Pipeline scanning: Novel technology for detection of voids and internal defects in non-conductive buried pipes

Underground non-metallic infrastructure including concrete and vitrified clay pipes, culverts and tunnels are deteriorating and an internal inspection procedure is necessary to establish the extent of rehabilitation work required. The most popular means of inspecting buried gravity driven pipes is a CCTV which is mounted on a robotic platform and designed to capture and transmit photographic images of the pipe wall. Though CCTV is an effective tool for identifying visible defects on the internal wall of pipelines, the possibility of seeing behind the pipe’s inner surface is limited. In order to overcome this limitation several companies use high frequency GPR units mounted on robotic platforms. The radars used for this purpose operate at high frequencies (1-3 GHz) with a narrow bandwidth. These radars are capable of providing some information regarding discontinuities and other structural defects in the pipe wall. However, these units suffer from several shortcomings including limited penetration depth and the need for a highly experienced geophysics professional to interpret the results. Also, most systems operate within a narrow range of frequencies, making it difficult to optimize their performance in the highly variable conditions present in and around buried pipe systems (wall thickness, medium electrical and magnetic properties, medium temperature and moisture content).

This paper describes the development of an innovative technology capable of providing higher resolution of the pipe wall and a greater penetration depth. The technology, named P-Scan, is based on ultra wide band (UWB) antennas capable of transmitting and receiving electromagnetic pulses in the nano and picoseconds ranges. Following a theoretical background of UWB, a custom-written numerical code written specifically to simulate the application of UWB antenna for pipeline scanning is presented. Experimental tests currently underway to experimentally validate the numerical model are also described.

UWB signals are typically very short duration pulses (in the nano- to picosecond range) having a bandwidth of several GHz and pulse repetition frequency of several hundred thousands to billions of pulses per second. An extensive literature is available about UWB and a good review source is Taylor (2002). UWB technology, though not a new one and dating back to the 1960s, had limited usage in the U.S market due to several reasons including federal regulations. In 2002, Federal Communications Commission (FCC) allocated particular bandwidths for civil applications including communication applications (3.1 – 10.6 GHz) and GPR type applications (< 960 MHz). Moreover UWB antennas have rarely been available commercially until recently (Brocato, 2004; Andrews, 2003).

In the development of an UWB sensor for condition assessment of buried pipes it is desired to operate in the picosecond range because pulse width in this region is several centimeters, a distance equal to or less than the wall thickness of most non-ferrous buried pipes. Subsequently, it is possible to obtain the resolution needed for detecting small defects within the pipe wall (e.g., cracks and thickness loss). In designing antenna systems for such smaller pulse width, parameters such as dimensions and geometry require careful consideration. Numerical simulation is a cost-effective approach for determining the anticipated performance of antenna system alternatives, allowing for rapid and economical prototype development. The following sections discuss the theoretical formulations behind the simulation code, followed by results of a numerical investigation of clay pipes that exhibited specific defects. A brief discussion of the experimental validation of the numerical validation, currently underway, is also presented.

Theoretical formulation
The finite difference time domain (FDTD) method is widely used to simulate the transient electromagnetic phenomena in many areas of engineering including the study of antenna radiation patterns in communications, tumor detection in biomedical engineering and detection of buried objects in geotechnical engineering. The relative simplicity in implementing variety of material types, such as soils and biological materials (e.g., tissues) over a wide frequency bandwidth coupled with the ability to model structures with arbitrary geometry have gained the FDTD method increasing popularity.

Simulation of electromagnetic fields through FDTD involves solving the Maxwell’s curl equations. Since Yee (1966) suggested a formulation to discretize the curl equations in Cartesian grid, the method has evolved to allow, among other things, the usage of a non-orthogonal co-ordinate system. In the case of a buried pipe the modeling space exhibits a cylindrical symmetry. Thus, the researchers formulated a cylindrical coordinate system for the analysis of buried pipes. The natural placement of the pipeline within this co-ordinate system is by aligning the z-axis along the longitudinal axis of the pipe and varying the radius (r) and the angle (θ) across its radial cross section. Considering the pipeline to be of infinite length, there exits an axial symmetry in either direction of the z-axis with the origin placed at the center of the antenna. Thus, the simulation space is a two dimensional domain of radial cross-section with r and θ variations. Assuming a 2-D idealized non-conductive medium (i.e., lossless), the number of Maxwell’s equations relating the electric field intensity E and magnetic field intensity H, reduces to 3, shown below as Eq. 1. The discretization of Eq. 1a is shown as Eq. 2.

In Eq. (2) n is the time step, μ is the magnetic permeability, ε is electrical permittivity and i, j are the spatial increments. For numerical stability of the difference equation in 2D, the maximum duration of the time step Δt is limited by the coordinate invariant stability condition given by Eq 3:

where c is the speed of light. In addition the size of the Yee cell is limited to approximately 0.1λ, where λ is the wave length. In the simulation presented herein the radial step size was set at 3 mm and angular step size at 1 degree. Grid size of such small increments requires careful management of computer resources. One method to conserve memory and computational resources is to restrict the size of the area to be simulated. In other words, boundaries are imposed to terminate the spatial domain. To avoid reflections occurring from the artificially imposed outer boundaries, a boundary condition called perfectly matched layer (PML) was imposed. In a cylindrical coordinate system the absorbing boundary is cylindrically symmetric, and so the PML was placed in the r-direction. A modified version of an un-split PML formulation proposed by Sullivan (1996) was used. Figure 1 shows the propagation and absorption of a differentiated Gaussian pulse (Taflove, 2000) at three time steps in a semi-circular cross-sectional area. Figure 1(a) shows the pulse starting from a cylindrical source, followed by the pulse approaching the PML (Figure 1b), and the pulse being absorbed by the PML (Figure 1c). The effectiveness of the PML is demonstrated in Figure 2, which shows that the magnitudes of the reflected signal from the PML boundary is approximately 1% of the magnitude of the transmitted signal, resulting in negligible noise.

Simulation setup
A schematic diagram for the simulation model in shown in Figure 3. The simulation domain consist of a radial cross-section with a pipe layer (vitrified clay) surrounded by a layer of soil (sandy loam with approximately 10 % moisture content). The outer diametrical boundary is terminated by a 20 cell-thick PML layer. The antenna is represented by two perfect electric conductors (PEC), each 50 cells in length, separated by 60 degrees. The same antenna functions both, as transmitter and receiver, and hence termed ‘trans-receiver’. A circular source between the two PEC boundaries is excited with a differentiated Gaussian pulse of 80 picoseconds (ps) wide. The inner and outer radii of the pipe are 0.48 m and 0.56 m, respectively. The surrounding soil layer is about 0.1 m thick. Strictly speaking, electrical properties (e.g., dielectric permittivity) of geotechnical materials are frequency dependant (Francisca et. al, 2003). However, for simplicity the dielectric permittivity of the verified clay and soil were considered to be constants in this work and their values were set to be 3 and 10, respectively (Hippel et. al,1954).

Results
Three different cases are studied during the numerical experiment. The first case represents an ideal pipe-soil section, while the remaining two cases represent non-ideal pipe-soil sections (i.e., presence of voids). In Case II, void approximately 4 cm thick is present within the soil surrounding the outside wall of the pipe, but the pipe wall was intact. In Case III, the pipe has wall thickness loss as well as a void running across both the soil and the pipe. Figure 4 shows snapshots of the pulse traveling inside an ideal pipe-soil cross-section. In Figure 4(a) the pulse is within the antenna, while in Figure 4(b) the pulse has traveled outside the antenna. In Figure 4(c) shows two individual reflected signals, one from the air-pipe inner wall interface and other from the pipe outer wall-soil interface.

The transmitted and reflected signals measured over time at a cell just in front of the antenna are given in Figure 5. Figure 5(a) represents an ideal pipe-soil interface, with the two positive peaks (0.2 V/m) marking the inner and pipe walls. Figure 5(b) show the resulting signal in the case of a void outside of the pipe. Alongside the two positive peaks mentioned above a third negative peak (-0.4 V/m) is also detected. This third peak is the reflection from a void present in the soil bedding just outside the pipe. Figure 5(c) display the signal signature for the case where the pipe wall experienced loss of thickness. The data revealed that the third negative peak shifted slightly between the two positive peaks due to the shift of the void into the pipe wall. The reflection signature from each of the three cases is unique, enabling to distinguish and properly describe each of the three scenarios.

The proposed technology also provides a measurement of the pipe wall thickness (h), enabling to detect internally and externally corroded sections by converting the time difference between the two positive peaks shown in Figure 5 to distance. Such conversion is performed using the following expression:

where c=speed of light (3x10⁸ m/s); Δt=two-way travel time; and ε_r=dielectric constant of the layer. Eq. 4 was used to compute the wall thickness in the simulation cases shown in Figures 5a through 5c, using a dielectric constant, ε_r=3.0, for the vitrified clay pipe. The two-way travel time for cases 5a and 5b are 0.915x10^-9 s and 0.892 x10^-9 s, respectively. The computed wall thickness for cases 5a and 5b were 790 mm and 770 mm, respectively. These values agree well with the actual value of 800 mm. In case 5c (thinner wall section) the two-way travel time was 0.348x10^-9 s, resulting in a computed wall thickness value of 300 mm, a value equal to that used in the simulation. In real world situations the dielectric constant, ε_r, is not known. In such cases the dielectric constant can be measured in the laboratory, assumed based on typical values published in the literature for the material in question or back calculated using a forward modeling algorithm based on reflected frequency spectrum such as the one proposed by Loulizi et al. (2003). Such an algorithm can be codified to automatically compute the thickness of the wall around the pipe circumference. This information can be then presented numerically or graphically, providing vital information for rehabilitation and replacement decisions.

Advantages of the proposed system

• The numerical simulation presented in this paper demonstrated the advantages of using a directional antenna inside the pipeline in comparison with more conventional GPR systems. The increased directivity of the antenna and the use of ultra-short pulses enable a more detailed investigation (i.e., higher resolution) of the pipe wall while maintaining adequate penetration depths.
• The pipe wall along with the soil acts as a dielectric concave lens system to help focusing the reflected signal back into the antenna. Consequently, the signal to noise ratio is maximized, thus increases the reliability of the data collected.
• Since the same antenna functions both as a transmitter and receiver, the placement of antenna inside the pipe is straightforward. Rotation of antenna in the circumference direction coupled with longitudinal advancement along the pipe can be processed to produce a three dimensional contour map of the pipeline. These features are more difficult to incorporate with traditional GPR units, where the transmitter and receiver shape and size affect the operational frequency, so antenna configuration is not easily altered to suit survey configurations.
• The thickness of the pipe wall and other distinct layers (i.e., thermoplastic liner, cement mortar lining) can be measured with relatively high precision in a continuous manner. Forward processing algorithms are available to back calculate the dielectric constant of the various materials intercepted by the pulse, eliminating the need for special technical training and/or experience for interpreting the collected data.
• The transmitted signal has a broad bandwidth and thus the analysis could be carried within wide frequency range in a single run.

Experimental validation
The authors are currently undertaking an experimental program to validate the results of the numerical model presented herein. An experimental setup placed at the TTC/CAPS nano-pulse laboratory is shown in Figure 6. Following the completion of the model validation, a prototype system will be constructed and tested in the TTC full-scale soil-structure interaction chamber. Results of these tests are expected to be available in the summer of 2007.

Conclusions
The UWB technology is introduced and the theoretical aspects involved in simulation of an UWB antenna, including the performance of a perfectly matched absorbing boundary condition, discussed. The results of a numerical simulation study conducted on a vitrified clay pipe-soil interface for condition assessment purposes are presented. It was demonstrated the UWB technology is capable of identifying voids in the pipe cross section and in the soil envelope surrounding it. In addition, the technology is capable of precise measurements of the pipe wall thickness in an automatic and continuous manner. The advantages of using UWB technology for buried non-ferrous pipes compared with existing methods (i.e., CCTV and GPR) are discussed. Other potential applications of UWB technology are also listed.

References
Andrews, J R, 2003, UWB Signals, Sources, Antennas and Propagation, Picosecond Pulse Labs Appl.Note, AN-14a, pp.3.

Francisca, F M & Rinaldi, V A, 2003, Complex Dielectric Permittivity of Soil–Organic Mixtures (20 MHz– 1.3 GHz), J. Envir. Engrg., Volume 129, Issue 4, pp. 347-357.

Hippel V & Arthur R, 1954, Dielectric Materials and Applications, M.I.T. Press, Cambridge, MA.

Loulizi, A., Al-Qadi, I.I. and Lahouar, S. 2003. Optimization of Ground-Penetrating Radar Data to Predict Layer Thicknessess in Flexible Pavements. ASCE, Journal of Transportation Engineering, Vol 129(1), pp. 93-99.

Robert W. Brocato, R W, 2004, FDTD Simulation Tools for UWB Antenna Analysis, Sandia Report, SAND2004-6577, Sandia National Laboratories.

Taflove, A & Hagness, S C, 2000, Computational Electrodynamics: The Finite-Difference Time- Domain Method 2nd edn, Artech House, Narwood. Taylor, J D, 1995, Introduction to Ultra-Wideband Radar System, RC Press LLC,Boca Raton.

Yee, K S, 1966, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propagat., vol. AP-17, pp. 585-589. 

¹ Research Assistant, Trenchless Technology Center, Louisiana Tech University, Ruston, USA
² Associate Director, Trenchless Technology Center, Louisiana Tech University, Ruston, USA
³ Associate Professor, Center for Applied Physics Study, Louisiana Tech University, Ruston, USA