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\chapter{\uppercase{Conclusions}}

\noindent This dissertation presents an experimental study that establishes the feasibility of using electrical resistivity imaging and induced polarization for estimating the final depth of bridge foundations where this pertinent information is no longer available.  Forward models are created to identify influencing in situ parameters that can not be systematically experimentally tested such as increasing foundation depth, the effect of multiple foundations, and the spacing between multiple foundations.  From these models it is shown that ideally only one foundation should be tested at a time and the electrode spacing should be equal to or less than the width of the foundation.

Foundations made of reinforced concrete and steel H-piles can be successfully imaged to estimate the depth of the foundation where it is unknown.  This is demonstrated using foundations at a NGES and four bridges in the Bryan TxDOT district that are both shallow and deep, in different soil conditions, and in one case, through the presence of water.  The experimentally determined setup for using ERI and IP for determining the depth of bridge foundations are listed below.

\begin{enumerate}
\item Arrange the array so that the foundation is in the middle of the electrode line
\item The central electrodes (14th and 15th in a 28 electrode line) should be placed on either side of the foundation
\item SS electrodes should be next to the foundation and NP electrodes offset by less than 0.3 m for a side scan survey
\item The IP cycle time should be two seconds
\item The dipole-dipole array should be used
\item For concrete structures, the foundation must contain reinforcement
\end{enumerate}

If it is determined after an initial survey that the foundation is deeper than the depth to which data are collected, the length of the array should be increased.  There is a tradeoff between the depth of penetration and image quality when the electrode spacing is increased to lengthen the survey line.  If deeper data are needed, additional electrodes should be used so that the electrode spacing remains equal to or less than the width of the foundation.

The two limitations of the method at this time are related to the soil type.  If the soil is very loose, like a loose sand, the interconnected pore space will allow the signal to dissipate lowering the quality of the data collected and the resulting inversion.  Data can be improved by using a bentonite slurry around the electrodes to increase the amount of current that is injected into the subsurface, but if the soil profile remains a loose sand to the depth of penetration of the survey the results will not be significantly increased.  Also, little can be seen in an inversion if the response of the soil is similar to the response of the reinforced structure, lowering the contrast between the two materials.  Table~\ref{con:tab} summarizes the conditions under which different foundations in different soils will yield a very good, fair, or poor result.  This table should be used as a general guideline when considering using IP for predicting the depth of an unknown foundation.  Note that timber piles were never tested, but because steel is necessary to gather a measurable IP response the data quality of a timber pile test is assumed to be poor.

\begin{table}[!ht]
\centering
\caption{In Situ Parameter Guidelines}
\begin{tabular}{|p{5cm}|p{1.5cm}|p{1.4cm}|p{1.4cm}|p{1.4cm}|p{1.4cm}|}
\hline
Foundation & Clay & Clayey Sand & Silty Sand & Well Graded Sand & Poorly Graded Sand \\
\hline
Spread footing  \newline L $\leq$ 5 m   & Very good  & Very good & Very good & Fair & Fair \\
\hline
Reinforced concrete pile \newline 0$\leq$ L $\leq$ 10 m  \newline d $\leq$ 1 m & Very good & Very good & Fair & Fair & Poor\\
\hline
Reinforced concrete pile \newline 0$\leq$ L $\leq$ 10 m \newline  d $\geq$ 1 m  & Very good & Very good & Very good & Fair & Poor\\
\hline
Reinforced concrete pile \newline L $\geq$ 10 m \newline  d $\leq$ 1 m   & Very good & Fair & Fair & Fair & Poor\\
\hline
Reinforced concrete pile \newline L $\geq$ 10 m \newline  d $\geq$ 1 m    & Very good & Very good & Very good & Fair & Poor\\
\hline
Unreinforced concrete foundation  & Poor & Poor & Poor & Poor & Poor\\
\hline
Steel piles \newline  0$\leq$ L $\leq$ 10 m & Fair& Fair & Fair & Poor & Poor\\
\hline
Steel piles \newline  L $\geq$ 10 m   & Fair& Fair & Fair & Poor & Poor\\
\hline
Timber pile  & Poor & Poor & Poor & Poor & Poor\\

\hline
\end{tabular}
\label{con:tab}
\end{table}

A quantitative post processing algorithm is created to remove the qualitative uncertainty of interpreting the inversions from each experiment.  This algorithm can be used for high and low quality data, but surveys with resulting high RMS models should still be interpreted with caution as it is a measure of the goodness of fit of the numerical model to the measured data.  After all tested bridges and two shallow foundations at the NGES have been post processed the predicted depths and known foundation depths are used to create a probability of non-exceedence curve showing the probability that the actual depth of the foundation is less than the depth predicted by IP.  Using this curve the depth predicted by IP can be reduced or increased depending on the acceptable level of confidence for the bridge that is being tested.  This curve should be used to provide an acceptable level of certainty depending on the situation of the inversions when used in practice.  The steps for data reduction and probability failure of the foundation prediction are as follows: 

\begin{enumerate}
\item Conduct an ERI/IP survey with the experimentally determined setup above
\item Process the data and visually interpret the inverted IP section
\item Estimate D$_{\textrm{pred}}$ using the post processing algorithm for the inverted IP model
\item Decide on the target probability of non-exceedance for the infrastructure considered
\item Read $\xi (p) $ from the probability of non-exeeedance curve
\item Write $D_{\textrm{actual}} = \xi (p) D_{\textrm{pred}}$
\item State the results as, ``there is a (target probability value) probability that the foundation is at least $\xi (p) D_{\textrm{pred}}$''
\end{enumerate}



Finally, a bridge with foundation details unknown to the researcher is successfully tested to validate the use of ERI and IP for truly unknown foundations.  The data are collected and post processed using the procedure defined in Chapter~\ref{chap:Stats} and predicted to be 7.89 m with a 21.53\% probability that the actual depth is more shallow than predicted.  The actual depth of embedment for the pile is 9.75 m so the pile length is under predicted by 19\%.  It is also shown that the method can be used for imaging other subsurface structures.  An 11.43 cm gas line is imaged.  More testing of buried lines with varying diameters, varying depths of embedment, and in different soil conditions is still required to evaluate the full potential of ERI and IP for locating buried lines. 

