) with PE-foam coating layer in (c) loose sand, and (d) compacted sand (1bar 690

applied pressure). Grey shaded area represents near field. 691

32

Figure 5. Attenuation measurements as a function of frequency and Disperse simulation fits 692

(solid lines) for FBE-coated pipe compared to bare pipe [24] in loose and compacted sand 693

cases: (a) T(0,1) mode (diamonds and squares) and (b) L(0,2) mode (circles and triangles) in 694

the loose sand case; (c) T(0,1) mode (diamonds and squares) and (d) L(0,2) mode (circles and 695

triangles) in the compacted sand case. 696

Figure 6. Attenuation of the T(0,1) mode as a function of non-dimensional frequency (the 697

product of the frequency times the thickness over the shear velocity in the coating) for a pipe-698

coating-sand system: varying the impedance of a finite-thickness coating layer while keeping 699

sand properties constant (ρSand=1620kg/m3; CS,Sand=121m/s). Grey lines (dash, dash-dot, solid 700

and dotted) – increasing the impedance of the coating layer; black lines (dash, dash-dot and 701

dotted) – decreasing the impedance of the coating layer; and black solid line – pipe-sand 702

system without coating present. 703

Figure 7. Attenuation measurements as a function of frequency in air for bare pipe, FBE-704

coated pipe and FBE-PE-foam-coated pipe: (a) T(0,1) mode (diamonds and squares) and (b) 705

L(0,2) mode (circles and triangles). 706

Figure 8. Ultrasonic interferometry for the measurement of the shear velocity and damping in 707

PE-foam: (a) sketch of the apparatus comprising a viscoelastic material sample clamped 708

between two steel rods. Torsional mode guided wave is excited and received using 709

piezoelectric transducers; (b) signal reflected from the steel rod in air (without the sample in 710

(a)); (c) signal reflected from the interface between the first steel rod and a 2.5mm long PE-711

foam cylindrical specimen. The PE-foam is clamped between two rods as shown in (a); (d) 712

signal transmitted through the PE-foam specimen in the same configuration as (c); (e) 713

transmission coefficient spectra for the PE-foam, measured values (circles) and best fit (solid 714

line) obtained for CS,PE=312 m/s and αS,PE = 0.48 Np/wavelength. 715

33

Figure 9. Attenuation measurements as a function of frequency for FBE-PE-foam-coated pipe 716

in loose and compacted sand: (a) T(0,1) mode (diamonds) and (b) L(0,2) mode (circles), 717

compared to attenuation measurements (squares and triangles) and Disperse simulation fits 718

(solid lines) for FBE-coated pipe. 719

Figure 10. Attenuation as a function of frequency for FBE-PE-foam-coated pipe buried in 720

compacted sand (ρSand= 1635kg/m3; CS,Sand= 131m/s). Simulated for various values of shear 721

damping (αS,PE-foam= 0-0.75 Neper/wavelength) in the PE-foam layer (19 mm thickness; ρPE-722

foam= 85kg/m3; CS,PE-foam= 312m/s): (a) T(0,1) mode and (b) L(0,2) mode. Vertical grey 723

dashed lines represent the through-thickness resonant frequencies. 724

Figure 11. Attenuation of the T(0,1) mode from the FBE-PE-foam-coated pipe buried in 725

compacted sand (ρSand=1635kg/m3; CS,Sand=131m/s), obtained by experimental measurement 726

(black solid line) and Disperse simulation (grey solid line). Also shown Disperse simulation 727

for a case of infinite layer of PE-foam (grey dashed line). Measured acoustic properties of 728

PE-foam (see Figure 8) were used in the simulations (ρPE-foam=85kg/m3; CS,PE-foam=312m/s; 729

αS,PE-foam=0.48 Np/λ). 730

Table 1. Material properties and thickness dimensions used in Disperse simulations. 731

Figure 1.

Schematic of a coated pipe buried in soil. An access pit is excavated in order to perform

guided wave inspection, where a guided wave transducer ring is attached to the pipe.

(Online version in colour)

Figure 2.

(a) (b)

Dispersion curves of the zero-order guided wave modes of interest in this study: (a) group

velocity, and (b) attenuation. Solid lines: 8” carbon steel pipe (Schedule 40, 9 mm wall

thickness, ρSteel=7932 kgm-3; CL,Steel=5960 ms-1; CS,Steel=3260 ms-1), coated with fusion-

bonded epoxy (0.3 mm thickness, ρFBE=1170 kgm-3; CL,FBE=2610 ms-1; CS,FBE=1100 ms-1)

and embedded in sand (ρSand=1620 kgm-3; CL,Sand=500 ms-1; CS,Sand=120 ms-1); and dashed

lines: 8” carbon steel pipe without coating embedded in sand (properties of the pipe and sand

are identical to properties in coated case).

(Online version in colour)

Figure 3.

(a) (b)

(c) (d)

Full-scale experimental apparatus: (a) Side view drawing, (b) front view drawing, (c)

photograph of the operating apparatus with the FBE-coated pipe embedded in sand in the

container, the transducer ring attached to the pipe and the data acquisition system, (d)

photograph of the FBE-coated pipe with additional layer of PE-foam coating being embedded

in sand; sand is poured from a bulk bag.

(Online version in colour)

Figure 4.

(a) (b)

(c) (d)

Typical experimental results from the coated buried pipe tests: amplitudes (in arbitrary units)

as a function of distance from the transducer ring, located adjacent to the container entrance,

using T(0,1) mode at central frequency of 23.5 kHz. FBE-coated pipe in (a) loose sand, and

(b) compacted sand (1bar applied pressure); and FBE-coated pipe (same as used in (a-b))

with PE-foam coating layer in (c) loose sand, and (d) compacted sand (1bar applied pressure).

Grey shaded area represents near field.

Figure 5.

(a) (b)

(c) (d)

Attenuation measurements as a function of frequency and Disperse simulation fits (solid

lines) for FBE-coated pipe compared to bare pipe [24] in loose and compacted sand cases: (a)

T(0,1) mode (diamonds and squares) and (b) L(0,2) mode (circles and triangles) in the loose

sand case; (c) T(0,1) mode (diamonds and squares) and (d) L(0,2) mode (circles and

triangles) in the compacted sand case.

Figure 6.

Attenuation of the T(0,1) mode as a function of non-dimensional frequency (the product of

the frequency times the thickness over the shear velocity in the coating) for a pipe-coating-

sand system: varying the impedance of a finite-thickness coating layer while keeping sand

properties constant (ρSand=1620kg/m3; CS,Sand=121m/s). Grey lines (dash, dash-dot, solid and

dotted) – increasing the impedance of the coating layer; black lines (dash, dash-dot and

dotted) – decreasing the impedance of the coating layer; and black solid line – pipe-sand

system without coating present.

Figure 7.

(a) (b)

Attenuation measurements as a function of frequency in air for bare pipe, FBE-coated pipe

and FBE-PE-foam-coated pipe: (a) T(0,1) mode (diamonds and squares) and (b) L(0,2) mode

(circles and triangles).

Figure 8.

(a)

(b)

(e)

(c)

(d)

Ultrasonic interferometry for the measurement of the shear velocity and damping in PE-foam:

(a) sketch of the apparatus comprising a viscoelastic material sample clamped between two

steel rods. Torsional mode guided wave is excited and received using piezoelectric

transducers; (b) signal reflected from the steel rod in air (without the sample in (a)); (c) signal

reflected from the interface between the first steel rod and a 2.5mm long PE-foam cylindrical

specimen. The PE-foam is clamped between two rods as shown in (a); (d) signal transmitted

through the PE-foam specimen in the same configuration as (c); (e) transmission coefficient

spectra for the PE-foam, measured values (circles) and best fit (solid line) obtained for

CS,PE=312 m/s and αS,PE = 0.48 Np/wavelength.

Figure 9.

(a) (b)

Attenuation measurements as a function of frequency for FBE-PE-foam-coated pipe in loose

and compacted sand: (a) T(0,1) mode (diamonds) and (b) L(0,2) mode (circles), compared to

attenuation measurements (squares and triangles) and Disperse simulation fits (solid lines) for

FBE-coated pipe.

Figure 10.

(a) (b)

Attenuation as a function of frequency for FBE-PE-foam-coated pipe buried in compacted

sand (ρSand= 1635kg/m3; CS,Sand= 131m/s). Simulated for various values of shear damping

(αS,PE-foam= 0-0.75 Neper/wavelength) in the PE-foam layer (19 mm thickness; ρPE-foam=

85kg/m3; CS,PE-foam= 312m/s): (a) T(0,1) mode and (b) L(0,2) mode. Vertical grey dashed

lines represent the through-thickness resonant frequencies.

Figure 11.

Attenuation of the T(0,1) mode from the FBE-PE-foam-coated pipe buried in compacted sand

(ρSand=1635kg/m3; CS,Sand=131m/s), obtained by experimental measurement (black solid line)

and Disperse simulation (grey solid line). Also shown Disperse simulation for a case of

infinite layer of PE-foam (grey dashed line). Measured acoustic properties of PE-foam (see

Figure 8) were used in the simulations (ρPE-foam=85kg/m3; CS,PE-foam=312m/s; αS,PE-foam=0.48

Np/λ).

Table 1. Material properties and thickness dimensions used in Disperse simulations.

Material Thickness mm

Density kgm-3

CS ms-1

CL ms-1

Steel 9 7932 3260 5960 Fusion-Bonded Epoxy 0.3 1200 1100 2610 Sand (loose)* ∞ 1485 93 400 Sand (compacted)* ∞ 1635 131 800 PE-Foam 19 85 313 500 Sand (loose)† ∞ 1475 93 400 Sand (compacted)† ∞ 1630 131 800 *In buried FBE-coated pipe case. †In buried FBE- PE-foam-coated pipe case.