Modeling of an obstacle detection sensor for horizontal directional drilling (HDD) operations

Modeling of an obstacle detection sensor for horizontal directional drilling (HDD) operations

Automation in Construction 20 (2011) 1079–1086 Contents lists available at ScienceDirect Automation in Construction j o u r n a l h o m e p a g e : ...

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Automation in Construction 20 (2011) 1079–1086

Contents lists available at ScienceDirect

Automation in Construction j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a u t c o n

Modeling of an obstacle detection sensor for horizontal directional drilling (HDD) operations A.P. Jaganathan a, J.N. Shah a, E.N. Allouche a,⁎, M. Kieba b, C.J. Ziolkowski b a b

Trenchless Technology Center (TTC), Louisiana Tech University, Ruston LA, USA Gas Technology Institute (GTI), Des Plaines, Illinois, USA

a r t i c l e

i n f o

Article history: Accepted 5 April 2011 Available online 7 May 2011 Keywords: Look-ahead Numerical modeling Differential impedance Obstacle detection Horizontal directional drilling

a b s t r a c t Horizontal Directional Drilling (HDD) is a commonly used construction method for the installation of underground pipelines, conduits and cables in urban areas and across obstacles such as rivers, railways and highways. A key concern in using the HDD method is the risk of hitting existing buried utilities during the pilot boring operation, which could potentially result in significant economic losses, disruption of services and injuries and/or loss of life. The Differential Impedance Obstacle Detection (DIOD) is a “look-ahead” sensory system, developed for the purpose of detecting metallic and thermoplastic pipes in the path of the boring head. The DIOD sensor was numerically simulated, and the model was validated by comparing its predictions with experimental measurements performed on a physical prototype in a controlled environment. Following validation of the model, a parametric study was undertaken to predict the performance of the DIOD under various scenarios that could be encountered in practice. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Beneath the US landscape lie a vast network of buried utilities and pipelines, stretching for nearly 10.6 million miles, which include natural gas lines, power lines, water distribution and collection systems and optical-fiber communication lines [1]. The need for laying new utilities to support new technologies (i.e., the ‘last mile’ program), coupled with increasing demands of an ever growing population, has resulted in a highly congested underground space, particularly in urban areas. A parallel trend is the increase in the utilization of newer construction methods that minimize excavation, and reduce disruption to traffic patterns and the built environment. Horizontal Directional Drilling (HDD), a trenchless method for installing pipelines and conduits underground, has become in recent years a midstream construction method due to its versatility, cost effectiveness and relatively small foot print [2]. A major concern in employing the HDD method is the occurrence of an inadvertent utility strike during the boring process. As the drill head advances underground, it might damage an existing utility located along its path. Such utility strikes can cause significant economic losses (i.e., service interruptions, damage to a buried utility or building foundation) as well as injuries and fatalities if a hazardous utility (i.e., flammable liquid lines, electrical conduits, natural gas lines) is hit. Thousands of inadvertent utility strikes have been reported over the past fifteen years, some with severe consequences. The Damage ⁎ Corresponding author at: Trenchless Technology Center, College of Engineering and Science, Louisiana Tech University, 600 Arizona West, Ruston, Louisiana, 71272, USA. Tel.: + 1 318 257 2852, + 1 318 257 4072; fax: + 1 318 257 2777. E-mail address: [email protected] (E.N. Allouche). 0926-5805/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.autcon.2011.04.009

Information Reporting Tool (DIRT), sponsored by the Common Ground Alliance, reported 258 HDD related utility hits in 2005 alone across the country [3]. A specific concern during HDD installations in urban areas is the accidental placement of a natural gas line in a way that it transects a lateral connection or a gravity sewer line. Such occurrences, commonly named ‘cross-bores’, could create a long-term risk as an attempt to remove blockade in the drain (induced by the presence of the transecting gas line) could compromise the gas line, resulting in leakage of natural gas into adjacent homes via the sewer system [4]. Fig. 1 shows photographs of typical ‘cross-bores’ created during HDD installations. Between 1996 and 2006 at least 20 explosions occurred in 13 states due to attempts to clear sewer laterals that were blocked by a natural gas line, resulting in loss of life, severe injuries and over one hundred million dollars in damages. In one case (Madill, Oklahoma), the explosion (November 14, 2007) occurred 15 years following the installation of the natural gas line (1992). Projects undertaken by various utilities for identifying legacy cross bores resulted in the detection of an average of 2 to 3 cross bores of natural gas lines into sewer mains and laterals per each mile of sewer main inspected, which translate into several hundred cross-bores for some cities [5]. Current practices for avoiding physical damage during HDD operations include search of GIS based databases (i.e., One Call system in U.S) to identify existing buried utilities within the project boundaries and surface surveys using geophysical tools such as cable locators, ground penetrating radar (GPR) and other locating methods. However, in some cases the One Call system is not fully effective due to inaccurate (or non-existing) records, cluttered environment (e.g., utilities that are stacked vertically or that are braided horizontally), excessive environmental noise (e.g., overhead

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Fig. 1. Utility hits (cross-bore) resulting from HDD installations.

power lines, reinforced concrete pavement) and/or loopholes in local legislations that exempt owners of non-pressurized pipeline networks from the need to locate their assets in advance of construction projects [6]. In recent years there were multiple efforts to develop a ‘look-ahead’ sensor technology that can be incorporated within the HDD drill head in an effort to eliminate HDD related utility hits. A literature review of current and emerging ‘look-ahead’ technology development efforts is presented. Thereafter, a description of the Differential Impedance Obstacle Detection (DIOD) system developed by the Gas Technology Institute (GTI) in collaboration with the Trenchless Technology Center (TTC) is provided. The DIOD system induces a low frequency electric field within the soil medium surrounding the drill head. The obstacle is detected by measuring changes in impedance occurring due to distortion of the electric field caused by the presence of the obstacle [7]. This paper describes the development and validation of a comprehensive 3-D numerical model created to predict and optimize the performance of the DIOD system. Following experimental validation of the numerical model, an extensive parametric study was undertaken to study the performance of the DIOD under varying conditions expected to be encountered in practice, including various soil types, different orientations of the obstacle with respect to the advancing drill head and different pipe (or ‘obstacle’) materials. 2. Current and emerging borehole technologies for obstacle detection To avoid a utility strike, HDD operators have to detect buried utilities before a physical contact between the drill head and the utility takes place. In recent years several efforts have been made to

develop sensor technology that could be incorporated into the HDD drill head with the capablity of detecting both, metallic and nonmetallic obstacles in near real-time. Nakauchi et al. [8] developed a small ground-penetrating radar system that is incorporated within a HDD drill head. It consists of a pair of antennas located at the cutting edge of the drill head and protected by a ceramic cover, a signal generator, a receiver and a communication link for transfering data gathered to the ground surface. The principle of operation behind this technology is similar to that of a pulsed GPR, where an electromagnetic signal with duration of 0.6 ns is transmitted ahead of the drill head and the backscattered electromagnetic wave is used to discriminate the obstacle [8]. Another GPR based technology for HDD was reported by Hirsch [9]. This particular radar employed electromagnetic signals with frequencies between 25 MHz and 500 MHz. Hirsh reported that a proof-ofconcept for the sensor was tested by pulling the prototype device through a 100 mm diameter polyethelene conduit, simulating the borehole created by a HDD rig, while attempting to locate metallic and non-metallic pipes located adjucent and perpendicular to the polyethelene conduit from a distance of 1 to 2 m ahead. California Energy Commission (CEC) [10] reported the development of a multisensory platform named SafeNav™ for HDD operations. The SafeNav system has been coupled with the AccuNav™ guidance system, used for establishing the location of the drill head [11]. SafeNav and AccuNav work in conjunction to detect underground obstacles, and also to communicate the information gathered by the various sensory systems to the surface [12]. The system consists of 25 sensors including two sets of magnetometers for detecting buried electrical power lines, two sets of triaxial sensors for tracing specific frequencies for the purpose of detecting

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telecommunication lines, geophones for detecting acoustic signals, accelerometers for tracking the drill head's position, and temperature sensors for monitoring the operating condition of the electronics in the harsh operating conditions often associated with HDD operations. The sensors were designed to locate obstacles situated either parallel or perpendicular to the trajectory of the drill ahead. The design is compatible with most conventional directional drilling rigs. Various field tests were conducted resulting in several design enhancements [12]. SoniPulse Inc. has developed a seismic based obstacle detection system for HDD. It employs an array of geophones located on the ground surface above the HDD path for detecting the seismic signals generated by the drill head [13]. The seismic energy generated by the drill head is scattered by the buried obstacles along its path, and this scattered energy is recorded by geophones located 0.3 m apart. The geophones were coupled with the ground such that the signal-tobackground noise ratio was minimized. The high-intensity sound was continuously monitored, cross-correlated, and processed to detect peaks in the intensity. As the sound waves generated by the drill head are too weak to detect below a certain depth, a noisemaker consisting of a rotating hammer that generates specific sound frequency was added to the drill head assembly. The technology has been tested for detecting large-diameter pipes at distances of 5 to 10 m and smalldiameter pipes at distances of 2 m ahead of the drill head. 3. Differential impedance obstacle detection (DIOD) sensor The operating principle of the DIOD sensor is based on the Wheatstone bridge circuit. When the sensor is buried within a homogeneous soil with no obstacles (e.g., metallic pipe) in its vicinity, the bridge circuit is in a balanced state with the differential output between the sensing electrodes returning a null value. As the sensor approaches the obstacle, the impedance of the soil medium changes, and as a result the bridge reaches an unbalanced state with differential voltage observed between each pair of diametrically placed sensing electrodes. Fig. 2 shows an image of a prototype DIOD sensor integrated within a mock HDD drill head as well as a 3-D CAD rendering of the sensory system. The prototype drill head is 900 mm long and 63 mm in diameter. The cutting edge (blade) of the drill

head is used to inject a low frequency (50–500 kHz) signal into the formation. There are four electrically isolated sensing copper electrodes placed orthogonally around the circumference of the drill head, which are in resistive contact with the ground. In an earlier version of the sensor, the copper electrodes were capacitively coupled with the soil (copper electrodes were covered with an external plastic tube and were not in direct contact with the soil). In later versions the copper electrodes were redesigned to have a resistive coupling with the soil (direct contact with the soil) to improve contact potential [14]. A practical implication of this modification is that the width of the slanted face ‘duck-bill’ will need to be approximately equal diameter of the drill rod. A potential difference is maintained between the blade and the sleeve, such that the electric field originating from the blade intersects the sleeve. The differential voltage between the diametrically placed copper electrodes is measured after amplification and filtering. In a homogeneous soil medium, the output signal from the electrodes will remain steady as the drilling rod advances forward. However, when an obstacle is presents the output signal changes indicating its presence. Compared with expensive and complex high frequency electronics used in GPRs, which generally operate at from few hundred megahertz to about 2.5 GHz, the low frequency electronics (50– 500 kHz) used in the DIOD sensor is significantly lower in cost and complexity. This cost-effective technology concept has the potential for detecting metallic and nonmetallic objects in the soil medium, as well as identifying the position of the buried obstacle with respect to the drill head. A limitation of the DIOD sensor when compared with ground penetrating radar technology is that GPR has better spatial resolution due to shorter signal wavelength. Also, with DIOD sensor it is difficult to directly estimate the distance to the detected obstacle, whereas in a GPR the time-of-flight principle is used to calculate the separation distance from the sensor to the obstacle. 4. Finite element modeling Numerical modeling of the DIOD sensor was carried out using the commercially available finite element software COMSOL Multiphysics with AC/DC module [15]. Since the wavelengths of the electric signal used in DIOD are very large compared with the dimensions of the

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Fig. 2. A HDD drill mounted with DIOD; original device (top) and the corresponding CAD model (bottom).

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Fig. 3. 3-D mesh of the numerical model containing a HDD drill mounted with DIOD.

modeled structure, the problem was treated as static/quasi-static in nature [15]. Two separate numerical models were created using the electrostatic and quasi-static modes available in COMSOL AC/DC module. The electrostatic mode was used to predict the performance of the sensor while the drill head was suspended in open space (i.e., surrounded by air; έ = 1), while the quasi-static mode was used to predict the performance of the sensor within a partially conductive dielectric medium (i.e., the soil formation). During simulations using the quasi-static mode, two separate cases were considered. In the first case, approximations were made by neglecting the coupling between the magnetic and electric fields using the ‘quasi-static electric current mode’. In the second case, the coupling between the electric and magnetic fields was considered using the ‘quasi-static electromagnetic mode’. A 3-D rendering of the numerical model (approximately 220,000 interior elements and 19,500 exterior elements) is shown in Fig. 3. The cutting edge of the drill was assigned a value of +30 V and the sleeve was assigned a value of − 30 V, similar to the actual system. The external boundary of the modeled domain was assumed to be grounded as it was sufficiently distanced from the modeled device. The interfaces between the dielectric mediums were assigned ‘electrical continuity boundary’ condition. To electrically isolate each electrode from directly influencing every other electrode, a grounded metallic cylinder was placed within the Teflon cylinder. In simulations conducted using the electrostatic mode, the four electrodes were assigned a ‘floating potential boundary’ condition. In simulation runs

where the quasi-static electromagnetic mode was deployed, the exterior boundaries were assumed to be magnetically insulated and the electrodes were assigned ‘impedance boundary’ conditions, a condition commonly used for modeling conductive films [16]. The geometry of the borehole was modeled based on the assumption that the soil was in contact with the drill head. 5. Comparison of the numerical results with the experimental data The numerical model was validated by comparing the predicted values with experimentally obtained data. Fig. 4 shows the experimental set-up used for validation purposes. The experimental tests were conducted in an indoor laboratory at the Gas Technology Institute's campus, Des Plaines, Illinois. A drill head equipped with the DIOD sensory system was fixed vertically using a fixture, such that the drill head was free to rotate about its longitudinal axis. The obstacle was suspended from the ceiling with an orientation perpendicular the drill head (Fig. 4). A 102 mm diameter aluminum pipe was used to simulate the obstacle utility. The drill head was rotated and potentials values recorded for pre-determined angular rotation values. During experimentation electrical potentials values measured between each pair of copper electrodes were passed through an amplification and signal conditioning circuitry, shown in Fig. 5. To properly account for this amplification, a model of the amplification and signal conditioning circuitry was constructed using Simulink®, dynamic modeling software. The electrical potential values between each opposite pair of

Fig. 4. Experimental setup used for validating the numerical model.

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Fig. 5. Schematic of the DIOD circuitry.

Step 1: FEM modeling of DIOD using COMSOL Step 2: Results from COMSOL used as input for Simulink model to include the effect of signal modification circuitry Step 3: Comparison of results from Simulink with experimental data Step 4: Following validation COMSOL model used to conduct a parametric study Fig. 6. A flow chart showing various steps involved in the numerical modeling work.

electrodes predicted by the numerical model were inputted into the Simulink® simulation, allowing to mimic the amplification in the experimental setup, such that the gain in the potentials obtained from the numerical model resembled that of the actual electronic circuitry. Fig. 6 shows a flow chart representing the steps taken during numerical modeling exercise. Fig. 7 displays a side-by-side comparison of the numerical and experimental setups used during the validation phase. The exterior boundaries of the numerical model was grounded, and the minimum distance between the drill rod and the nearest exterior boundary had a clearance of at least twice the length of the drill rod, so that exterior boundaries had minimal effect on the performance of the sensor. Similar care was taken during physical experimentation by placing the setup apart from neighboring objects. The relative position and orientation of the drill head with respect to the obstacle pipe are represented using Z, R andθ (see Fig. 8). Z represents the separation distance between the centerline of the obstacle pipe and the tip of the drill head along its longitudinal axis. The origin of the Z axis is assumed to be at the tip of the drill head, and a positive Z value represents a position forward of the drill tip. R represents the radial distance from the drill head's longitudinal axis to the outermost fiber of the obstacle. The

rotation angle of the drill head along its longitudinal axis is represented using θ. Comparison of potentials obtained experimentally as the drill head approaches a 102 mm diameter metallic pipe and the corresponding numerically predicted values are shown in Figs. 9 and 10 for the asymmetric and symmetric electrode pairs, respectively. It can be seen that the numerical data follow the same trend as the experimental observations. However, the amplitudes predicted by the numerical simulation were higher than those measured experimentally. It is believed that this difference in amplitude is due to signal loses that occurred in the experimental setup, as well as from the less than optimal sensitivity of the electrodes. It is expected that a dedicated electronics board mounted on the drill head closer to the electrodes will reduce losses, hence improving the sensitivity of the sensory system. Following validation of the numerical model, a parametric study was conducted using the numerical model to gain further insight to the performance of the DIOD sensor. 6. Parametric study A series of numerical simulations were undertaken to predict the performance of the DIOD under various conditions that could be encountered in the field. Parameters studied in this exercise include soil type, material type of the obstacle (i.e., metallic and non-metallic pipes), the separation distances between the drill head and the obstacle, and the orientation of the obstacle with respect to the longitudinal axis of the drill head. In this section selected results obtained during the parametric study are presented. The soil medium was assumed to be a lossy dielectric medium and the values of its permittivity (ε) and conductivity (σ) in the frequency range of interest (50–500 kHz) were assumed to be these given by Arthur [17]. In the model, non-metallic obstacles were represented by a dielectric constant of 3, which is a good approximation for the dielectric constant of a variety of materials used for manufacturing non-metallic

Fig. 7. Side-by-side comparison of the experimental setup and numerical model used for validation.

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Target pipe

θ R

Z Separation distance

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Fig. 8. Location of drill head with respect to the target pipe as seen from both top and side views.

0.7 m. It should to be noted that voltage values used in Fig. 11 were calculated using COMSOL prior to amplification and signal processing. Next, the effect of a drill head approaching the obstacle (metallic pipe) at various orientations was investigated. Fig. 12 shows the distribution of the electric equipotential lines generated for two different orientations of the obstacle pipe with respect to the drill head. For both angular positions shown in Fig. 12, the distance between the center of the obstacle and the tip of the drill head was 0.5 m. Fig. 13 shows the change in voltage predicted on individual electrodes for orientations of the obstacle pipe with respect to the longitudinal axis of the drill head ranging between 60° and 120°. It can be seen that the DIOD sensor is most sensitive to the presence of the obstacle pipe when its orientation is somewhat parallel to the drill

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pipes including PVC, HDPE, vitrified clay pipe and non-reinforced concrete [17]. The first parameter examined was the effect of the separation distance between the drill head and an obstacle pipe placed perpendicular to the longitudinal axis of the drill stem and buried in sandy soil with conductivity of 0.02 S/m. Fig. 11 summarizes the predicted voltages for each of the electrode for three separation distances ranging from 0.45 m to 1.0 m. As seen from Fig. 11, the values of the resulting voltage increase as the drill head approaches the obstacle, suggesting that the sensor is capable of detecting a metallic obstacle perpendicular to the trajectory of the pilot bore as the drill head approach it. Also, as seen in Fig. 11, the sensitivity of the sensor decreases when the distance to the obstacle is greater than

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Fig. 11. Numerically predicted potentials from individual electrodes for different separation distances between the drill head and a buried metallic pipe.

Fig. 13. Numerically obtained potentials for different orientations of a metallic pipe as shown in Fig. 11 (the distance between the longitudinal center of the pipe and the tip of the drill head is 0.5 m).

head longitudinal axis (i.e., the angle between the pipe and the drill head longitudinal axes is less than 70°). This is attributed to better coupling of the electrical field generated by the drill head with the pipe while both objects are somewhat parallel to each other. During a typical HDD operation the drill head rotates at a rate of about 10 to 30 revolutions per minute about its longitudinal axis while advancing forward. As a result of this rotation, the orientation of the sensor electrodes alternates with respect to a potential obstacle. Thus, it was of interest to predict the response from the sensors as a function of the rotation angle of the drill head with respect to a fixed obstacle (metallic pipe). The predicted changes could play an important role in the development of algorithms for detecting the presence of an obstacle along with its relative position with respect to the drill head. Fig. 14 presents the response in terms of sensor voltage for various angles of rotation of the drill head for a fixed separation distance (Z = 0.15 m & R = 0.17 m) from the obstacle. Fig. 14 presents the results obtained for both, metallic and non-metallic pipes of similar dimensions (102 mm diameter). It can be seen that the curve obtained for the metallic obstacle exhibits phase reversal twice for a single cycle of rotation, while results from the non-metallic obstacle display a single phase reversal for a 360° rotation of the drill head. Simulations were also carried out to predict the effect of different soil types on the response of the DIOD sensor by varying the dielectric permittivity of the soil medium between 2 and 10. Based on the simulations, the predicted performance of the DIOD revealed limited sensitivity to changes in the dielectric of the surrounding medium.

7. Conclusion A sensory device named DIOD aimed at detecting buried utilities ahead of, or to the side of, an advancing directional drilling boring head was described. A numerical model of a DIOD sensor housed within the drill head was developed using COMSOL Multiphysics and validated by comparing its predictions with experimentally observed values. The amplification and gain circuitry employed in the experimental setup were duplicated numerically using a SimuLink model. Following validation of the numerical model, an extensive parametric study was undertaken to examine the performance of DIOD under various field conditions. The results suggest that the sensitivity of the sensor to the presence of a nearby buried pipe increases when the angle between the target pipe and the advancing drill head is less than 70° due to enhanced coupling between the target and the drill head. Results from the simulation also showed that the sensor is less sensitive when the separation distance between the sensor and the obstacle is greater than 0.7 m. Furthermore, simulation results suggest that the system is capable of distinguishing between metallic and non-metallic targets based on the number of phase changes experienced during each revolution of the drill head. The numerical analysis demonstrated that experimental results did not represent the optimal performance of the system. This was attributed to excessive losses in the experimental setup used, which employed generic laboratory equipment rather than a custom electronic board for signal conditioning and amplification. Numerical modeling was proven to be an invaluable tool in the development of the DIOD by

Fig. 12. Electric equipotential lines obtained for two angular orientations of the target with respect to the drill head.

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predicting the performance of the system under various field conditions without having to perform complex and costly physical experimentation. References [1] R.L. Sterling, J. Anspach, E. Allouche, J. Simicevic, C.D.F. Rogers, K. Weston, K. Hayes, Encouraging innovation in locating and characterizing underground utilities, Report prepared for the Transportation Research Board NAS-NRC under Contract # SHRP-R-01, 2008 209 pp.

[2] E.N. Allouche, S.T. Ariaratnam, J.S. Lueke, Horizontal directional drilling – profile of an emerging industry, Journal of Construction Engineering and Management, ASCE 126 (1) (2000) 68–76. [3] DIRT, Annual report of damage information report tool, https://www.damagereporting.org/dr/download/2005_DIRT_Report.pdfvisited on august 15, 2008. [4] W.W. Richard, WUCA from the Trenches, Wisconsin Underground Contractors Association, 2005, p. page 2. [5] Crossboresafety, Preventing and eliminating crossbores – increasing safety and reducing risk, http://www.crossboresafety.org/visited January 2009. [6] R. Sterling, J. Anspach, E.N. Allouche, J. Simicevic, C.D.F. Rogers, Encouraging innovation in locating and characterizing buried utilities for U.S. transportation projects, 12th International Conference on Ground Penetrating Radar, June 16–19, 2008, Birmingham, UK, 5 pp. [7] M. Kieba, E.N. Allouche, Obstacle Detection Sensor for HDD, No-Dig Conference, San Diego, CA, 2007 (10 pp., on conference CD). [8] T. Nakauchi, H. Hayakawa, I. Arai, A Small GPR for Horizontal Directional Drilling System”, The 10th International Symposium on Recent Advances in Exploration Geophysics (RAEG 2006), Kigam, Korea, 2006, March 30–31, 4 pp. [9] V. Hirsch, Drill-mounted radar for horizontal directional drilling, Federal Laboratories Consortium Workshop, 2000. [10] CEC, Trenchless Burial Equipment, Public Interest Energy Research (PIER) Program Final Report, P600-00-032, California Energy Commission (CEC), 1999http://cacx.org//pier/index.html 50 pp. [11] Maurer Technologies, http://www.maurertechnology.com/Engr/Products/safeNav.aspvisited on November 6, 2007. [12] S. Wirsching, Strategic Energy Research, Trenchless Burial Equipment, Public Interest Energy Research California Energy Commission, October 1999. [13] K.M. Kothari, G.T. Pittard, R. Cribbs, Obstacle detection systems for utility construction operations, 22nd World Gas Conference, 2003. [14] M. Kieba, C.J. Ziolkowski, Differential soil impedance obstacle detection, Report prepared for the U.S Department of Energy under DOE, 2005 Contract #: DE-FC2602NT41318. [15] COMSOL Multiphysics, User's Guide, Version 3.3, 2007. [16] J.N. Shah, A. Jaganathan, E.N. Allouche, M. Kieba, C.J. Ziolkowski, 3-D modeling of a differential impedance obstacle detection sensor for horizontal directional drilling operations, Comsol Conference, Boston, 2007. [17] R.V.H. Arthur, Dielectric materials and applications, M.I.T Press, 1954.