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\chapter{\uppercase{Validation}}
\label{chap:NavasotaRiver}

\section{Introduction}
All of the experiments in Chapters~\ref{chap:Model} and~\ref{chap:Experiment} are conducted on foundations with documented depths of embedments that were known prior to testing.  Known foundations are used to validate the use of ERI and IP for identifying bridge foundation depths and to determine the correct procedure for conducting field experiments on bridge foundations.  To emphasize the use of ERI and IP for identifying unknown bridge foundation depths a blind study is conducted.  

\section{Navasota River Relief Bridge}
The data are collected at a bridge that was constructed in 2011 on SH 21, 0.83 km southwest of the Brazos/Madison County line, shown in Figures~\ref{fig:21setup} and \ref{fig:21bridge}.  This bridge is labeled as 'Unknown Bridge' in Fig.~\ref{fig:map}. 
 \begin{figure}[!ht]
     \centering
           \begin{subfigure}[Test site]
             {\includegraphics[width=70mm, height=60mm]{figures/21} \label{fig:21setup}}
       \end{subfigure}
       ~
     \begin{subfigure}[Experimental setup]
       {\includegraphics[width=70mm, height=60mm]{figures/212} \label{fig:21bridge}}
 \end{subfigure}
 \caption{SH 21 over Navasota River Relief Bridge}
 \end{figure}
\noindent The Navasota River Relief Bridge is 515.1 m long with 14 bents spaced every 19.81 m.  There are three piles on each bent with 0.762 m diameters.  A 1 m electrode spacing is used with 28 SS and 28 NP electrodes.  The two lines of electrodes are parallel with a 0.3 m space between.  A total station is used to account for the variable ground level, particularly around the pile where some localized scour has occurred.  
 
\begin{figure}[!ht]
\setlength{\unitlength}{0.8cm}
\centering 
\begin{picture}(18.89,11.5)
\put(0,0){\includegraphics[width=\textwidth]{figures/sh21}} 
\put(0,10){(a)}
\put(0,4.6){(b)}
\end{picture}
\caption{Navasota River Relief Bridge central pile on bent three:  (a) inverted resistivity section; (b) inverted IP section}
\label{fig:valid}
\end{figure}

From this survey, again, an isolated zone of resistivity that is higher than the surrounding soil is noted where the pile is located from the superstructure to less that 1 m into the subsurface.  The ERI section converges in only seven iterations to an RMS of 2.61\%.  The IP inversion shows a zone of high chargeability directly beneath the pile that expands radially larger than the diameter of the pile at the surface.  Using visual inspection of Fig.~\ref{fig:valid} it is inferred that the pile is embedded at least 6.1 m.  

The results of the inversion shown in Fig.~\ref{fig:valid} are post processed using the procedure defined in Chapter~\ref{chap:Stats}.  Fig.~\ref{fig:charge21} is the vertical ratio of the elements over the foundation.
\begin{figure}
\setlength{\unitlength}{0.8cm}
\centering
\begin{picture}(18.89,10)
\put(1.2,0){\includegraphics[width=0.85\textwidth]{figures/charge21}}
\put(5,4.28){Element 1}
\put(5,3.74){Element 2}
\put(5,3.2){Element 3}
\put(5,2.66){Element 4}
\put(5,2.12){Data Depth}
\put(5,1.58){Predicted Depth}
\put(3.2,0.75){0}
\put(4.2,0.75){0.2}
\put(5.42,0.75){0.4}
\put(6.67,0.75){0.6}
\put(7.93,0.75){0.8}
\put(9.22,0.75){1.0}
\put(10.42,0.75){1.2}
\put(11.71,0.75){1.4}
\put(12.94,0.75){1.6}
\put(14.2,0.75){1.8}
\put(15.59,0.75){2}
\put(2.5,1.2){-15}
\put(2.8,3.125){-12}
\put(2.8,5.075){-9}
\put(2.8,7.06){-6}
\put(2.8,9.01){-3}
\put(2.8, 10.95){ 0}
\put(1.75,4.5){\rotatebox{90}{Depth (m)}}
\put(9.27,0){$R$}
\end{picture}
\caption{Chargeability ratio for Navasota River Relief}
\label{fig:charge21}
\end{figure}
From the chargeability ratio the foundation depth is predicted as 7.49 m.  Next, the gradient of the elements is plotted.

\begin{figure}
\setlength{\unitlength}{0.8cm}
\centering
\begin{picture}(18.89,10)
\put(1.2,0){\includegraphics[width=0.85\textwidth]{figures/slope21}}
\put(5,4.28){Element 1}
\put(5,3.74){Element 2}
\put(5,3.2){Element 3}
\put(5,2.66){Element 4}
\put(5,2.12){Data Depth}
\put(5,1.58){Predicted Depth}
\put(2.85,0.75){-40}
\put(4.4,0.75){-30}
\put(6,0.75){-20}
\put(7.55,0.75){-10}
\put(9.4,0.75){0}
\put(10.8,0.75){10}
\put(12.425,0.75){20}
\put(14,0.75){30}
\put(15.5,0.75){40}
\put(2.5,1.2){-15}
\put(2.8,3.125){-12}
\put(2.8,5.075){-9}
\put(2.8,7.06){-6}
\put(2.8,9.01){-3}
\put(2.8, 10.95){ 0}
\put(1.75,5.5){\rotatebox{90}{Depth (m)}}
\put(9.27,0){$F'$}
\end{picture}
\caption{Gradient for Navasota River Relief}
\label{fig:slope21}
\end{figure}
From the gradient of the elements in Fig.~\ref{fig:slope21} the foundation is predicted as 9.09 m.  The depths where the two criteria exclusively match (from 7.119 m to 8.6 m) are averaged for the prediction.  The foundation depth is estimated as 7.89 m beneath the subsurface with a 21.53\% probability that the actual foundation depth is less than predicted.  

After this prediction is made, the bridge plans are handed to the researcher to determine the prediction error from the blind study.  Pile three in Fig.~\ref{fig:navplans} is the pile tested.  These plans are the drawings for the scour analysis for this bridge.
\begin{figure}[!ht]
\includegraphics[width=\textwidth]{figures/navplans}
\caption{Navasota River Relief Bridge plans}
\label{fig:navplans}
\end{figure}
The as-built bridge plans indicate that the foundation is 9.75 m beneath the subsurface; the pile is under predicted by 19\%.   
\clearpage
\section{Validation Summary}
\noindent A newly constructed bridge is tested to increase the likelihood that the plans could be located after the testing and foundation depth estimation are complete.  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 less than predicted.  The true depth of embedment for the pile is 9.75 m so the pile length is under predicted by 19\%.  Thus the use of the method and corresponding probability of non-exceedance curve for predicting the depth of unknown foundations are validated.
