mechanical properties of granite from the taourirt tan afella massif, algeria

22 Pages·2009·0.46 MB·English

TID-4500, UC-35
L5
LAWRENCE UVERMORE LABORATORY
U*^ty&CaHoa&/UwmmCaltOtnitf/S4550
UCRL-51296
MECHANICAL PROPERTIES OF GRANITE FROM THE
TAOURIRT TAN AFELLA MASSIF, ALGERIA
fi. N. Schock
A. E. Abey
H. C. Heard
II. Louis
MS date: November ",, 1972
-NOTICC-
Tliii report wos prepircd as on account of work
sponsored by the United Stales Government. Neither
the United States nor the United Slates Atomic Energy
Commission, nor any of their employees, nor any of
their contractors, subcontractors, or Ihcu employees,
makes any warranty, cxircss or Implied, or assumes an;'
legal liability or rcsponiiblllly for the accuracy, com­
pleteness or usefulness of any Information, apparatus,
pjoduct or process disclosed, or represents that Its uso
would not infringe privately owned rights.
• i r- ";,;~'"-'r^i
1 1 ••', V • • -III
I)
\
Contents
Abstract I
introduction 1
Pressure-Volume Determinations 3
Determination of Shear Strength at High Pressure 5
Uniaxial Compression Tests 6
Torsion Tests 7
Brazil Tests 11
Acoustic Velocity Determinations 11
Three-Dimensional Stress-Strain Determinations 13
Uniaxial Stress 14
Uniaxial Strain 16
References 19
MECHANICAL PROPERTIES OF GRANITE FROM
THE TAOURIRT TAN AFELLA MASSIF, ALGERIA
Abstract
The mechanical properties of a granite granites that have been studied extensively.
from the French Hoggar test site in The failure envelope was determined to
Algeria were measured to provide input 30-kbar mean stress with no evidence of
for numerical codes seeking to predict ductile behavior. Stress-strain experiments
rock response to a stress wave and to reveal the presence of long narrow cracks
assist in formulating models on which which close at stress libels below 0.5 kbar.
these codes are based. The measured The rock at atmospheric pressure was
properties include pressure-volume found to have a bulk modulus of 330 kbnr
behavior, failure envelope as a function and a shear modi'lus jf 290 kbar. These
of mea.i pressure, compressional and yield an elastic compressional velocity of
shear velocities as a function of pressure, 5.24 km sec" , in good agreement with
and three-dimensional stress-strain laboratory measurements on small
measurements along various loading and samples and with field experiments within
unloading paths. This granite responds the massif over distances of several tens
to stress in much the same way as other of meters.
Introduction
As part of an exchange program between test site and expe; Imental conditions Is
the French Commissariat a L'Energie given by Stephens.
Atomique (CEA) and the United States The Hoggar test site consists primarily
Atomic Energy Commission, related to of Taourirt Tan Afella (24° 03' N, 5° 02'
the peaceful use of nuclear explosives, E) and the surrounding plains. The
we have received a suite of rock samples samples received (henceforth called
from a 765-m borehole in the Taourirt Hoggar) were from a borehole drilled
Tan Afella massif, on the Hoggar test into the massif to within 40 m of the shot
site, in what was formerly French point, prior to the Monique explosion
Algeria. The French have conducted (117 kT). A cross-section of the massif
several underground nuclear explosions through the borehole is shown in Fig. i.
in this massif. A summary of previous We received samples from every 20 or
technical exchanges and a bibliography ot 30 m between the surface and 750 m.
the French reports describing the Hoggar Each sample is approximately 10 cm in
-l-
AltituHo -— m
SW NE
2000-
— /"""•"^.^ Borehole T 71
1800-
J IOOP"^*^. TAOURIRT TAN AFELLA
1600-
30o\-
1400-
500V-
1200-
700 m\- Projection of mino shaft \
= {extonding to the north from
11000000-- Point 0 point 0 for about 1230 m)
Scalar 1/10,000
Fig. 1. Southwest-Noriheast section through Borehole T. 71.
_j i_ 1_
10 20 30 40 50 60 70 80 90
cm
Fig. 2. French CEA photograph of granite samples.
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Table 1. Properties of the granite of motion, and wave propagation. Since
Taourirt Tan Afella.3
these calculational codes require mech­
Mineralogical analyses anical properties as input, ivo have chosen
Quartz 3 57o Ch aye's to concentrate first on the rock samples
index 64
Microcline 37% closest to the explosion. The deepest
Plagioclase 25% sample (7 50 m) is from just outside the
Biotite 2.1% region in which the cavity was produced,
Muscovite 0.6% and where peak stresses are of the order
of tens oC kilobars.
Chemical analyses
We have experimentally determined
Si0 7 5.80% K0 4.7 9%
2 2 the pressure-volume loading behavior to
AlO 12.49% Ti0 0.08%
2 s 2 35 kbar, the failure envelope to 50 kbar
1.30% o.oi/o
Fe2°3 P2C5 mean pressure, and acoustic velocities to
MnO 0.04% co 0.13%
2 10 kbar. In addition, the stress-atrain
MgO 0.03% H0+ 0.48%
2 relationships in quasi-static loading have
CaO 0.59% H0- 0.06%
2 bvi^n measured to 15 kbar to determine
Na0 3.80%
2 such parameters as the stress and path
dependence of the shear modulus, and the
length by 5 cm in diameter, althougu the properties on unloading from peak stresses
size and core diameter vary slightly below the failure envelope. The experi­
(Fig. 2). The samples were coherent, mental techniques used have been de-
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appeared relatively unaltered and showed cribed in detail elsewhere. The aver­
little evidence of fracturing. Chemical age density of the material studied is
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and mineralogical analysis of the granite 2.61 g cm and varied between 2.604 and
body are given in Table 1. 2.617. All stresses are referred to a
One of the primary goals of this ex­ cylindrical coordinate system witn a,, a„
change of rock samples is to compare and a„ the maximum, intermediate, and
numerical simulation techniques that seek minimum principle stresses. Stress is
to predict such explosion induced features taken as positive and strain as negative
as cavity dimensions, fracturing, ground in compression.
Pressure-Volume Determinations
The pressure-volume relationship for volume relationship is determined from
Hoggar granite was determined on four measurements of force and piston dis­
different samples from 700 m. Two of placement. The results from the two
these samples (1.15 cm diam X 2.54 cm 3 5-kbar quasi-hydrostatic runs are shown
cylinders) were compressed to 35 kbar by the symbols O and A in Fig. 3. The
in a quasi-hydrostatic piston cylinder remaining two samples (1.91 cm diam
apparatus. This apparatus uses tin as X 2.54 cm) were tested in a hydrostatic
the pressure medium. The pressure- apparatus to 14 kbar. These sampies
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0.94 0.95 0.96 0.97 0 98 0.99 1.00
v/v
0
Fig. 3. Pressure-volume relationship for Hoggar granite. Climax Stock gronodiorite,
and Westerly granite. Pressure-volume relationships are shown for com­
parison.
were jacketed in 0.02-cm lead to prevent
penetration of the pressure fluid into the v/v'o = - AZ ciCpi ,P•' , (i)
n
rock. Strain was measured as a function l»0
of pressure by foil strain gap that are where C, is a constant and P-> l Ii_s pressure
bonded to the lead jacket. Tho results for in kbar. The bulk modulus, K, can be
the hydrostatic tests are shown as D and expressed as a ratio of power series
V in Fig. 3. For comparison. Fig. 3
also shows the pressure-volume relation- 9
C.P
ships for Climax Stock granodiorlte and
i
K =-q-^ . (2)
Westerly granite.
I" i • C • P*1-1'
The results from all four runs appear t
to be in good agreement in the overlapping i=l
region. A curve '«* drawn through the Table 2 gives the values for C,. Equa­
experimental data up to 35 kbar. These tion 2 gives a bulk modulus at P = 0 of
data may be expressed as a power series, 326 kbar.
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Table 2. Polynomial coefficients in
Eq. 2 and derived pressure-
volume data.
[ Ct
0 1.000000000
1 -3.06201539X 10"3
2 1.50892659 X 10"4
3 -1.64618743 X 10"5
4 1.05764000 X 10"6
5 -3.22663929 X 10"8
6 1.45310915 X 10"10
7 1.86230791 X 10"11
8 -4.99569603 X 10-13
9 41 .12613182 X 10" 5
P v/v K
(kb) 0 (kb)
0 1. 326
0.5 0.9985 342
1 0.9971 357
5 0.9872 436
10 0.9765 487
15 0.9672 56S
20 0.9594 675
25 0.9529 770
30 0.9468 795
35 0.9409 810
Determination of Shear Strength at High Pressure
The differential stress-strain behavior 1.9 cm diam by 3.0 cm long at 1 bar
of this granite was determined in three pressure. The compression tests were
types of tests: 1) uniaxial compression carried out in a fluid medium using
on cylinders 1.2 cm diam by 2.5 cm long jacketed samples. Pressures wrere
under confining pressures ranging up to determined from the resistance change of
22 kbar, 2) torsion of solid disks 0.25 cm manganin wire coils and the axial loads
diam by 0.7 cm long under pressures imposed on the sample were measured
ranging up to 50 kbar, and 3) indirect within the pressure vessel with a force
tensile tests (Brazil) on right cylinders gage placed in mechanical series with the
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test sample. Changes in sample length Tabic 3. Compression,teats, Jloggar
granodiorite.
were determined from external piston
displacements. Accuracies of measure­ •i ni r.i •'> " ~' <\ K
ment are estimated at 0.5 to 1.0% after
calibration. General descriptions of the 2007 n 0 0 I04T. 0 GftS 0
apparatus as well as discussions of gen­ 31(52 f) 0 o tono 0 f?0 0
eral techniques used are described else- s-r'.4n0o 42 210000 aa isoo 3:>(1.i0o 2.i7n 3;o0 1 r-"3r0. i 23<0>(1300 tiirnji
where. The torsion tests were carried :o2ro «520 1000 toiio 4C40 I?20 (010 233d
woo J4!>0 1000 1040 44*0 12.10 lifO Ifl (10
out in a solid-pressure medium appara­ 15030 C7C0 21.00 20110 6S20 3*40 tuso 3MO
14370 "310 3010 21.10 GlflO .10*0 nuo 4150
tus. The mean prersures as well as
innri OliO 3000 :. n o coso 300O 7fi4.1 :<l 10
the torques and twists applied to the I 7340 i mo .TOM- :il -o "120 4040 7 7 SO Nl -10
1P020 14600 3C?'' 3840 7fi7r> 1.100 P7G0 ?+3P
sample disk were measured externally. I 7*70 3430 3020 "MfJO 7330 3130 7fi30 5270
Accuracies for these tests are believed 1DP30 11470 4000 42:0 7P70 3G30 9.110 iCSO
aieso 15050 soso 3? 10 0300 0 ion no S310'
to be about 5%. The indirect tensile tests 31)70 13300 5100 MOO D040 .14 50 1-1-10 7700
23010 CSIO 60C0 (1510 (1700 0 11*110 r.ni 0
were made in a standard testing machine
25760 7300 70 BO 7.100 !>350 0 133PS 7.10.11
having accuracies of <0,S%. All three 2 MOO 7300 70GO 73P0 «00 y 1.1J !>0 7300
33020 12350 13350 1 23 SO 10750 0 I0-.20 12350
test types were carried out at room 37110 153(50 153C0 153G0 toono 0 2?r,m 153 GO
•4 43700 202C0 202KO 30360 11370 0 2'7tV. 3^ .0
temperature and at stra'n rates of 10 4 3330 21030 21030 31^30 11700 0 30730 71M0
tto 10"5/sec. flntnn proooufo. All fallm 11, ir. >>v UriHlo fr -aclurc.
T. 713toi it nnmpli en from COO to 7 5'0 rtl.
UNIAXIAL COMPRESSION TESTS
the single or occasionally conjugate shear
Differential stress-axial strain curves fractures in these samples did not punc­
at each pressure were calculated from ture the thin-wall jacketing material. For
the raw force-displacement data and the the highest pre93ure tests, displacements
initial sample dimensions. Intercomparl- on the fracture surfaces were sufficient
son of these curves over v .e range of to penetrate the jacket and allow the fluid
pressures investigated along with visual pressure access to the rock with conse­
observations on the deformed test samples quent drop in stress to zero. Total
then yielded an internally consistent pat­ permanent strains before onset of fracture
tern of behavior with pressure for the were about 1 to 2% with the tendency to
Hoggar granite. increase somewhat with pressure. Be­
In each ease, the stress-strain curve havior of all samples could thus be termed
showed a quasi-elastic portion followed brittle.
by a narrow region of yielding (both ir, The principal stresses at the point of
stress-:as well as in strain) which finally fracture la., a,) as well as the stresses
terminated in fracture. In most tests, supported by tl e granite ir mediately after
with the exception of those at the highest fracture (aj, cri) are summarized inTable3.
pressures, the stress after fracture did From this table it is apparent that a or
not drop to zero but remained at about the shear stress -r, [a - o~'i/2, markedly
one-half the ultimate (fracture) value. increases with confining pressure o„.
The tensile fracture planes as well as Sucih btihavior Is to be expected if the
-6-
."qiluro mechanism responsible <s depend- at which the dominant .'iiechynisn: of
e it upon normal stress. Shear fracture deformation became plastic flow in the
and frictional sliding of adjacent surfaces component crystals (ductile behavior)
arc two such mechanisms. Figure -J prompted us to extend our measurement?
illustrates this increase in strength with to tho highest preus<irt, * possible. Com­
pressure up to pressures of 22 kbar. pression testing i'ecomen very difficult
12
Results on the same roclt to S kbar are in fluido at pressure:; above about 25 kbar.
also shown. Agreement between the two Thus, ~.-o initiated a limited pr< gram of
sets of data is considered very good at the strength measurements in torsion in tho
lower pressures but only fair in the 2 to pressure region 21 to 50 kbnr in a ."olid
4 kbar range. Discrepancies diminish at pressure medium apparatus.
the highest comparable pressure and it Re-outta from the torsion tests in the
>-.ppears the two curves might cross and form of torque-twist curvej as well as
diverge if higher pressure data were the deformed samples had the same
available. Also shown for comparison characteristics as the compression data
are data for tw< similar rocks—tho discussed above. Values for the prlncip;
Westerly grafjit"; to 20 kbar and the stresses at fracture, as calculated in Uv
Climax Stock granodiorite to 8 libar. The outer flboru of the deformed disk, are
esterly results are nearly parallel to oummcrli'.ed in Table -t for comparison
that of the Hoggar to the highest pres­ with those for compression (Table 3).
sures; the only significant difference is From these tables it appears the fracti.r
the 3 to 4 kbar offset in fracture strength strength lu apparently still increasing t
at pressures above about 10 kbar. Tho the highest pressures mea&ured. Gr: uc
Hardhot granodioritc apparently la stronger comparison of both sets of results ar<
than b ••) granites.
Results for both the iloggar and
Table 1. Torsion tests, Hoggar grano­
Westerly granites are also shown as
diorite.3
failure envelopes in shear stress-mean
pressure space (Fig. 5). In addition, tho
strength of the Hoggar samples after
fracture is shown for comparison. It is kb
apparent that this granite retains con­ 41.2 21.0 0.8 10.1 21.0
siderable strength under pressure even 41.2 21.0 0.0 10.1 21.0
though all cohesion is destroyed. Avail­ 44.5 21.0 -2.5 11,8 21.0
able data ior the Hardhat and Westerly 56.2 29.0 1.8 13.5 ?9.0
rocks also indicate comparable strengths 56.6 29.0 1.4 13.8 29.0
after fracture. 63.2 35.0 6.8 14.1 35.0
dl.4 35.0 8.6 IS.2 3 5.0
TORSION TESTS 79.5 50.0 20.5 14.8 50.0
80.6 50.0 19.4 1 5.3 50.0
The desire to determine the limiting
All failure is by brittle fracture.
shear strength as well as the pressures T. 71 test samples from 600 to 7 50
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0 5 10 15 20 25
a, — kbar
Fig. 4. Axial stress difference at failure as a function of confining pressure for Hoggar
and Westerly granites and Climax Stock granodiorite.
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