Strain rate effect on the compressive strength of frozen sand

Engineering Geology, 13 (1979) 223--231

223

© Elsevier Scientific Publishing Company, Amsterdam - - Printed in The Netherlands

STRAIN RATE EFFECT ON THE COMPRESSIVE STRENGTH OF FROZEN SAND

T.H.W. BAKER

Division of Building Research, National Research Council of Canada, Ottawa (Canada) (Received June. 15, 1978)

ABSTRACT Baker, T.H.W., 1979. Strain rate effect on the compressive strength of frozen sand. Eng. Geol., 13: 223--231. Cylindrical specimens of fine Ottawa sand (A.S.T.M. designation C-109), compacted at the optimum moisture content and saturated before unidirectional freezing, have been tested in uniaxial compression at a cold room temperature of --5.5°C and strain rates between 10 -7 and 10 -2 s-1. The results agree with an extrapolation of data obtained by Sayles and Epanchin [1 ], but are much higher than those obtained by both Goughnour and Andersland [2] and Perkins and Ruedrich [3] at strain rates below 10 -s s-~. There is evidence that this may be due to variation in total moisture (ice) content, the conditions under which the specimens were frozen (closed system or an open system) and to the end effects at the platen--specimen interface.

INTRODUCTION

Several investigators have studied the strength and deformation behavior of naturally and artificiallyfrozen sands under various conditions of temperature, pressure and loading rate. In comparing the results,the author noted a change in the strain-rate dependence of the unconfined compressive strength at a strain rate of about 3 × 10 -s s-~ (Fig.l). This is of concern when trying to establish the long-term stress--strainbehavior required for the design of foundations in frozen soil by extrapolation from short-term tests. It should be recognized that Sayles and Epanchin's data [1] in Fig.1 extend to higher strain rates and that only part of the data are shown here. This paper gives observations of the strength and deformation behavior of artificiallyfrozen sand--ice specimens tested in the same range of strain rates as those presented in Fig.1. EXPERIMENTAL PROCEDURE

Sample preparation Fine Ottawa sand (A.S.T.M. designation C-109) was compacted in layers in a Plexigiass split mould at optimum moisture content (14% by dry weight)

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GOUGHNOUR AND ANDERSLAND

I21 AT -7.5, -12"C

(-9

10 5

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..........

PERKINS ANDRUEDRICH

I31 A T - 3 . 9 ' C

--.--

PERKINS ANDRUEDRICH

/3/ A T - 6 . 7 C

-

SAYLES

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--

M

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STRAIN

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RATE,

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Fig. 1. Strain rate d a t a for O t t a w a fine sand.

as determined by a standard Proctor compaction test. The mould was connected to a vacuum pump, after compaction, and evacuated and saturated with de-aired distilled water prior to freezing. Loose insulation was placed around the mould to ensure uniaxial freezing at a cold room temperature of --5.5°C. Following complete freezing, which took about three days, the sample was taken from the mould and machined and faced in a lathe to obtain a specimen 75 mm in diameter and 150 mm in length. Specimen characteristics are listed in Table I. A more detailed description of the procedures followed in the preparation of these specimens can be found in refs. [5] and [ 6 ] . During the freezing phase, four specimens (of a total o f 55) expanded in the mould by as much as 10 mm. No ice lenses were visible on the surface of these specimens, but their densities were slightly lower than those of the remainder. The specimen moulds were designed to allow water to be expelled from the bottom during uniaxial freezing. A heater wire used to prevent freezing o f expelled water malfunctioned in four cases so that these specimens were frozen in an essentially closed system. Their volume expansion was due to in-situ freezing of the pore water [ 7 ] .

Testing program All specimens were tested in compression using an Instrom universal testing machine (Model 1127, capacity 25,000 kg). The limiting strain rates in this program were due to the minimum speed of the testing machine and its

225

TABLE I Specimen characteristics No. of spec.

Mean avg.

Stand. dev.

Moisture content (%) Dry density (g/cc) Void ratio Moisture saturation

55

19.3

1.3

Ice saturation

55

1.68

0.03

55 55

0.577 0.97

0.024 0.03

55

1.07

0.03

maximum load capacity. Some tests were performed with the specimen immersed in a kerosene bath, others in air with the specimen covered b y a membrane to reduce sublimation. The kerosene bath did n o t significantly affect the results except in very long-term tests (approximately 10 -7 s-l). Some o f the long-term tests using the bath had to be discarded because the bath temperature increased as a result of heat given off b y the gears in the loadframe. This could have been overcome b y using a refrigerated bath. Four platen types were used to investigate the influence o f various end conditions (Fig.2). The disk and end-cap platens are most c o m m o n l y used in testing brittle materials [8]. Flexane compliant platens were developed [9, 10] to reduce the effects of rough specimen ends and to provide a uniform normal stress. Maraset compliant platens [11, 12] were designed to provide an elastic match between specimen and platen in order to reduce interface radial shear stresses. They were the only t y p e that did n o t affect the unconfined compressive strength of frozen sand specimens of different slenderness (length/diameter) ratio [ 1 1 ] . Load was measured b y a load transducer m o u n t e d between the specimen and the loadframe cross-head. Load was converted to stress b y dividing it b y the cross-sectional area o f the specimen. The maximum (failure) stress in each test was taken to be the unconfined compressive strength. Axial deformation o f the specimen was determined from displacement of the crosshead. Linear displacement transducers (DCDT) were m o u n t e d on some specimens tested with each platen type. By comparing cross-head m o v e m e n t and actual specimen deformation measured b y the transducers a correction factor was obtained for each platen type. This factor was used to obtain the specimen deformation from the cross-head displacement and to correct for deformation in the platens. O u t p u t from all transducers was recorded at regular time intervals on a data acquisition system. TEST RESULTS Fig.3 shows the relation o f unconfined compressive strength a m ~ to the strain rate ~ for all o f the tests performed for this study. Compressive strength

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ALUMINUM

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FLEXANE

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FLEXANE

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ALUMINUM

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76 mm COMPLIANT

PLATEN

Fig. 2. Platen types.

was found to be related to strain rate by: am~x = A ~ b

(1)

Values for the regression coefficients A and b, the correlation coefficient R and the number o f tests N, are given in Table II. Fig. 4 shows the relation of axial strain at failure el, to time to failure tf, for all o f the tests performed for this study. The axial failure strain was found to be related to the time to failure by: ef = C t ~

(2)

Values for the regression coefficients C and d, the correlation coefficient R and the number of tests N, are given in Table III. The effect on unconfined compressive strength of varying the moisture

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1 ALL PLATENS 2 HEAVEDSPECIMENS 3 SAYLESAND EPANCHIN111 (EXTRAPOLAED)

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STRA N RATE, $-1 Fig.3. Strain rate versus unconfined compressive strength.

(ice) c o n t e n t b e t w e e n a b o u t 17 and 24% is s h o w n in Fig.5 f o r a strain rate o f 10-s s-'. T h e m o i s t u r e c o n t e n t d e p e n d e n c e o f t h e u n c o n f i n e d compressive s t r e n g t h o f f r o z e n fine sand f o r t h e range 5 - - 1 0 0 % is s h o w n in Fig.6 f o r a strain r a t e o f 2.2 × 10 -6 s -~ and a t e m p e r a t u r e o f --12°C. DISCUSSION It m a y b e seen in Fig.3 t h a t t h e a u t h o r ' s d a t a are in g o o d a g r e e m e n t w i t h t h e e x t r a p o l a t i o n o f t h e d a t a f r o m Sayles and E p a n c h i n [ 1 ] f o r a similar t e m p e r a t u r e . Change in strain-rate d e p e n d e n c e r e p o r t e d b y o t h e r a u t h o r s ( F i g . l ) at a b o u t 3 × 10 -s s - ' d o e s n o t a p p e a r in t h e p r e s e n t d a t a . S t r e n g t h s h o w e d n o t e n d e n c y t o p l a t e a u f o r strain rates a b o v e 3 × 10 -s s - ' , as s h o w n TABLE II C o n s t a n t s for e q . l : a m • x ffi A~ b w h e r e a m • x is in kPa, ~ is in s - ' Platen

A

b

R

N

Aluminum disks Aluminum end caps Flexane compliant Maraset compliant All platens

28960

0.090

0.52

19

24099

0.051

0.72

14

29397

0.088

0.58

11

7577

---0.057

0.54

11

24796 27610

0.066 0.131

0.41 0.96

55

Heaved specimens

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OTTAWA SAND ASTM C-1~ TEMPERATURE -5.5°C

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Fig.4. T i m e to failure versus axial strain to failure.

by Perkins and Ruedrich [3] (Fig.l). Lower unconfined compressive strengths were found in samples t h a t had expanded during the freezing process. The expansion of pore water during freezing lowers the relative compaction o f the sand grains, thereby reducing interparticle friction of sand grains. The correlation coefficient determined for the combined data from all platen types is very low. As will be discussed, this is mainly due to the variation in total moisture c o n t e n t o f the specimens. The results indicate t h a t unconfined compressive strength increases uniformly with increasing strain rate in the range 10 -~ s-l--10 -2 s-1. TABLE III Constants for eq.2: ef = C t d where ef is in %, tf is in seconds Platen

C

d

R

N

Aluminum disks Aluminum end caps

1.203

0.134

0.48

19

0.933

0.176

0.88

14

Flexane compliant Maraset compliant All platens Heaved specimens

7.011

---0.030

0.04

11

1.402

0.132

0.87

11

1.143 0. 34

0.154 0.262

0.58

55

0.71

4

229 18000

~

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16000 O n

Z

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14000

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ST'RAIN RATE 10-$ s-1 -5.5°C

A

g

TEMPERATURE

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0

12000

o

V

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m

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OTTAWA SAND A STM C -109

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10000

V

8000 V

O

6000

V

PLATENS A ALUMINUM DISKS rl END CAPS o FLEXANE V MARASET

4000 Z

o

2000 I

0 17

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18 19 20 21 22 TOTAL MOISTURE

23

CONTENT,

24 %

Fig. 5. Total moisture content and unconfined compressive strength.

7000

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6000 5000

4000

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FINE

SAND

I

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STRAINRATE 2.2x 10-6 s -1 TEMPERATURE-12°C

0

3000

2000 I 0 Z

o

1000

0

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GOUGHNOUR ANDANDERSLAND 121

.~

o BAKER 1131

Z

I I0

I 20

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30

40

TOTAL

MOISTURE

50

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60

10

CONTENT,

%

I

80

Fig.6. Effect o f total moisture content on unconfined compressive strength.

I

90

| 100

230 Data presented in Fig.4 show that axial strain to failure increases as the time to failure increases in the range 1--104 s. Axial strain to failure was also d e p e n d e n t on moisture content. Specimens frozen without permitting water exudation had a lower strain to failure than expected. Neither the unconfined compressive strength nor the axial strain to failure appear to depend significantly on the t y p e o f platen. The modes of failure at low strain rates were different for each platen type. End-cap platens and disk platens induced bulging at mid-height on the specimen. Flexane compliant platens induced bulging only after the specimens came in contact with the ring. Maraset compliant platens did n o t produce any noticeable bulging. All the platens produced conjugate shear failure planes at high strain rates. In a previous study [ 1 1 ] , use of friction reducers was found to induce tensile splitting at low strength values. Considerable care was taken to control the total moisture content of the test specimens. Slight variation from sublimation influenced unconfined compressive strength (Fig.5). Strength of frozen soil is d e p e n d e n t on moisture content, as shown in Fig.6; strength increases until the soil is fully saturated with ice, and then decreases until the soil particles no longer influence it [ 1 3 ] . All specimens in this study were oversaturated with ice. CONCLUSIONS Observations show that unconfined compressive strength of saturated frozen sand at a temperature of --5.5°C increases uniformly with strain rate in the range 10 -7 s-~ to 10 -5 s-'. Axial strain to failure increases from 1 to 5% as the time to failure increases from 1 to 104 s. The strength results agree with an extrapolation of data obtained b y Sayles and Epanchin [ 1 ], b u t they are much higher than those reported by both Goughnour and Andersland [2] and Perkins and Ruedrich [3] at strain rates below 10 -s s-1. Low values reported b y other investigators may be related to the total moisture (ice) content o f the specimens, expansion of the specimen during freezing, or the use of inserted friction reducers at the specimen--platen interface. Reasons for the systematic change in strain rate dependence found by Perkins and Ruedrich [3] at 3 × 10 -s s-~ were not determined in the present study. Variation in the total moisture (ice) content influenced unconfined compressive strength. The results from several specimens tested at the same strain rate (10-s s-l) indicated that specimens with the highest moisture content had the lowest strength. This was typical of frozen sands slightly oversaturated with ice. Specimens that expanded during freezing showed a reduction in unconfined compressive strength and strain to failure. They had strength values similar to those reported b y Goughnour and Andersland [2] and Perkins and Ruedrich [3 ]. The four platen types investigated did not significantly affect the value o f the unconfined compressive strength or the strain to failure. The mode o f

231 failure at t h e l o w e r strain rates was d i f f e r e n t f o r each p l a t e n t y p e . Maraset c o m p l i a n t platens p r o d u c e d t h e m o s t u n i f o r m d e f o r m a t i o n , w i t h n o specim e n bulging. A previous investigation [11] has s h o w n t h a t these platens are m o s t useful in d i s t r i b u t i n g load u n i f o r m l y and in r e d u c i n g f r i c t i o n b e t w e e n p l a t e n and specimen. In tl~e same investigation, f r i c t i o n - r e d u c i n g inserts p r o d u c e d vertical tensile failures at m u c h l o w e r compressive strengths t h a n other platen types. ACKNOWLEDGEMENTS T h e a u t h o r wishes t o t h a n k Dr. V.R. P a r a m e s w a r a n , G. M o u l d and C. H u b b s , D . B . R . / N . R . C . , f o r t h e i r h e l p in carrying o u t these tests. This p a p e r is a c o n t r i b u t i o n f r o m t h e Division o f Building Research, N a t i o n a l Research Council o f Canada, and is published w i t h t h e permission o f t h e D i r e c t o r o f t h e Division. REFERENCES 1 Sayles, F.H. and Epanchin, V.N., 1966. Rate of Strain Compression Tests on Frozen Ottawa Sand and Ice. U.S. Army CRREL, Tech. Note, 54 pp. 2 Goughnour, R.R. and Andersland, O.B., 1968. Mechanical properties of a sand--ice system. A.S.C.E.J.S.M.F.E., 94(SM4): 923--950. 3 Perkins, T.K. and Ruedrich, R.A., 1973. The mechanical behaviour of synthetic permafrost. Soc. Petrol Eng. J.(Aug.): 211--220. 4 Sayles, F.H., 1974. Triaxial constant strain rate tests and triaxial creep tests on frozen Ottawa sand. U.S. Army CRREL, Tech. Rep. 253, 29 pp. 5 Baker, T.H.W., 1976. Preparation of artificially frozen sand specimens. N.R.C. of Canada, Div. Build. Res., N.R.C.C. 15349, 16 pp. 6 Baker, T.H.W., 1976. Transportation, preparation and storage of frozen soil samples for laboratory testing. A.S.T.M. Spec. Tech. Publ. No.599, pp.88--112. 7 McRoberts, E.C. and Morgenstern, N.R., 1975. Pore water expulsion during freezing. Can. Geotech. J., 12(1): 130--141. 8 Hawkes, I. and Mellor, M., 1970. Uniaxiai testing in rock mechanics laboratories. Eng. Geol., 4: 177--285. 9 Kartashov, Y.M. et al., 1970. Determination of the uniaxiai compressive strength of rocks. Soy. Min. Sci., No.3 (May--June): 339--341. 10 Haynes, F.D. and Mellor, M., 1976. Measuring the uniaxial compressive strength of ice. Syrup. Appl. Glaciol., Cambridge, 25 pp. 11 Baker, T.H.W., 1978. Effect of end conditions on the uniaxiai compressive strength of frozen sand. Proc., Int. Conf. Permafrost, 3rd, Edmonton, 1: 608--614. 12 Law, K.T., 1977. Design of a loading platen for testing ice and frozen soil. Can. Geotech. J., 14(2): 266--271. 13 Baker, T.H.W., 1976. Compressive Strength of Some Frozen Soils. M.Sc. Thesis, Dept. Civ. Eng., Queen's Univ., Kingston, Ontario, 245 pp.