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Laboratory creep tests of frozen gravels
Cold Regions Science and Technology, 13 (1986) 1 0 1 - 1 0 4
101
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
Short Communication LABORATORY CREEP TESTS OF FROZEN GRAVELS Scott L. Huang and Robert C. Speck Department of Mining and Geological Engineering, University of Alaska-Fairbanks, Fairbanks, Alaska 99775-1190 (U.S.A.)
(Received February 25, 1986; accepted in revised form April 21, 1986)
As part of a continuing effort to develop a relationship between convergence of full-scale underground openings in permanently frozen gravel and laboratory creep strength tests of frozen gravels, two uniaxial creep tests of reconstituted gravel were conducted at the University of Alaska-Fairbanks. The authors here present a description and the results of those tests.
LABORATORYPROCEDURE The gravel materials for testing were sampled directly from the U.S. Army CRREL permafrost tunnel at Fox, Alaska. Before sieve analysis, these materials were oven dried at l l0°C (230°F) for 8 hours. Particles passing through the 1.27 cm (0.5 in.) sieve were collected for preparing reconstituted specimens. Figure 1 shows the particle distributions of the in-situ gravel materials and the reconstituted specimens. The in-situ gravel materials contain a large portion of particles in the size of coarse sand or larger. The curves CR25 and CR29 indicate the particle-size distribution of the two reconstituted specimens which were tested later at -3.9°C (25°F) and -1.7°C (29°F), respectively. The removal of particles larger than 1.27 cm (0.5 in.) in diameter was necessary due to the fact that large grains within the specimens caused premature failure under uniaxial loading. Sample preparation consisted of placing the -1.27 cm (-0.5 in.) particles in two 15.24-cm-diameter and 30.48-cm-height (6-in..diameter and 12-in.height) molds. The first layer of gravel in each mold was tamped 20 times with a standard Proctor 0165-232X/86/$03.50
hammer. The top two layers were then compacted 25 times each. After the molds were filled with gravel and compacted, they were placed in a sink and wetted from the top by allowing a small amount of water to drip through the samples for several hours. This saturation procedure provided an average moisture content of 10.1% for CR25 specimen and 8.9% for CR29 specimen. The moisture contents are in a range similar to that measured in the field (8.910.3%). Upon the completion of the saturation process, the specimens were frozen in a walk-in type cold room at the University of Alaska, Fairbanks. The top surface of each specimen was wrapped with an 80 W battery blanket and the top half of the gravel sample was insulated with fiberglass. On top of the battery blanket a layer of styrofoam was applied to reduce heat loss through the top end of the sample. The first sample was then placed in the cold-room and the refrigeration unit was turned on. When the cold-room temperature stabilized at -3.9°C (25°F), the battery blanket was also turned on in order to allow any entrapped air to escape through the warmer top end during the gradual freezing of the sample. After 3 hours the blanket was turned off and the entire sample was permitted to freeze. The second sample was frozen at a cold-room temperature o f - 1 . 7 ° C (29°F), and the battery blanket was turned on for 6 hours. The samples were frozen within a period of one or two days. Before removing the frozen specimens from the molds, a thin layer of silt slurry was sprayed on the top end of each sample to obtain a smooth end surface and avoid local stress concentrations where large sand and gravel grains might contact the loading
© 1986 ElsevierScience Publishers B.V.
102 U.S. STANDARD
SIEVE SIZE 12
4
30
70
200
100 i
80
o.. 0
, N - S i . U GRAVE . CR29
z to
S.1 .~
ECONS"TO'EO GRAVEL
60 i
a. w ~
40
a.
20
.1
10 GRAIN
.O1
.001
SIZE, INCHES
Fig. 1. Particle size analyses of in-situ gravel and reconstituted gravel sample.
plates. After the slurry froze, the specimen was removed from the mold and placed under a loading frame for creep strength testing. The creep strength test was performed at a constant stress level of approximately 18% of the uniaxial compressive strength at the particular temperature (i.e. -3.9°C [25°F] and -1.7°C [29°F]). The load was applied to the specimen by means of a 44.5 kN (10000 lb) mechanical screw jack. The magnitude of the applied load was recorded with a 22.4 kN (50 000 lb) load cell during the creep test. The applied load was manually adjusted to the predetermined magnitude. During the tests, the applied loads slowly dissipated because of the deformation of the sample. Periodic adjustment of the applied loads were performed every quarter hour for the first hours and every two hours for the next six. The intervals of adjustment were increased to 8 hours for the next one and a half days and were maintained at 12 hours for the rest of the test. Average axial deformation of the test specimen was measured using two dial gauges with a 0.0265 mm (0.001 in.) sensitivity mounted on the loading frame. Deformation and applied load were checked frequently for a period of one week until cracks occurred around top or bottom end of the specimen.
TEST RESULTS
Data from the laboratory test are shown in Fig. 2. The strain-time curve CR25 illustrates the measurements of an ice-poor frozen gravel sample at -3.9°C (25°F) under an average applied stress of 1.46 MPa (212 psi). The initial axial strain was 7.0X10 -a which occurred almost instantaneously. As noted from the diagram, specimen CR25 exhibits a secondary creep behavior approximately 36 hours after loading. The later portion of the creep curve can be approximated by a straight line having a slope of 6.0 X 10 -s h -1 . The intercept, pseudoinstantaneous creep as defined by Andersland et al. (1978), was 10 × 10 -3. Curve CR29 summarizes the creep strain and time relationship under a stress of 1.05 MPa (153 psi) and test temperature o f - 1 . 7 ° C (29°F). The curvilinear trend, again, indicates that deformation of the specimen reached the secondary creep stage. The intercept of the straight line portion of the curve gives a pseudoinstantaneous creep of 3.1 × 10 -2, which is higher than the observed initial strain of 4.2 X 10 -a. The secondary creep rate was estimated to be 8.1 × 10 -s h -1. In order to evaluate the possible erratic responses due to testing procedure error, the measurements of
103
And, the theoretical creep rate can be presented as follows:
-'0--CR25 ---e---CR29
•(c) = C' t b' ep
~ ............
where C is a constant, t is the test time, ~c is an arbitrarily selected normalizing creep rate (~:10 -s min-1), o is the uniaxial normal stress applied, Oc is the material creep modulus (= {(~c/b)b/Co )l/n), n, b are temperature dependent material constants, C', b ' are temperature dependent material constants, Co equals C at o = 1. Evaluation of b and C for a given frozen soil can be made if the experimental creep strain and time data linearize on a plot of log e vs. log t. Figure 4 shows the creep strain vs. time curves for CR25 and CR29 plotted on log-log coordinates. By intercepting the linear line with Y-axis at time = 1 h, the constant C was calculated. The C value for sample CR25 was 7.3 X 10 -3 and was 7.9 × 10 -3 for CR29. Slopes of the lines represent the temperature-dependent material constant b. The coefficient b was estimated to be 0.0793 for sample CR25 and was 0.3457 for CR29. The strain rate vs. time relationships for the samples were also analyzed by fitting the creep strain rates with a linear trend in a log-log scale (Fig. 5). The constants C' and b' were estimated directly from the curves. The b' values calculated from the slopes of the time-strain rate curves were --0.3401 and -0.6136 for specimens CR25 and CR29, respectively. The coefficient C' was 2.5 X 10 -4 for CR25 and was 2.9 X 10 -3 for CR29. It is interesting to note from the analysis that the strain rate was also apparently a temperature dependent factor. The imposed primary creep strain and creep strain rate of frozen gravel by a 1.46 MPa (212 psi) stress at -3.9°C (25°F) can be described as follows:
,..,/
~ O 30
*/
x
/i
Z
/
/
rr
I-- 20 (n
/
/
..-~-,~-.~ ~o,,o I
I
I
I
!
I
25
50
75
100
125
150
TIME, h Fig. 2. Creep strain distributions o f testing specimens.
creep strain of the frozen gravel specimens were plotted in conjunction with the creep data of frozen Ottawa sand collected by Sayles (1968). Figure 3 shows the comparison between two types of materials. Although the testing conditions varied slightly, both sets of curves indicate a similar trend. The primary creep of frozen soil under constant stress at constant temperature is dependent upon time duration and material type. The creep strain can be described by the creep law (Andersland et al., 1978): ep(C) = C t b
(1)
50 --
- - - SANO 40
?o ao
~////
~t
////
i ~
L1.O3 MPa,-0.6°C /'
GRAVEL
,: - 1.OSMP*, - t . 7 ° C
/
I //
" ' - / ///
~
(c) ep = 7.3 X 10 -a t °'°~a
/ / ///// ~
//
2o
(2)
(3)
and . . . 1.46 MPa, -3,9°C
~ ~ ~.
~(c) = 2.5 X I0 -4 f-o.34oI
(4)
10
o 0
I
I
I
I
I
I
25
50
75
100
125
150
175
TIME,h Fig. 3. C o m p a r i s o n o f creep responses b e t w e e n frozen gravel Ottawa sand (data o f f r o z e n sand: Sayles, 1968).
The primary creep strain and creep strain rate due to a 1.05 MPa 0 5 3 psi) of applied stress at -1.7°C (29°F): e(e) = 7.9 X 10 -a "t 0"34s7
and
F
and
(5)
104 +6 +
-O.- C R 2 5 • "~-+ C R 2 9
~..
£~)= 7.gx103t °`3457 /" /
2 ~ Z
"/'~"
p.
--~
~
CI~) = 73 . x I03t 0"0793
~
o
+,5:'
I 1(~1
I
I
I
1
I
10
I 10 2
h
TIME,
Fig. 4. Primary creep strain vs. testing time on log-log scale. +61 CR25 I~(¢) ==
•- e ' - "
2 . 9x11) 3 t " ° . e l a e
CR29
7
ui
~(~>= 2,5 xlO-4t - 03401
Z
~.
o
lb=
I 101
I 1
o~
I
~
I lO TIME,
I
I lO 2
h
Fig. 5. Primary creep strain rate vs. testing time on log-log scale.
~(pe) = 2.9 X 10 -3 t -0"6136
(6)
where e(pe) is the creep strain at a given temperature •(e) is the creep strain rate, and applied stress, and ep t is time (h).
ACKNOWLEDGEMENTS The authors wish to thank Mrs. Alice Baergen for her assistance in typing this manuscript. This work
was conducted with the Financial support from the Generic Center, U.S. Bureau o f Mines.
REFERENCES Andersland, D.B., Sayles, F.H. and Ladanyi, B. (1978). Mechanical properties of frozen ground. In Andersland and Anderson (ed), Geoteehnical Engineering for Cold Regions, McGraw-Hill Book Company, pp. 216-275. Sayles, F.H. (1968). Creep of frozen sand, U.S. Army CRREL Technical Report TR 190, Hanover, N.H.
101
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
Short Communication LABORATORY CREEP TESTS OF FROZEN GRAVELS Scott L. Huang and Robert C. Speck Department of Mining and Geological Engineering, University of Alaska-Fairbanks, Fairbanks, Alaska 99775-1190 (U.S.A.)
(Received February 25, 1986; accepted in revised form April 21, 1986)
As part of a continuing effort to develop a relationship between convergence of full-scale underground openings in permanently frozen gravel and laboratory creep strength tests of frozen gravels, two uniaxial creep tests of reconstituted gravel were conducted at the University of Alaska-Fairbanks. The authors here present a description and the results of those tests.
LABORATORYPROCEDURE The gravel materials for testing were sampled directly from the U.S. Army CRREL permafrost tunnel at Fox, Alaska. Before sieve analysis, these materials were oven dried at l l0°C (230°F) for 8 hours. Particles passing through the 1.27 cm (0.5 in.) sieve were collected for preparing reconstituted specimens. Figure 1 shows the particle distributions of the in-situ gravel materials and the reconstituted specimens. The in-situ gravel materials contain a large portion of particles in the size of coarse sand or larger. The curves CR25 and CR29 indicate the particle-size distribution of the two reconstituted specimens which were tested later at -3.9°C (25°F) and -1.7°C (29°F), respectively. The removal of particles larger than 1.27 cm (0.5 in.) in diameter was necessary due to the fact that large grains within the specimens caused premature failure under uniaxial loading. Sample preparation consisted of placing the -1.27 cm (-0.5 in.) particles in two 15.24-cm-diameter and 30.48-cm-height (6-in..diameter and 12-in.height) molds. The first layer of gravel in each mold was tamped 20 times with a standard Proctor 0165-232X/86/$03.50
hammer. The top two layers were then compacted 25 times each. After the molds were filled with gravel and compacted, they were placed in a sink and wetted from the top by allowing a small amount of water to drip through the samples for several hours. This saturation procedure provided an average moisture content of 10.1% for CR25 specimen and 8.9% for CR29 specimen. The moisture contents are in a range similar to that measured in the field (8.910.3%). Upon the completion of the saturation process, the specimens were frozen in a walk-in type cold room at the University of Alaska, Fairbanks. The top surface of each specimen was wrapped with an 80 W battery blanket and the top half of the gravel sample was insulated with fiberglass. On top of the battery blanket a layer of styrofoam was applied to reduce heat loss through the top end of the sample. The first sample was then placed in the cold-room and the refrigeration unit was turned on. When the cold-room temperature stabilized at -3.9°C (25°F), the battery blanket was also turned on in order to allow any entrapped air to escape through the warmer top end during the gradual freezing of the sample. After 3 hours the blanket was turned off and the entire sample was permitted to freeze. The second sample was frozen at a cold-room temperature o f - 1 . 7 ° C (29°F), and the battery blanket was turned on for 6 hours. The samples were frozen within a period of one or two days. Before removing the frozen specimens from the molds, a thin layer of silt slurry was sprayed on the top end of each sample to obtain a smooth end surface and avoid local stress concentrations where large sand and gravel grains might contact the loading
© 1986 ElsevierScience Publishers B.V.
102 U.S. STANDARD
SIEVE SIZE 12
4
30
70
200
100 i
80
o.. 0
, N - S i . U GRAVE . CR29
z to
S.1 .~
ECONS"TO'EO GRAVEL
60 i
a. w ~
40
a.
20
.1
10 GRAIN
.O1
.001
SIZE, INCHES
Fig. 1. Particle size analyses of in-situ gravel and reconstituted gravel sample.
plates. After the slurry froze, the specimen was removed from the mold and placed under a loading frame for creep strength testing. The creep strength test was performed at a constant stress level of approximately 18% of the uniaxial compressive strength at the particular temperature (i.e. -3.9°C [25°F] and -1.7°C [29°F]). The load was applied to the specimen by means of a 44.5 kN (10000 lb) mechanical screw jack. The magnitude of the applied load was recorded with a 22.4 kN (50 000 lb) load cell during the creep test. The applied load was manually adjusted to the predetermined magnitude. During the tests, the applied loads slowly dissipated because of the deformation of the sample. Periodic adjustment of the applied loads were performed every quarter hour for the first hours and every two hours for the next six. The intervals of adjustment were increased to 8 hours for the next one and a half days and were maintained at 12 hours for the rest of the test. Average axial deformation of the test specimen was measured using two dial gauges with a 0.0265 mm (0.001 in.) sensitivity mounted on the loading frame. Deformation and applied load were checked frequently for a period of one week until cracks occurred around top or bottom end of the specimen.
TEST RESULTS
Data from the laboratory test are shown in Fig. 2. The strain-time curve CR25 illustrates the measurements of an ice-poor frozen gravel sample at -3.9°C (25°F) under an average applied stress of 1.46 MPa (212 psi). The initial axial strain was 7.0X10 -a which occurred almost instantaneously. As noted from the diagram, specimen CR25 exhibits a secondary creep behavior approximately 36 hours after loading. The later portion of the creep curve can be approximated by a straight line having a slope of 6.0 X 10 -s h -1 . The intercept, pseudoinstantaneous creep as defined by Andersland et al. (1978), was 10 × 10 -3. Curve CR29 summarizes the creep strain and time relationship under a stress of 1.05 MPa (153 psi) and test temperature o f - 1 . 7 ° C (29°F). The curvilinear trend, again, indicates that deformation of the specimen reached the secondary creep stage. The intercept of the straight line portion of the curve gives a pseudoinstantaneous creep of 3.1 × 10 -2, which is higher than the observed initial strain of 4.2 X 10 -a. The secondary creep rate was estimated to be 8.1 × 10 -s h -1. In order to evaluate the possible erratic responses due to testing procedure error, the measurements of
103
And, the theoretical creep rate can be presented as follows:
-'0--CR25 ---e---CR29
•(c) = C' t b' ep
~ ............
where C is a constant, t is the test time, ~c is an arbitrarily selected normalizing creep rate (~:10 -s min-1), o is the uniaxial normal stress applied, Oc is the material creep modulus (= {(~c/b)b/Co )l/n), n, b are temperature dependent material constants, C', b ' are temperature dependent material constants, Co equals C at o = 1. Evaluation of b and C for a given frozen soil can be made if the experimental creep strain and time data linearize on a plot of log e vs. log t. Figure 4 shows the creep strain vs. time curves for CR25 and CR29 plotted on log-log coordinates. By intercepting the linear line with Y-axis at time = 1 h, the constant C was calculated. The C value for sample CR25 was 7.3 X 10 -3 and was 7.9 × 10 -3 for CR29. Slopes of the lines represent the temperature-dependent material constant b. The coefficient b was estimated to be 0.0793 for sample CR25 and was 0.3457 for CR29. The strain rate vs. time relationships for the samples were also analyzed by fitting the creep strain rates with a linear trend in a log-log scale (Fig. 5). The constants C' and b' were estimated directly from the curves. The b' values calculated from the slopes of the time-strain rate curves were --0.3401 and -0.6136 for specimens CR25 and CR29, respectively. The coefficient C' was 2.5 X 10 -4 for CR25 and was 2.9 X 10 -3 for CR29. It is interesting to note from the analysis that the strain rate was also apparently a temperature dependent factor. The imposed primary creep strain and creep strain rate of frozen gravel by a 1.46 MPa (212 psi) stress at -3.9°C (25°F) can be described as follows:
,..,/
~ O 30
*/
x
/i
Z
/
/
rr
I-- 20 (n
/
/
..-~-,~-.~ ~o,,o I
I
I
I
!
I
25
50
75
100
125
150
TIME, h Fig. 2. Creep strain distributions o f testing specimens.
creep strain of the frozen gravel specimens were plotted in conjunction with the creep data of frozen Ottawa sand collected by Sayles (1968). Figure 3 shows the comparison between two types of materials. Although the testing conditions varied slightly, both sets of curves indicate a similar trend. The primary creep of frozen soil under constant stress at constant temperature is dependent upon time duration and material type. The creep strain can be described by the creep law (Andersland et al., 1978): ep(C) = C t b
(1)
50 --
- - - SANO 40
?o ao
~////
~t
////
i ~
L1.O3 MPa,-0.6°C /'
GRAVEL
,: - 1.OSMP*, - t . 7 ° C
/
I //
" ' - / ///
~
(c) ep = 7.3 X 10 -a t °'°~a
/ / ///// ~
//
2o
(2)
(3)
and . . . 1.46 MPa, -3,9°C
~ ~ ~.
~(c) = 2.5 X I0 -4 f-o.34oI
(4)
10
o 0
I
I
I
I
I
I
25
50
75
100
125
150
175
TIME,h Fig. 3. C o m p a r i s o n o f creep responses b e t w e e n frozen gravel Ottawa sand (data o f f r o z e n sand: Sayles, 1968).
The primary creep strain and creep strain rate due to a 1.05 MPa 0 5 3 psi) of applied stress at -1.7°C (29°F): e(e) = 7.9 X 10 -a "t 0"34s7
and
F
and
(5)
104 +6 +
-O.- C R 2 5 • "~-+ C R 2 9
~..
£~)= 7.gx103t °`3457 /" /
2 ~ Z
"/'~"
p.
--~
~
CI~) = 73 . x I03t 0"0793
~
o
+,5:'
I 1(~1
I
I
I
1
I
10
I 10 2
h
TIME,
Fig. 4. Primary creep strain vs. testing time on log-log scale. +61 CR25 I~(¢) ==
•- e ' - "
2 . 9x11) 3 t " ° . e l a e
CR29
7
ui
~(~>= 2,5 xlO-4t - 03401
Z
~.
o
lb=
I 101
I 1
o~
I
~
I lO TIME,
I
I lO 2
h
Fig. 5. Primary creep strain rate vs. testing time on log-log scale.
~(pe) = 2.9 X 10 -3 t -0"6136
(6)
where e(pe) is the creep strain at a given temperature •(e) is the creep strain rate, and applied stress, and ep t is time (h).
ACKNOWLEDGEMENTS The authors wish to thank Mrs. Alice Baergen for her assistance in typing this manuscript. This work
was conducted with the Financial support from the Generic Center, U.S. Bureau o f Mines.
REFERENCES Andersland, D.B., Sayles, F.H. and Ladanyi, B. (1978). Mechanical properties of frozen ground. In Andersland and Anderson (ed), Geoteehnical Engineering for Cold Regions, McGraw-Hill Book Company, pp. 216-275. Sayles, F.H. (1968). Creep of frozen sand, U.S. Army CRREL Technical Report TR 190, Hanover, N.H.