1、Designation: D 6982 03Standard Practice forDetecting Hot Spots and Buried Objects Using Point-Net(Grid) Search Patterns1This standard is issued under the fixed designation D 6982; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the
2、 year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) 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 proba
3、bilitiesof detecting hot spots (that is, localized areas of soil orgroundwater contamination) and buried objects using point-net(that is, grid) search patterns. Hot spots, more generallyreferred to as targets, are presumed to be invisible on theground surface. Buried objects may include former surfa
4、ceimpoundments, waste disposal pits, and utilities that have beencovered by soil or paving materials. Hot spots may also includecontaminant plumes in ground water or soil gas.1.2 For purposes of calculating detection probabilities, hotspots or buried objects are presumed to be elliptically shapedwhe
5、n projected vertically to the ground surface, and searchpatterns are square, rectangular, or rhombic. Assumptionsabout the size and shape of suspected hot spots are the primarylimitations of this practice, and must be judged by historicalinformation.Afurther limitation is that hot spot boundaries ar
6、eassumed to be clear and distinct. Alternative approaches to hotspot detection using discrete sampling should also be consid-ered where feasible, such as surface geophysical measurements(see Guide D 6429).1.3 Search sampling would normally be conducted duringpreliminary investigations of hazardous w
7、aste sites or hazard-ous waste management facilities (see Guide D 5730). Samplingmay be conducted via drilling or by direct-push methods. Incontrast, guidance on sampling for the purpose of makingstatistical inferences about population characteristics (for ex-ample, contaminant concentrations) can b
8、e found in GuideD 6311.1.4 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
9、 to use.2. Referenced Documents2.1 ASTM Standards:2D 5730 Guide for Site Characterization for EnvironmentalPurposes With Emphasis on Soil, Rock, the Vadose Zoneand Ground WaterD 6051 Guide for Composite Sampling and Field Subsam-pling for Environmental Waste Management ActivitiesD 6311 Guide for Gen
10、eration of Environmental Data Re-lated to Waste Management Activities: Selection andOptimization of Sampling DesignD 6429 Guide for Selecting Surface Geophysical Methods3. Terminology3.1 Definitions:3.1.1 hot spota localized area of soil or groundwatercontamination.3.1.1.1 DiscussionA hot spot may b
11、e considered as adiscrete volume of buried waste or contaminated soil where theconcentration of a contaminant of interest exceeds someprespecified threshold value. Although elliptically shaped hotspots or targets are assumed for the purposes of calculatingprobabilities of detecting hot spots, hot sp
12、ots are more likely tohave variable sizes and shapes and not have clear and distinctboundaries. However, the concept of hot spots is consistentwith known historical patterns of contaminant distributions.3.1.2 sampling densitythe number of borings (that is,sampling points) per unit area.3.1.3 semi-ma
13、jor axis, aone-half the length of the longaxis of an ellipse. For a circle, this distance is simply theradius.3.1.4 semi-minor axis, bone-half the length of the shortaxis of an ellipse.3.1.5 targetthe object or “hot spot” that is being searchedfor.1This practice is under the jurisdiction of ASTM Com
14、mittee D34 on WasteManagement and is the direct responsibility of Subcommittee D34.01.01 onPlanning for Sampling.Current edition approved Nov. 1, 2003. Published January 2004.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For
15、 Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.1.6 threshold concentrationthe concentration of a con-taminant above
16、which a hot spot is considered to be detected.3.1.7 unit cellthe 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 60/120rhombus comprised of two equilateral triangles with a commonside.3.2 Symbols:a
17、= 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= pab.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
18、 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= QG2. For a 60/120 rhombus, Arh=(=3)/2G2. The inverse
19、 of ACis the sampling densityb = the probability of not detecting a hot spot (that is,“consumers risk”)P(hit) = probability of detection (that is, 1 b)4. Significance and Use4.1 Search sampling strategies have found wide utility ingeologic exploration where drilling is required to detectsubsurface m
20、ineral deposit, such as when drilling for oil. Usingsuch strategies to search for buried wastes, subsurface contami-nants, and underground structures is a logical extension ofthese strategies.4.2 Systematic sampling strategies are often the most cost-effective method for searching for hot spots or b
21、uried objects.4.3 Search sampling patterns may also be used to optimizethe locations of ground water monitoring wells or to optimizethe location of vadose zone monitoring devices.4.4 This practice may be used to determine the risk ofmissing a target of specified size and shape given a specifiedsampl
22、ing pattern and sampling density.4.5 This practice may be used to determine the smallesttarget that can be detected with a specified probability andgiven sampling density.4.6 This practice may be used to select the optimum gridsampling strategy (that is, sampling pattern and density) for aspecified
23、risk of not detecting a hot spot or buried object.4.7 By using the algorithms given in this practice, one canbalance the cost of sampling versus the risk of missing a hotspot or buried object.5. Assumptions5.1 One or more targets (for example, hot spots) exist andare equally likely to occur in any p
24、art 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
25、 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. Fordetection of b
26、uried solid objects, this should present littledifficulty. However, for buried contaminants, such an assump-tion presumes that the full depth of a boring would be subjectto analysis as contiguous intervals of the boring. If samplingintervals are discontinuous, then contamination might bemissed if it
27、 occurred between sampled intervals. If samplingFIG. 1 Projection of Boundaries of Subsurface Contamination to the Ground SurfaceD6982032intervals are too long, then a hot spot may not be detectedbecause of dilution of a hot spot with less contaminatedportions of the sampled interval. The criteria f
28、or detection ofcontaminants may be prespecified threshold concentrations (forexample, screening levels) that would trigger further investi-gation 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 pract
29、ice assume that borehole or direct-pushdevices have no area, but rather are treated as a vertical line.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 historica
30、l 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 or the presence of buried waste orobjects such as underground storage tanks.Areas wit
31、h differentexpected probabilities of detection of a hot spot or other targetshould be clearly 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
32、be overlain. Areas with higher expectedoccurrence of hot spots or buried objects should have corre-spondingly higher sampling densities compared to areas withlower expected occurrence. However, areas with greater hazardfrom missing a hot spot should also have correspondinglyhigher sampling densities
33、 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 willde
34、pend 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 samp
35、led 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 with otherlayers of soil or waste. Further, a hot spo
36、t confined to a discretelayer may be missed entirely by not sampling that layer. Forthis reason, continuous sampling is recommended.6.4 Detection of contaminant levels in samples abovethreshold concentrations or the detection of buried objects maytrigger further action requiring possibly more detail
37、ed drillingand sampling to better define spatially the location of hot spotsor buried objects. Again, a grid sampling strategy will be themost efficient. If new boring locations are centered at themidpoints of the unit cells, the total number of borings will beexactly doubled.7. Computing Hot Spot D
38、etection Probabilities7.1 Case IIf the longest dimension of an elliptical target isless than or equal to the grid spacing (that is, 2a#G), then theFIG. 2 Grid Patterns for Detecting Hot Spots. Borings are Made at the Grid NodesD6982033target can only be hit once and the probability P of detectingthe
39、 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 2If 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 develop
40、edby Singer and Wickman (1)3employing 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. Singersalgorithm
41、s 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 TargetThe probabilityof detecting a target,
42、 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 c
43、alculate 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 interpolatebetwee
44、n 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 ahoriz
45、ontal line from the prespecified probability of a hit to thecurve 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 al
46、so 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 TargetIf the orientation of t
47、heelliptical 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 t
48、arget (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
49、 over another when searching for a target is3The boldface numbers in parentheses refer to the list of references at the end ofthis standard.FIG. 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.D6982034measured 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 a triangular grid and asquare grid, respectively. By extension
