Preparing correlation plots – which involve plotting two or more variables against each other rather than against time – is a useful way to analyze data collected by dam safety monitoring devices. Correlation plots are particularly useful for monitoring dams where reservoir water levels vary significantly.
By Eugene B. Gall
Proper instrumentation plays an important role in monitoring the safety of a dam. Equally important is proper interpretation of the data collected by the instrumentation. The two primary ways to plot instrumentation data with regard to a specific stimulus (such as reservoir level) are:
–On the same axis with the stimulus, against time (producing a time-history plot); or
–Against the stimulus (producing a correlation plot).
Typically, personnel produce time-history plots of various data, such as piezometer level and reservoir water level for embankment dams. However, this practice gives rise to several questions:
–Does this type of plot provide all the information available from the data?
–Should the dam owner select threshold/action levels based on slope stability, historical readings, or both?
–If the reservoir at a pumped-storage project is at a low level or even mid-level, how does the project owner evaluate safety of the embankment dam after an earthquake? What is the threshold level in this case?
The above questions can be answered by plotting and interpreting the correlation between the reservoir water level and piezometer level. Correlation plots generally are underutilized because, in most cases, the behavior of the dam is clear enough on the time-history plot, especially for a reservoir with a quasi-constant level. However, correlation plots illustrate some aspects of the piezometric response of embankment dams better than time-history plots. Correlation plots are a valuable tool and are regularly used by some organizations,1,2,3 but they are not used as often as they should be. Under the right circumstances, correlation plots can be indispensable in analyzing data gathered from instrumentation.
Correlation plots can be used in many simple applications, including identifying stimulus and evaluating piezometer clogging.1,4
Understanding correlation plots
Conventional correlation plots present the reservoir water level along the x-axis and the piezometer level along the y-axis. Each point on the correlation line is a piezometer/reservoir reading, taken at a moment in time, which does not necessarily represent the steady-state condition. If the piezometer level is influenced only by the reservoir water level and no significant lag effect is present, the plot shows a straight line. In general, the larger the distance or gradient between the piezometer and the reservoir, the weaker the correlation and the flatter the slope. Mathematically, the limit cases are:4
–Full correlation for a piezometer connected to a reservoir, when the piezometer reading equals the reservoir level, is represented by a 45-degree line for equal scales on both axes; and
–No or zero correlation, with a horizontal line representation, when the piezometer level is constant regardless of the reservoir level.
If the piezometer is influenced by and thus lags behind the reservoir level when it rises or falls, the points scatter along a sloped line (correlation line). On correlation plots, the lag for a certain reservoir level is expressed as the deviation in piezometer level from the correlation line. It is expressed in feet, rather than in time (as it is on the time-history plot).
Alternately, random scattering along a constant piezometer value for constant reservoir level shows that a different stimulus exists (such as runoff, aquifer fed from an uphill source, or tailwater level variation) that may need to be identified.
Correlation plots are especially sensitive to several factors. These are:
–Changes in the piezometric regime. Any new development or action that significantly affects the cause or effect of a correlation requires building a new correlation plot. Factors affecting both the phreatic line in the dam or foundation (i.e., grouting, installation of dewatering wells, etc.) and the piezometer itself (i.e., flushing, recalibration, etc.) are examples of such changes.
–Instrumentation data collection errors. If the reservoir and piezometer levels are not recorded at the same time, this time gap will be interpreted as an additional (but false) lag and will lead to an incorrect correlation. This interval depends on the rate of variation of the reservoir level. This is especially important for relatively rapid reservoir level variation, as in pumped-storage projects where a variation of several feet per hour is common.
–The “scale” effect. Selection of a too-detailed scale for piezometer readings visually exaggerates the reading variation and may mislead the reader into believing that a correlation exists.
Using correlation plots
The use of correlation plots is particularly helpful when analyzing data from instrumentation at storage and dewatered projects, at pumped-storage projects, and when monitoring potential failure modes (PFMs).
Storage and dewatered projects
Complex monitoring is required at projects that store water, during initial filling of a reservoir, or during dewatering and refilling of a reservoir at a run-of-river plant. These situations call for the use of correlation plots in addition to history plots.
Take the example of an embankment dam on glacial till with a central core. The reservoir impounded by the dam was being dewatered to repair the embankment. Monitoring was necessary for two situations:
–Uncontrolled reservoir level rise due to floods while repairs were being completed; and
–Controlled slow refilling of the reservoir after repairs were completed. The average rate of refill was 0.14 foot per day, and the piezometers were allowed to stabilize at intermediate stages.
Monitoring was complicated by flushing of the old standpipes (some of them were partially clogged) and installation of dewatering wells at the toe of the dam. These activities improved responsiveness of some piezometers and lowered the phreatic line through the dam, respectively. Not all piezometers were affected by these activities, but new correlation plots had to be reconfigured after each modification for the ones that were affected. These plots had to use only the post-modification data collected during several floods that occurred in the dewatering interval and during refill operation.
The correlation plots for piezometers in pervious layers (clean sand, in this case) directly connected with the reservoir were relatively simple. They exhibited a sloped straight-line plot, meaning they were clearly influenced by the reservoir. The apparent lag is zero for all practical purposes.
The correlation plots for piezometers in low-permeable or impervious layers were more complex. Figure 1 shows the response for a standpipe in the silty core of the embankment dam, along the centerline. The piezometer level drops only 2 feet during a 50-foot rapid reservoir dewatering from the initial steady-state point A (full reservoir) along line AB. The piezometer drops another 9 feet toward a second steady-state point C (under stationary dewatered reservoir) along line BC. Then the plot shows a slow-refill correlation (line CA) that includes stabilization at each refill stage.
The readings part of the CA correlation could be contained either between two straight lines or within a closed envelope. I prefer to use an elliptical visually-determined “best fit” envelope because it highlights the smaller range of the piezometer readings variation that corresponds to the lower rate of reservoir variation for the extreme levels. The “loops” below line CA are due to the 2006 and 2007 floods when the piezometer could not keep up with the fast-rising reservoir level and dropped below the correlation envelope. These readings are outside of the “normal” operation envelope but do indicate a fast rate of reservoir variation rather than an adverse development. Any readings outside the envelope should be carefully evaluated before any action is taken.
The correlation plot shows at a glance the consistency and accuracy of the correlation, the historical range of the piezometer readings, and the deviation of the current reading for any reservoir level. The history plot does not offer this information.
The piezometer lag is somewhat easier to recognize on a time-history plot for a pumped-storage project because the reservoir reaches the same elevation several times a week and the corresponding piezometer levels can be compared. However, one still cannot accurately quantify this lag and recognize incipient negative trends at a glance.
For pumped-storage projects, the piezometer readings perform daily loops inside a well-defined envelope, specific for each rate of reservoir variation depending on the number of units running. For these correlation plots, the visual best-fit elliptical envelope is used again. The slope of the longitudinal axis of this ellipse shows the degree of correlation, and the vertically-measured range is twice the instantaneous lag for each water level.
Note that, due to variation in reservoir level of up to 40 feet in several hours at pumped-storage projects, piezometer readings represented by the points on the correlation plot do not necessarily correspond to the steady-state level for that reservoir level. Deviation from the equilibrium line is generally smaller for piezometers in pervious layers and larger for piezometers in impervious layers.
The behavior of two piezometers in the lower embankment of a pumped-storage project (see Figures 2 and 3) illustrates the characteristics of correlation plots produced. Readings and plotting were done under both normal pumped-storage operation and full lower reservoir held under constant level while the upper reservoir was dewatered for inspection and repairs. This dewatering lasted a couple of months, and the steady state for full lower reservoir was attained for all practical purposes.
Figure 2 shows a correlation plot for a vibrating wire piezometer in a clean sand aquifer in the dam foundation, at the toe of the lower embankment. During the normal weekly pumped-storage operation, the reservoir level varies 37 feet and the piezometer level 13 feet.
The piezometer stabilized fast once the reservoir was held under constant level, with an apparent increment in piezometer level of only several inches. The piezometer equilibrium level aligns well with the longitudinal axis of the normal operation envelope, which, for this case, can be considered representative for both operation and steady-state conditions.
Applications of this plot are:
–A benchmark for future readings;
–A benchmark for checking dam condition after a major event, such as an earthquake, regardless of the reservoir level. This is based on the location of the piezometer reading at that time on the correlation plot, i.e., in or out of the plotted ellipse representing the expected or historical range for that particular reservoir level.
–A determination of water pressure in an aquifer in the dam foundation at the toe during floods, to be used in calculation of heaving or lifting safety factor for the impervious layer that covers the aquifer. This is done by extrapolation of the correlation line and reading for flood reservoir level. (This is valid only for piezometers in pervious material.)
–A benchmark for prolonged high water level in the lower reservoir while the upper reservoir is dewatered for inspection and/or repairs. (This is valid only for piezometers in pervious material.)
Figure 3 shows a correlation plot for a hydraulic piezometer in the clay core of the embankment at the same pumped-storage project, for the same time period. It took about a month from when the reservoir level was held constant until this piezometer reached the steady-state level. The piezometer level increment from apparent equilibrium to steady-state level was about 10 feet. This point falls way out of the normal operation correlation envelope that, in this case, is representative for piezometer only in “standard” pumped-storage operation but not for the steady-state condition. The points inside the envelope are “floating” with the reservoir level, but they are not stabilized for any particular level.
Applications of this correlation plot for a piezometer in an impervious layer include use as a benchmark for readings during both regular inspections and inspections after a major event, regardless of the reservoir level.
Another recent application was initiated by elevated readings at a couple of piezometers at the toe of the upper sealed reservoir of a pumped-storage project. The project did not have an automated data acquisition system. The reservoir levels were not routinely recorded at the time of reading of piezometer levels, so correlations could not be obtained from the historic data. A three-day hourly recording of simultaneous piezometer and reservoir levels under 40 foot daily variation supplied data necessary to produce correlation plots for all piezometers. It was found that the elevated piezometers did not respond to the reservoir level variation, and a different stimulus was identified. However, three other piezometers did, so apparently the reservoir seal was leaking at a location in the general area of these piezometers.
When the reservoir was dewatered, several cracks were found in the reservoir floor liner. Although this trend could be seen in the time-history plot, it was more evident in the correlation plot.
A more general application involves the presentation of threshold levels against the reading data for monitoring PFMs. The threshold level is a reading that indicates a significant departure from the normal range of readings and prompts an action.5 (However, exceeding the threshold by itself usually does not imply an instability of the structure.) Multiple thresholds sometimes are designated in relation to the same failure mode.
The threshold levels are routinely determined based either on position of the actual pore pressure level relative to the level considered in the slope stability calculation, or the deviation from the historical readings. However, the design limit (design basis value5) corresponds to only one particular reservoir level, i.e., the level considered in a stability calculation. In addition, the historic limit cannot be easily read on a time-history plot for a specific reservoir level. In fact, each approach covers a different failure mode and these approaches can be represented, read, and interpreted on the correlation plot as a unitary concept (see Figure 4). The more complex plot for a piezometer in the pumped-storage clay core embankment (shown in Figure 3 on page 65) was used for illustration, and the origin of the threshold is labeled.
Note that there are out-of-range readings on Figure 4, labeled as Potential Failure Mode 2 and Potential Failure Mode 3. These are related to specific PFMs that could be identified only by their deviation from the historical range of readings, and they do not exceed the level used in stability calculations. In Potential Failure Mode 2, the penstock leakage pressurizes the core in the zone of influence of the piezometer without reaching the design limit (at least in the incipient stages). In Potential Failure Mode 3, piping developing in the zone of influence of the piezometer will not exceed the stability threshold limit and even drop below the correlation envelope as long as the pipe behaves like a drain, lowering the pore pressure. The advantage of the correlation plot is that abnormal readings that may indicate development of an adverse condition could be instantly visualized for any reservoir level.
Correlation plots are essential in evaluating the behavior of an embankment dam where reservoir levels are not constant, such as at storage projects and at projects during dewatering and filling. They clearly define the piezometric range of readings for any reservoir level (unlike time-history plots) and consequently allow for a better evaluation of action levels. Consequently, correlation plots are an ideal tool for evaluation of the embankment during both regular inspections and inspections after unusual events, such as floods and earthquakes.
Correlation plots also are useful in evaluating performance of weirs, slope inclinometers, and crack monitors.
Mr. Gall may be reached at Federal Energy Regulatory Commission, New York Regional Office, 19 West 34th Street, Suite 400, New York, NY 10001; (1) 212-273-5950; E-mail: [email protected]
The examples and statements in this paper are based on the author’s 15 years of experience with projects located in the northeastern U.S. under the jurisdiction of FERC.
- Guidelines for Instrumentation and Measurements for Monitoring Dam Performance, American Society of Civil Engineers, Reston, Va., 2000.
- Kuperman, Selmo C., M. Regina Moretti, Julio C. Pinfari, and Edvaldo F. Carneiro, “Placing ‘Limit Values’ on Instrument Readings,” HRW, Volume 15, No. 3, July 2007, pages 24-31.
- Harris, Craig, and Alex Grenoble, Instrumentation and Monitoring Training Classes for the Division of Dam Safety and Inspections, Federal Energy Regulatory Commission, Washington, D.C., 1996.
- Gall, Eugene B., “Correlation Plot – A Modern Tool in Dam Safety Monitoring,” USSD Annual Meeting and Conference, United States Society on Dams, Denver, Colo., 2007.
- Engineering Guidelines for the Evaluation of Hydropower Projects, Chapter 14, Appendix J, Federal Energy Regulatory Commission, Washington, D.C., 2008.
Eugene Gall, P.E., is a dam safety engineering supervisor in the New York Regional Office of the Federal Energy Regulatory Commission.