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Synthesizing Bulk Density for Soils with Abundant Rock
Fragments
Kirk
R.
Vincent* and Oliver A. Chadwick
ABSTRACT
Bulk density is a fundamental soil property that is difficult to
determine for gravelly to extreme!y gravelly soils because results vary
significantly with sample volume. For such coarse soils, the representative
volume (for whole-soil bulk density) should be large, but guidelines for
selecting an appropriate sample volume do not exist. We evaluate the
representative volume for a soil with abundant rock fragments, by comparing
measured properties of
sarnplcs
ranging in volume from 0.03 to 410 liters,
For whole-soil bulk density determination, the representative volume is 4
liters or larger for a soil horizon containing
34?40
gravel (by volume) and is
between 5 and 50 liters for a soil horizon containing
54V0
gravel. Intact-
sarnplcs
of that size are prohibitively large, so an alternative approach
is
dcvclopcd that starts with measurement of fine-earth bulk density. For
fine-
earth bulk density, the sample volume needed for representative results is
between 0.2 liters and 1 liter for gravelly to extremely gravelly soils. The
alternative approach reliably synthesizes whole-soil bulk density using
1)
fine-earth bulk density from modest sized samples, 2) mass size-distribution
from large (>40 kg) representative disturbed samples, and 3) rock fragment
bulk densities. The mass and volume of rock fragments that “should be” in a
sample are added to the mass and volume used to calculate fine-earth bulk
density. ‘I’he method allows integration of lateral variability in the soil
without the consequence of averaging properties over a large depth range.
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*
K,R.
Vincent, Dep. of Geoscience, Univ. of Arizona, Tucson, AZ, 85721; and
O.A.
Chadwick, Jet Propulsion Laboratory, California Institute of Technology,
4800 Oak Grove Dr., Pasadena, CA, 91109. *Corresponding author.
The importance of accurate measurement of soil bulk density and
porosity is clear — they are fundamental
so~l
properties. Pedologists and
soil
geomorphologists need whole-soil bulk density to determine the volumetric
content of soil constituents, such as secondary carbonate (Mach
ette,
1985),
or the volumetric consequence of soil weathering (Chadwick et al., 1990).
Measurement of bulk density for soils
ccmtaining
abundant coarse fragments
is problematic, however, because results vary with sample volume, and
whole-soil bulk density may differ appreciably from the bulk density of
fine-
earth (soil with all fragments
>2
mm removed, Soil Survey Staff, 1992).
Although understanding of the influence of coarse fragments on the
properties and proccsscs of soils is increasing
(SCC
review by Childs and
Flint, 1990) practical sampling
problcrns
remain. For example, a variety of
sampling methods exist for determination of soil bulk density and porosity—
each with unique strengths and wcakncsscs (Flint and Childs, 1984a). Most
published studies compare sampling methods (Andraski, 1991; Flint and
Childs, 1984a; Howard and Singer, 1981: Shipp and Matclski,
1965;
and
McLintock, 1959), but curiously the appropriateness of sample sizes were
not evaluated. We know of no published investigations specifically designed
to define the representative
sarnplc
volume for determination of bulk
density for soils containing abundant
rc)ck
fragments.
in this paper we define the sample volume required to dctcrminc
representative whole-soil bulk density for a soil containing abundant rock
fragments. The resulting rcprescntativc volumes arc prohibitively large and,
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consequently, we develop an alternative approach. We substantiate a
theoretical procedure of synthesizing whole-soil bulk density using 1)
fine-
earth bulk density, 2) rock fragment bulk densities, and 3) representative
particle-size distribution.
DEFINITIONS, OBJECTIVES and CONCEPTUAL FRAMEWORK
Several terms are used here in a broader sense than their most strict
definition. The terms “gravel”, “coarse fragments”, and “rock fragnlents” are
used interchangeably to indicate all particles larger than 2 mm regardless of
their specific sizes and shapes. “Pebble” is used to indicate a single particle
of gravel without implying a specific size class. The term “gravelly soil”
is
used to indicate any soil that has physical properties influenced by the
presence of rounded gravel or angular rock fragments. A sample has
“representative volume” if
it
is the smallest sample whose measured
properties do not differ from that measured for larger volume samples. If a
smaller volume sample was selected the measurement results would be
unreliable. Its volume is also optimal, because selection of a larger volume
sample would create unnecessary, extra effort.
The first objective of this study is to define the representative sample-
volume required to determine bulk density for a soil with major horizons
containing 34°/0, 54°/0, and 77°/0 gravel by volume. We compare the bulk
densities of samples, ranging in volume from 0,03 to 410 liters, to
dctcrminc graphically the minimum, optimal sample volume.
The second objective is to evaluate the possjbjlity of reliably using
intact soil samples that are smaller than a soil’s representative volume. We
evaluate a procedure of substituting rcprcscntative-mass size distribution for
representative intact volume: a procedure best explained using the following
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example. Consider
aloam
soil containing very few rock fragments larger
than 2
mm.
If a rare pebble is discovered inside an undisturbed soil sample
after measurement of intact volume, It is acceptable to subtract the mass and
volume of the pebble from that of the sample before calculating bulk density
(Soil Survey Staff, 1992, p.83). Technically, the result is the bulk density of
the fine-earth
(<2
mm fraction) and, in this hypothetical case, the result is
also representative of the whole soil because coarse fragments are so rare.
Using that procedure we calculate the fine-earth bulk density and porosity
for intact samples of our gravelly soil. Then we reverse the process by
adding the mass and volume of gravel (determined for a disturbed sample
that is large enough to adequately characterize the mass size-distribution) to
the mass and volumes used in the calculations of fine-earth properties. the
term “synthesized” is used to identify the results of this procedure.
Synthesized whole-soil bulk densities are compared by sample volume to
evaluate whether results are indeed representative of the whole soil.
Soils are composed of many volume elements each with potentially
unique density. It is useful to group these elements of the whole-soil volume
into two categories: first, the bulk volume of gravel (where each pebble is
dominated by
the fine-earth
voids). Thus,
is included in
mineral solid, but may also contain pore space); and second,
bulk volume (containing mineral solids, organic solids and
in
this conceptualization, the volume of a void inside a pebble
the calculation of rock fragment bulk density, whereas the
volume of a void bounded in part by the surface of a pebble is included in the
calculation of fine-earth bulk density. In contrast, the National Cooperative
Soil Survey includes the volume of voids inside gravel in the calculation of
fine-earth bulk density (Soil Survey Staff,
1992).
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MATERIALS AND METHODS
General Environmental and Soil Properties
The sample site is located in east central Idaho, 35 km northwest of
the town of Mackay in Custer County, at an altitude of 2100 m (6900 ft), and
at the center of the SW 1/4 of Section 28, T 10 N, R 22 E. The soil is
located on an alluvial fan composed of well-washed gravel deposited at the
end of the latest glacial
(=15
ka)
and subsequently covered by a 10 to 20 cm
thick blanket of loess (Pierce and Scott, 1982). Mean annual precipitation
is about 25 cm and mean annual temperature
is
about 1.3° C. Vegetative
cover is approximately 500/0 and is dominated by ~rtemisia tridentat~.
The study soil is classified as a sandy-skeletal, carbonatlc, frigid
Xerollic Calciorthid. Detailed soil description revealed the following
horkons
to a depth of 1.2 m: A, ABk,
Bkl,
Bk2, Bk3,
13Ck,
and
C13k
(depth
increments are noted on Fig, 3). For sampling purposes, we grouped the
first three horizons into a major horizon designated
“AT3k”,
the next two
horizons into a major horizon designated
“Bk”,
and the bottom two horizons
into a major horizon designated
“CBk”.
Soil properties not listed In Table 1
jncludc the following. Whole-soil mass percents are: ABk horizon — 58%
coarse fragments
(>2
mm), 27°/0 sand (2 to 0.043 mm), and 15°/0 silt plus
clay sized particles(<O.043 mm); Bk horizon —
72V0
coarse fragments, 25%
sand, and 3% silt plus clay;
C]3k
horizon —
80?40
coarse fragments,
17V0
sand, and 3°/0 silt plus clay. Coarse fragment lithologics are limestone
(87%), dolomite
(49to),
and shale, volcanic rocks and sandstone (9%). Their
b-axis diameters did not cxcecd 15 cm, and few exceeded 10 cm.
Sample Types
Four types of samples were obtained (names are undcr]ined) and are
summarized here for clarjty.
1
) An entire pedon was sampled so that
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results would be limited by measurement imprecision, and not
by
lateral
variability. The pedon was subdivided into three major horizons
(ABk,
Bk,
CBk) and together these three pedon
subsarndes
totaled 2.5 Mg of soil
excavated from a pit 1.26 ms in volume (Tables 1 and 2). 2) Seventeen
intact
soil
clods were sampled, at various depths from the wall of the soil
pit, with sample volume ranging from 0,03 to 6.1 liters (Table 3). Bulk
densities and porosities of the clod samples were determined in the
laboratory and compared to that of the corresponding pcdon subsamples. 3)
Disturbed samples were raked from the pit wall and sieved to determine
representative size-distribution of the soil mass. Three disturbed samples
were obtained, with mass ranging from 32 to 43 kg, one for each of the
three major horizons (Table 2). 4)
~a-vel
samdes,
from each disturbed
sample mentioned above, were organized by size class and each class was
ana]yzed for rock fragment bulk density, fragment porosity, and fragment
particle-density (Table 4). This information was then used to subtract (and
add) the influence of gravel from (to) the properties
Many equations exist for density and porosity
of intact samples.
Calculations
(Brakcnsiek et al.,
1986); all are fundamentally rooted
in
the laws of conservation of volume
and conservation of mass, and in the definitions of density and porosity. We
derived equations appropriate for our measurements and objectives. Here
we use the sample worksheet in
Fig,
1 as a vehicle to present a summary of
all equations and measured, calculated, or synthesized variables. In addition,
Fig.
1 can be used as a model format for computer sprcadshcct
implementation of our procedures.
The values quoted for gravel content by mass and by volume were
determined for the pedon subsamplcs (Table 1). They
arc
not estimates by
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eye. The particle mass size-distributions (Table 2) were determined by
sieving and weighing, as discussed below. The percent gravel by volume was
determined by converting gravel mass to bulk volume using rock fragment
bulk density mentioned below. We estimate the uncertainty of these volume
percent values to be about
A2
percentage points.
To determine densities and porosities for samples of variable size, we
measured volumes directly, as well as masses, and no specific gravity
measurements were made. Elemental volumes not measured were
calculated by addition or subtraction of directly measured volumes with two
exceptions. First, the volume of mineral solids
C2
mm in size was calculated
as the mass of fines divided by the average particle density of rock
fragments, because those particle densities are quite uniform (Table 4) and
clay content in the soil is minimal. Second, rock fragrncnt properties were
not measured for every pebble, rather they were determined for large
sub samples.
‘1’bus, average rock fragment bulk density was used to calculate
the bulk volumes of individual pebbles contained inside samples
(Fig,
1).
13ulk
densities for individual pebbles probably differ from the average for
many. In retrospect, results could be Improved by measuring the bulk
volume of coarse fragments actually contained in each sample and
subtracting that from sample volume to obtain fine-earth volume.
Processing of Mass
The methods for measuring volumes for each samp]c type, and other
procedures, are discussed under the appropriate headings below. The
methods for measuring soil mass and rock fragment size, however, can be
discussed in general,
Soil mass was passed by hand through
from
64
to 2 mm and weighed. All soil from
7
nested sieves with openings
the intact clod samples and
the
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disturbed samples were oven
clried,
sieved, and weighed on an electronic
balance. For the larger samples, however, only a subsample of the
<4
mm
fraction was sieved. The entire pcdon subsamples were weighed in the field
using calibrated spring scales, after all material was passed through sieves
with 64 to 13.2 mm openings. Only a subsample of the
c
13.2 mm fraction
was passed through the smaller sieves. Field weight was corrected for
moisture content which was
<1
YO
of mass for gravel and ranged from 2 to
5V0
for fine earth. Roots greater than one centimeter in length or one
millimeter in diameter were
segregatecl,
but these macro-organics are
insignificant at
eO.3Vo
of soil mass.
To ensure that a representative
Pedon Subsamples
volume for the gravel soil was
obtained, construction worker tactics were employed to sample an entire
soil pit. A 1.26
rns
pit was excavated by back hoe and back-filled with a
known volume of water. First, a plot frame (0.92 m by 1,83 m), constructed
of two-by-four lumber, was staked to the ground such that each side board
was horizontal. Later the pit was excavated inside this frame. A moveable
screed board was placed on the plot frame providing an elevation datum
from which the vertical distance to the soil surface (and later the pit
bottom) could be measured. Marks, spaced 0.1 m apart, on both the plot
frame and the screed in effect created a horizontal grid. At each grid
intersection point, the distance below the elevation datum was measured;
thus 100 to 105 measurements were made for each computation of average
elevation of the soil surface or pit bottom.
After measuring the elevation of the soil surface, the
A1lk
horizon was
excavated. The pit bottom was made
rcmghly
horizontal, loose material was
removed by hand, and the excavated material was placed on a ground
cloth
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and covered. The elevation of the base of the ABk horizon was then
measured, This process was repeated for the Ilk horizon and then for the
CBk horizon. The pit walls were roughly vertical and did not ravel or
collapse. Fine soil was unfortunately lost to the wind during excavation, and
our estimates of loss ranged from 0.8%0 to
2.30/o
of the sample mass.
The original volume occupied by the excavated soil was determined
using a variation of the compliant cavity method (Soil Survey Staff, 1992,
p,101 ). A measured volume of water was poured into the pit after it had
been lined with a doubled sheet of construction grade plastic. Water was
poured into the pit using previously calibrated stainless steel buckets and
the sheet was regularly inspected to make sure its loose folds conformed to
the shape of the pit walls. After every 5 or 10 cm rise in water
lCVC1
the
vertical distance of the water surface below the elevation datum was
measured. Water surface elevation data was graphed against volume of water
in the pit to determine the pit volumes below horizon boundaries. Filling
the pit with water took about 2 hours. After the pit was full, the water level
was monitored and leakage, under maximum hydraulic head, was
~nsignificant (3.6 liters pcr hour). Implications of other potential errors are
dcvclopcd in the results and discussion section. Relevant data for the three
pcdon subsamples arc found in Tables 1 and 2.
Intact Clod Samples
Intact soil clods were taken from the pit wall, after the pit had
drained and dried, were coated with paraffin in the field and their volumes
were dctcrmincd in the laboratory by immersion, Samples were successfully
removed intact from the
A1lk
and
Dk
horizon but not from the CBk horizon.
Although the CBk horizon structure is massive the bonding between
particles is weak, consequently soil aggregates could not be kept intact even
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with wax coatings. Small clods (<300 ems) were placed in a hair net and
dipped into molten paraffin, but
large
clods (1000 to 6000 cm3) were
partially excavated and coated in situ, The large clods were then detached
so that the bottom of the sample could be sealed.
The volumes of wax-coated clods were determined by water
displacement, not by weight in water (Soil Survey Staff, 1992,
p.83),
because
a balance capable of weighing the large intact samples was not available.
Water volume displaced by submerging a sample in a container was
accomplished with the aid of a point-gauge: a device common to hydraulics
laboratories and used for precise measurement of water level. Wax coatings
were pried free of the clods and loose soil was removed from them. The
volumes of (remelted) paraffin coatings were determined by volume
displacement, because the coatings were thick
(=4
mm) and contained
variable amounts of soil, Intact clod “sample volume”, as used here, means
coated-sample volume minus the volume of the coating. Loss of soil mass
was minimal; thus, accuracy was primarily limited by volume precision.
Relevant data for intact clods are found in Table 3.
Disturbed Samples and Gravel Samples
Large disturbed samples were raked from the pit wall and sieved to
dctcrminc the size-distribution of soil mass (Table 2), A sample was
obtained from the entire vertical exposure of each of the three major
horizons, A “five gallon” bucket was placed in an undercut just below the
sample horizon and filled. The samples were oven dried, sieved, and
weighed in the laboratory.
Gravel samples, subsets of the disturbed samples, were used to”
evaluate the physical properties of gravel and the dcpcndcncc of those
properties on particle size (Table 4). l’article size is denoted here as the
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opening-size of the sieve retaining the fragments. The gravel sample masses
(Table 4) ranged from 500 to 2000 g for all but the smallest size classes.
These sample masses were designed to contain several hundred to several
thousand particles, assuring representative mix of lithologies. Only the
largest size classes consisted of a few stones and, thus, could have a biased
lithological mix,
Gravel properties were measured using a significant modification of
ASTM method C97 (1992, p. 69)
folloting
the suggestions of Flint and
Childs (1984a, p. 93). The gravel was washed to remove fine earlh
(secondary carbonate rinds were not removed), oven dried for 24 hours, and
weighed. The gravel was then submerged under water inside a bell jar that
was placed under vacuum for 40 hours. After the pores within the gravel
were saturated by this procedure, the gravel was toweled to remove surface
water, and then was quickly weighed and placed into a calibrated container
for volume determination. Saturation of pores assured precise rneasurcment
of gravel bulk volume, and allowed calculation of pore volume as the
difference
jn
wet and dry mass divided by the density of water. The specific
gravity of fragments was not measured. Rock fragment properties (bulk
density, porosity, and particle-density
cm
Table 4) were calculated using the
definition of those properties.
RESULTS AND DISCUSSION
Representative Volume for Whole-Soil Density
Whole-soil bulk density increases significantly with gravel content
(Table 1), It is 1.38, 1.97 and 2,38 g
cm-s
for the ABk,
13k
and CBk pedon
subsamples, respectively. These horizons are dense, the lower ones in
particular, because they have gravel contents of
34?10,
54?40
and 77?40 by
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volume; or
58?40,
720/o
and
800/o
by mass, respectively. Whole soil porosity,
acting In concert with density, decreases with increasing gravel content and
ranges from 48% to 10O/O.
Our first objective was to determine the representative volume for
whole-soil bulk density. This is done graphically on Fig. 2A, by plotting
sample bulk density against sample volume and utilizing the lines drawn to
envelop the data for each horizon. Ideally, the density data would be highly
scattered for small samples, but with increasing sample size would converge
to define a value no longer dependent on size. The approximate
representative volume could be chosen from the graph as that minimum
sample-volume yielding results similar to (within 5%
of)
that for larger
samples. At the onset of sampling, we assumed that a large pcdon
subsample would provide the “best” bulk density datum, but have
subsequently learned that it may not. Although the reasons for this
conclusion are developed in the next section, it is important to state now
that the most reliable estimate of whole-soil bulk density is 1.45 g
cm-s
for
the ABk major horizon and is about 1.9 g
cm-s
for the Bk horizon,
Sample bulk density for gravelly soils is influenced strongly by sample
volume, as shown on Fig. 2A, For both major horizons, the density of intact
clod samples generally increases in magnitude with sample volume,
illustrating that coarse fragments are under-represented by small samples.
The scatter of density data diminishes with increasing sample volume and
converge toward a uniform value, For example, all intact clod samples from
the ABk horizon yield results within 20?40 of 1.45 g
cm-s,
Samples larger
than 200
ems,
however, yield results within
-8?40
and +
lVO
of 1.45 g
cm-s,
and the two largest intact samples
(=
6,000
cma)
yield results within
20/o
of
1.45 g
cm-s.
We infer from Fig. 2A that the representative volume (for
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whole-soil bulk density determination) for the ABk horizon is 4 liters or
greater — substantially larger than the (100 to 300
cma)
volume commonly
sampled for bulk density measurement. Although the number of samples for
the Bk horizon are limited, the representative volume is no doubt large. We
infer the representative volume to be at least 5 liters and it may be as large
as 50 liters. The minimum estimate,
5
liters, is two orders of magnitude
larger than some intact samples retrieved from the field.
Rock Fragment Properties
In general, rock fragments in soils can contain considerable pore
volume; as much as 20 to
60?10
porosity (Flint and Childs, 1984a).
Furthermore, gravel properties may depend on particle size due to more
thorough weathering of smaller particles (Childs and Flint, 1990; after
Schmidt, 1988). Bulk density and porosity of gravel from the study soil vary
with particle size (Table 4). Rock fragment porosity, for example, ranges
from 2 or
3V0
for large cobbles and up to 10 or
15V0
for small pebbles, with
the higher values for gravel from the surface horizons.
We tested the possibility that not all of the pores inside the gravel
were saturated with water while under vacuum as follows. Rock fragment
particle-density was formulated as dry mass divided by volume of solids (bulk
volume less pore volume) and as such has larger accumulation of errors than
rock fragment bulk-density or porosity. Nevertheless, rock fragment
particle-densities in Table 4 are nearly identical demonstrating the
reliability of the saturation method. This result also confirms that the mix of
rock fragment lithologies in the samples was indeed representative.
Synthesizing Whole-Soil Density
Fine-earth bulk density is a commonly measured property, although it
is
not a substitute for whole-soil bu]k density if the gravel content influences
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the physical properties significantly. Fine-earth bulk density is, specifically,
the mass of mineral soil
<2
mm in size plus mass of organics, divided by the
cumulative volume of fine-grained mineral solids, organic soljds, and voids
(except, as defined here, those voids inside gravel) (Fig. 1). This density can
be determined by subtracting the mass and the bulk volume of gravel inside
an intact sample from the whole mass and whole volume of that sample,
respectively (Soil Survey Staff, 1992, p.83). Our premise is that the reverse
process should be a viable means of determining whole-soil bulk density.
One should be able to synthesize a reliable whole-soil bulk density by
starting with fine-earth mass and fine-earth bulk volume, from a relatively
small intact sample, and adding in an appropriate mass and volume of gravel.
At the close of this project, we learned that calculations such as this have
been used by the National Cooperative Sojl Survey, but
the
method has not
been published (Bob Grossman, pcrs. comm,, 1993).
I-Icre,
we refer to this
as
“synthcsizccl”
whole-soil bulk
clcnsity
in contrast to sample bulk density.
The mass of gravel that “should be” in the sample is calculated using
equations in
Fig,
1, but the calculation is described below for clarity. First,
hypothetical total whole-soil mass equals fine-earth mass (in the intact
samp]c) divided by percent of total mass that is fine graincd for a large
disturbed sample. The mass of gravel then equals total mass minus
fine-
earth mass, The volume associated with the gravel mass would equal that
mass divided by measured rock fragment bulk density. The procedure is
simple
~f
gravel properties (e.g. porosity) do not vary with particle size, such
as for example, the gravel dominated by
quarbzite
from the
E
12 soil on Table
4. The properties of gravel from the study soil do vary with particle size,
and thus the gravel mass within each size class was treated as individual
volume clcmcnts with unique properties (Fig. 1).
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16
17
18
19
20
21
22
23
24
25
26
27
The premise of synthesizing a reliable whole-soil bulk density is
indeed viable, as illustrated in Fig. 2. Synthesized whole-soil bulk density
data (Fig. 2B) have less scatter compared to the original intact-sample bulk
density data (Fig. 2A), More importantly, the data are no longer strongly
dependent on intact-sample volume, which we consider a positive result.
We can make a stronger case for the reliability of this method after
developing two subtleties.
First, does a pedon subsample produce the “best” results? Large soil
pit samples may not be the most reliable means of determining physical
properties of soils because field measurements are often less precise than
laboratory measurements. For example, results from previous investigations
that used water to determine volumes of small pits were largely
unsatisfactory (McLintock,
1959;
IIoward and Singer, 1981). Our field
measurements
arc
limited by problems such as loss of mass to the wind, and
the need to correct for variable moisture content, but two other problems
arc potentially more significant. First, it is possible that soil from the
A13k
horizon was dislodged from the pit wall during excavation of the
13k
horizon,
and erroncous]y ascribed to the mass of the
13k
pcdon subsamplc.
lhc
second problem is that as the pit was filled with water the increasing
hydrostatic head might have forced the plastic liner more tightly against the
pit wall. It is possible, therefore, that water ascribed to the volume of the
ABk sample might have actually flowed down into the space of the
Bk
pedon
subsample. These two potential
problcrns
would have the same
consequence, namely to underestimate the ABk pedon subsample bulk
density and, at the same time, to overestimate the
Bk
pedon subsamplc bulk
density. Notice in
Fig,
2B
(and Fig. 3), the bulk
dcmsity
of the
Allk
pcclon
subsample is less than the whole-soil bulk densities synthesized from clod
15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
2)
22
23
24
25
26
27
data; but in contrast, the bulk density of the Bk pedon subsarnple is greater
than the whole-soil bulk densities synthesized using intact clods from that
horizon. Evidently, the large soil volumes
did
not entirely compensate for
the problems described above.
The second subtlety is caused by soil properties changing with depth
in the Bk horizon. The surface
horkon
is
discussed first for comparison.
Within the ABk horizon, soil properties Including fine-earth bulk density and
gravel content do not change significanUy with depth. Our results for the
ABk horizon indicate that synthesized whole-soil bulk density is uniform
with depth (Fig. 3), and does not depend on field-sample volume (Fig.
213).
The mean of the eleven synthesized whole-soil bulk density values is 1.45 g
cm-s,
with ranges about the mean of tO.07 g
cm-s
and standard deviations of
~0.04
g
cm-a
or
*2.80/o.
The ABk results clearly demonstrates the utility of
our method of synthesizing whole-soil bulk density. Results for the
Bk
horizon are affected by changing properties with depth. Below a depth of 27
cm, both fine-earth bulk density (data
in
Table 3) and gravel content
increase with depth. On
Fjg,
3, synthesized whole-soil bulk density values
increase with depth in the
13k
horizon, and offer an explanation of the slight
dependence that the data has on sample volume in Fig.
2B
— smaller
samples with lighter densities were taken, quite by accident, from higher
in
the soil profile. With this observation, we suggest that the Bk horizon data
set also supports our method of synthesizing whole-soil bulk density.
One last point is that the large disturbed samples were taken from
whole
clepth
range of the major horizons, but intact samples were only 5
20 cm thick, The synthesized whole-soil bulk density values for the
13k
the
to
horizon in Fig. 3, therefore, are not spcciflc to the minor horizons
sarnplcd
because they were forced by the calculations
(Fig,
1)
to resemble the average
16
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
condition of the Bk horizon. Thus the increase in estimated densities with
depth in
F~g.
3 is entirely the artifact of increasing fine-earth bulk density
with depth, Disturbed samples should be taken from only the horizon whose
average conditions are of interest, be that an entire soil profile or a thin
horizon.
The discussions above
lead
us to conclude that knowledge of the
representative volume of a soil of a given texture is not all that is required to
produce accurate and useful results. The position of a sample In space, and
its three dimensional shape, are also important because soil properties vary
laterally as well as with depth. In pedon sampling the lateral variability of
soil properties is often considered noise, whereas the changing of
properties with depth is considered the information signal. A small sample
(<100
crns)
will not obscure the signal, but cannot integrate the noise.
L.argc
pit samples, such as our pcdon subsamples, are inevitably about as
deep as they are wide. ‘l’hey absorb lateral variability, but in the process also
integrate properties over a significant depth range. Bulk density synthesis
can alleviate this signal/noise problem in gravely soils. For example,
consider the objective of determining whole-soil bulk density for a 10 cm
thick gravelly horizon, intact loaf-sized (>) 000 ems) samples could easily be
obtainccl
for measurement of fine-earth bulk density, and a large
(>4
O kg,)
disturbed sample could, with care, be extracted over a wide area of that thin
horizon for measurement of representative mass-size distribution. The
rcsultjng synthesized whole-soil bulk density would integrate lateral
variability without obscuring the horizon-specific signal.
Having established that together representative-mass size distribution,
gravel properties, and fine-earth bulk densities can be used to synthesize
whole-soi] bulk densities, we should know two things:
1
) the minimum
17
sample volume required to obtain reliable fine-earth bulk densities, and 2)
the minimum sample mass required to obtain reliable particle size-
distribution.
Representative Volume for Fine-Earth Density
The representative intact volume for fine-earth bulk density
determination is much less than that for whole-soil bulk density
determination. For ABk horizon intact samples (Table 3), which range in
volume from 105 to 5455
ems,
the average fine-earth bulk density is 0.96 g
cm-s with standard deviation of 0.04 g
cm-s
or
40/o.
More importantly, there
is no dependence of fine-earth bulk density on sample size.
Because no samples were smaller than 100
ems,
we can not determine
whether the representative volume is smaller than that. Therefore,
in
the
future we will take samples with volumes larger than 200 cms from horizons
with 30 to 40% gravel (by volume) for determination of fine-earth bulk
density. For the Bk horizon, there is a slight dependence of the data on
volume due to increasing fine-earth bulk density with depth as discussed
previously. Conclusions are therefore limited, thus in the future we will
attempt to take samples with volumes close to 1000 cms for determining
fine-earth bulk density of horizons with
50-60?40
gravel by volume,
Representative mass for particle-size distribution
Choosing a dkturbed sample mass that will yield accurate particle
size distribution is important for utilizing our method of synthesizing
whole-soil properties. Two citations (ASTM, 1992; sections D 75 and D
2487) provide guidance for choosing an appropriate sample mass, but their
suggestions are large and may be cxccssive. Both methods rely on
maximum or “maximum nominal” size of aggregates. Our study soil
contains fcw rock fragments larger than 10 cm, and no rocks larger than
18
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
15 cm. Extrapolation of the ASTM linear relationship (section D 75, p. 70,
Table
1)
suggests we should used a sample mass of 200 or 300 kg to
determine particle size distribution. This mass is large, half of themass”of
our
A13k
pedon subsample, but admittedly, the purpose of that guideline
includes sampling prospective gravel mines. For the purpose of classifying
soils, ASTM (section D 2487, p. 327) provides a table of data that
constitutes a semi-logarithmic relationship of suggested sample size,
however their maximum particle size does not exceed 7.5 cm.
Extrapolating their relationship to 10
cm
indicates a mass of 200 kg
should be used. Extrapolation for soils with larger rock fragments,
although probably, indicates thousands of kilograms should be used.
Wc have data that are relevant to this problem. First, it should bc
stated that for our synthesis method the critical information is the percent
of whole soil mass that
is
larger than 2 mm. The distribution of mass
within the
var~ous
large size-classes is of secondary importance. In Fig. 4,
therefore, percent of total mass that is larger than 2 mm is plotted against
sample mass. Scatter in the data indicates that samples less than 10 kg
are unreliable, but the more massive samples have nearly identical percent
gravel values. For our gravely to cxtremc]y gravely horizons wc used
=4
O kg
samples for determining the entire mass-size distribution, the same as the
compromise mass suggested by the Soil Survey Staff (1992, p. 76).
Samples >400 kg are impractical and appear to be unnecessary.
CONCLUSIONS
1)
The representative volume for whole-soil bulk density is large for soils
with significant gravel content. For the soil horizon containing 34?40 gravel
by volume it is 4 liters or larger, and for the soil horizon containing
54?40
19
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
gravel by volume it is at least
5
liters and possibly as large as 50 liters. For
similar soils, measurement of whole-soil bulk density may be in error if
field-sample volumes are smaller than the above guidelines.
2)The representative volume for fine-earth bulk density determination
is
smaller than that for whole-soil bulk density determination. For the soil
horizon containing
34?40
gravel, the representative field-sample volume may
bc less than 0.1 liters. However, for gravelly to extremely gravelly soils we
strongly recommend field-sample volumes between 0.2 liters and
1
liter for
fine-earth bulk density determination.
3) Whole-soil bulk density and porosity can be reliably synthesized
know]ng:
1)
fine-earth bulk density and porosity, 2) rock fragment bulk
densities and porosities, and 3) representative particle-size distribution,
This is a viable alternative to
~)roccssing
large, intact, representative volume
samples; and is a positive conclusion for two reasons. First, truly
representative intact samples may be too large to handle. Second, previous
studies of gravelly soil that produced unreliable bulk densities because
sample volumes were too small (or where only fine-earth properties were
calculated) need not bc discarded. The situation can be reconciled by
obtaining a large
(>4
O
kgl
disturbed sample from the original soil and
following the procedure described here.
4)Our method of synthesizing whole-soil properties promjscs to be quite
useful for detailed investigations of soils with thin horizons. The method
allows integration of lateral variability in the soil without averaging
properties over a large depth range.
5) Sampling entire soil pits with very large volumes
(>
100,000 Liters)
arc not necessary or
porosities of gravcl]y
even desirable for mcasurcmcnt of
clcnsitics
and
soil,
This conclusion is fortunate considering the
20
1
extreme effort required
to
obtain such samples. On a theoretical level, huge
2
samples integrate lateral variability in the soil at the expense of averaging
3 properties over a large depth range. This consequence may be inconsistent
4
with research objectives. On a practical level, a huge soil volume may not
5 entirely compensate for potential errors involving measurement of mass,
6 and the uncertainty in measurement of large volumes in the field.
7
6)It is impossible to extract an intact sample from some soils. We found
8 this to be the case for the CBk horizon of our study soil which contains
77Q40
9 gravel by volume and 80% gravel by mass.
In
such cases, jn situ volume
10 measurement is
unavo~dable
and we recommend a device (refined by Flir
11
and Childs,
1984b)
that measures the volume of small
(<15
liters) soil pi
12
or irregular holes using lightweight epoxy beads, Our method of
13 synthesizing results may still be employed If 15 liters is not considered
14
adequate or cannot be obtained.
15
ACKNOWLEDGMENTS
16
17
18
19
20
21
22
23
24
25
26
27
t
s
We would like to acknowledge Gordon Vaden for back hoe expertise,
Wiley Smith and the Mackay Volunteer Fire Department for delivering
water, and Mat Gleason for help sieving and weighing gravel. We appreciate
Bob Enis and the U.S. Forest Service for land-use permits, David Hendricks
and Sheri Musil for advice and laboratory equipment, and Elise Pendall and
Laurie Wirt for review of an early manuscript. This paper was improved
significantly by editorial reviews by W. D. Ncttleton,
R,
Grossman, and an
anonymous rcvicwcr. Research support was provided,
~n
part, by the Jet
Propulsion I.aboratoW on contract
to
NASA Land Processes Division,
REFERENCES
ASTM.
1992,
Annual nook of ASTM Standards. Construction, Section 4.
Volume 04.08. Am. Sot, for Testing Materials. l’hiladclphia
PA,
21
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Andraski,
B.J.
1991. Balloon and core sampling for determining bulk density
of alluvial desert soil. Soil
Sci,
Sot.
An~.
J.
55:1188-1190.
F3rakensiek,
D.
L,,
W,J.
Rawls,
and G
,R,
Stephenson. 1986. A note on
determining soil properties for soils containing rock fragments.
Journal of Range Management 39:408-409.
Chadwick, O.A., G.H Brimhall,
D.M.
lIendricks, 1990. From a black box to a
gray box -– Mass balance interpretation of pedogenesis.
Geomorphology 3:369-390.
Childs, S.W., and A. I.. Flint, 1990. Physical properties of forest soils
Flint,
Flint,
containing rock fragments. p. 95-121.
~
S.
Gessel
(cd.)
Proc.
7th
North American Forest Soils Conference. Edmonton Alberta.
A,I.,,
and S.
Childs.
1984a. Physical properties of rock fragments and
their effect on available water in skeletal soils. p. 91-103.
~
J. Il.
Nicols,
P. I..
13rown,
and W.J. Grant (cd.) Erosion and productivity of
soils containing rock fragments. Special Publication #13. Soil
Sci.
Sot. Am. Madison, WI.
A.I,., and S, Childs.
1984b.
Development and calibration of an
irregular hole bulk density sampler. Soil
Sci,
Sot. Am. J. 48:374-
378.
Iloward, R. F., and
M.J.
Singer. 1981. Measuring forest soil bulk density
using irregular hole, paraffin
CIOCI,
and air permeability. Forest Sci.
27:316-322.
McI.intock, T.F, 1959. A method for obtaining soil-sample volumes in stony
soils. Journal of Forestry 57:832-834.
Machctte,
M,N.
1985, Calcic soils of the American southwest.
@
D.L.
Wcide
and
M.L.
Faber
(eds.)
Soils and Quatcrnary
gcolo.gy
of the
southwestern United States.
Spec.
Pap.
Gcol.
Sot, Am. 203:1-22,
22
b
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Pierce, K, L., and W.E. Scott. 1982. Pleistocene episodes of alluvial-gravel
deposition, southeastern Idaho. p. 685-702,
~
B. Bonnichsen and
R,M.
Breckenridge (cd.) Cenozoic geology of Idaho. IBMG
Bull.
26.
Idaho Bureau of Mines and Geology. Moscow, ID.
Schmidt,
M.R,
1988. Classification of upland soils by geomorphic and
physical properties affecting infiltration at Yucca Mountain, Nevada.
M.E,
thesis. Colorado
Sc}~ool
of Mines, Golden CO.
Shipp, R. F.,
ancl
R,P.
Matelski. 1965.
13ulk-density
and coarse-fragment
determinations on some Pennsylvania soils. Soil
Sci.
99:392-397.
Soil Survey Laboratory Staff. 1992.
So~l
Survey Laboratory Methods Manual,
SSIR #42, 2,0:400,
Figure Captions
Ng.
1. All equations used in
t}~is
study for calculations of bulk densities and
porosities, and example data and results for intact soil clod #5.
Fig. 2. Graphs of bulk densities plotted against field-sample volume. Open
circles are used for the ABk horizon
(340/o
gravel by volume) and closed
circles are for the Bk horizon
(540/o
gravel), The size of plotted symbols
indicate sample type:
small
symbol — intact clod; large syInbol —
pedon
subsamples.
Fig. 3. Synthesized whole soil bulk densities (closed circles) are plotted
against depth, with intact-sample
clcpth
ranges shown as bars, Pedon
subsamples are indicated by rectangles defined by bulk density error ranges
and sarnple-depth ranges.
Fig. 4. Percent of total mass, that js larger than 2 mm, is plotted against
sample mass for samples from gravely to extrcmc]y gravely horizons.
23
*
Table 1: Data and Properties of Pedon Subsamples
Description Label Units ABk Bk
CBk
Horizon Horizon Horizon
Depth Range
Mass of gravel, (>2 mm)
Estimate of fines lost
Mass of all fines (<2 mm)
Mass Total
Mass Error
Volume of sample
Volume Error
% of VT as bulk gravel
Vol. of voids in gravel
Bulk Density of sample
Compounded BD Error
Porosity of sample
Bulk Density of fines
Porosity of fines
M>2
M<2
MT
M*
VT
v*
%Vbk>z
XVV>2
BD
BD~
P
BD<2
P<2
cm
kg
kg
kg
kg
kg
L
L
9’0
L
g
cm-s
g
cm-a
‘/0
g
cm-s
‘/0
O-27
254
20
183
437
10
317
10
34
10
1.38
0.07
47.6
0.87
66.9
27-6262-109
584
10
226
810
10
410
10
54
17
1.97
0.07
29.4
1.19
54.8
1008
20
251
1259
10
528
10
77
27
2.38
0.06
10.2
2.07
21.8
Table 2: Particle Size Distributions for Pedon Subsamples and Disturbed Samples.
ABk
Horizon
Bk Horizon CBk Horizon
Size Pedon Disturbed Pedon
Disturbed Pedon Disturbed
Class
Subsample Sample
SubsamPe
Sample
Subsam~le
Samt31e
mm
?40
%70 %
%
940
64
45
32
22.4
16
13.2
11.2
8
5.7
4
2.8
2
2.1
2.8
3.7
5.3
6.0
3.7
5.4
8.7
7.2
5.3
4.2
3.6
2.0
1.8
2.4
4.6
6.7
4.2
5.5
8.9
7.4
5.5
4.3
3.7
8.8
10.4
9.3
9.2
8.0
4.0
2.9
5.0
4.6
3.2
:::
14.0
11.2
7.8
8.2
6.5
2.9
2.9
4.9
4.5
3.1
3.4
3.2
6.0
7.2
7.7
10.7
10.0
5.1
5.5
7.9
6.8
4.8
4.4
4.0
10.6
7.4
9.7
12.4
10.5
4.7
4.6
6.6
5.7
4.0
3.7
3.4
<2
42.0
43.0
27.9
27.4 19.9 16.7
Mass, g
437,000 32,580 809,000 42,660
1,259,000
69,860
.,
Table 3: Data and Results for Intact Soil
Clods
by
Sample
Number.
ABk
Horizort
Bk
Hotizotl
Messumd
for
SLWIDIQ
Depth
of Sample
Mass
d
gravel (.2 mm)
M86s
d
firm
(<2
mm)
%Of
TOtsf-<2mm
Macrcxxganks
Mass Total
Mass
Error
Vdutm
of
UMPIQ
Vdunu
Error
@lcu!sted
for
Smv3fS
Bulk
Demity
of sample
Conqmun&d
80
Error
PwOdfy
of
samfio
Bulk
Demify
of
fines
POrOdfy
of
flne9
<2
mm
*2
&z
%w2
k%
MT
m
VT
v*
BD
BLM
P
BD.2
P<2
m
thesized
for
whole
SOU
(
●
)
Ms8s
Tow
“
m
cm
5-17
9
1579
9
1365
%
47
9
10
9
2974
6
$
2?90
m+ 18
g
CWT3
1.36
g
CM-* 0.()?
%
46.5
g
c+
0.91
%
65.4
9
335s
#2 *3
#4
5-20
4430
4233
49
2
6662
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61OI
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2-27
669
1051
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1940
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1463
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~
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0.97 0.97
62.0
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774 2363 567
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7.49
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46.7
43.3 445
M.4
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o
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9
1.16
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1.34
47.2
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70
747
1?2
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o
253
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176
7
7.44
0.06
45.4
0.96
63.5
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f.45
44.6
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0.04
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1.03
60.9
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61
62
57
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7
124
0.08
52.6
092
65.0
WI
46
7.41
46.3
#3P2
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20m
202 676
tst
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47
49
0 0
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7332
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3
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646
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tm
lA1
O.M
0.02
46.6 46.5
0.97 0.99
63.2
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lst7
lot
as
1A6
t.46
44.6
43.6
:5
:6
#7
#bPt
#bP2
40-50 35-60
3545
2050
7t16
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1431
3495 617
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33 27
0
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3461 1C613
2295
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20%?
579t
1236
33
40
23
1.66
1 .s3
1.65
0.03
0.01
O.w
36.3 30.s 29.9
1.16
?
22
1.12
55.3 53.6
57.6
5227127672252
1546
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6@3
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7.93 1.65
26.3 27.2 30.0
32
14
2s
65
0
34
1
3t
6
127
0.23
S2.O
i
.02
67.5
e2
27
T.n
33.0
32
126
74
37
0
202
T
117
7
*.n
0.11
34A
7.t7
55,6
m
60
1.69
26.6
f
bP3
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792
159
45
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351
f
223
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1.57
0.05
40.3
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“Ii
Table
4:
Densities, and Porosity of Rock Fragments.
Sieve Size Sample
Fr&gu~:nt
BDi
~
Fragment
Pit
Fragment
PD*
t
Masa
Porosity Particle
Density Density
mm
9
ABk
Horizon
64 .
45
32
350
22.4 902
16
1018
13.2
526
11.2
929
8
715
5.66 844
4115.1
2,8 90.8
2
76.7
J3k
Horizom
64
45
32
22.4
16
13.2
11.2
8
5.66
4
2,8
2
1753
.
1205
1099
1029
535
593
965
865
86.9
91.7
86.8
CB
k Horizon
64 836
45
1256
32
1243
22.4 1142
16
959
13.2
838
11.2
923
8
765
5.66
712
4
106.3
2.8
99.1
2
90
EliM.dls
64 2079
45
1687
32
1870
22.4 894
16
760
13.2
317
g
cm-3
g
cm”3
.
2.49
2.49
2.47
2.39
2.41
2.34
2,31
2.25
2.20
2.27
2.59
.
2.52
2.49
2.42
2.41
2.38
2.35
2.32
2.30
2.30
2.29
2.71
2.58
2.56
2.51
2.49
2.48
2,44
2.42
2.40
2.34
2.36
2.32
2.69
2.63
2.68
2.60
2.65
2.62
0.07
0.03
0.02
0.04
0.02
0.03
0.02
0.02
0.02
0.03
0.01
.
0.02
0.02
0.02
0.04
0.04
0.02
0.02
0.04
0.22
0.24
0.03
0.02
0.02
0.02
0.02
0.03
0.02
0.03
0.03
0,02
0.02
0.02
0,01
0,02
0.O1
0.03
0.03
0.08
%
.
5.0
6.3
6.5
9.1
8.8
11.1
11.8
14.1
14.8
13.6
3.5
.
4,4
5.9
7.8
8,6
9.6
11.0
12.6
13.0
13.0
10.8
1.6
2.9
4.5
6.2
6.2
6.5
7.4
7.9
9.5
9.9
10.5
10,3
1.8
3.3
2.4
2.9
2.8
3.3
%
g
cm-3
g
cm”3
1.5
0.6
0.5
1.0
0.6
0.8
0.6
0.5
0.6
0.7
0.3
.
0.4
0,5
0.5
1.0
0.9
0.6
0.6
0.7
6.0
6.2
0.7
0,4
0.4
0.5
0.6
0.6
0.6
0.7
0,8
0.5
0.6
0.6
0.3
0.3
0.3
0.6
0,7
1.7
2.62
2.65
2.54
2.63
2.65
2.63
2.62
2.62
2.58
2,63
2.63
+
2.69
.
2.63
2.64
2.63
2,63
2.63
2.64
2.65
2.54
2.64
2.57
2.64$
2.75
2.66
2.68
2,68
2.66
2.65
2.64
2.63
2.65
2.60
2.63
2.59
2.65
~
2,74
2.72
2.74
2.68
2.73
2.71
2.72
i
0.11
0.04
0.04
0.08
0.04
0.05
0.05
0.03
0.04
0.05
0,02
.
0.03
0.04
0.04
0.07
0.07
0.04
0.05
0.09
0.45
0.45
0.05
0.03
0.03
0.04
0,04
0.05
0.04
0.05
0.06
0,04
0.04
0.04
0.02
0,03
0.02
0.05
0.06
0.13
t
Compounded, worst case error due to imprecision
$
Average particle density for all rock fragment size classes
~
Data for nearby soil E12 dominated by
quarlzite
for comparison
Example Worksheet for Intact Soil Clod Data and Calculations
“Gravel”
(>2
mm)
Propetiles
by Size Class
MBKb2
P*2
VbL2
VV*2 %M2
M’
Vbk>2*
VV>2*
Size Class,
Mass Dry Gravel
Gravel
Bulk Vol. Pora Vol. Pit Wall Estimated Bulk Vol. Pore Vol.
Retaining Bulk
Porosity of Gravel in Gravel % of M2T Dry Mass of Gravel in Gravel
Sieve Density
mm 9g cm-3 %
cm9
c~s
%
9
cm3
cf.r13
Note: #1 #2
#3
#4
#IJ
#6 #7 #8 #9
64
2.59 3.55 014.10 736.89
11:
284.39
10.09
45 2.54
4.00
4!.88
1,80
11.16
563.18 229.60 9.18
32
67.8
2.52
4.38 26.95
1.18
7.84 409.75 162.88 7.14
22,4
324.1 2,49
5.88 130.34 7.67
8.17
427.05 171.74
10.10
16 282.1
2.42 7.77 116.43 9.05
6.47 338.41
139.67
10.85
13.2 168.1
2.41
8.55
69.82 5.97 2.90 151.72 63.02
5.39
11.2 128.9 2.38 9.62
54.21
5.22 2.86 149.25 62.76 6.04
8
210.9
2.35
10.98
89.58 9.83
4.88
255.02 108.32
11.89
5.66
210.8 2.32
12.61
90.86 11.45 4.52 236.45 101.92
12,85
4
182.9 2.30
12.97
79.53
10.31 3.15
164.46
71.51 9.27
2.8 184 2.30
13.03
80.10
10.43
3.36 175.80 76.53
9.97
2
176 2.29
10.81
76.86
8.31 3.22
168.24 73.52 7.95
<2
mm
1431
..
27.38
Measured for Whole Sample
:
Notes for above:
Mass of all gravel
M>2
2049.5 g
#1 Measure for intact sample
Mass of fines
(<2
mm)
M<2
1431 g
#2
&
#3 Measured for gravel taken
‘A
of Total mass <2 mm
%M<2
41.11 %
from sample or appropriate horizon
Macro.
organics Mo
0.2 g
#4
Vbk>2
= M
I
BD>2
Mass Total MT
3480 g
#5
VV>2
=
(Vbk>z)
‘
(P/1 00)
Mass Error
Mi3g
#6
Measured for pit wall sample M2
Volume of sample v-r 2072
cms
#7 M’ = (MT*) ●
(“AM2)
Volume Error
Vk
33
~m3
#8
Vbk>2*
= (M*)/ B D>2
Particle Density <2 mm
PD<2
2,64
g
cm-3
#9
VV>2*
=
(Vbk>2’)
●
(P>2/1
00)
.-
Calculated for Sample
Buk
Vdune
dgavel
~Vbk>2
859.6 cm3,
Sum
for
all
slev~
●
i~es
22
mm
O/’d
VTastx&gyavel
%Vbk>2 41.5
% =
(XVbk>2
/
VT)
●
100
Vol. of voids in
gavel XVV>2
81.2
ems,
Sum for all sieve sizes
22
mm
Bulk Density of
sampla
BD
1.68 gem-3=
MT/W
Compounded BD Error
BD~
0.03
g cm-a=
BD
. ((MT-Mi)
/
(VT+V~))
Porosity of sample
P
36.28 % =
[(VV>2
+
(Vbk<2.Vs<2))
/ Vt]*l 00
Bulk Volume of fines
Vbk<2
1212.4
cm3
=
VT -
Vbl@2
Volume of solid fines
Va<2 542
~m3
=
M<2
/
pD<2
Bulk Density of fines
BD<2
1,18
g
cm-s
.
M<2
I
Vbk<2
Porosity of bulk fines
P*2
55.3
%
x
[
(Vbk<2
-
Vti2)
/
Vbk<2
] *1OO
Synthesized for whole soil (*)
Mass Total MT* 5227.3
g = M<2 /
(%M2<2
/ 100)
Bulk Volume of gravel
~Vbb2*
1545.9
cm3,
Sum
for
all
sieve
sizes
>2
mm
Vol. of pores in gravel IYV>24
110.7
cm3,
Sum
for
all
sieve sizes
~
2 mm
Bulk Density BD’
1.90 g cm-a= MT’/
(Vbk<2
+
ZVbk>2*)
Porosity P’
28.3
‘k
-
-
[(D/v>2*
+
{Vbk<2
-
VSC2})
/
(xVbk>2*
+
Vbk<2)]
*
100
Fig 1- Vincent
4’
‘“’
2.2
2.0
s
,-
Cfa
c
ts
1.6
● ✍
0
01.2
1.0
2.2
.;
‘“8
U)
c
~
1.6
x
E
m
1.4
1.2
1.0
10
1001,00010,000100,000 1,000,000
Volume of Field Sample, cm
3
Fig 2- Vincent
0
10
20
30
40
50
60
70
80
90
100
110
Soil Bulk Density, g cm
-3
1.4 1.6
1.8
2.0 2.2 2.41.0 1.2
I
A
ABk
Bk 1
Bk 2
Bk 3
BCk
1——————————’1—
!
●
●
●
CBk
,
1
,
11
II
1
Fig 3- Vincent
