# ASTM D6982-09 (Reapproved 2016)

Designation: D6982 − 09 (Reapproved 2016)Standard Practice forDetecting Hot Spots Using Point-Net (Grid) Search Patterns1This standard is issued under the fixed designation D6982; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice provides equations and nomographs, and areference to a computer program, for calculating probabilitiesof detecting hot spots (that is, localized areas of soil orgroundwater contamination) using point-net (that is, grid)search patterns. Hot spots, more generally referred to as targets,are presumed to be invisible on the ground surface. Hot spotsmay include former surface impoundments and waste disposalpits, as well as contaminant plumes in ground water or thevadose zone.1.2 For purposes of calculating detection probabilities, hotspots or buried contaminants are presumed to be ellipticallyshaped when projected vertically to the ground surface, andsearch patterns are square, rectangular, or rhombic. Assump-tions about the size and shape of suspected hot spots are theprimary limitations of this practice, and must be judged byhistorical information. A further limitation is that hot spotboundaries are usually not clear and distinct.1.3 In general, this practice should not be used in lieu ofsurface geophysical methods for detecting buried objects,including underground utilities, where such buried objects canbe detected by these methods (see Guide D6429).1.4 Search sampling would normally be conducted duringpreliminary investigations of hazardous waste sites or hazard-ous waste management facilities (see Guide D5730). Samplingmay be conducted by drilling or by direct-push methods. Incontrast, guidance on sampling for the purpose of makingstatistical inferences about population characteristics (forexample, contaminant concentrations) can be found in GuideD6311.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D5730 Guide for Site Characterization for EnvironmentalPurposes With Emphasis on Soil, Rock, the Vadose Zoneand Groundwater (Withdrawn 2013)3D6051 Guide for Composite Sampling and Field Subsam-pling for Environmental Waste Management ActivitiesD6311 Guide for Generation of Environmental Data Relatedto Waste Management Activities: Selection and Optimiza-tion of Sampling DesignD6429 Guide for Selecting Surface Geophysical Methods3. Terminology3.1 Definitions:3.1.1 hot spot—a localized area of soil or groundwatercontamination.3.1.1.1 Discussion—A hot spot may be considered as adiscrete volume of buried waste or contaminated soil where theconcentration of a contaminant of interest exceeds someprespecified threshold value. Although hot spots are morelikely to have variable sizes and shapes and not have clear anddistinct boundaries, ellipitically shaped hot spots or targetswith well defined edges are assumed for the purposes ofcalculating detection probabilities. The assumption that hotspots have elliptical shapes is not inconsistent with knownhistorical patterns of contaminant distribution.3.1.2 sampling density—the number of soil borings (that is,sampling points) per unit area.3.1.3 semi-major axis, a—one-half the length of the longaxis of an ellipse. For a circle, this distance is simply theradius.3.1.4 semi-minor axis, b—one-half the length of the shortaxis of an ellipse.3.1.5 target—the object or “hot spot” that is being searchedfor.1This practice is under the jurisdiction of ASTM Committee D34 on WasteManagement and is the direct responsibility of Subcommittee D34.01.01 onPlanning for Sampling.Current edition approved May 1, 2016. Published May 2016. Originallyapproved in 2003. Last previous edition approved in 2009 as D6982 – 09. DOI:10.1520/D6982-16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3The last approved version of this historical standard is referenced onwww.astm.org.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.1.6 threshold concentration—the concentration of a con-taminant above which a hot spot is considered to be detected.3.1.7 unit cell—the smallest area into which a grid can bedivided so that these areas have the same shape, size andorientation. For a triangular grid, the unit cell is a 60°/120°rhombus comprised of two equilateral triangles with a commonside.3.2 Symbols: a = length of the semi-major axis of an ellipseb = length of the semi-minor axis of an ellipseAT= area of target or hot spot. For an ellipse, AT= πab.AS= search areaS = the “shape” of an elliptical target (that is, the ratio of thelength of the semi-minor axis to the length of the semi-majoraxis of an ellipse, b/a)G = the distance between nearest grid nodes of a unit cellQ = the ratio of the length of the long side of a rectangulargrid cell to the length of the short sideAC= the area of the unit cell. For a square, Asq= G2. For arectangle Are= Q·G2. For a 60°/120° rhombus, Arh=[(√3)/2]G2. The inverse of ACis the sampling densityβ = the probability of not detecting a hot spotP(hit) = probability of detection (that is, 1 − β)4. Significance and Use4.1 Search sampling strategies have found wide utility ingeologic exploration where drilling is required to detectsubsurface mineral deposit, such as when drilling for oil andgas. Using such strategies to search for buried wastes andsubsurface contaminants, including volatile organiccompounds, is a logical extension of these strategies.4.2 Systematic sampling strategies are often the most cost-effective method for searching for hot spots.4.3 This practice may be used to determine the risk ofmissing a hot spot of specified size and shape given a specifiedsampling pattern and sampling density.4.4 This practice may be used to determine the smallest hotspot that can be detected with a specified probability and givensampling density.4.5 This practice may be used to select the optimum gridsampling strategy (that is, sampling pattern and density) for aspecified risk of not detecting a hot spot.4.6 By using the algorithms given in this practice, one canbalance the cost of sampling versus the risk of missing a hotspot.4.7 Search sampling patterns may also be used to optimizethe locations of additional ground water monitoring wells orvadose zone monitoring devices.5. Assumptions5.1 One or more targets or hot spots exist and are equallylikely to occur in any part of the search area.5.2 When projected vertically upward to a level groundsurface, the target appears as an ellipse or a circle (Fig. 1). Theprobable size and shape of a hot spot can only be guessed frompast site or facility records, known layout of the site or facility,and personal knowledge.5.3 The search pattern is either a square, a rectangular, or anequilateral triangular grid. Borings are made at the intersec-tions of grid lines (that is, nodes) (Fig. 2).5.4 Borings or direct-push devices are directed downwardvertically and the detection of the target is unambiguous. Suchan assumption presumes that the full length of a boring wouldbe subject to analysis as contiguous intervals of the boring. Ifsampling intervals are discontinuous, then contaminationmight be missed if it occurred between sampled intervals. Ifsampling intervals are too long, then a hot spot may not bedetected because of dilution of a hot spot with less contami-nated portions of the sampled interval. The criteria for detec-tion of contaminants may be prespecified threshold concentra-tions (for example, screening levels) that would trigger furtherinvestigation of sites or facilities.5.5 The area of the borehole or direct-push device isinfinitely small compared to the target area. The algorithmsused in this practice assume that boreholes or direct-pushdevices have no area, but rather are vertical lines projecteddownward from grid nodes.6. Preliminary Considerations6.1 Before designing a hot spot detection strategy, a pre-liminary investigation of the area containing possible hot spotsor targets should be conducted. From historical records, physi-cal layout of buildings and equipment, known transportationpathways, landscape features, and eyewitness accounts, onemay be able to identify areas with a high probability ofsubsurface contamination. Areas with different expected prob-abilities of detection of a hot spot or other target should beclearly mapped.6.2 Within areas of relatively uniform expected probabilityof hot spot or target detection, sampling grids of prespecifiedgrid spacing G and type (for example, square, rectangular, ortriangular) may be overlain. Areas with smaller hot spotsFIG. 1 Projection of Boundaries of Subsurface Contamination tothe Ground SurfaceD6982 − 09 (2016)2should have correspondingly higher sampling densities com-pared to areas with large hot spots. However, areas with greaterhazard from missing a hot spot should also have correspond-ingly higher sampling densities than areas with a lesser hazard.Ideally, the starting point for each grid and its orientationshould be randomly determined.6.3 When searching for hot spots, threshold concentrationsfor detection may be established by a regulatory authority.Whether or not a threshold concentration is exceeded willdepend upon the physical distribution of the contaminant, thevolume of the sampling device, the sampling intervals selected,and the sensitivity of the analysis. If contamination occurs in adiscrete layer, then the probability of detecting a hot spot willdecrease with increasing volume of material sampled in a borehole or if the sampling interval exceeds the depth of thediscrete hot spot layer. The analytically determined contami-nant concentration may then be less than the threshold concen-tration because of the dilution of the hot spot layer withuncontaminated layers of soil or waste. Further, a hot spotconfined to a discrete layer may be missed entirely by notsampling that layer. For this reason, continuous sampling isrecommended.6.4 Detection of contaminant levels in samples abovethreshold concentrations may trigger more detailed sampling tobetter define the spatial extent of hot spots or buried contami-nation. Again, a grid sampling strategy will be the mostefficient.7. Determining Hot Spot Detection Probabilities7.1 Case I—If the longest dimension of an elliptical target isless than or equal to the grid spacing (that is, 2a ≤ G), then thetarget can only be hit once and the probability P of detectingthe hot spot is simply equal to the ratio of the area of the targetATto the area of the unit cell AC(that is, P = AT/AC).7.2 Case 2—If the longest dimension of an elliptical targetis greater than the grid spacing (that is, 2a G), then the targetmay be hit more than once. In this case, algorithms developedby Singer and Wickman (1)4employing affine transformationsand programmed in FORTRAN by Singer (2) are required tocalculate the exact probability of detecting the target. Thisprogram is limited to ellipses having a shape S between 0.05and 1.0 and the ratio a/G between 0.05 and 1.0. Singer’salgorithms have been adapted by J. R. Davidson (3) to thepersonal computer (PC) running under the MS DOS operatingsystem. Supporting documentation for this program,ELIPGRID-PC, is available from Oak Ridge National Labora-tory (4, 5).7.3 Randomly Oriented Elliptical Target—The probabilityof detecting a target, P(hit), of a specified size a shape S and fora specified grid G spacing can be obtained from nomographsshown in Figs. 3 and 4 for square and equilateral triangular gridsampling patterns, respectively. Data for these nomographswere generated using the ELIPGRID-PC program. To use thesegraphs, first calculate the ratio a/G. Then draw a vertical linefrom the point represented by the ratio a/G on the x-axis of thegraph to the curve representing the prespecified shape of theellipse. Then draw a horizontal line to the y-axis. For shapesother than those shown on the graphs, one must interpolate4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.FIG. 2 Grid Patterns for Detecting Hot Spots. Borings are Made at the Grid NodesD6982 − 09 (2016)3between curves with closest values of S. The value on they-axis represents the probability of at least one hit of the target.Using these same graphs, one can also determine the requiredgrid spacing to detect an elliptical target of shape at aprespecified probability of detection. In this case, draw ahorizontal line from the prespecified probability of a hit to theFIG. 3 Nomograph Relating the Probability of Detecting a Single Hot Spot to the Ratio a/G for Selected Shapes (b/a)Using a Square Grid with Grid Spacing G.FIG. 4 Nomograph Relating the Probability of Detecting a Single Hot Spot to the Ratio a/G for Selected Shapes (b/a)Using a Triangular Grid with Grid Spacing G.D6982 − 09 (2016)4curve representing the prespecified shape of the ellipse. Thendraw a vertical line down to the x-axis. From the ratio a/G atthe point of intersection with the x-axis, one can determine theminimum required grid spacing. Similarly, one can also deter-mine the smallest sized hot spot of a given shape that can bedetected for a given grid spacing and probability of detectionby calculating a from the ratio a/G and grid spacing G.Alternatively, one can use the computer program ELIPGRID-PC.7.4 Oriented Elliptical Target—If the orientation of theelliptical target with respect to the grid lines is specified, thenthe probability of detecting the target must be determined usingthe computer program ELIPGRID-PC.8. Comparing the Relative Efficiencies of Search Patterns8.1 The efficiency of a search pattern is measured as theprobability that a target (for example, hot spot) will be hit atleast once. Given the same sampling density, a samplingpattern with a higher probability of hitting a target will be moreefficient than a sampling pattern with a lower probability ofhitting the same target. The relative efficiency, RE,ofonesampling pattern over another when searching for a target ismeasured as the percent difference in the efficiency of twoequivalent density sampling patterns. For example, RE =100 % (PTRI− PSQR)/PSQRwhere PTRIand PSQRare theprobabilities of detecting a target with an equilateral triangulargrid and a square grid, respectively. By extension, for the sameprobability of detecting a target, a more efficient samplingpattern wil