ASTM D6982-03
(Practice)Standard Practice for Detecting Hot Spots and Buried Objects Using Point-Net (Grid) Search Patterns
Standard Practice for Detecting Hot Spots and Buried Objects Using Point-Net (Grid) Search Patterns
SIGNIFICANCE AND USE
Search sampling strategies have found wide utility in geologic exploration where drilling is required to detect subsurface mineral deposit, such as when drilling for oil. Using such strategies to search for buried wastes, subsurface contaminants, and underground structures is a logical extension of these strategies.
Systematic sampling strategies are often the most cost-effective method for searching for hot spots or buried objects.
Search sampling patterns may also be used to optimize the locations of ground water monitoring wells or to optimize the location of vadose zone monitoring devices.
This practice may be used to determine the risk of missing a target of specified size and shape given a specified sampling pattern and sampling density.
This practice may be used to determine the smallest target that can be detected with a specified probability and given sampling density.
This practice may be used to select the optimum grid sampling strategy (that is, sampling pattern and density) for a specified risk of not detecting a hot spot or buried object.
By using the algorithms given in this practice, one can balance the cost of sampling versus the risk of missing a hot spot or buried object.
SCOPE
1.1 This practice provides equations and nomographs, and a reference to a computer program, for calculating probabilities of detecting hot spots (that is, localized areas of soil or groundwater contamination) and buried objects 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. Buried objects may include former surface impoundments, waste disposal pits, and utilities that have been covered by soil or paving materials. Hot spots may also include contaminant plumes in ground water or soil gas.
1.2 For purposes of calculating detection probabilities, hot spots or buried objects are presumed to be elliptically shaped when projected vertically to the ground surface, and search patterns are square, rectangular, or rhombic. Assumptions about the size and shape of suspected hot spots are the primary limitations of this practice, and must be judged by historical information. A further limitation is that hot spot boundaries are assumed to be clear and distinct. Alternative approaches to hot spot detection using discrete sampling should also be considered where feasible, such as surface geophysical measurements (see Guide D 6429).
1.3 Search sampling would normally be conducted during preliminary investigations of hazardous waste sites or hazardous waste management facilities (see Guide D 5730). Sampling may be conducted via drilling or by direct-push methods. In contrast, guidance on sampling for the purpose of making statistical inferences about population characteristics (for example, contaminant concentrations) can be found in Guide D 6311.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Standards Content (Sample)
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Designation:D6982–03
Standard Practice for
Detecting Hot Spots and Buried Objects Using Point-Net
(Grid) Search Patterns
This standard is issued under the fixed designation D6982; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 2. Referenced Documents
1.1 Thispracticeprovidesequationsandnomographs,anda 2.1 ASTM Standards:
reference to a computer program, for calculating probabilities D5730 Guide for Site Characterization for Environmental
of detecting hot spots (that is, localized areas of soil or Purposes With Emphasis on Soil, Rock, the Vadose Zone
groundwatercontamination)andburiedobjectsusingpoint-net and Ground Water
(that is, grid) search patterns. Hot spots, more generally D6051 Guide for Composite Sampling and Field Subsam-
referred to as targets, are presumed to be invisible on the pling for Environmental Waste Management Activities
ground surface. Buried objects may include former surface D6311 Guide for Generation of Environmental Data Re-
impoundments,wastedisposalpits,andutilitiesthathavebeen lated to Waste Management Activities: Selection and
coveredbysoilorpavingmaterials.Hotspotsmayalsoinclude Optimization of Sampling Design
contaminant plumes in ground water or soil gas. D6429 Guide for Selecting Surface Geophysical Methods
1.2 For purposes of calculating detection probabilities, hot
3. Terminology
spots or buried objects are presumed to be elliptically shaped
when projected vertically to the ground surface, and search 3.1 Definitions:
3.1.1 hot spot—a localized area of soil or groundwater
patterns are square, rectangular, or rhombic. Assumptions
aboutthesizeandshapeofsuspectedhotspotsaretheprimary contamination.
3.1.1.1 Discussion—A hot spot may be considered as a
limitations of this practice, and must be judged by historical
information.Afurtherlimitationisthathotspotboundariesare discretevolumeofburiedwasteorcontaminatedsoilwherethe
concentration of a contaminant of interest exceeds some
assumed to be clear and distinct.Alternative approaches to hot
prespecified threshold value. Although elliptically shaped hot
spot detection using discrete sampling should also be consid-
eredwherefeasible,suchassurfacegeophysicalmeasurements spots or targets are assumed for the purposes of calculating
probabilitiesofdetectinghotspots,hotspotsaremorelikelyto
(see Guide D6429).
1.3 Search sampling would normally be conducted during have variable sizes and shapes and not have clear and distinct
boundaries. However, the concept of hot spots is consistent
preliminary investigations of hazardous waste sites or hazard-
ouswastemanagementfacilities(seeGuideD5730).Sampling with known historical patterns of contaminant distributions.
3.1.2 sampling density—the number of borings (that is,
may be conducted via drilling or by direct-push methods. In
contrast, guidance on sampling for the purpose of making sampling points) per unit area.
3.1.3 semi-major axis, a—one-half the length of the long
statistical inferences about population characteristics (for ex-
ample, contaminant concentrations) can be found in Guide axis of an ellipse. For a circle, this distance is simply the
radius.
D6311.
1.4 This standard does not purport to address all of the 3.1.4 semi-minor axis, b—one-half the length of the short
axis of an ellipse.
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro- 3.1.5 target—the object or “hot spot” that is being searched
for.
priate safety and health practices and determine the applica-
bility of regulatory limitations prior to use. 3.1.6 threshold concentration—the concentration of a con-
taminant above which a hot spot is considered to be detected.
This practice is under the jurisdiction of ASTM Committee D34 on Waste
Management and is the direct responsibility of Subcommittee D34.01.01 on For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Planning for Sampling. contactASTM Customer Service at service@astm.org. ForAnnual Book ofASTM
Current edition approved Nov. 1, 2003. Published January 2004. DOI: 10.1520/ Standards volume information, refer to the standard’s Document Summary page on
D6982-03. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D6982–03
3.1.7 unit cell—the smallest area into which a grid can be 4.4 This practice may be used to determine the risk of
divided so that these areas have the same shape, size and missing a target of specified size and shape given a specified
orientation. For a triangular grid, the unit cell is a 60°/120° sampling pattern and sampling density.
rhombuscomprisedoftwoequilateraltriangleswithacommon 4.5 This practice may be used to determine the smallest
side. target that can be detected with a specified probability and
3.2 Symbols: given sampling density.
a= length of the semi-major axis of an ellipse 4.6 This practice may be used to select the optimum grid
b= length of the semi-minor axis of an ellipse sampling strategy (that is, sampling pattern and density) for a
A = area of target or hot spot. For an ellipse, A = pab. specified risk of not detecting a hot spot or buried object.
T T
A = search area 4.7 By using the algorithms given in this practice, one can
S
S= the“shape”ofanellipticaltarget(thatis,theratioofthe balance the cost of sampling versus the risk of missing a hot
length of the semi-minor axis to the length of the semi-major spot or buried object.
axis of an ellipse, b/a)
5. Assumptions
G= the distance between nearest grid nodes of a unit cell
Q= the ratio of the length of the long side of a rectangular
5.1 One or more targets (for example, hot spots) exist and
grid cell to the length of the short side
are equally likely to occur in any part of the search area.
A = the area of the unit cell. For a square, A = G . For a
C sq 5.2 When projected vertically upward to a level ground
rectangle A = Q·G . For a 60°/120° rhombus, A =[(=3)/
re rh surface, the target appears as an ellipse or a circle (Fig. 1).The
2]G . The inverse of A is the sampling density
C probablesizeandshapeofahotspotcanonlybeguessedfrom
b= the probability of not detecting a hot spot (that is,
pastsiteorfacilityrecords,knownlayoutofthesiteorfacility,
“consumer’s risk”)
and personal knowledge.
P(hit)= probability of detection (that is, 1 − b)
5.3 Thesearchpatterniseitherasquare,arectangular,oran
equilateral triangular grid. Borings are made at the intersec-
4. Significance and Use
tions of grid lines (that is, nodes) (Fig. 2).
4.1 Search sampling strategies have found wide utility in 5.4 Borings or direct-push devices are directed downward
geologic exploration where drilling is required to detect vertically and the detection of the target is unambiguous. For
subsurfacemineraldeposit,suchaswhendrillingforoil.Using detection of buried solid objects, this should present little
suchstrategiestosearchforburiedwastes,subsurfacecontami- difficulty. However, for buried contaminants, such an assump-
nants, and underground structures is a logical extension of tion presumes that the full depth of a boring would be subject
these strategies. to analysis as contiguous intervals of the boring. If sampling
4.2 Systematic sampling strategies are often the most cost- intervals are discontinuous, then contamination might be
effective method for searching for hot spots or buried objects. missed if it occurred between sampled intervals. If sampling
4.3 Search sampling patterns may also be used to optimize intervals are too long, then a hot spot may not be detected
the locations of ground water monitoring wells or to optimize because of dilution of a hot spot with less contaminated
the location of vadose zone monitoring devices. portions of the sampled interval. The criteria for detection of
FIG. 1 Projection of Boundaries of Subsurface Contamination to the Ground Surface
D6982–03
FIG. 2 Grid Patterns for Detecting Hot Spots. Borings are Made at the Grid Nodes
contaminantsmaybeprespecifiedthresholdconcentrations(for 6.3 When searching for hot spots, threshold concentrations
example, screening levels) that would trigger further investi- for detection may be established by a regulatory authority.
gation of sites or facilities. Whether or not a threshold concentration is exceeded will
5.5 The area of the borehole or direct-push device is depend upon the physical distribution of the contaminant, the
infinitely small compared to the target area. The algorithms volumeofthesamplingdevice,thesamplingintervalsselected,
used in this practice assume that borehole or direct-push and the sensitivity of the analysis. If contamination occurs in a
devices have no area, but rather are treated as a vertical line. discrete layer, then the probability of detecting a hot spot will
decrease with increasing volume of material sampled in a bore
6. Preliminary Considerations
hole or if the sampling interval exceeds the depth of the
discrete hot spot layer. The analytically determined contami-
6.1 Before designing a hot spot detection strategy, a pre-
nantconcentrationmaythenbelessthanthethresholdconcen-
liminary investigation of the area containing possible hot spots
tration because of the dilution of the hot spot layer with other
or targets should be conducted. From historical records, physi-
layersofsoilorwaste.Further,ahotspotconfinedtoadiscrete
cal layout of buildings and equipment, known transportation
layer may be missed entirely by not sampling that layer. For
pathways, landscape features, and eyewitness accounts, one
this reason, continuous sampling is recommended.
may be able to identify areas with a high probability of
6.4 Detection of contaminant levels in samples above
subsurface contamination or the presence of buried waste or
thresholdconcentrationsorthedetectionofburiedobjectsmay
objectssuchasundergroundstoragetanks.Areaswithdifferent
trigger further action requiring possibly more detailed drilling
expected probabilities of detection of a hot spot or other target
and sampling to better define spatially the location of hot spots
should be clearly mapped.
or buried objects. Again, a grid sampling strategy will be the
6.2 Within areas of relatively uniform expected probability
most efficient. If new boring locations are centered at the
of hot spot or target detection, sampling grids of prespecified
midpoints of the unit cells, the total number of borings will be
grid spacing G and type (for example, square, rectangular, or
exactly doubled.
triangular) may be overlain. Areas with higher expected
occurrence of hot spots or buried objects should have corre-
7. Computing Hot Spot Detection Probabilities
spondingly higher sampling densities compared to areas with
lowerexpectedoccurrence.However,areaswithgreaterhazard 7.1 Case I—Ifthelongestdimensionofanellipticaltargetis
from missing a hot spot should also have correspondingly lessthanorequaltothegridspacing(thatis,2a# G),thenthe
higher sampling densities than areas with a lesser hazard. target can only be hit once and the probability P of detecting
Ideally, the starting point for each grid and its orientation the hot spot is simply equal to the ratio of the area of the target
should be randomly determined. A to the area of the unit cell A (that is, P = A /A ).
T C T C
D6982–03
7.2 Case 2—If the longest dimension of an elliptical target Using these same graphs, one can also determine the required
isgreaterthanthegridspacing(thatis,2a> G),thenthetarget grid spacing to detect an elliptical target of shape at a
may be hit more than once. In this case, algorithms developed prespecified probability of detection. In this case, draw a
by Singer and Wickman (1) employing affine transformations horizontal line from the prespecified probability of a hit to the
and programmed in FORTRAN by Singer (2) are required to curve representing the prespecified shape of the ellipse. Then
calculate the exact probability of detecting the target. This draw a vertical line down to the x-axis. From the ratio a/G at
program is limited to ellipses having a shape S between 0.05 the point of intersection with the x-axis, one can determine the
and 1.0 and the ratio a/G between 0.05 and 1.0. Singer’s minimum required grid spacing. Similarly, one can also deter-
algorithms have been adapted by J. R. Davidson (3) to the mine the smallest sized hot spot of a given shape that can be
personal computer (PC) running under the MS DOS operating detected for a given grid spacing and probability of detection
system. Supporting documentation for this program, by calculating a from the ratio a/G and grid spacing G.
ELIPGRID-PC, is available from Oak Ridge National Labora- Alternatively, one can use the computer program ELIPGRID-
tory (4, 5). PC.
7.3 Randomly Oriented Elliptical Target—The probability 7.4 Oriented Elliptical Target—If the orientation of the
ofdetectingatarget, P(hit),ofaspecifiedsize ashape Sandfor
elliptical target with respect to the grid lines is specified, then
a specified grid G spacing can be obtained from nomographs
theprobabilityofdetectingthetargetmustbedeterminedusing
showninFigs.3and4forsquareandequilateraltriangulargrid
the computer program ELIPGRID-PC.
sampling patterns, respectively. Data for these nomographs
weregeneratedusingtheELIPGRID-PCprogram.Tousethese
8. Comparing the Relative Efficiencies of Search Patterns
graphs, first calculate the ratio a/G. Then draw a vertical line
8.1 The efficiency of a search pattern is measured as the
from the point represented by the ratio a/G on the x-axis of the
probability that a target (for example, hot spot) will be hit at
graph to the curve representing the prespecified shape of the
least once. Given the same sampling density, a sampling
ellipse. Then draw a horizontal line to the y-axis. For shapes
patternwithahigherprobabilityofhittingatargetwillbemore
other than those shown on the graphs, one must interpolate
efficient than a sampling pattern with a lower probability of
between curves with closest values of S. The value on the
hitting the same target. The relative efficiency, RE,ofone
y-axisrepresentstheprobabilityofatleastonehitofthetarget.
sampling pattern over another when searching for a target is
measured as the percent difference in the efficiency of two
equivalent density sampling patterns. For example, RE =
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
100% (P
...
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