The purpose of this VSP boundary module is to set up a sampling design that uses multiple increment (MI) soil samples along the boundary of a contaminated military training range or similar site to determine if explosive residue or other contamination in soil has migrated beyond the boundary. VSP determines the number of segments using the length of the boundary and the specified width of a contaminant plume (hot spot) that would be of concern if it is present at the boundary or extends beyond the boundary line. The boundary is divided into segments, with one or two MI samples collected per segment. VSP assumes that each MI sample collected in a segment consists of 25 small soil samples (increments) that have been collected in sets of 5 small samples clustered around each of 5 equally spaced Primary Sampling Locations along the segment. The spacing depends on the specified width of the hot spot of concern at the boundary. It is assumed that either: 1) measurements of the contaminants in soil aliquots from the MI sample are normally distributed, or 2) that the computed mean based on those measurements is itself normally distributed.
VSP provides two versions of the design: one for enclosing boundaries and one for partial (open-type) boundaries. Partial boundaries represent a dividing line, with contamination on one side and no contamination on the other side. VSP provides special tools for creating and manipulating open-type sample areas.
An upper confidence limit (UCL) on the mean concentration for each contaminant for each segment is computed and compared to an appropriate threshold value. If the UCL for a given segment exceeds the threshold value for one or more of the contaminants of concern, then VSP extends the boundary line for that segment outward to form a triangle whose sides have the same length as the initial boundary segment. Each new side is a new segment. Then one or two MI samples (each composed of 25 small soil samples) are then taken from each of the two segments (sides) of the triangle and a UCL test conducted for each segment. The final enclosing boundary for the site is the boundary that exists when all new UCL tests indicate no new segments need to be bumped out.
VSP does not consider all aspects of the sampling plan such as the methods of sample collection, the physical size, shape, and depth of soil samples collected, and the handling, transport and laboratory analysis procedures.
The following steps are used:
1. The VSP user specifies the width (feet, meters or inches) of a contaminant plume that would be of concern if it extended beyond the current boundary line. The dialogue box in VSP uses diameter of hot spot to denote this specified width of plume. On the Analytes page of the dialog box, the VSP user also specifies the contaminants of concern along with their respective action limits and units of measure. By default, VSP uses the following analytes and action levels: TNT (16 ppm), RDX (4.4 ppm), and HMX (3100 ppm).
2. VSP calculates the optimum segment length (OSL) along the current boundary line, where all segments have the same length:
OSL = 5 x (VSP user-specified width of the contamination plume of concern),
where 5 is the number of equally spaced Primary Sample Locations within each segment. A Primary Sample Location is a point along the boundary line around which a cluster of 5 small soil samples is collected. VSP assumes there are 5 Primary Sample Locations equally spaced in each segment. VSP does not consider the spatial pattern and spacing among the 5 small soil samples at each Primary Sample Location.
3. The number of segments along the boundary is computed by dividing the perimeter length (total length of the enclosing boundary) by the OSL and rounding up to the nearest whole number. This ensures that the spacing between Primary Sampling Locations will not exceed the specified width of the contamination plume.
4. The actual length of the segments is computed by dividing the length of the boundary by the number of segments.
5. For each segment, VSP assumes that the field crew will collect 5 soil increments in a cluster around the 5 evenly spaced primary sampling locations for a total of 25 increments per segment. It is assumed that these 25 increments are thoroughly mixed to form a single multiple increment sample for the segment.
6. VSP requires at least 5 segments or 10% of the segments to have a second (duplicate) MI sample collected using the same sampling pattern used for the first MI sample. However, the VSP dialogue box allows the VSP user to specify a larger number or percent of segments if desired. The purpose of duplicate MI samples is to estimate the relative standard deviation (RSD) of the data so that an UCL test can be conducted for each segment (see discussion below).
7. If the enclosed boundary of the site is very irregular, e.g., has various indentations, the VSP user can specify in the dialogue box that VSP should change the boundary to a convex hull. This has the effect of smoothing out the boundary irregularities, but it also enlarges the area enclosed by the initial boundary. In practice, the VSP user can try this option and view the resulting initial boundary to see if the new boundary is acceptable. (Note: the user should save a copy of the initial boundary because the act of converting a sample area to a convex hull cannot be undone.) The convex hull option in not available for partial boundaries.
The following steps are used:
1. A concentration value for each analyte of concern for each MI sample is entered into VSP. These data are entered into VSP by right-clicking on any of the five primary sample locations on the map or by copying data from the clipboard into the Coordinate view (see the details about the format of clipboard data).
2. For each analyte of concern, VSP uses the data from all the segments along the initial boundary that have duplicate MI samples to estimate the relative standard deviation (RSD). This estimated RSD (defined below) is assumed to apply to all segments along the initial boundary, including those for which only one MI sample was obtained.
3. For each segment, VSP multiplies the estimated segment mean for the analyte by the RSD to estimate the standard deviation for the segment.
4. VSP uses the estimated standard deviation and mean for the segment to compute the one-sided upper confidence limit (UCL) on the segment mean for the analyte. The VSP user inputs into the VSP dialogue box the confidence level desired, e.g., 0.90 (90%) or 0.95 (95%). The UCL is computed assuming that the analyte measurements of the MI samples are normally distributed.
5. If the UCL for any initial segment equals or exceeds the action level for the analyte, then the boundary for that segment is moved outward (bumped out) in the shape of a triangle. The base of the triangle is the initial segment. The length of each side of the triangle is the length of the initial segments. Depending on the shape of the enclosing boundary, the bump-out may not always be a triangle; sometimes it will fill an indentation when necessary to maintain a boundary that does not cross over itself. The UCLs for the segments are not computed until all the data for segments that have duplicate MI samples have been entered into VSP. There are two special cases where VSP will bump out a triangle before the UCL is computed: 1) when only one MI sample is collected in a segment and the measurement for that sample exceeds the threshold, and 2) when two MI samples are collected in a segment and the mean of those samples exceeds the threshold.
6. One or two new MI samples are formed for each of the new bump-out segments (sides of the triangle) using the same sampling design used along the initial segments (i.e., 25 soil samples per MI sample). VSP computes the UCL for each new bump-out segment to determine if any of these new segments should be further bumped out. This iterative process continues until none of the segments are bumped out. The rule used by VSP to determine if one or two MI samples are used in a new bump-out segment is as follows: If the VSP user specified in the dialogue box that a specific number of segments with duplicate samples is required, then VSP designates those among the initial segments and no new bumped-out segment has a duplicate MI sample; but if the VSP user specified that a percentage of the segments should have duplicate MI samples, then that percentage of the bumped-out segments will have duplicate MI samples.
7. The UCLs for new (bumped-out) segments are computed using updated estimates of the RSD based on additional duplicate MI samples, the number of which is specified by the VSP user. The following procedure is used to assure that previous bump-out decisions are not affected by the additional data and updated RSD:
Define:
Set 1 to be the segments on the initial boundary,
Set 2 to be the bump-out segments from Set 1 segments,
Set 3 to be the bump-out segments from Set 2 bump-out segments, and so forth.
Then compute the RSD and UCL for:
Segments in Set 1 using only the duplicates in Set 1,
Segments in Set 2 using the duplicates in Sets 1 and 2,
Segments in Set 3 using the duplicates in Sets 1, 2 and 3, and so forth.
Using this process the UCLs and decisions for Set 1 segments will not change if further bump-outs occur. Similarly, the UCLs and decisions for Set 2 won't change if further bump-outs occur, and so on.
The following steps are used:
1. Compute the relative standard deviation (RSD) for the initial set of \(n\) segments for which two MI samples were obtained:
\begin{equation} RSD = \sqrt{\frac{1}{n}\displaystyle\sum_{i=1}^{n}\frac{s_i^2}{{\bar{x}}_i^2}} \end{equation}
where
\(s_i^2 = \displaystyle\sum_{j=1}^{2}(x_{ij} - {\bar{x}}_i)^2\) is the variance of the two MI sample measurements from the \(i\)th segment
\({\bar{x}}_i = \frac{1}{2}\displaystyle\sum_{j=1}^{2}x_{ij}\) is the mean of the two measurements from the \(i\)th segment
2. Compute the standard deviation for the \(i\)th segment among all the segments along the initial boundary, even those segments that had only one MI sample:
\begin{equation} {SD}_i = (RSD)({\bar{x}}_i) \end{equation}
where
\({\bar{x}}_i = \frac{1}{m_i}\displaystyle\sum_{j=1}^{m_i}x_{ij}\) is the mean of the MI sample measurements in the \(i\)th segment
\(m_i\) is the number of MI sample measurements (\(m_i\) = 1 or 2) for the \(i\)th segment
3. Compute the 100(1- \(\alpha\)) percent UCL for the \(i\)th segment
\begin{equation} {UCL}_i = {\bar{x}}_i + t_{1-\alpha, n}\frac{{SD}_i}{\sqrt{m_i}} \end{equation}
where
\(n\) is the number of segments for which two MI samples were obtained
\(t_{1-\alpha, n}\) is the \(100(1-\alpha)\) percentile of the t distribution with \(n\) degrees of freedom
and \({SD}_i\) is computed using Equation (2).
4. Conduct the UCL test for the \(i\)th segment
If \({UCL}_i \geq \) action level, then bump-out the \(i\)th segment, where \({UCL}_i\) is computed using Equation (3.0). Note: the segment is bumped out if \({UCL}_i \geq\) action level for one or more of the analytes.
5. Update the estimate of the RSD using the duplicate multiple increment measurements in Sets 1 and 2.
\begin{equation} RSD = \sqrt{\frac{1}{n^*}\displaystyle\sum_{i=1}^{n^*}\frac{s_i^2}{{\bar{x}_i}^2}} \end{equation}
where
\(n^*\) is the \(n\) + (number of new bumped-out segments that have two MI samples).
6. Compute the standard deviation and the UCL and conduct the UCL test for each segment in Set 2.
Compute Equation (2) and Equation (3) for the newly bumped-out segments.
7. Repeat Steps 5 and 6 until no new segments are bumped out.
The field crew will collect 5 small soil samples in a cluster around the 5 evenly spaced Primary Sampling Locations for a total of 25 small soil samples per MI sample.
The 25 small soil samples are thoroughly mixed to form a single MI sample for the segment.
If a second MI sample is needed for a segment, the same sampling pattern (5 small soil samples in a cluster around each of the 5 evenly spaced Primary Sampling Locations) should be used.
Analyte measurements of the MI samples from the segment of a set have a normal (Gaussian) distribution.
The RSD computed for a given set of segments (Set 1, Set 2, Set 3, etc.) applies to all segments in the set, that is, the RSD is assumed to be constant for all segments.
If more than one measurement is obtained from a MI sample, then \(x_i\) in Equations 1.0, 2.0, 3.0 and 4.0 in this Appendix is the average of the several measurements.
The sampling design (one or two MI samples per segment and 25 small samples per MI sample) results in a sufficiently high (unspecified) power (probability) that the UCL test will indicate when a segment should be bumped out.
There is no spatial correlation of the concentrations along the boundary line.
Diameter of Hot Spot that Must be Detected at the Boundary
% of segments that need field duplicates
Number of segments that need field duplicates