final report robert 0. goetz - michigan
TRANSCRIPT
TA 710.5 G63 1971
-;?7
.. · 335130-1-F
Investigation Into Using Air in the Permeability Testing of Granular Soils
· FINAL REPORT
ROBERT 0. GOETZ
LIBRARY michigan department of
state highways
lANSING
June 1971
Michigan Department of State Highways Contract No. 70-0580 Lansing, Michigan
~\\TY IJ;:-~~t Depa<tment of c;v;l Eng;nee,;ng
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THE UNIVERSITY OF MICHIGAN
COLLEGE OF ENGINEERING Department of Civil Engineering
Final Report
INVESTIGATION INTO USING AIR IN THE PERMEABILITY TESTING OF GRANULAR SOILS
Robert 0. Goetz Associate Professor of Civil Engineering
ORA Project 335130
LIBRARY michigan department of ' state highways
LANSING
under contract with:
MICHIGAN DEPARTMENT OF STATE HIGHWAYS CONTRACT NO. 70-0580
lANSING, MICHIGAN
administered through;
OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR
June 1971
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SYNOPSIS
The investigation involved the permeability testing of four soils using
both water and air as the permeating fluid. The four soils selected for
testing were a 20-30 standard Ottawa sand, a 2NS concrete sand, a dune sand,
and a 22A graveL The last three are representative of materials used as
porous backfill by the Michigan Department of State Highways. From the re-
sults of the tests, it is concluded that, for the range of gradations tested,
the coefficient of permeability determined by the air test is, for practical
purposes, the same as that found using water.
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INTRODUCTION
The permeability test procedure used in the Testing Laboratory of the
Michigan Department of State Highways for determining the coefficient of per-
meability of porous materials (bases, subbases, and backfills) was developed
in the 1930's. The procedure follows, with some modification, "Method ST-22:
Method of Test for the Permeability and Capillarity of Soils and Soil Mix-
tures" found in Ref. l. In this method, the sample is placed in the permea-
meter at the required density. The sample is saturated and the rate of flow
determined under a constant hydraulic gradient at least twice a day for 7 days
or more to determine if a steady state has been reached. The apparatus used
by the Department for performing the test does not readily permit the varying
of the hydraulic gradient and the tests are usually run at only one gradient.
If the coefficient of permeability is required at different densities, the
whole procedure must be repeated for each density.
The above procedure is very time consuming. In addition, it is subject !,''
to the problems of using water-test procedures. The most bothersome of these
is the clogging of the void spaces in the sample with air or solid contami-
nants. To minimize these problems, deaired distilled water is normally used,
and the hydraulic gradients are kept low to prevent the movement of fines in
the sample.
The purpose of the present investigation is to determine if air can be
used as the permeating fluid instead of water in determining the coefficient
of permeability, and, in this way, overcome the problems of the water-test
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procedure. The major advantages of using air are:
l. The problems of air dissolved in the water and trapped air in the sample are eliminated.
2. The density of the sample can be changed by vibrating the soil in the permeameter. The same sample can be tested over a. wide range of densities without tearing down the entire apparatus.
3· Steady state flow can be reached in a short period of time.
4. The gradient through the sample can be varied readily.
5· Measurable flows for very dense soils can be attained without the use of excessive gradients.
The primary aim of this investigation is to find if the coefficient of
permeability determined from water tests can be predicted from air tests with
sufficient accuracy for practical purposes. With a. test procedure that is
less time consuming, the Department would be in a. position to expand the rou-
tine permeability testing of porous materials.
BACKGROUND INFORMATION
Taylor (Ref. 2) presents an equation for Darcy's Law for granular soils
based on laminar flow through a. nest of circular tubes:
v
where v = discharge or superficial velocity, q = rate of flow, A = cross-
sectional area of flow, D = effective or average particle diameter of the s
(l)
soil, ~ = the viscosity of the permeating fluid, e = void ratio of the soil,
C = a. factor depending on the shapes and arrangement of the pores, and
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i ~ pressure gradient. p
.2 3 For a. given soil mass, the D , e /(l+e), and c terms s
are constant and can be replaced by K, the permeability of the soil, a.s dis-
cussed in Muskat (Ref. 3). The permeability, K, then, is independent of the
permeating fluid and depends only on the soil structure. Therefore, Equation
(l) can be rewritten as:
v ~
K i
fl p (2)
The study of seepage problems in Civil Engineering involves almost exclu-
sively the flow of water through the soil under a. hydraulic gradient. For
this condition, the pressure gradient may be expressed a.s a. hydraulic gradient
and the viscosity, except for temperature effects, may also be absorbed in a.
new constant, k, the coefficient of permeability. Equation (2) then becomes:
v ~ ki ( 3)
where i ~ hydraulic gradient ~ i ly and y ~ unit weight of water. The coef-p' w w
ficient of permeability, then, is a. function of both the permeating fluid and
the soil structure. It will vary with temperature since the viscosity of
water varies with temperature. Equating Equations (2) and (3) leads to the
following relationship between K and k:
where fl w
k ~ K
viscosity of water.
3
liBRARY michigan department of
state highways
LANSING
(4)
SELECTION OF MATERIALS
Four granular materials were selected for testing: standard 20-30 ottawa
sand, 2NS concrete sand, a dune sand, and a 22A gravel. The gradations of the
four samples were determined and are presented in Figure l. In addition to
the gradations, the specific gravities were found and are also given in
Figure l.
The standard 20-30 Ottawa sand was selected because it has been used by
other investigators. The remaining three were chosen as typical of porous
materials used by the Department.
TESTING APPARATUS AND PROCEDURE
WATER
A schematic drawing of the apparatus used in finding the coefficient of
permeability using water as the fluid is shown in Figure 2(a). The essential
elements are a source of distilled water, constant-head filter tank, overflow
chamber, permeameter, two manometers, and the necessary piping and valves.
·l The constant-head filter tank contains sand through which the water flows in
order to remove any entrapped air that might be in the distilled water. This
tank also contains an overflow weir. The head on the sample is controlled and
kept constant by means of the overflow chamber. This chamber can be adjusted
up and down so that the sample may be tested under different constant heads.
The permeameter is a plastic cylinder mounted between a. top plate and a.
:l ' base plate. There is an inlet in the top plate and an outlet in the bottom
4
plate to permit the flow of water through the sample. The plastic cylinder
is fitted with two outlets for connection to the manometers for measuring the
head loss through the sample. Figure 3 presents the main details of the per-
meameter.
The apparatus described in the previous paragraphs conforms to the stan-.-,
l
dard test method for the "Permeability of Granular Soils (Constant Head),"
l
·! ASSHO Designation: T215-70 and ASTM Designation: D2434-68. The test proce-
dure used to find the permeability also followed these standard methods.
Briefly, the procedure involves placing the sample in the permeameter and
saturating it. The weight and height of the sample are determined so that the
void ratio can be computed. Some difficulty was encountered with segregation
in the 22A gravel, and with saturating the 22A gravel and the 2NS concrete
sand.
After saturation, the inlet valve is opened, the overflow chamber is ad-
justed, and water is allowed to flow until a steady state is reached as indi-
cated by little or no drift in the manometer levels. The head loss, 6h, as
i determined by the difference in level in the manometers, the quantity of flow,
Q, the time, t, to collect Q, and the water temperature, T, are measured and
recorded. The overflow chamber is then moved to produce a different constant
'.} head on the sample and the measurements are repeated. A typical data set is
shown in Table 1. The whole procedure is repeated at a number of different
void ratios for each soil.
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AIR
The apparatus used to determine the coefficient of permeability using
air as the fluid is shown in Figure 2(b). It consists of a constant pressure
regulator, permeameter, well-type manometer, and flow meters. The constant
pressure regulator is connected to the compressed air line in the lahoratory.
The regulator permits the reduction of the line pressure to the wanted value
and then holds the pressure constant. The permeameter is the same one as used
in the water tests. The well-type manometer is connected to the permeameter
through three-way valves so that the pressure difference between outlets and
pressure at the entering end can be measured. The quantity of air flowing
through the sample under the pressure gradient is determined by means of the
flow meters.
The soil is placed in the permeameter as loose as possible using the same
procedure as in the water tests. The inlet pressure is adjusted by means of
the regulator to give a measurable flow. After the steady state is achieved,
the rate of flow, q, the pressure difference, p1
-p2
, and the inlet pressure,
p1
, are measured and recorded, where p2
is the outlet pressure. The inlet
pressure is changed by means of the regulator and the measurements are re-
peated. A typical data set is presented in Table 2. The sample is vibrated
to a lower void ratio and the measurements repeated, until the dense state is
reached.
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DATA ANALYSIS
WATER
Equation (3) is used to analyze the data from the water tests. From the
recorded data the hydraulic gradient can be determined from:
i
where L = the distance between manometer outlets in the permeameter. The
velocity can be computed from:
v ~ At
=
where A = the cross-sectional area of the permeameter.
The next step in the analysis is to plot the velocity versus the gradi-
ent. The points should lie along a straight line which indicates laminar
flow. Any significant and consistent departures from the line at higher gra.-
dients would be indicative of turbulent flow. A straight line is fitted to
the points by means of linear regression techniques. The slope of this
straight line is the best estimate of the coefficient of permeability for the
sample.
Equation (l) indicated that the coefficient of permeability should be a.
function of e3j(l+e). Therefore for each soil, the coefficients of permeabil
ity at the different void ratios are plotted against e3j(l+e). Again, a.
straight line is fitted to the points by linear regression methods.
As discussed previously, the coefficient of permeability will vary with
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temperature. In the present series of tests, the average water temperature
in each test was about 2)°C. Therefore, the coefficients of permeability
presented are for approximately 2)°C.
AIR
The use of air introduces complicating factors into the analysis of the
data. In contrast to water, air is compressible under the pressures used.
At the entering end of the sample the air is at p1
• As the air passes through
the sample, the pressure drops to p2
resulting in an expansion of the air.
Muska.t discusses this situation and gives the equation,
K 1-l qL a
where q ~ rate of flow at the mean pressure (p1
-p )/2 and 1-l ~ viscosity of 2 a
( 5)
air, for computing the permeability of the soil. In addition, the flow meter
measures the rate of flow, q, of the air at atmospheric pressure and not at
the mean pressure in the sample. The ideal gas law can be used to determine
q from q as follows:
q (p' +p' )/2 ' l 2
~
2p q a.
p +p +2p l 2 a
where p ~ atmospheric pressure, p' ~ p + p and p • ~ p + p • In analyzing a l la. 2 2a
the data for this project, p is taken as 29.0 in. of Hg or 394.4 in. of a
water.
(6)
The next step in the analysis is to substitute Equation (5) into Equation
(4) which gives
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k 1-l qL y
a w
In this equation the hydraulic gradient is given by
i =
and the velocity is
v =
(7)
(8)
The average temperature of the air as measured during the tests was also 23"c,
and this temperature was used in analyzing the data. The viscosity of the
air was computed from the following equation given in Ref. 4:
0.0001702 (1 + 0.00329T + 0.0000070T2
)
where 1-l is in poises and T is in degrees centigrade. a
After determination of the hydraulic gradient and the velocity of flow,
the analysis followed the same procedure as is used for the water data. Plots
of velocity versus gradient are made and straight lines put through the points
by regression techniques. The coefficients of permeability are then plotted
against e3/(l+e).
DISCUSSION OF RESULTS
Figures 4 through 8 present the plots of the velocity versus the gradient
for the four soils using water as the permeating fluid. The same relationships
9
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for the air tests are presented in Figures 9 through 12. On each figure, the
void ratio, e, the equations of the regression lines, the correlation coeffi-
cients, r, and the computed test statistics, ~", from the analysis of variance
are given. The F value at the '7/o significance level used in testing the hy-
pothesis that the slope is zero is also given. As would be expected, the cor-
relation coefficient and the F values show that the relationship between the
gradient and the velocity can be considered linear.
Visual examination of the plots reveals that straight lines from the re-
gression analysis fit the data very well with the possible exception of the
22A gravel with water as the fluid. Close study of the results shows that
the slopes have a tendency to decrease as the gradient increases instead of
being constant. In other words, curves might fit the points better than
straight lines. While there is the possibility that there was turbulent flow,
it is felt that results observed were due to movement of fines as the gradient
increased.
In Figures 13 through 16, the coefficients of permeability are plotted
versus e3/(l+e). For each soil, the water and air results are presented in
the same figure for comparison purposes. As in Figures 4 through 12, the
equations for the two regression lines and the results of the statistical
analysis are given. Except for two cases, the r and F values indicate again
that the relationship can be considered linear. The exceptions are for the
2NS concrete sand using water and the dune sand using air. Visual examination
of these two lines reveal that they fit the points as well as or better than
in some of the other cases. In these two cases the number of tests performed
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are too small for a significant statistical analysis. It is believed that if
additional tests were run on these materials the results would be significant
at the 5% level.
It should also be noted that the air test for the 22A gravel in the
loosest state was not used in the regression analysis. It was not possible
to conduct a test using water at this void ratio as the sample would compact
during saturation. The indication is that the relationship is not linear at
the higher void ratio.
When comparing the coefficients of permeability from the two methods, it
should be kept in mind the practical use that is made of permeability test
results. One is in the area of acceptance testing where the test is used to
determine if a porous material has an acceptable coefficient of permeability.
In this case, all that is needed is to know if the coefficient of permeability
-4 is greater than about 10 em/sec. Whether it is 0.0053 or 0.0063 em/sec is
not significant. Another use is in the area of seepage computations. Here
again, great accuracy in the permeability determination is not required in
light of the other variables involved in the problem.
Study of Figures 13 through 16 show that, for all four materials, the
value of the coefficient of permeability predicted from the regression line
for the air data is, for practical purposes, the same as that predicted from
the line for the water data.. This conclusion is verified by the analyses
which are presented in Tables 3 through 6. In these tables, the first column
contains the void ratio and the second gives e3/(l+e). The third column is
the measured coefficient of permeability, k . In the fourth column appears m
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the coefficient of permeability, k , predicated from the water regression line w
while column five contains the predicted value, k , from the a.ir regression a.
line.
The last three columns give residuals. The residual R1
is the difference
between the measured value of the coefficient of permeability and the pre-
dieted value from the water line (R1
= km- kw). The average residual, ii1
,
which is reported at the bottom of the column, is found by squaring each re-
sidual, summing the squares, dividing by the number of values, and taking the
square root as indicated in the equation:
R
Two comparisons are made in the final two columns. In column seven is
shown the differences between the coefficients of permeability as predicted
by the water and a.ir regression lines (R = k - k ) . 'rhese residual values 2 w a
and the average residual, R2
, show how well the air predicated values dupli-
cate the water predicted values. The last column presents the differences
between the coefficients of permeability as measured in the water test and
those predicted from the air regression line (R = k - k ) • These residuals 3 m a
indicate how close the air regression line fits the water test data.
Table 3 presents the analysis of the residuals for the 20-30 standard
Ottawa sand. Study of this table shows that the R2
resid,Jals are on the same
order of magnitude as the R1
values. The R2
value of 0.041 is only slightly
greater than R1
= 0. 036. These results indicate that the air regression line
can predict, with the same degree of confidence, the coefficient of
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permeability with respect to the 1vater regression line as the water line pre-
diets the actual measured values. The R3
residuals and the R3
~ 0.056 indi-
cate that the air regression line fits the measured water values almost as
well as the water regression line. Examination of the residual analyses for
the other three soils s~ow the same behavior.
CONCLUSIONS
The following conclusions can be reached on the basis of the stU<jy pre-
sented in this report.
l. The apparatus and procedures used in this study resulted in reliable and consistent measures of the coefficients of permeability, using water and air as the permeating fluid. Care must be exercised in placing the sample to prevent segregation, and to insure complete saturation.
2. The use of water as the fluid is more time consuming. It took 3 to 4 hours at each void ratio to determine the coefficient of permeability. A new sample has to be prepared for each void ratio.
3. The coefficient of permeability using air is much less time consuming. It took less than 2 hours to conduct the test for all void ratios. The steady state of flow is achieved faster, and the same sample is used for all void ratios.
4. The analysis of the data from the air test is more complicated. Charts or graphs could be developed to reduce the work.
5· For the range of soil gradations tested, the coefficient of permeability predicted from using air and one sample is within the accuracy needed for practical purposes.
6. Further study is needed to determine the lower limit that air can be used in permeability testing. Clays adsorb water on their surfaces which would have an effect on the permeability. Air would not duplicate this effect.
13
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ACKNOWLEDGMENT
This research wa.s financed by the Michigan Department of State Highways.
The investigation was conducted in the Soils Laboratory of the Department's
Testing Laboratory.
Personnel of the Department's Testing Laboratory under the general super-
vision of Howard E. Barnes were most cooperative in providing the soil tested
and sharing laboratory space. Special thanks are due to Louis D. Bertos of
the Soils Section who aided in some of the testing.
Thanks are also due to Ronald E. Miller, graduate student a.t The Univer-
sity of Michigan, who assembled and built the apparatus used. He also made
most of the tests and aided in the analysis of the data. and the preparation
of this report.
liBRARY michigan department of
state highways
LANSING
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LIST OF REE'ERENCES
1. Housel, w. s., Applied Soil Mechanics, Laboratory Manual of Soil Testing Procedures, Edwards Brothers, 1957, pp. 119-130.
2. Taylor, D. w., Fundamentals of Soil Mechanics, Wiley, 1948, p. lll.
3. Muskat, M., The Flow of Homogeneous Fluids Through Porous Media, McGrawHill, 1937, pp. 69-79·
4. Lamb, H., Hydrodynamics, 6th Ed., Cambridge University Press, p. 576.
15
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TABLE 1
TYPICAL PERMEABILITY TEST DATA USING WATER
Test No: 7 Date of Test: 1-7-71 ------Description of Soil: 20-30 Ottawa Sand
~~~~~~--------------------Remarks:
Diameter, D ~ 11.43 em
Area, A~ 102.609 cm2
Length, L ~ 11.43 em
Specific Gravity, G ~ 2.66
llh
(em)
1 4. 3 Height Before, H1
~ ___ _ em
14. 3 em
2501 Height After, H2 ~ --~
Weight of Soil, W ~ _.::..::...::...:_ __ GAH Void Ratio, e ~ -w- -
v ~ _.9. · At
(em/sec)
l ~ 0.561
0.28 0.00530 0.216
~~0~.5~0~·--~--~2~3~7____ _30JL_ __ r~o~·~0~4~3.~7--~~~o~·~o~o~7~70~+-~o~·~17~6~~
1_~1'-'.--'-o-'-o _____ _ __ 4_0 _8 ___ c-_ 3 o SJ---r---2-~-· o_8_75 o . o 1 3 2 o . 1 5 L_ l--_:__1 :.:· 3::.:5=------ji----'6:..::2:..::5 ____ +--~-~oo _____ _():_!2§ ______ o'-'.'-'o-"2--"occ3 __ +---'o-'-.-'-1 -'-7=-2 ---1
1.65 470 200 0.144 0.0229 0.159 '----'---·---+- ~--~·-·- ----j--~--------- __ :_:_::::::::~~--='-'-'...::..::.--1
_l_. 9 5 57 0 2 0 0 --- r-_o_,_l]j ___ _ 0 • 0 2 7 8 -- _ _Q~~-'--'1 6"'3.___, 2.60 730 200 0.227 0.0356 0.156 3.20 875 200 0.280 0.0426 0. 15 2 3.70 515 100 0.324 0.0502 0.155
-----~~- ---·-· ~-------. -----~
4.20 590 100 0.367 0.0575 0. 156 5.05 725 100 0.442 0.0706 0. 160
~-... ---- -5. 70 500 60 0. 499 0.0812 0.163
0.560 0.0926 0. 16 5 0. 59 5 0. 1 01 0. 169
0.647 0.109 0. 168
6.40 t . ::: 60 6. 80 60
7.40 60
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TABLE 2
TYPICAL PERMEABILITY TEST DATA USING AIR
Test No: 2 Date of Test: 4-27-71 Description of Soil: 20-30 Ottawa Sand
Remarks:
Diameter, D = 11.43 em Height Before, Hl = 16. 5 em
Area, A= 102.609 2 Height After, H2 16. 5 em = em
Length, L = 11.43 em Weight of Soil, w = 2652 gm
Specific Gravity, G = 2.66 Void Ratio, GAH l 0.698 e = - = w
-- i =
pl-p2 .!"aq L¥w
v =--pl - p2 pl q q )J-WA k
(in H20) (in H20) (lpm) (lpm) (em/sec) (em/sec)
0.05 1. 40 2.0 1. 99 0.0111 0.00634 0. 5 71 ----·--0.13 4.65 4.0 3.95 0.0289 0.0126 0.435 -- -~~---- f---0.20 9. 80 6. 0 5.86 ' 0.0444 0.0186 0.419 0.25 13.60 8.0 7~ 0.0556 0.0246 0.443 -0.32 21 . 70 1 0. 0 9.48 0.0711 0.0302 0.424 ---------,-------0.30 9.05 1 0. 0 9. 78 ! 0.0667 0.0311 0.467 -------- --------· -t--------------------0. 40 1 3. 1 0 1 3. 0 -~-2. 5_9____j_ 0 . 0 8 89 0.0400 0. 451
~--------- ·-------·------- ---0.45 1 4. 9 0 15.0 14.46 0.100 0.0460 0.460
0.60 24. 1 0 20.0 18.86 0. 1 3 3 0.0600 0.450 0.75-----35.70 25.0 22.94 0.167 0.0730 0.438
- ------------- r---- -~----~----··
--'--
pl - p2 pl - p2 in. H20 ,(2.54) (0.9976g:mLcm3 ) i = = (11.43) (0.9976) X 3 X ·
L.l'w (em) (gm/cm ) :Ln.
= 0.2222(pl - p2)
f<aq (l.837lxl0-4 ) (g) (poises) (lpm) (1000 cm3 ) (min) v = ~wA = -(-9~.~3~8x~l~0-=3~)~(l-0~2L.~6~0L9--) x(poises) (cm2 ) x(liter) (60 sec)
= 0.00318lq
'""''"'""...;_, "~----"" ·,
TABLE 3
ANALYSIS OF RESIDUALS FOR 20-30 STANDARD OTTAWA SAND
.
I Void
3 k k k Rl = R2 = R3 = Ratio e m w a k - k k - k k - k e l + e (cmjsec) (em/sec) (em/sec) m w w a I m a
0.557 0 . 11 1 0.262 0.226 0.255 0.036 -0.029 0.007 --0.561 0. 1 13 0. 16 5 0.232 0.259 -0.067 -0.027 -0.094 0. 577 0. 1 2 2 0.284 0.259 0.278 0.025 -0.019 0.006 0.646 o. 164 0.388 0.385 0.366 0.003 I 0.019 0.022
G6~2 0. 1 89 0.478 0. 461 0.419 0. 0 1 7 0.042 0.059 .688 0. 1 9 3 0.459 0. 4 72 0.427 -0.013 H,045 0.032
l 0. 701 0.203 0,542 0.502 0.448 0.040 .054 0.094 0. 71 5 0. 21 3 0.493 0.534 0.470 1 -0.041 0.064 0.023
R1-0.036 R2-0.041 R3-0.056
TABLE 4
ANALYSIS OF RESIDUALS FOR 2NS CONCRETE SAND
I i
Rl = R = R = Void 3 k I k k 2 3 Ratio e m I w a k - k k - k - k l + e (cmjsec) i (em/sec) (em/sec) k m w w a m a e
- l 0.374 0.0382 0.0174 0.0164
I 0.0158 0.0010 0.0006 0.0016
0. 461 0.0669 0.0382 0.0378 0.0339 0.0004 0.0039 0.0043
0. 501 0.0839 0.0400 0. 0 50 4 0.0446 -0.0104 0.0058 -0.0046 0.514 0. 0 89 7 0.0638 0.0548 0.0482 0.0090 0.0066 0.0156
R1;0.0069 R2; 0. 0048 R3; 0.0084
Void Ratio
e
0.609
0.722
0. 772
Void Ratio
e
0. 140
0. 21 8
0.260
3 e 1 + e
TABLE 5
ANALYSIS OF RESIDUALS FOR DUNE SAND
k \1 k !I Rl = R = :1 R3 = m kw , a , 2
(em/sec) (em/sec) j (em/sec) i km - kw kw - ka I km - ka
0.0154 I 0.0153 ! 0.0149 I 0.0001 0.0004 0.0005
o . o2 5o ! o . o 2 52 I o . o 2 4 4 I -o . o o o 2 o . o o o 8 I o . o o o 6
0.0307 1 0.0306 1 0.0295 r 0.0001 o.oon , 0.0012
jR1 = 0.0002 R2= 0.0008 R3= 0.0009
TABLE 6
ANALYSIS OF RESIDUALS FOR 22A GRAVEL
I I k I kw ka Rl = R = 2
k - k w a
R = 3 k -k m a 1 (cm/~ec) i (em/sec) (em/sec) km - kw
t------+----+-------+----+·--------1----··---f-------+------i 0.245 0.0118 0.0110 ! 0.0081 0.0103 0.0029 -0.0022 0.0007
~ 0.292 0.0194 I 0.0238 I 0.0214 0.0245 0.0024 -0.0031 -0.0007
0.360 0.0342 0.0358 i 0.0475 0.0525 -0.01171-0.0050 -0.0167
'-1 _o_._4_1_3_L-_o_._o_4_9_8-+-_o_._o_8_1_4_+-[_o_. o_7_4_9__._ __ ~ . o 81 8 o . o o 6 5 - o . o o 6 9 - o . o o o 4 --R1 = 0.0070 R2= 0.0047 R3= 0.0084
SIEVE g .~ OPENING MM. c;; c;;
I 00
90
80
70
~ 60
z
"' "' < 0- 50
= = ~ = 0 -.
~ 0
= N
= = = 0 ... ~ ~
= = =
v ~
·.,;~.~"""" ~·;;:~·_::c.;,~,j,'
= 0 ~ = ~
'\
I I
j I
1/
1/
0 = M
/
/
0 0 = = 0 = ..,;. 10 CD
v
_/ v
/ v
./ ~
z w I/ v 0
= w 40 0-
I / /
30 I /
_/_ v
20 1 L ~ _L .L'/
I 0 .!L.'Z ... 1---7L
0 v / 820-30 OTTAWA SANO. G • 2.66
I!
I _j_
t v
= = = N
v
= 0
= M
= = = 0 = 0
0 0 = ... ~ ~
Ll.OUNE SAND, G • 2.64
02 NS CONCRETE SAND, G • 2.66 022A GRAVEL. G • 2.60
FIGURE I. GRADATION CURVES FOR SAMPLES TESTED
0 = = = 0 = ~ = - 0
I 0
20
30
40
50
60
70
80
90
100
= w z < ~
w = ~ z w 0 = w 0-
l '
i
I
.. j ~:\
I ,j
-~
i :j
.;;
l '
.:1
I -.-!
i J
~--.1
T
AIR SUPPLY
DISTillED WATER SUPPLY TANK MANOMETERS
-- -- =11 . . : .. u . .
~ .. ~
~ ~ ~ u ~
;: ~
VALVE I ~ ~ ~
CONSTANT HEAD ~
FILTER TANK ~
~ OCi1 ADJUSTABLE ~
~ OVERFLOW CHAMBER
OVERFLOW
.0.
VA~E 3
PERMEAME TER
FIGURE 2A SCHEMATIC DIAGRAM OF PERMEABiliTY APPARATUS FOR WATER
PRESSURE REGULATOR
~
PERMEAMETER
VAl:!_ 5
WEll-TYPE MANOMETER ~
VAL; 4 l '41
FIGURE 2B
3 2
FLOWMETERS
SCHEMATIC DIAGRAM OF PERMEABiliTY APPARATUS FOR AIR
11
c VALVE 2
-,.-, --J
<1 j
·:-l 1 ') :)i -~
1 j
~~~j
j
:t j
-J l J
MANOMETER--I--,_ OUTLET
0
m
SOIL SAMPLE
·. ·: ·P.b~o.li~ · .s1QNC ·_-: . . . . . . . . .
TRANS PARENT I++----PLASTIC CYLINDER
1---5.5."' DIA (13.97 CM)----..1
FIGURE 3 DETAILS OF PERMEAMETER
.:::i .<i '}
.:)
'J\
,•'1
I
., -•,J ,,::j . .'}
·-;, .i
J
j '':1 ' J
>~-.I
l :;
• :·1 I ~
-"l
,-'i
--)
.. -j
:·-_1)
-.J
0.12 r--------,r--------,--~z----.---------,--------.---------~---,
1,~6 / o o/ /__ 1 o/1 o
~ I 0.10 r-------~--------~T---~---+--~!---~--------~--------+---~
t I II f£ I v;o
o.oa r----t----:f-jr ----J."Ii ___ o7)/+---+---+-----1------l
f ;' II 0 I/ I
~ o.os ~--t!);-,0/r:-/-~;---,./--+vl-; ---+--4----+---~
rl ;I 0.04 r-----t-A-H~b '---1+------+--~+--~-+---+----~
0. 02 1---,d~'l/--;l-:l--l------+----t------+------!-----1--J
O.B----~L-----~~----~~----~L-----~L_ ______ L__j o 0.1 o .2 o.3 0.4 0.5 o.a
GRADIENT
e=0.682 0 0 VEL= -0.0008 + 0.4778 GRAO
r=0.994, F= 1600.6, F_ 95 ( 1 , 18 )~4.41
•=0.715 6_ __ --A VEL= -0.0012 + 0.4933 GRAD
r = 0.999, F = 9055 •. 3, F_ 95 ( 1 , 15 J = 4.54
e=0.646 0-- ---0 VEL= 0.0015 + 0.3879 GRAD
r = 0.999, F = 11617.2, F_ 95 ( 1 , 15 J = 4.54
e = 0.577 o-- --0 VEL = 0.0001 + 0. 2842 GRAD r = 0.997, F = 4907.8, F_ 95 ( 1 , 23 J = 4.28
F I GUllE 4 VELOCITY vs GRADIENT FOR 20-30 OTTAWA SAND USING WATER
i j
i i
.I
~ ~
0.12
0.1 0
o.oa
~ I
J,.
/
f ~ I
J I
/ I / .,/ I
ol I -
It / v"'o
~ c,_, 0.06 ~
// 7 0
,I //
II/ ~:0 /"'O 0 d
~ 1/ 0 I/o
/Ia // /'0
t~l ) //
/' l/6
~,/ r f I
~ 1/ ~i/'
,_ ~ 0 ~ ~
>
0. 04
0. 02
0
0 0.1 0,2 0.3 0.4
GRADIENT
e ~ 0.701 (}---------()VEL= -0.0034 + 0.5417 GRAD
r = 0.977, F = 486.2, F. 95 <1 • 23 l = 4.28
e = 0.688 "'---- .1:.VEL = -0.0010 + 0.4588 GRAD
r=0.999, F= 11754.6, F_ 95 <1 , 21 l=4.32
e = 0.557 0- ---0 VEL= -0.0014 + 0.2622 GRAD
r = 0.997, F = 2290,7, F. 95 ( 1 , 14 l = 4.6D
e=0.561 o-- -QVEL = co:0007 + 0.1655 GRAD r = 0.998, F = 4962.4, F. 95 <1 , 14 ) = 4.60
FIGURE 5
//
/' /
// .e
/
0.5 0.6
VELOCITY vs GRADIENT FOR 20-30 OTTAWA SAND USING WATER
LIBRARY michigan department of
state highways
LANSING
c /
>I
--,, '
J.
l I
J I
--" --1
j '
. fo
I 1,
I I If I
I
/i/ / //
/j f i, I c
I I !! / 16
/; /
v/ // /
0,09
0.08
0.07
0.06
I /t.} //
// /; /6
v ;r,; 4
/'
/ / .£" l} /
// // ,./ ' 0.0
I /I //u '~ 0 514
v ~VEL ~ 0, 0002 + 0. 0636 GRAD
(; // r~ 0.999,F~11677.5,F. 95 ( 1 , 13 J=4.67
/ ~ '~0.501 fr.-- -6. VEL~ 0.0005 + 0.0400. GRAD
2 r ~o. 999, F ~ 14617.4, F . 95 <1 , 13 ) ~4. 67
Ll [.,/ ' //
1'1 ' ~ 0.461 o- --oVEL~ 0.0000 +0.0363 GRAD
/ r~0.99B,F~3690.7,F. 95 ( 1 , 13 J ~ 4.67
i ' ~ 0.374 1
rY/ o- - -QVEL ~ -0.0005 + 0. 0175 GRAD
l" / r ~o. 999, F ~ 16113. o, F. 95 <1• 13 J ~ 4. 67
/ 0 f//
0. 0
0.0
0 0.5 1.0 1 . 5 2. 0 2. 5 '. 0 3.5
GRADIENT
FIGURE 6 VELOCITY vs GRADIENT FOR 2NS CONCRETE SAND USING WATER
o. oa
/
1/ I /if
/
0. 07
I /
t/ I
/ y I
/
I / //
0,08
0. 05
0. 03
I /
// 6/ /
/
// f'
//-v
lor/
;(; /'
// ,/ ~/
0 !/;/ //
;; // 0// /'
;; /
jY
0. 02
i:: 0.04
0. 01
0
l I
0 0,5 LO 1,5 2.0 2,5 3 '0 3 '5 GRADIENT
'~ 0.772 0 0 VEL~ 0.0000 + 0,0307 GRAO, r ~ 0.999, F ~ 34380.8, F. 95 (l,ll) ~ 4,84 ,,
! '
e~0.722 D.- ----L>VEL ~ 0,0001 + 0.0250 GRAD, r ~ 0.999, F ~ 25550.7, F.s5(J,l1) ~ 4.84
' ~ 0. 609 D--- --DVEL~O.OOOO+O.OI54GRAD, r~0.999, F~l3857.2, F. 95 (l,l3)~4.67
FIGURE 7 VELOCITY vs GRADIENT FOR DUNE SAND USING WATER
0,09 :7 0
e-0.413 o---o VEL~ D.DD82 + D.D814 GRAD r ~ D.992, F ~ 531.9, F.oS(l,SJ ~ 5.12
Oo 07
':1, )
' ~~
·::\~ 0,06
J
-~-~\ ~
' ~
' = 0.05 :•) " '" ~ >
:.;·\ ~
~ i = ~ ..
~· ~
~
0, 04 ., ·.'· j
0. 03
'.\
: . -."I
0. 02
.J
0. 01
' ~ D.36D
I t:... - - -<1. VEL ~ D. DD45 + .0. 0351 GRAD
r ~ 0.993, F ~ 666.5, F.S5(l,lOJ~ 4.96 '~ 0.292 D-- -lJ VEL ~ 0. D040 + 0. 0238 GRAD
r ~ 0.995, F ~ 951.6, F.S5(l,l OJ~ 4.96
I ' = 0.245 0-- -om~ D.DOD6 + 0.0110 GRAD
r ~ 0.998, F ~2296.2, F.95(l,10J ~4.96
I I
/
l I
I
v~ /> I
I I
/ /
1/ I
/ I
I / I I
/ I I ~ I
7 //
1 "'II / I / I
I I/
7 0
I / I t./ 0/ I
0// I I
l ? "/ I ;/ I ,.A)
"'I ll v--/ o/ _..,./--
v / I// ~,..
I o? J..
1/ /) ~
~ // 7
/
I o --~/ _.,0
o/ ~..----
~--_.--A)
0,08
0
0,5 1.0 1.5 2.0 2. 5 GRADIENT
FIGURE B VELOCITY vs GRADIENT FOR 22A GRAVEL USING WATER
1
1 .J
.\ ~ ~
l ~
;;., ~
~
-~}
,_ ;:;
I = ~ ~
>
J
0.08
I / I I /!
I / 1/ 1/ / / / I
I _/ I
1/ .II / /
/; /1 I' l l/ I II
/
/ / /
1/ / / ./ a/ol Pj ./
J /II I I /
./:, /;1 II // ~/ / ~-l
II~// I/ .'
~~~ v·/
0.07
0. 06
0. 05
0. 04
0. 03
2 I l//
.M ~f;P/~
0. 0
o .. o
r/'
.V 0 0.05 0.10 0.15 0.20 0.25
GRADIENT
~VEl~ 0.0004+ 0.4414 GRAD, r~ 0.996, F~ 2729.4, F 95 (1,a)~ 5.32
J:.:~·~5:.C.VEL~ -0.0020+0.3606 GRAD, r ~ 0.996, F~ 1969.3, F. 95 ( 1 , 5 )~ 6.61
e ~ 0.616 0-- ---DVEL~ -0.0006+0.3273 GRAD, r ~ 0.996, F~ 1406.9, F. 95 ( 1 , 5 )~ 6.61
e=0.575 o-- --0VEl ~ -0.0004+0.2613 GRAD, r ~ 0.997, F ~ 622.2, F.Q5(1,a) ~ 6.61 e ~ 0.533 .
8--. --o VEL~ 0.0003 + 0.2246 GRAD, r ~ 0.997, F ~ 907.6, F, 95 (1 , 5) ~ 6.61
FIGURE 9
/
VELOCITY vs GRADIENT FOR 20-30 OTTAWA SAND USING AIR
/-j
v
0.30 0.35
-~ '1
"1 I
~: J
l '1 ' l
.0
··:'\ j 'j
·>~
1 .~_-) . -·r
:;
-A
--1
j
J
·--1 :=J
)
J :?
- ·(
0.07
0.06
o. 05
0.04
~ ~
"" " '"' ~ 0.03 ~· !:::: ~
"' .... ~
>
0.02
0. 01
0
• I
// / / I / / / //
I 7 // I I o/
/~/ I I
II 7 I ,,/
I 7 ·" / / II / /./ /.
ll II //"' .v v·~
I I 0 / ;,. ,I /~ v.:
1/ /o /•
~/-v·
"'l/ It/ /' 0 0.5 1.0 1.5 2.0 2.5 3.0
GRADIENT
e = 0.523 Q----0 VEL= -0.0008 + 0.0519 GRAD, r = 0.997, F = 1945.2, F. 95 <1.s) = 5.12
e = 0.494 b-- --1). VEL= -0.0005 + 0.0425 GRAD, r = 0.992, F = 583.3, F. 95 (l,S) = 5.12
e = 0.455 et-- --0 VEL= -0.0000 + 0;0314 GRAD, r = 0.998, F = 2362.4, F. 95 (l,S) = 5.12
e = 0.417 0- _ -o VEL= 0.0001 + 0.0234 GRAD, r = 0.998, F = 3537.3, F. 95 (1.S) = 5.12
(:;_~~VEL= -0.0000 + 0.0140 GRAD, r = 0.998, F = 2112.4, F. 95 (1.B) = 5.32
FIGURE I 0 VELOCITY vs GRADIENT FOR 2NS CONCRETE SAND USING AIR
0. OJ
-, ..l ' '
·"'!
l J
~ ~ <X>
"'" :.. .I ~
:.; ~ -"j >-~
= ''';3 ~
.I ~
> I
i I ~-
1 ' ' ' ,,
-;
::'-1 :-~
::}
) 0
0.06 I /
// ~ /
/ // I
/ /
/, / // 0 _/ 1/ // /
1//// /, I /: ~
/:.' /tf / ~ /0
//,
); ~.6>/~
/ /
o];!J/ 1/ .
0.05
0.04
0.03
0. 02
o. 01
0 0.5 1.0 2. 0 2.5 1.5
_<} GRADIENT
:]
:_j
e= O.B22 0------0 VEL= 0.0001 + 0.0346 GRAD. r = 0.99B, F = 2926.D, F. 95 <1 , 12 ) = 4.75
e=0.767 A---...t>YEL=-0.0005+0.0297GRAD, r=0.994, F= 1042.1, F. 95 ( 1 , 12 )=4.75
-) J
_.--] e=0.724 o-- -oVEL=-0.0005 + 0.0241 GRAD, r = 0.996, F = 1562.5, F. 95 ( 1 , 12 ) = 4.75
i FIGURE II j VELOCITY vs GRADIENT FOR DUNE SAND USING AIR
l J
'_j
:<j .::[
I
j
l ~) i ·' ~,-:,
j '· j
;:;:
I . J
0.07 r-------,.-----.------,..------r-----..,
I I 0.06 1------.lr--+--l---+-----~i-------+-------1
I I I I
o.05 1----+-+'r>/--J/'---
0-~-~-ft-----1----/--+------1
I o /
I / "/ 0.04 f--+--*.~---;+-----+------11---, /.L----+------1
~ / / /v
§ / ./ /( ~0.03 1-~r-~~--+~----+--~-e-~---·----+-~-----1 ~ l v /{ /' f I // .............. .......-.
i /- /b /.-----: 0.02 f-f--f-l-/+
0-1------, ,(.L--+-------1-,...-L ,-::_ _ _:__+-------!
[I ;//" ~-/"·· £; \/ _/. I / /.,...-
0 0.5 1.0 1.5 2.0 2. 5 GRADIENT
e = 0.462 0. 0042 + 0. 1545 GRAD, r = 0.999, ~ VEL = f=3887.5, F.9511,Bl = 5.32
e =0.407 0. 0032 + 0. 0790 GRAD, r = 0.997, .6,. - - -t:, VEL = f = 1604.5, F.95(1,Bl = 5.32
e = 0. 361 0- --D VEL = 0. 0026 + 0. 0482 GRAD, r = 0.990, F = 441.2, F .9511 ,9) = 5.12 e =0.300 0-- --o VEL = -0.0003 + 0. 0252 GRAD, r = 0.990, F = 386. 0, F.9511 ,6) = 5.32 e = U. 245 e- · -.:.:e VEL = 0.0000 + 0.0121 GRAD, r = 0.978, F=156.7, f = 5.59 .95(1 '7)
FIGURE 12 VELOCITY vs GRADIENT FOR 22A GRAVEL USING AIR
I I
0.55
I I
~,
I 0.50 I
~'
' :_1 -·--j
,_, __ j
I 0.45
I I
~~ '
~~,
I
'~I ::1
0.40 ~ ~ 0?
;;. ~
>-,_ --:~ _, ' 0.35 ) "" .. ..... ..
"' ..... 'J ~
.] u.. -:·.!, = ,_
= ..... ,.,1
~ 0. ~1 0
j u..
"' ..... = ~
I 0.25
. >1 I
J 0.20
I !
.,.~
0.15 .i
l l
_,]
)
I J
I I ',
. -~-~
I
I _,3
/ o/ //
/il
0
0.1 0 0.12
()----{)USING WATER:
e.-- -euSING AIR:
;(v 0
. L v /"'
.....
/ /
/ /
/ ........
/. / , .... /
/.... /
',/
~/ ;...-
/j v/
0.14 0.16 0.18 0.20 0.22 · e3/1 +e
k = -0.1069 + 3.0051 e3/1 +B, r = 0.958, f = 67.3, F. 95 ( 1 ,B) = 5.99
k = 0.0226 + 2.0972 e3/1 +e, r = 0.998, f=1207.2, F. 95 ( 1 • 3 )=lO.l3
FIGURE 13 COEFFICIENT OF PERMEABiliTY vs e3/l +8 FOR 20-30 OTTAWA SAND
j ,-J ,:..)
',1 ''I
··'i
' .. ) .-'\
I J J
·;>:~ ,, ·,;j -,, J
-:~:)
.·1
j
·::-a ,I
·~·-1 ~
"i I
d
' 1 d
.)
I j
j
'-' ..... "' "" "' '-' >-,__ .... "" "" ..... "" "' ..... 0..
..... = ,__ "" ..... "' "-..... ..... = '-'
0.07
0 v 0.06 I
/
0,05
o. 04
'/ '
/ /
I /
/
~/
f/ 0. 03 I /'
/ /
/
" 0.02 //
f/
l /
./ /
o. 01 0.02 0.04 0. 06 O.OB 0.10 0.12
(}---()USING WATER: k" -0.0121 + 0. 7452 e3/J +B
r "0.907, F" 9.3, F. 95 ( 1,, 2 ) "18.51
e-----4itUSJNG AIR: k "-0.0083 + 0.6308 e3/1 +e
r "0.998, F" 804.2, F. 95 ( 1 , 3 )" 10.13
FIGURE 14 COEFFICIENT OF PERMEABiliTY vs ea/1 + e FOR 2NS CONCRETE SAND
·;;1
J >,J
"'·)
i ~j
~~! ;.! ~ l
cd
" cl
''1,
i ~:1
I :·d
-1 '-':
._.j ~
1
_I
l J
'-' "-'
"' "'--== '-'
>-1-_,
"' ... "-'
"" = "-' "-
"-= 1-:z: "-' '-' "-"-"-' = '-'
0. 036
/ • / /
/
o. 032 /
0,028 J
v / /
/ /
w/ 0 .024 ~ ~/
0,020 '
0.016 I'
I
Q----()USING WATER: k = -0.0025 + 0.1271 e3/1+e
r = 0.999, F = 1271.8, F. 95 (l,ll = 161.4
e.----USING AIR: k = -0.0022 + 0.1217 e3/1 + e
r = 0.991, F = 54.9, F. 95 (l,U = 161.4
FIGURE 15 COEFFICIENT OF PERMEABILITY vs e3/f +e FOR DUNE SAND
'-' ~ .., ;;, '-'
>->-.... = -~ "' "' ~· 0..
..... = >-z ~
'-' ..... ..... ~ = '-'
:j '
J
0.16 r----------,---------.----------~---------,---------,----------,
0.14
0.12
0.1 0
0.06
0.06
I/~/
/ It/
/v 0.04 1------~r---_/-~-;-'-,.f------t-----t-----+------1 , "'v/ 0
/ 0.02 ~----~e._/_/_/+7"'-1----+-----+-----11-------+-----1
0.0 0.01 0.02 0.03 0.04 0.05 0.06 0. 07
e 3/1 + e
0---QUSING WATER: k = -0.0127 + 1.7597 e3/1 +e, r = 0.905, F = 27.0, F. 95 ( 1 ,2
) = 18.51
·-- ... USING AIR: k = -0.0119 + 1.8810 e3/1 +e, r = 0.998, F = 604.9, F = 18.51 .95(1,2)
FIGURE 16 COEFFICIENT OF PERMEABILITY vs e3/l + e FOR 22A GRAVEL