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Fo: publication in the Proccella:
of the Sixth Symposium o! Picek
Mechanics, Kollit, Mo., L:.. 28-30, 13
SEP - 1999
ORAL-P- 202
CONF-702-/

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CORRELATION OF CONVERGENCE
MEASUREMENTS IN SAIT MINES
WITH LABORATORY CREEP-T'EST DATA*
MASTER
By R. L. Bradshaw, W. J. Boegly and F. M. Empson
Costu w tymtoto mm.
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Cowanie
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LEGAL NOTICE -
Health Physics Division
Oak Ridge National Laboratory
Oak ridge, Tennessee
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.
INTRODUCTION
b.t the Cak Ridge National Laboratory we are studying salt mine stability
to determine the design parameters for the ultimate disposal of high-level
radioactive wastes in salt mines... To be able to predict the effects of
elevated temperature (due to heat generated by decay of radioactive wastes)
on creep and mire stability, an understanding of creep efi'ects at ambient
temperature is necessary.
S. Serata in 1959, suggested that creep 19tes (or cłosure mtes) of mined
openings always decrease with time. In 1959, both ORNL and Serata (then at
the University of Texas) installed several vertical and horizontal cor.verger.ce
measuring stations in the Carey Salt Company's mine at Hutchinson, Kansas.
Since that time, ORNL has added additional stations at the Carey mines in both
Hutchinson and Lyons, Kansas. These stations were designed to determine the
effects of both age of the opening and pillar stress on creep rates. Data from
these stations tended to indicate that Serata's hypothesis of steadily
*Research sponsored by the US Atomic Energy Conmission under contract with
the Union Carbide Corporation
decreasi: vertical convertince was correio, ni least for the pillar stress
10:1s encountered in the Kansas ines.
I: Kirch 1953 Serata indicated trai
toe mad successfully extrapolated creep data t'ron laboratory pillar models
to creep rates in mined openings."
PILLAR MODEL TEST RESULTS
L. Obert, of the Applied Physics Laboratory of the U. S. Bureau of Mines,
has developed a somewhat different techr.ique for performing creep tests on
pillar models. At our request the Applied Physics laboratory carried out 1000
hour creef tests on model pillars which they rachined fro:n 6 in. dian. cores of
Lyons' mine salt. Steel restraining rings were epoxied around the upper
and lower ends cf the specimens and then the centers of the specimens were
ground out to form the pillar, and surroundinis roof and floor. The model
pillars had a diameter-to-height ratio of 4, and tests were run with average
pillar stresses of 4, 5, 6, 7, 8, 10, and 12 thousard psi. Vertical shortening
of the pillars, as a function of time and stress, was measured by means of
dial gages mounted between the steel restraining rings.
In the 12,000 psi test, flow was rupid and the pillar was considered to
have failed due to excessive flow; however, there was no evidence of catastrophic
(sudden or brittle) failure. The 10,000 psi model exceeded 20% deformation
before the 1000 hr of the test was completed.
Based on the cumulative deformation curves supplied to us by Obert, we
prepared Figure 1 showing the creep rates as a function of time, obtained by
taking the tangents to Obert's curves at the indicated times. Data from these
curves can be fitted by an equation of the om:
į = Bota
where
Ė = strain rate (vertical convergence S. Olivro Inches per irich per day
a
5
B = a constant (dependent on units of Ć)
= average pillar stress (psi)
slope of é vs o on a log-log plct (positive)
t = time (nr.)
n = slope of ė vs t on a log-log plot (negative)
A reasonable fit is obtained with:
ė = 9 x 10-3 03.1 -0.6
The exponent of the stress dependent ter. is in reasonable agreement with
those obtained by the USBM with salt and similar rocks from other localities.
The 0.6 slope obtained for the time function appears to be significantly different
than the range of 0.8 to 1 (obtained from unpublished data of USBM and S.
Serata) for selt from a different locality. However, extrapolation of the
above equation out to periods up to 70 years (:in excess of 600,000 hrs.)
produces predicted creep rates which agree reasonable well with those actually
measured in the Hutchinson and Lyons mines, whereas agreement was poor when
compared with extrapolation of the data from models made from salt from the
other localities. It thus appears that the creep behavior of the Lyons and
Hutchinson salt is somewhat different than that of salt from some other
formations, and that data from one m..ne should not be presumed to be representative
of that from mines in different salt formations.
TC
CORRELATION OF VERTICAL CONVERGENCE MEASUREMENTS
WITH PILLAR MODEL TESTS
Tables 1 and 2 show the results of vertical and horizontal convergence
masurements in the Hutchinson and Lyons mines, respectively. (It should be
noted that the Lyons station numbers which were omitted are either different
type measurements, have not yet been installed, or sufficient data has not
yet been octainer to establish convergence ruties. Figures 2 and 3 show the
locations of the measuring stations. Horizontal closure rates (in inches
per year) in the Hutchinson nine, are believed to be subject to abou' + 0.02
in error due to use of a less accurate type of gage installation than that
used for the other measurements. For the other measurements, (both horizontal
aná vertical) anchors are set approximately 18 in. Into the salt, and readings
are taken with a dial gage which reads to 0.001 in.: however, other variables,
such as minor seasonal variations in mine air temperature, reduce the accuracy
of the results to perhaps + 0.005 in./yr.
Figure 4 corapares the vertical convergence rates in both the Hutchinson
and Lyons mines (tables 1 & 2 plus additional data) with the convergence
rates predicted by the empirical equation derived from the pillar-model
tects. After an opening is about 10 years old, approximately two years of
data are necessary to establish two points of sufficient accuracy on the
convergence rate vs time plcts due to the slow decrease in rate of closure.
Thus each of the points for Hutchinson stations 2, 3, and 7 is the rate
established by taking the total deformation for a period of one year, converting
it to the proper units, and plotting it as the rate at mid-year. Only
one point is shown for the older stations since, for example, in a 30 year
old opening, about five years of data would be required to produce two
significant points. Most of the gaging stations in the Hutchinson mine are
located near the boundaries of the mined-out area and thus the adjacent pillars
would not be expected to be supporting the calculated dead weight of the
overburder as should be the case if the pillars were in the center of a very
large panel of rooms. That this is true (at least for openings up to a few
years of age) is shorn in Figure 4 by the behavior of Hutchinson Station No. 6.
A short time after the excavation in the area of Station 8, mining was
discontinued on the west side and shifted to the east side of the north parel. When
the orening at Station 8 was about three years old, ühe apparent stress in the
pilar was about 1700 psi (sue Table 3 as well as Figure 4). At this time,
mlning was resumed near Station 8 and the western boundary was extended beyond
that shown in Figure 2. The rapid rise in vertical convergence rate indicates
that the pillur had not been fully loaded after the initial mining; however, it
should not be assumed that the load increased to more than 3000 psi (as might be
inferred from Figure 4). With the incremental load added some three years after
the opening was created, the time scale would have to be shifted to take into account
the fact that the creep due to the incremental load essentially begins at a new
zero on the time scale. With the points plotted, as shown, as a function of time
after the original loading (initial creation of the opening) the convergence rate
would have been expected to show a more rapid decrease as the pillar stabilized
under its new load. Unfortunately, the gaging station had to be removed before
this stage was reached. It is expected that Station 1 will show a similar behavior
when mining is again resumed on the west side of the north panel.
In general, the stations located nearest the centers of large mined-out areas
tend to approach the stress calculated by assuming an infinitely large mined area
(see Table 3). Hutchinson Station No. 6, for example, while located near the
eastern boundar, is in the center of a panel which is very long in the N-S direction,
..
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'
and the atress value obtained from Fig. 4 approaches the calculated value.
On
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the other hand, Hutchinson Stations 5, 9, and 10, located near a northern boundary
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as well as the large irregular pillar left around the mine shaft, indicate stresses
considerably below the calculated values.
SY
Lyons Stations 1 through 13 are located in the area around the shaft (no
large shaft pillar was left in this mine) where the mining pattern was very
irregular and the estimated extraction ratio is no better than a guess. Therefore
the calculated pillar loads for these stations (Table 3) may be too high. The
vertical convergence rates at stations 8 and 9 are anomalous, and the
29
INN

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anoraly is definitely known to be due to a parting separation and resultant
ceiling sag. Stations 26 through 33 are progressively nearer a western boundary
and the convergence rates seem to reflect this fact, although it is believed
thathere may be some ceiling sag contributing to the cor.vergence at 16 and
possibly at 20.
Referring again to Table 3, it should be noted that stress measurements
made in the Hutchinson mine by the USBM (using stress relief techniques)?,0
tend to confirm the general validity of the pillar-nodei extrapo.lations. The
1300 psi figure was measured one pillar away from Stations 9 and 10, and the
1600 psi was measured in a pillar near Station 8, soon after Station 8 was
installed.
RELATIONSHIPS BETWEEN VERTICAL
AND JIORIZONTAL CONVERGENCE RATES
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If it is assumed that the shortening of a pillar in & mine is similar
to squeezing a parallelepiped body between two parallel plates; that the pillar
volume displaced in the vertical direction is redistributed by equal expansion
on all sides of the pillar; ard that the change in height is small compared to
the original height , it can be shown that, for a rectangular pillar of
height A, width W, and length L = nw, the change in width (AW) is related to
the change in height (AH) by:
Am I )
AW = n
A
null
For a rouni pillar (of diameter D) under the same assumptions, the relationship
is:
D
=
F
Thus, if it is assumed that expansion is equal on all sides of a pillar
(round, square, or rectangular), and since Hutchinson pillars are square and
most pillars in Lyons are roughly square or at most 2:1 rectangular, it
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min.:
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would be expectea that the masured ratio of rorizonial to vertical convergence
(Fcriz/A Vert) should be between 1/2 and 2/3 times the width-to-height rat?c.
If it is assumed that horizontal expansion is directly proportional to
the horizontal dimension, it can be shown that:
&
ic
.. and
Thus, if pillars are not round or square, the results are dependent upon
which direction the horizontal convergence is measured in. If convergence is
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'=
measured between the long sides of two rectangular pillars, the reasured
value 18 AW, and A Horiz/A Vert is thus 1/2x(w/A). If convergence is
measured between short sides, the measured value is AL (= na w, and A Horiz/Avert
is n/2x(W/H). Thus for the case of a pillar with 1 = 2w, the ratio of the
measured values Alloriz/overt would equal W/A. If the convergence is measured
between a long and a short side, the measured ratio (Horiz/vert) would
thus be (1+n)/4x(W/A), or 3/4X(W/A) for the case where I = 2w.
Thus it would appear that, if horizontal expansion volume is equal to
vertical contraction volume, (assuming uniform shortening throughout k pillar),
then no matter whether the pillar is round or rectangular with long dimensions
up to twice the short dimension, no matter which sides of the pillars the
convergence measurements are made between, and no matter whether horizontal
expansion is uniform all around or is greatest in the direction of the longer
dimension, the measured ratio of horizontal convergence to vertical convergence
in both of the Carey mines should lie between 1 (W) and (w where w is the short
dimension and A is the height.
The foregoing assumes, of course, that convergence measurements are not
influenced by ceiling sags due to parting separation, or pillar spalling. It
also assumes that the horizontal expansion of the pillars is uniform over the
i
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vertical extent of the pillars. This last assumption is an oversimplification:

A
CT
Honever, if the horizontal expunsion is rorurilcim in the vertical plan, it
... to be expected that the greater expansion rouid take place at the vertic: 1
center of the pillar.' Under these conditions, the horizontal measurements
reported here would tend to be on the high side, since the horizontal gages
are located at the vertical centers.
In the Hutchinson mine the pillars are very nearly square and W/A ratios
at our res suring stations run from about 3.7 to 4.7. The data also indicate
that there is little or no parting separation since the clusure rates near
the pillar and in the center of the room are nearly equal. Thus it would be
expected that measured Aforiz/vert should be about 2. However, at all the
Hutchinson stations the measured ratio (last colwan, Table 1) is less than,
or approximately equal to unity.
In the Lyons mine, the Aforiz/Avert ratio would be expected to range up
to about 3. Instead, at stations which do not show evidence of parting
separation, the ratio is approximately unity (last column,
Table 2). Thus the bebavior in the Lyons and Hutchinson mines is similar
in that horizontal expansions of the pillars do not seem to be great enough
to account for the apparent shortening of the pillars.
There are a number of possible explanations for this apparent anomaly.
One plausible explanation is that part of the pillar volume expands into the
room via the floor and roof thus contributing to the vertical closure. If
2.3:
this is true, then the existing data indicate that the expansion is such that
after the first couple of years, it produces a nearly uniform vertical convergence
ali the way across the room. A point which tends to support this hypothesis
is the fact that parallelepiped samples compressed uniaxially do not behave in
the same manner (as regards creep rates) as do pillar models (with the same
relative pillar dimensions as the parallelepiped samples) which include the
3
roof, floor, and currounding opening wivi rastrainin; rings simulating the
center ot the surrounding opening by restricting the horizontal flow of the
roof and floor. There appears to be some flow of salt at the junctions
between the pillar and the floor and roof.
The data are not sufficient to establish relationships between horizontal
closure rates and pillar stress, but, unless the Autchinson Station 1 data
are anomalous, it does appear that the horizontal closure rates in in./yr.
(which are an indirect measure of transverse pillar expansion races) are
siguificantly lower than the vertical closure rates during the first few
years after creation of an opening. After about 10 years, the vertical
and horizontal closure rates in in./yr. appear to become approxiinately equal.
CONCLUSIONS
Laboratory pillar model tests, of 1000 hr or less duration, run at
several different values of average pillar stress, appear to be sufficient
to allow the development of an empirical equation which can be used to predict
vertical closure rates in salt mine openings up to 70 years old.
Vertical convergence rates have been shown to continue to decrease with
☆
tiine in openings up to 12 years old where the pillar stress is well. below
the ultimate strength. Accumulation of data at individual stations in
2.
-..
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olaer openings is not yet sufficient to determine with certainty if the
:
closure rates are still decree.sing after several decades, but the data from
the collective stations seem to indicate that rates are still decreasing after
70 years.
Horizontal closure rates (and thus transverse pillar expansion rates)
appear to be considerably lower than the vertical closure rates for the
first few years after an opening is created. It is thus possible that transverse
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pillar expansion tends to approach a nearly constant rate after a short period
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of time, aithough the cata also indicate that, after about 10 years, the
trarsverse expansion ryte in in./yr, tends to approach the vertical
convergence rate.
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REFERENCES
1. R. L. Bradshaw, W. J. Boegly, Jr., F. M. Empson, A. Kubota, F. L. Parker,
J, J. Perona, and E. G. Struxness, "ultimate Storage of High-Level Waste
Solids and Liquids in Salt Formations". Treatment and Storage of High-
Level Radioactive Wastes, International Atomic Energy Agency, Vienna, 1963,
pp. 153-175.
2. R. L. Bradshaw, F. M. Empson, W. J. Boegly, Jr., A. Kubota, F. L. Parker,
aná E. G. Struxness, "Properties of Salt Important in Radioactive Waste
Disposal", Proceedings of the International Conference on Saline Deposits,
Houston, Texas, Nov. 12-17, 1962 (In pres).

3.
.
.
S. Serata, and E. F. Gloyna, Development of Design Principle for Disposal
Into Underground Salt Cavities, Technical Report to the Atomic Energy
Commission, Dept. of Civil Engineering, Sanitary Engineering Research
Laboratory, Univ. of Texas, January, 1959, Chapter 10.
#. $. Serata, Dept. of Civil Engineering, Michigan State Univ., March, 1963
(Personal Communication).
5. L. Obert, Stress Determinations and Borehole Deformation Studies, Report
APRL, E 40.1, us Bureau of Mines, Applied Physics Laboratory, college
Park, Maryland.

6. L. Sbert, "In Situ Determination of Stress in Rock", Mining Engineering,
August, 1962, pp 51-58.
7. J. D. Sayder and L. F. Dellwig, "Plastic Flowage of Salt in Mines at
Hutchinson and Lyons, Kansas", State Geological Survey of Kansas,
Bulletin 152, Part 2, University of Kansas Publications, Lawrence,
Kansas, 1961.
TABLF. 1. CREFP MEASUREMENTS IN THIE HUICHINSON MINE
Hutchinson1
Suation
No.
Approximatic
Ago or
Oxoning
11. Your:
Total Closure Rate in
Incheo Por Yeur
Vortical
Horizontal
Next to Pilar Centor or Room Contor of Pillar
Avamy
Pillar Holght
in Inches
Vortimul Cloruro
Rate in
win/in-duy
(Noxt to Pillar)
Alor..
World
0.23
130
14.0
2.16
1.3
121
0.11
0.17
3.5
0.16
0.014
0.05
0.06+0.02
0.0740.02
0.1810.02
0.02+0.02
0.02.40.02
0.1740.02
0.11+0.02
1.6
0.19
0.10
10.4
28
ho
0.02
0.25
.1.1.3
0.116
No longer in Oxl::lonce
ho
0.02
0.:)
0.05
0.010.1
(1.740..!
1.100.1
0.600.5
1.011.0
0.700.1
(1.810.1
36
200
118
0.3
0.66
5.7
0.25
10
O.
HO
260
0.2
1. Detin ne or suplember 1963
b. S1:10.1013 local.oil 100 rib pillar pelo
c. Sinion Joented in an airwiny
Nie
TABLE 2. CREEP MEASUREMENTS IN THE LYONS MINEC
Aloriz
Avert
0.23
1.1
186
7.6
204
Hoooo mů ñ
2.3
Approximate
Approximate Vertical
Total Closure Rate
Lyons
Age of
Vertical Gage Closure Rate
Station
Opening
in Inches Per Year
Length in
in
No.
in Years verticala Horizontal
Inchesb
min/in-day
0.20
204
2.7
0.22
0.20
204
2.9
0.52
0.20
0.37
0.19
10.4
0.22
2.9
0.17
204
0.25
244
4.7
0.14
144
0.19
174
0.08
120
186
0.08
0.03
186
1.
ETR8-TI (center of 30
0.06
1.5
opening)
E7R8-T2 (next to 30
0.05
108 1.3
- pillar)
a. Data 4s of Ceptoruber 1963
b. Also assumed to be the effective pillar height
c. Vertical gages 8 and 9 are anchored in sagging roof slabs.
d. Due to rounded openings most gages are in the center of the openings.
Pigeon in Sinô
In 149*661462999
2.6
1.8
1.4
0.10
0.10
1.0
1.0
108
--,
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Table 3. Pillar Stresses Estimated by Different Methods
Pillar Stress
Calculated Calculated Measured
from Dead
from Pillar by USBMC
Station
Weight of
Model
(Stress
Number
Overburden Extrapolation Relist Method)
Hutchinson
30008
2900 €
800 van F wr
3000€
25004
22006
3800
3950 €
26000
1800
2100
2600
2400
1500
3300
2600
1700
1600
1400
22000
1600
1300
1300
22000
Lyons
Ons
40000
40000
4000 a
4000 a
40000
40000
3400
3400
4700
5200
3400
3200
3400
29000
2900
2800
2500
2500
25008
3000
2600
2400
2200
2400
33
2500
25004
E7R8-TI
Based on actual measurement of room and pillar areas.
Based on nominal extraction ratio in the whole panel of rooms.
"Report APRL, E 40.1, Stress Determinations and Borehole Deformation
Studies, by L. Obert, USBM, Applied Physics Research Laboratory,
College Park, Maryland.
Based on estimated extraction ratio.
.
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UNCLASSIFIED
ORNL-DWG 64-6011
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AVERAGE PILLAR
STRESS
ė , VERTICAL CONVERGENCE RATES (u in. in. 4 day-1).
--
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HIT 10,000 psi;
til 8000
0 7000
6000
it 5000
PF 4000
102
10
100
1000
TIME (hr)
10,000
Creep Rate Data on Lyons Pillar - Models (USBM Tests).
FIG. 1
.
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ORML LA DWG 126/9#

MORTH PAMEL
MOONS: $0 $0 NI
PILLARS: 501 50 11
CEILINO: 13 II MUNCH
- MINE SHAFT
MOOMS: 60 1300 11
PILLARS: 20 17 mot
CELINO: 6 11 HKOH 91
L
NOOMS: 50.800 11
PILLARS: 20 I1 WIDE
CEILING: 6 19 HNOM
MOOMS: 50*300 11
ALLMS 2011 WIOTC
CEKL MNO: 6 II HUCH
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MOOMS: 50 300 11
ICMLLARS: 20 I1 WIDE
CEMANG 6 11 HICH
mooms: 50*300 11
MULAS: 20 11 Woc
CEILIMO: 6 11 HIGH
MOOWS: 501 300 11
MUMS: 20 ft WIDE
CEILING: 6 IT MIGH
ROOMS: 50 - 50 11
PILLARS: 50 * 50 11
CELLING: NO 11 MICH
NOTE:
ALL HAUL AGE WAYS ANO AMWAYS, 30 11 WIDE
• LOCATION OF MEASURING STATION
AOOMS: 50 * 50 11
PILLARS: 40 X 40 11
CEILING: NO 11 HIGH
5000
500
1000
FEET
Plan of Hutchinson Mine, Showing Locations of Convergence Measuring Stations.
FIG. 2

.
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Partial Plan of Lyons Mine Showing Locations
of Convergence Measuring Stations.
FIG. 3
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-
- --
-
-
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-
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-
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UNCLASSIFIED
ORNL-DWG 64-6010
Q3000 psi IN PILLAR MODEL
WA
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2500
-
ON
140
R
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hinong
¿, VERTICAL CONVERGENCE RATES (min. in.-1 day -").
M32
2011
E7R8T1
•,0 HUTCHINSON MINE
A LYONS MINE
- 103
2
5
106
5 104 2 5 105 2
TIME SINCE CREATION OF OPENING (hr)
Measured Mine Convergence Rates Superimposed on Plots of Equation
Derived from Model Tests.
FIG. 4

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DATE FILMED
11/ 20/64
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LEGAL NOTICE
The report was prepared as an account of Government sponsored work. Neither the United
Buata, vor the Commission, nor any person acting on behalf of the Commission:
A. Makas any warranty or representation, expressed or implied, with respect to the actu-
racy, completeness, or wefulness of the taformation contained in talo roport, or that the wo
of any taformation, apparatus, method, or procesi dinclound in this report may not infringe
prinately owned retta; or
B. Asumas any liabilities with respect to the wool, or for damages routing from the
une of any information, apparatus, method, or procon dieclound in this report.
As wood tan the abova, "person acting on behalf of the Commission" includes ny
ploys or contractor of the Commission, -or-employer of sucha contractor, to the adient that
auch employee or contractor of the Commission, or employee of mucha contractor preparos,
disseminates, or provides acces ko, Information pursuant to Wo employment or contract
with the Commission, or we employment with sucha contractor.
END
Wh