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\chapter{\uppercase{Underground Utility}}
\label{chap:pipe}
\section{Introduction}
\noindent Near surface geophysical methods are limited in their applications due to a common variable, depth of penetration. The depth of penetration for most methods, including IP and ERI, is limited by available space for testing. When testing bridges, for example, the length of the array may be limited by personal property fences on each side of the bridge. The depth of penetration is also related to the signal to noise ratio.  In addition to bridge foundations, there are many ``shallow'' buried objects that may require nondestructive imaging.  One example of this is infrastructure mapping of unknown buried gas, water, or sewer lines.  Particularly in urban areas, while theoretically the location of these subsurface lines should be known, older maps may not be accurate or as in the case of unknown bridge foundations, the plans may have been lost over time.  

In this Chapter, a buried gas line is imaged.  In most geophysical studies, the influence of man-made objects on an ERI or IP survey is seen as a nuisance \citep{Sum} but for civil engineering studies these structures are the desired targets.  Another objective of testing the gas line is to reduce the size of the imaged anomaly.  In Chapter~\ref{chap:Experiment} it is shown that IP can successfully imaged bridge foundations to provide an estimation of the depth.  While the depth of the foundation can be inferred from these images, the width of the foundation cannot.  Knowing that all deep foundations in this research have been straight shaft piles, the results often appear much wider than the dimensions of the substructure.  In this Chapter, a natural gas line on the North side of the Texas A\&M University Riverside Campus is imaged using 12 arrays.  Each array is centered about the same point and varied by 15$^\circ$ to narrow the apparent width of the pipe.

\section{Gas Line Description}
\noindent The natural gas line on the North side of the Texas A\&M University Riverside Campus is located between SH 21 and Warehouse Loop as shown in Fig.~\ref{fig:gas}.  It is owned and operated by Atmos Pipeline and is an in-service gas transmission system.  The pipeline is 11.43 cm in diameter and is buried 1.5 m beneath the surface.
\begin{figure}[!ht]
\centering
\includegraphics[width=0.75\textwidth]{figures/pipemap}
\caption{Map of the natural gas transmission system}
\label{fig:gas}
\end{figure}
As previously mentioned, the same point over the pipe is tested by rotating the array by 15$^\circ$ from a central point.  The central point is located following a preliminary test used as an example for a classroom field trip.  Fig.~\ref{fig:origpipe} is the field study that initiated further testing of the gas line.
\begin{figure}[!ht]
\setlength{\unitlength}{0.8cm}
\centering 
\begin{picture}(18.89,11.5)
\put(0,0){\includegraphics[width=\textwidth]{figures/origpipe}} 
\put(0,10){(a)}
\put(0,4.6){(b)}
\end{picture}
\caption{Preliminary field study of the Atmos gas line:  (a) inverted resistivity section; (b) inverted IP section}
\label{fig:origpipe}
\end{figure}
The ERI and IP profiles here send conflicting messages.  The gas line is located between the 13th and 14th electrodes.  The location of the gas line is estimated using the gas line markers, the yellow sign in Fig.~\ref{fig:pipemiddle}.  
\begin{figure}[!ht]
\centering 
\begin{subfigure}[Experimental setup]
{\includegraphics[width=70mm, height=90mm]{figures/pipemiddle}\label{fig:pipemiddle}}
\end{subfigure}
~~
\begin{subfigure}[Test site]
{\includegraphics[width=70mm, height=90mm]{figures/pipearray}\label{fig:pipearray}}\end{subfigure}
\caption{Gas line test at Riverside Campus} \label{fig:pipepic}
\end{figure}
The depth of the gas line is approximately 1.5 m, so the depth on the ERI profile is accurate, though much larger than the 11.43 cm diameter galvanized steel pipe.  The inverted IP section makes the pipe appear to be buried approximately 3 m instead of 1.5 m.  The RMS of the IP section is 13.94 mV/V; the model is not a good fit for the inversion.  This data set is full of poor IP curves and negative apparent resistivities.  To improve the data quality, holes are dug and filled with a bentonite slurry for the rotating arrays.  The bentonite slurry allows for better contact with both the SS and NP electrodes allowing more current to be injected in the ground and higher quality decay curves.  The bentonite is necessary because the ground is so stiff that when holes are dug for the NP electrodes there are large voids surrounding the NP electrodes leading to a loss of signal.

\section{Experimental Setup and Results}
\noindent The results of the preliminary study are used to plan the survey.  The center of the resistivity anomaly is taken as the center point for the field set up.  From this point, lines are rotated by 15$^\circ$ and stretched radially out by 6.75 m.  This keeps the total length of the array at 13.5 m (28 NP and 28 SS electrodes spaced every 0.5 m) and the exact center point the same.  A diagram of the field set up for all 12 lines is shown in Fig.~\ref{fig:pipedia}.
\begin{figure}[!ht]
\centering
\includegraphics[width=0.75\textwidth]{figures/pipelines}
\caption{Aerial layout of array setup}
\label{fig:pipedia}
\end{figure}

The pipe is not successfully imaged by IP in most of the inversions.  This is most likely due to the small size of the pipe and the numerous poor decay curves despite the improvement from the bentonite slurry.  The ERI and IP inversion of each of the 12 lines are included in Appendix~\ref{app:pipe} along with the rotated image relative to Line 1.  Because the IP images do not successfully image the pipe, they are not included in the 3-D model.  Figure~\ref{fig:3dmodel} shows all of the results of the 12 lines combine.
\begin{figure}[!ht]
\setlength{\unitlength}{0.8cm}
\centering
\begin{picture}(18.89,9)
\put(0,0.6){\includegraphics[width=\textwidth]{figures/3dmodel}}
\put(0.6,2.85){-2.88}
\put(0.6,3.67){-2.04}
\put(0.8,4.5){-1.2}
\put(0.6,5.3){-0.36}
\put(0.75,6.1){0.49}
\put(0,3.25){\rotatebox{90}{Elevation (m)}}
\put(1.6,6.45){0.0}
\put(3.2,6.45){1.5}
\put(4.87,6.45){3.0}
\put(6.52,6.45){4.5}
\put(8.18,6.45){6.0}
\put(9.84,6.45){7.5}
\put(11.5,6.45){9.0}
\put(12.9,6.45){10.5}
\put(14.56,6.45){12.0}
\put(16.22,6.45){13.5}
\put(17.3,6.45){Ohm-m}
\put(18.1,2.85){1.0}
\put(18.1,3.67){2.7}
\put(18.1,4.5){7.1}
\put(18.1,5.3){18.8}
\put(18.1,6.1){50.0}
\end{picture}
\caption{Combined ERI inversions for a 3D model}
\label{fig:3dmodel}
\end{figure}

\clearpage
The line with the elevation labeled and the apparent resistivity values is Line 1 from Fig.~\ref{fig:pipedia}.  The scale of apparent resistivity is maintained the same for all 12 inversions.  Because the arrays are centered on the same point, the model of all 12 lines does not show the images clearly.  Line 1 is kept in all figures and each subsequent line is shown relative to Line 1 so the pipe can be seen. 

In order to show the increasing angle from Line 1, each slice is placed on its respective rotated plane relative to Line 1 in Solid Works.  Overlaying these images obscures some of the first line so it is shown in Fig.~\ref{fig:pir} alone.
\begin{figure}[!ht]
\includegraphics[width=\textwidth]{figures/p1r}
\caption{ERI Inversion of Line 1 in the gas line survey}
\label{fig:pir}
\end{figure}

The pipe can be seen as a circular zone of low resistivity between 6 m and 7.5 m centered approximately 1.6 m beneath the surface.  This anomaly is buried near the known depth of the gas line (1.5 m) but it appears much larger than the documented 11.43 cm diameter gas line.  An objective of this study is to reduce the side of ERI response of the pipe by changing the angle of the array respective to the gas line.  The 45$^\circ$ and 90$^\circ$ are included in this chapter.

The 45$^\circ$ line, Line 4, shows the reduced diameter of the gas line compared to Fig.~\ref{fig:pir} in Fig.~\ref{fig:model45}.  There is a small, circular zone of low resistivity beginning at 2 m to approximately 3 m.  This is a mathematical anomaly, because this section of the model is removed because of negative apparent resistivity values.
\begin{figure}[!ht]
\setlength{\unitlength}{0.8cm}
\centering
\begin{picture}(18.89,7.5)
\put(0,0){\includegraphics[width=\textwidth]{figures/Model45}}
\put(0,2.3){\rotatebox{90}{Elevation (m)}}
\put(0.8,2.1){-2.88}
\put(0.8,2.9){-2.04}
\put(1,3.7){-1.2}
\put(0.8,4.5){-0.36}
\put(0.95,5.3){0.49}
\put(1.9,5.75){0.0}
\put(3.6,5.75){1.5}
\put(5.15,5.75){3.0}
\put(6.7,5.755){4.5}
\put(8.4,5.75){6.0}
\put(10,5.75){7.5}
\put(11.65,5.75){9.0}
\put(13,5.75){10.5}
\put(14.56,5.75){12.0}
\put(16.22,5.75){13.5}
\put(17.3,5.75){Ohm-m}
\put(18.1,2.1){1.0}
\put(18.1,2.85){2.7}
\put(18.1,3.67){7.1}
\put(18.1,4.5){18.8}
\put(18.1,5.3){50.0}
\end{picture}
\caption{3D model of the 45$^\circ$ line in the gas line survey}
\label{fig:model45}
\end{figure}
The RMS for this inversion is 11.03\% despite having removed some of the negative values.  Despite this, a localized circular zone of high conductivity is seen over the location of the pipe in Fig.~\ref{fig:p4r}.  The conductivity of the pipe is higher at 45$^\circ$ and the diameter of the pipe is smaller.
\begin{figure}[!ht]
\includegraphics[width=\textwidth]{figures/p4r}
\caption{ERI inversion of Line 4 in the gas line survey}
\label{fig:p4r}
\end{figure}

Line 7, which is rotated 90$^\circ $ from Line 1, has an RMS of 7.51\% and again a region of low resistivity can be seen around 3 m from the front of the line.  The zone of high conductivity around the pipe is the smallest in Line 7, appearing around 20 cm, nearly twice the diameter of the pipe.
\begin{figure}[!ht]
\includegraphics[width=\textwidth]{figures/Model90}
\caption{3D model of the 90$^\circ$ line in the gas line survey}
\label{fig:pipe90}
\end{figure}
It is expected that there be a zone of low resistivity all along this profile around 1.5 m because Line 7 should have been directly over the pipe.  The significantly reduced diameter of the pipe, along with the lack of a layer of low resistivity indicates that this line is not directly over the pipe..   The line appears to run perpendicular to Warehouse Loop in Fig.~\ref{fig:gas}, but Line 1 may have not been exactly parallel to Warehouse Loop during testing.   
\begin{figure}[!ht]
\includegraphics[width=\textwidth]{figures/p7r}
\caption{ERI Inversion of Line 7 in the gas line survey}
\label{fig:p7r}
\end{figure}
A slight error  in the original layout of Line 1 leads to error propagation around the circle so that inside of testing directly on top of the pipe for Fig.~\ref{fig:p7r}, only a small section of the pipe is tested at the middle.  This may also be the cause of the response of the pipe appearing larger in diameter than in reality because of the close proximity of a highly conductive material along the line instead of an isolated section of the pipe.  Unfortunately, because of the slight skew of the lines the response of the gas line does not appear symmetric on the other half of the circle.  When comparing the 45$^\circ$ line and the 135$^\circ$ line, for example, the 135$^\circ$ appears much more spread out than Fig.~\ref{fig:p4r} and shifted slightly to under 6 m.

\section{Underground Utility Summary}
\noindent An objective of this research is to show that ERI and IP can be applied to other subsurface infrastructure.  IP is not successful at imaging the galvanized steel gas line due to low quality IP decay curves and possibly due to the small diameter of the pipe.  ERI, however, is successful at imaging the pipe.  By rotating the array by 15$^\circ$ the diameter of the pipe in the inversion is successfully reduced.  Unfortunately, the original line is not exactly perpendicular to the gas line so these images are not symmetric through the inversions.  Also, the exact depth of the gas line is not consistently achieved in this study.  Despite this another possible application of ERI for Civil Engineering investigations is proved.