Investigation of guided wave propagation in pipes fully and partially embedded in concrete

The application of long-range guided-wave testing to pipes embedded in concrete results in unpredictable test-ranges. The influence of the circumferential extent of the embedding-concrete around a steel pipe on the guided wave propagation is investigated. An analytical model is used to study the axisymmetric fully embedded pipe case, while explicit finite-element and semi-analytical finite-element simulations are utilised to investigate a partially embedded pipe. Model predictions and simulations are compared with full-scale guided-wave tests. The transmission-loss of the T(0,1)-mode in an 8 in. steel pipe fully embedded over an axial length of 0.4 m is found to be in the range of 32-36 dB while it reduces by a factor of 5 when only 50% of the circumference is embedded. The transmission-loss in a fully embedded pipe is mainly due to attenuation in the embedded section while in a partially embedded pipe it depend strongly on the extent of mode-conversion at entry to the embedded-section; low loss modes with energy concentrated in the region of the circumference not-covered with concrete have been identified. The results show that in a fully embedded pipe, inspection beyond a short distance will not be possible, whereas when the concrete is debonded over a fraction of the pipe circumference, inspection of substantially longer lengths may be possible.


I. INTRODUCTION
The assessment and monitoring of infrastructure, e.g., pipelines, are of crucial importance in the early detection of corrosion and thus in avoiding leakage and associated economic and environmental costs.Guided wave testing (GWT), which uses elastic waves that can propagate along the wall of the pipe, is an efficient method for a rapid and accurate nondestructive assessment of large lengths of pipes.][3][4] GWT employs low-frequency ultrasonic waves (<100 kHz) that are guided in the axial direction along the inspected pipework.Waves are excited and received in a GWT sensor that is attached at a single position along the pipe.GWT offers coverage of tens of meters from a single position in aboveground bare pipe configurations (e.g., Alleyne et al. 1 ); however, when applied to coated, buried or embedded pipes practical test ranges are significantly reduced due to high attenuation of the guided wave modes. 5,6ave propagation phenomena along guides have been described extensively (e.g., Auld 7 ) and form the basis for obtaining characteristic dispersion relations and throughthickness mode shapes in certain regular geometries, e.g., cylindrical waveguides and flat plates. 83][14][15] The SAFE method uses a FE representation of the cross-section of the waveguide, thus enabling definitions of irregular cross-sectional shapes, together with a harmonic description of the wave modes along the propagation direction (e.g., Predoi et al. 16 ).
The propagation of guided waves in embedded waveguides is accompanied with attenuation due to leakage of energy radiating out into the embedding material, and damping by energy-absorbing materials of the waveguide system, resulting in a reduction of the test range.The extent of leakage depends on the material properties of both the pipe and the embedding material.Leaky cylindrical waveguides embedded in infinite media have been treated in the literature (e.g., Lowe, 8 Parnes, 17 Viens et al. 18 ), and have been utilised to study various systems, including steel bars embedded in cement grout, 19 wires embedded in epoxy resin, 20,21 rock bolts embedded in rock strata, 22 reinforcing bars and anchor bolts embedded in concrete, 23 steel bars embedded in soil, 24 and pipes buried in sand. 5Recently, Leinov et al. 6 have presented the possibility of ultrasonic isolation of pipelines buried in soil, utilising a carefully specified pipe coating material promoting the trapping of ultrasonic guided wave energy within the waveguide rather than allowing it to leak.The attenuation of the guided wave modes in structures coated with materials having internal damping, e.g., bitumen, is also related to the fraction of energy in the mode that is carried in the coating layer and generally increases with frequency. 25,26FE and SAFE numerical simulations have been used to study coated pipes [27][28][29][30] and coated pipes buried in soil. 31The SAFE method has also been utilized to study the general case of a waveguide with arbitrary cross-section embedded in a solid medium (e.g., Castaings and Lowe 32 ).
In some practical applications pipes are embedded in concrete, e.g., wall penetrations, pipe anchors. 33The acoustic properties of concrete dictate extremely high attenuation values of the guided wave modes in steel waveguides embedded in concrete, resulting in very short practical inspection ranges (e.g., Pavlacovic et al., 19 Beard et al. 23 ).However, in practice the inspection of pipes embedded in concrete is generally unpredictable.In some installations the guided wave modes show strong attenuation while other, apparently similar, installations show lower attenuation and increased inspection ranges, indicating the pipe and concrete have debonded partially or completely.In the present study, we investigate the influence of the circumferential extent of fully attached embedding concrete around the pipe on the guided wave behaviour.Model predictions are used to provide dispersion relations of the generic symmetric system of a pipe fully embedded in concrete, FE and SAFE simulations are utilized to study symmetric and asymmetric systems where the pipe is either fully or partially embedded in concrete, and full-scale experiments are performed for validation.
This paper is organised as follows.The acoustic properties of concrete, the guided wave model, FE and SAFE numerical implementations are described in Sec.II.The experimental apparatus and measurement method are described in Sec.III.The results are reported and discussed in Sec.IV and the conclusions are provided in Sec.V.

A. Acoustic properties of concrete
Concrete reaches its characteristic mechanical properties after curing for 28 days; the final concrete properties depend on the treatment it undergoes at its application site.The efficiency of the consolidation and the effectiveness of the curing procedures are critical for attaining the full potential of a designed concrete mixture.
The acoustic properties of the embedding concrete dictate the amount of energy leakage from the wave modes guided along the pipe, and hence have a major role in the GWT inspection range obtained in practice.A large amount of work has been published in the civil and geotechnical engineering literature on the measurement of concrete material properties.A number of representative values of concrete acoustic properties found in the literature are presented in Table I.Although concrete is an intrinsically heterogeneous material, 34 for the purpose of the current investigation the concrete is assumed to be elastic and homogenous since the guided wave leakage phenomenon is mainly governed by the average acoustic impedance of the embedding material.

B. Disperse simulations
The analytical model of guided wave propagation in embedded cylindrical shells has been described in detail in Refs.6 and 8.The Disperse 42 modelling software is based on partial wave theory and the global matrix technique. 8It provides rigorous predictions for guided wave propagation and dispersion characteristics with frequency in simple waveguide geometries, e.g., pipes, and allows the embedding of the structure in solid materials.Dispersion curves are found iteratively in frequency, wave number and attenuation space.
The model used to generate dispersion curves in Disperse assumes guided wave modes propagate along an infinitely long hollow cylinder embedded in an infinite concrete medium.Continuity of displacements and stresses is imposed at the interface between the pipe and the concrete.The dispersion of the guided wave is due to geometrical effects and leakage of energy to the embedding medium; the concrete is assumed here to behave as an elastic solid material.The propagating mode displacements on the outer surface of the pipe excite bulk waves in the surrounding medium which radiate energy away from the pipe.Figure 1 presents an example of dispersion curves of the zero-order modes for a Schedule-40, 8 in.pipe embedded in concrete with representative acoustic properties.Figure 1(a) shows the group velocity and the corresponding attenuation of the fundamental modes is presented in Fig. 1(b).The attenuation

C. Finite-element simulations
The Disperse software can only be used to solve plate or axisymmetric systems.Therefore, in order to predict the effect of the circumferential extent of the embedding concrete on the propagation of the T(0,1)-mode as it propagates into an embedded section, explicit time domain FE simulations were performed using Abaqus (Dassault Syste `ms).The FE model consisted of a 4 m long, 8 in.steel pipe (9 mm wall thickness) embedded in concrete, as illustrated in Figs.2(a)-2(c).Two different axial lengths of embedding concrete were studied, 0.4 and 0.9 m, to allow comparison of the simulation results to the experimental measurements and to extract the attenuation of the wave propagating in the embedded section of the pipe.The 0.4 m long embedding length was not long enough to allow the extraction of the attenuation while avoiding the effect of the reflection from the exit of the embedded section; hence, the 0.9 m long embedding length was selected to allow a longer propagation distance for the signal within the embedded section.The embedding region extended for 1 m in the radial direction [Figs.2(a)-2(c)].The radial length of the embedding region was chosen to avoid reflections of the leaky waves from the domain edges by simply gating them out in time.The extent of the circumferential cover was varied from 22.5 to 360 (fully embedded).The mechanical properties of steel and concrete used in the simulations are given in Table II.
A mesh of linear hexahedral elements was used with four elements through the wall thickness of the pipe and 391 elements around the circumference of the pipe.The pipe and embedding region were meshed as a single part in Abaqus with 21.13 Â 10 6 elements.The mechanical properties of steel and concrete were assigned to the elements in each region using a MATLAB script before performing the simulations back in Abaqus.The MATLAB software was also used to post-process the simulation results.Excitation of the T(0,1)-mode was obtained by prescribing tangential forces of equal magnitude at the through-thickness nodes around the circumference of the pipe at a desired axial position, the excitation being either a two or a five-cycle Hanning windowed tone burst.Simulations were performed at different central frequencies in the range of 19-35 kHz.The simulation setup is presented in Fig. 2(c), the incident signal is excited in the plain pipe section at 1 m from the pipe-end and recorded at six positions along the pipe, at 0.4 m before entry and 0.5 m before the pipe-end, after the exit from the embedding region, and at four evenly spaced positions along the embedding region.Absorbing layers (ALID, e.g., see Castaings and Bacon 43 ) were implemented at the free end of the pipe near the excitation signal position to remove wave reflections from waves travelling at the opposite direction from the embedding region.

D. Semi-analytical finite-element simulations
The SAFE method was implemented to predict the propagating wave modes in the partially embedded section of the pipe in order to improve the understanding of the waveforms predicted by the response model of Sec.II C. The method uses a two-dimensional FE representation of a constant crosssection of the waveguide and the embedding medium.The model is based on three-dimensional elasticity, where no simplifications are made to the elastic tensor and the displacement field.Harmonic guided waves propagating along the axial direction, i.e., the axis perpendicular to the cross section, are considered.The equation of dynamic equilibrium is prescribed in the form of a characteristic eigenvalue problem with eigenvalue solutions in terms of wavenumber for chosen values of angular frequency (see Castaings and Lowe 32 ).Each set of solutions at a chosen frequency produces the wavenumber of all of the possible modes at that frequency.The full dispersion curve spectrum is found by repeatedly solving the eigenvalue problem at each frequency over the desired range of frequencies.The infinite embedding medium has to be modelled with finite extent in the model; reflections from the outer edge are suppressed by applying gradually increasing damping to the region of concrete outside an elastic inner shell, 32,43 as shown in Figs.

2(d) and 2(e).
In this study the SAFE method was implemented in Comsol Multiphysics 5.2 software (Comsol Inc.).Two cases of interest were modelled, namely, a pipe embedded in a full-wall of concrete [Fig.2(d)] and a pipe embedded in a half-wall of concrete [Fig.2(e)].The models consisted of an 8 in.steel pipe (9 mm wall thickness) embedded in concrete.The mechanical properties of steel and concrete used in the SAFE model are given in Table II.The embedding region consisted of a layer of elastic concrete (20 mm thick), and a layer of concrete with absorbing properties (310 mm thick).The thickness of the absorbing layer was approximated to be twice the maximum wavelength of the bulk waves expected to be radiated into the concrete when guided wave modes propagate along the steel pipe at a frequency of around 25 kHz.Increasing the length of the absorbing region further resulted in an increased number of spurious modes present in the solution for higher frequencies.Hence, this size was selected as a compromise and a reduced accuracy of the SAFE model was expected at frequencies below 25 kHz where the outer surface reflections would not be completely suppressed.The whole geometry was meshed with 8900 triangular elements in the full-wall case and with 5090 triangular elements in the half-wall case.Calculations were performed over a frequency range of 15-90 kHz in 5 kHz steps.Over 800 eigenvalue solutions were found at each calculation step; the solution values were filtered to obtain the modes with dominant motion in the steel pipe and eliminate waves with motion only in the embedding concrete.
The full-wall case was solved to provide validation of the SAFE solution by comparing it with the model predictions produced by Disperse software (Sec.II B).The same parameters used in the full-wall case were then implemented in the half-wall case.

III. GUIDED WAVE TEST SETUP
A full-scale laboratory apparatus was constructed to allow comparison between simulations and experimental measurements.Here we describe the apparatus and the measurement technique.

A. Full-scale experiments
Two cases of interest were selected for the experimental investigation, namely, a pipe fully embedded in concrete (full-wall case) and a pipe half-embedded in concrete (halfwall case).The embedded pipes experimental rig consisted of two 8 in.diameter schedule-40 carbon steel pipes; a 5.67 m long pipe was used in the full-wall case and a 6 -m long pipe was used in the half-wall case.Each pipe was supported by two support posts fitted with simple wooden supports.Two plywood moulds were prepared for the casting of concrete.The concrete dimensions extended a minimum of 0.5 m from the pipe in the radial direction; the exterior dimensions were 1.28 m (height) Â 1.53 m (width) in the full-wall case and 1.76 m (height) Â 1.41 m (width) in the half-wall case, with a gap exposing the bottom half of the pipe to air [Figs.3(a) and 3(b)].The embedding length along the axis of the pipe was 0.4 m to allow guided wave measurements to be performed within a dynamic range of 40 dB with a measurable signal past the concrete.A standard ready-mix batch of concrete was used (30/37 CIIB-VþSR, Cemex UK Materials Ltd.) with an average aggregate size of 10 mm (Thames valley flint).A total of 1.6 m 3 of concrete was used to cast both moulds from the same batch; the wooden moulds were removed 28 days after casting.Figures 3(a) and 3(b) presents photographs of the rig 30 days after casting; the concrete density was determined to be 2320 6 20 kg/m 3 following the completion of the testing programme by weighing each of the test specimens and knowing the weight of the pipes.The density measurement was confirmed using 4 concrete standard test cubes (0.1 m Â 0.1 m Â 0.1 m) which were set aside at casting for compression stress tests.The concrete test cubes were prepared by casting concrete into standard test cube moulds and were kept submerged in a tank of water for 30 days to provide a hydrated environment for the curing process after removing the cubes from the moulds 24 h after casting.The compression stress test (Automax 5, Controls) yielded an averaged compressive strength value of 48.62 6 0.05 MPa.The compressive strength was used to estimate the concrete Young's modulus using a standard correlation. 44uided wave tests were performed using the T(0,1) mode which was generated in the pipe using commercial transducer rings (Guided Ultrasonics, Ltd.); signals were transmitted and collected using the Wavemaker G4 instrument (Guided Ultrasonics, Ltd.).The transducer rings consist of dry-coupled piezoelectric transducer elements which are clamped to the pipe surface using an air-inflatable sleeve.
Guided wave tests were performed on both the full-wall and half-wall rigs in succession during the concrete curing process and after the concrete had matured for 28 days as required for attaining its compressive strength potential.Initially, tests were performed immediately after casting the concrete into both moulds; subsequently, tests were performed 48 h after casting and once a week until 7 weeks after casting.

B. Measurement technique
During the concrete curing, tests were performed in pulse-echo mode using a single transducer ring attached at the free section of each of the pipes, such that a reflection from the pipe-end near the transducer ring and a reflection from the pipe-end beyond the embedded section were received and recorded.Received signals obtained from the transducer rings were converted to the frequency domain via Fourier transform.Two different central frequencies, 16.5 and 23.5 kHz, were used to allow overlap of the frequencies in the range covered.
The transmission loss across the embedded section was obtained from the echo received from the end of the pipe beyond the embedded section, compared to that received from the near end, the factor 2 being introduced because the wave interacts twice with the embedded section.The transmission loss is a result of reflection and mode conversion at the two ends of the embedded section and the attenuation along it.The attenuation of the guided wave mode in the free section of the pipe was considered to be negligible. 5fter 2 weeks of the concrete curing, the signal reflection from the pipe-end beyond the embedding region could not be distinguished from the coherent noise level.Tests were then performed in a transmission mode using two separate transducer rings positioned at both sides of the concrete wall.In this configuration, a signal generated by one ring has been transmitted once through the entry and once through the exit from the embedded section before being recorded by the second ring.The transmission loss measurement in this configuration was obtained from where A 0,1 is the reference amplitude of the transmitting ring, A 0,2 is the reference amplitude of the receiving ring and A 1 is the amplitude of signal received from the transmitting ring at the receiving ring.The reference amplitude of each ring was obtained from a received echo from the free-end of the pipe corresponding to a signal generated and recorded in each ring.
IV. RESULTS

A. Finite-element simulations
Some example results from the 3D-FE simulations are given in Fig. 4. The A-scan signals at the different monitoring positions [Fig.2(c)] in the full-wall case for an incident wave at a central frequency of 28 kHz are shown in Fig. 4(a).The signals were obtained by summing the recorded signal traces at the nodes around the outer circumference of the pipe at the different monitoring axial-positions.The amplitude of the transmitted wave decreases considerably with the propagation distance along the embedded region of the pipe due to the leakage of energy into the embedding concrete.Figure 4(b) presents the reflection and transmission coefficients as a function of frequency in the full-wall case.The reflection and transmission coefficients were obtained from the ratio of the Fourier transform of the signal amplitudes at the monitoring positions before and beyond the embedded region to the incident signal, respectively.Here transmission refers to the wave transmitted beyond the embedding region onto the plain pipe region.The results show that almost no signal was transmitted through the 0.9 m long embedding region due to strong attenuation of the signal.The reflection coefficient is in the range of 0.1-0.22 and decreases with increasing frequency; this behaviour has been discussed in Vogt et al. 20,21 Figure 4(c) shows results obtained in the half-wall case, where the transmitted signal decreases only slightly with propagation distance along the embedded region of the pipe and a significant signal was recorded at the monitoring position beyond the embedded region.The reflection coefficient in the half-wall case [Fig.4(d)] has decreased to the range of 0.04-0.1,about half of its magnitude in the full-wall case, while the transmission coefficient has increased to 0.42-0.5 compared to practically no transmission in the full-wall case.
The effect of the concrete circumferential coverage around the pipe on the propagation of the T(0,1)-mode was addressed by studying several cases of different extent of concrete cover.Figure 5 presents the maximum signal amplitudes around the circumference of the pipe as a function of angle at the monitoring positions before and beyond the concrete-embedded region for four different circumferential extents.The amplitudes were normalised by the maximum amplitude of the incident signal.The results show that the transmitted signal, measured at the axial position beyond the embedded region, acts as an indicator of the position of the missing concrete around the circumference of the pipe.Larger amplitudes were measured in the exposed section around the circumference of the pipe at the given axial position, while smaller amplitudes were measured in the section in contact with the embedding concrete.As the concrete covers larger extents of the circumference of the pipe, the amplitude values were smaller.

B. Semi-analytical finite-element simulations
The SAFE method was implemented for two general cases, fully and half-embedded pipes in concrete, for a frequency range of 15-90 kHz.The full-wall case was initially modelled to allow comparison to the Disperse model predictions and to verify the parametric values of the absorption coefficient in the concrete absorbing region 32 [Figs.2(d) and 2(e)].Figures 6(a) and 6(b) present example results from the SAFE simulations at a single frequency of 40 kHz for two different modes, the T(0,1) [Fig.6(a)] and the F(1,2) [Fig.6(b)].These modes correspond to solutions with motion primarily in the steel pipe coupled to the surrounding concrete.Figures 7(a) and 7(b) presents the dispersion curves of the wave modes propagating in the steel pipe and radiating energy into the concrete.The solid curves are the Disperse model predictions for these modes as well as the L(0,2) and the F(1,3) modes and the markers are the SAFE solutions.Only the wave modes of circumferential order zero (axially symmetric) and order one (one harmonic order around the circumference) of relevance to the current study are shown while other modes are not shown for clarity.The phase velocity of the SAFE solutions [Fig.7(a)] was obtained by dividing the angular frequency by the real wavenumber, and the attenuation [Fig.7(b)] was obtained from the imaginary part of the wavenumber.Very good agreement is found between most of the SAFE solutions and the independently calculated dispersion curves from Disperse, though the SAFE phase velocity diverges from the Disperse calculated curves for frequencies smaller than 25 kHz.This divergence results from the selection of the size of the absorbing region in the SAFE model as mentioned in Sec.II D.
The same model parameters were then used to model the half-wall case.The zero-order axisymmetric modes, T(0,1) and L(0,2), do not exist in this case since the system is non-symmetric.However, other modes with predominant motion over half the circumference of the pipe were found; two modes with predominantly circumferential motion are shown in Figs.6(c) and 6(d).In one case the motion is concentrated in the embedded section of the pipe [Fig.6(c)] while in the other the motion is primarily in the free section of the pipe [Fig.6(d)].By analogy with the F(1,2)-mode of the axisymmetric system [Fig.6(b)], these have been termed F 0 (1,2) and F 00 (1,2), respectively.Modes similar to the F(1,3)-mode in the axisymmetric system with motion primarily in the embedded [F 0 (1,3)] and free [F 00 (1,3)] sections of the pipe were also found.The phase velocity and attenuation of the modes of interest as a function of frequency obtained from the SAFE model in the half-wall case are presented in Figs.7(c) and 7(d); also shown for reference are the dispersion curves for the full-wall case obtained from Disperse.Good agreement is found in the phase velocity; the modes concentrated in the embedded and exposed regions have very similar values of phase velocity to those in the full-wall case.The attenuation of the modes in the embedded region of the pipe in the half-wall case behave the same as in the full-wall case, while the modes in the exposed section of the pipe have practically no attenuation.Since the zero-order axisymmetric-modes do not exist in the partially embedded case, the T(0,1)-mode propagating in the plain pipe section before entry to the embedded region mode converts on entry to the embedded region to flexural modes, i.e., F 0 (1,2) and F 00 (1,2), and higher-order modes that are characteristic of the partially embedded region.The modes that exist in the embedded part of the pipe circumference are leaky-modes and the modes that exist in the exposed part have practically no attenuation.Beyond the embedded region these modes will reconvert to the T(0,1) and F(1,2) modes of the plain pipe.The same argument is applicable for the zero-order longitudinal mode, L(0,2), that will be converted to F 0 (1,3) and F 00 (1,3).

C. Guided wave tests
Results obtained from guided wave tests on the pipes embedded in the full-wall and the half-wall of concrete immediately after concrete casting are shown in Figs.8(a) and 8(b).The mode of excitation was T(0,1) at a central frequency of 23.5 kHz.The results are displayed as the amplitude of the Hilbert envelope of the recorded signal on a logarithmic scale as a function of distance from the transducer ring position.Reflections from both pipe-end positions are clearly evident, with the reflection from the near-end of  the pipe to the left of the transducer ring position and the reflection from the pipe-end beyond the embedded region to the right of the transducer ring position.The transmission loss measurement of the guided wave mode was obtained from the amplitudes of these reflections using Eq. ( 1).Figures 8(c) and 8(d) present results obtained 2 weeks after the concrete casting for both cases.In the full-wall case [Fig.8(c)], the pipe-end reflection from the near-end of the pipe is clearly evident while the reflection from the pipe-end beyond the concrete wall could not be clearly identified from the coherent noise level following the entry reflection from the concrete wall.This indicates that the concrete has established a good acoustic coupling with the pipe since there is energy leakage.Conversely, in the 2 weeks old concrete half-wall case [Fig.8(d)], the pipe-end reflection from beyond the concrete wall appears to be larger than it was in the test performed immediately after casting [Fig.8(b)], denoting that the attenuation has decreased; this indicated the concrete was not acoustically coupled to the pipe.Tests performed over the following 2 weeks have confirmed that the concrete was practically not in contact with the pipe.To verify this hypothesis, after the removal of the wooden moulds 28 days after casting, the pipe support posts [Fig.3(b)] were removed and indeed the pipe was found to be completely disbonded from the half-wall of concrete [Fig.3(c)].Therefore, in order to achieve acoustic coupling between the pipe and concrete, the pipe and half-wall of concrete were joined at the same location using a thin layer of epoxy adhesive (Araldite 2011, Huntsman) [Fig.3(d)].Tests were then performed immediately after the application of the epoxy, and 3 days later, after the epoxy had completely cured.
Figure 9 presents the transmission loss measurements of the T(0,1)-mode as a function of frequency during and after the concrete curing process in the half-and full-wall cases.The transmission loss in the half-wall case [Fig.9(a)] immediately after the concrete casting is in the range of 1.4-1.7 dB, after 2 days the transmission loss reduced to the range of 0.6-1.2dB, and after 2 weeks it was in the range of 0.1-0.2dB, indicating that the concrete was not acoustically coupled to the pipe and practically all of the guided wave energy remained in the pipe.After the application of the thin layer of epoxy between the pipe and concrete, the transmission loss had similar and even larger values compared to those obtained with fresh concrete; the transmission loss increased further after the epoxy had cured, to values in the range of 5.8-6.8dB, indicating that acoustic coupling between the pipe and concrete had been established.
The measured transmission loss immediately after the concrete casting in the full-wall case [Fig.9(b)] was higher than that measured in the half-wall case.The transmission loss increased dramatically in the full-wall 2 days after casting, from 1.4-2.7 dB to 12.5-15.5dB, implying the concrete was acoustically coupled to the pipe and energy leakage was promoted.The attenuation increased moderately over the next 2 weeks and after 4 weeks of concrete curing the measured attenuation has reached values of 18-28 dB with a strong frequency dependence.

D. Comparison between predicted and measured transmission loss
where A T is the amplitude of the transmitted signal beyond the concrete-embedded region and A I is the amplitude of the incident signal.The transmission loss includes the attenuation of the signal along the embedded section and the losses due to reflection and mode-conversion at the entry and exit of the embedded section.Figure 10 also presents the transmission loss due to attenuation in the embedded section, extracted from simulations of pipe embedded over 0.9 m in full-wall of concrete.The attenuation in the embedded section of the pipe was obtained from the recorded signal amplitudes at the monitoring positions within the embedded section [see Fig. 2 where A i is the amplitude of the signal at a monitoring position within the embedded section, A 0 is the amplitude of the signal at the first monitoring position within the embedded section and L is the distance between these monitoring positions.The transmission loss values due to attenuation were then obtained by multiplying the attenuation by the distance of 0.4 m.The full-wall case results show that the transmission loss is almost entirely due to attenuation along the embedded section.Good agreement is found with the Disperse model predictions, the maximum difference being 5%.The experimentally measured transmission loss values in the full-wall case are lower than the simulation values, in the range of 18-28 dB, and show a clear evidence of frequency dependence.It is recognised that the simple single uniform-layer model used in Disperse and in the simulations is not an exact representation since the mean properties of the concrete are likely to vary with distance from the pipe wall.Evidence of reduction in the volume fraction of aggregate (mean diameter of 10 mm) in the 10-20 mm of concrete adjacent to pipe has been found following the completion of the experimental campaign when a quarter of the full-wall of concrete was cut-out in the axial direction along the pipe, exposing the pipe-concrete interface.Therefore the effect of the presence of a thin layer of concrete with similar properties to those of plain cement (grout) on the attenuation has been investigated.A modified, two-layer model has been simulated in the Disperse software where a pipe is embedded in a medium consisting of an inner layer of material adjacent to the pipe and a surrounding second infinite-layer of concrete.A similar approach has been used by Leinov et al. 5 to explain the frequency-dependent attenuation in pipes buried in soil.The outer layer properties were set to be equal to the properties used to model the single uniform-layer of concrete (Table II).The thickness of the inner layer was approximated to vary in the range of 1-2 times the mean aggregate size of 10 mm and the acoustic properties of the layer were adjusted to fit the transmission loss values.Figure 11 shows the two-layer simulation best fit to the experimental measurements along with the single uniform-layer fit.A very good fit is obtained using the two-layer model to most of the measured transmission loss values.The two-layer model best-fit was obtained for acoustic properties of the inner layer that are between those of concrete and grout (Table I), and the best-fit thickness was found to be 16 mm.The twolayer model results, along with this observation, suggest that an interlayer with varying properties is the likely explanation for the lower, frequency dependent transmission loss.
In the half-wall case, the measured transmission loss values are much smaller than the full-wall case, in the range of 5.8-6.8dB (Fig. 11).Explicit 3D-FE simulations of pipe embedded over 0.4 m in half-wall of concrete were performed at the same frequencies as in the full-wall case; good agreement within 10%, was found between the transmission loss values obtained from the FE simulation of the half-wall case and the experimental measurements.The simulation values are slightly larger than the experimentally measured values due to the fact that in the tests the concrete actually covered 48.5% rather than 50% of the pipe circumference.

V. CONCLUSIONS
The propagation of the T(0,1) guided wave mode has been investigated in pipes fully and partially embedded in fully attached concrete using guided wave models, FE and SAFE simulations and full-scale laboratory experiments over the frequency range commonly used in guided wave testing.Model predictions of the transmission loss due to attenuation of the torsional mode in an 8 in.steel pipe fully embedded in concrete over 0.4 m of its length were found to be in the range of 32-36 dB.The FE simulations of a pipe fully embedded in concrete that is fully attached to the concrete have shown that the transmission loss is almost entirely due to attenuation along the embedded section and that losses from scattering and mode conversion at the entry and exit are negligible.Experimentally measured transmission loss in the fully embedded pipe were found to be lower than the predicted values, in the range of 18-28 dB, with clear evidence of frequency dependence.It was shown that the frequency dependence can be explained by the presence of a thin layer adjacent to the pipe with a lower acoustic impedance than the bulk of the embedding concrete due to a reduced volume fraction of aggregate in this region.
The transmission loss in a partially embedded pipe was found to be significantly lower than that in the fully embedded pipe and to be dominated by mode conversion.Predicted and experimentally measured transmission loss values in a pipe half-embedded in concrete over 0.4 m were found to be in the range of 5.8-7.6 dB.
The high transmission loss in a fully embedded pipe results in a very short guided wave inspection range.However, for pipes partially embedded in concrete or cases where the concrete is only partially bonded to the pipe, measurable signals would be obtained over significantly longer distances.The variability in the circumferential extent of the bonding between the pipe and the concrete can explain the unpredictability of test-ranges encountered in GWT and could be used to indicate whether the concrete is bonded to the pipe over the full-circumference.Nanyang Technological University, Singapore, for his support and advice on SAFE modelling and Dr. Anton Van-Pamel at Imperial College for valuable advice on FE modelling.

FIG. 3 .
FIG. 3. (Color online) Full-scale experimental rig: (a) and (b) photographs of the rig from two opposing faces with one pipe embedded in fullwall of concrete and a second pipe embedded in half-wall of concrete.(Photographstaken 30 days after casting); (c) photograph captured after removing the pipe support posts in the half-wall rig; the concrete was not coupled to the pipe after curing, (d) a thin layer of epoxy was applied between the pipe and the concrete to allow acoustic coupling.

FIG. 4 .
FIG. 4. (Color online) Data analysis of the FE simulations at a central frequency of 28 kHz.Full-wall case: (a) A-scans at the monitoring positions and (b) reflection (black) and transmission (red) coefficients; Half-wall case: (c) A-scans at the monitoring positions and (d) reflection (black) and transmission (red) coefficients.The signals in (a) and (c) are the axisymmetric component of the motion, obtained by summing the signal traces at the nodes around the circumference of the pipe at the different monitoring axial-positions.

FIG. 5 .
FIG. 5. (Color online) FE simulation results: normalised amplitudes around the circumference of the pipe at the monitoring positions before (black) and after (red) the 0.9 m concrete-embedded section of the pipe for different circumferential concrete coverage at 28 kHz central frequency: (a) 90 cover ( 1 4 -wall), (b) 180 cover ( 1 2 -wall), (c) 225 cover ( 5 8 -wall) and (d) 270 cover ( 3 4 -wall).Amplitudes are normalised by the incident signal amplitude.The scale in (d) is an order of magnitude smaller than the scale in (a-c).

FIG. 6 .
FIG. 6. (Color online) SAFE model example results.Cross-sectional distribution of the axial energy flow in the pipe for fully and partially embedded cases at 40 kHz for different modes.The grey area surrounding the pipe indicates the presence of concrete.Full-wall case: (a) T(0,1)-mode and (b) F(1,2)-mode; Half-wall case: (c) F 0 (1,2)-mode having motion primarily in the embedded section of the pipe, (d) F 00 (1,2)-mode having motion primarily in the exposed section of the pipe.The motion in all modes shown is predominantly torsional.The color scale represents the normalised axial energy flow in the pipe.The energy flow is normalised by the maximum value of energy flow for each of the modes.

A
comparison between transmission loss values obtained from Disperse model prediction and 3D-FE simulations and experimentally measured values in the guided wave tests performed after the concrete curing on the pipes embedded in full-wall and half-wall of concrete is presented in Fig. 10.The attenuation values predicted by the Disperse model for a pipe fully embedded in concrete [Fig.1(b)] were converted to transmission loss by multiplying the attenuation by 0.4 m of propagation distance in concrete to yield values of 32-36 dB over the frequency range of 10-40 kHz.

FIG. 8 .
FIG.8.Experimental results from the embedded pipes: Amplitudes of the Hilbert envelope of the recorded signal (in arbitrary units) as a function of distance from the transducer ring, located between the pipe end and the concrete, using T(0,1) mode at central frequency of 23.5 kHz.Grey shaded rectangle is the near field.Pipe embedded in (a) full-wall and (b) half-wall immediately after casting; (c) full-wall and (d) halfwall weeks after concrete casting.

FIG. 9 .
FIG. 9. (Color online) Transmission loss measurements as a function of frequency for pipe embedded over 0.4 m in (a) half-wall and (b) full-wall of concrete.

FIG. (
FIG. (Color online)Disperse model fit to the experimental transmission loss measurements in the full-wall case as a function of frequency: experimental measurements (circles), uniform single-layer model (q Conc.¼ 2320 kg/m 3 ; C S ¼ 2413 m/s; C L ¼ 3982.6 m/s) (blue solid line), and twolayer model (inner layer of concrete: 16 mm thickness; q Conc.,1 ¼ 1900 kg/m 3 ; C S,1 ¼ 1800 m/s; C L,1 ¼ 2900 m/s; outer layer of concrete properties are identical to the uniform single-layer properties) (black solid line).

TABLE I .
Material properties of concrete from the literature.

TABLE II .
Mechanical properties of steel and concrete used in this study.Value measured from standard concrete block specimen extracted from the casting batch and confirmed with weight measurement of the entire experimental rig.bValue extracted from compression stress tests performed on standard concrete blocks extracted from the casting batch; the compression stress was converted to Young's modulus using a relation given in Ref.44. a