Tectonophysics, 22 (1974) 311-334 o Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

THE INFLUENCE OF TEMPERATURE, STRAIN RATE AND INTER- STITIAL WATER IN THE EXPERIMENTAL DEFORMATION OF CALCITE ROCKS

ERNEST H. RUTTER Geology Department, Imperial College, London (Great Britain)

(Accepted for publication December 3, 1973)

ABSTRACT

Rutter, E.H., 1974. The influence of temperature, strain rate and interstitial water in the experimental deformation of calcite rocks. Tectonophysics, 22:311-334.

A series of experiments are described, which illustrate the effects of temperature, strain rate and the presence of pore water on the rheological behaviour of Carrara Marble and Solnhofen Limestone. All of the experiments were performed at an effective confin- ing pressure of 1.5 kbar.

The results of the experiments performed on dry samples are compared with previous- ly published data for Yule Marble. The rheological behaviour of all three rocks is broadly similar. Work hardening flow, with strength virtually independent of strain rate, occurs at temperatures below 4OO’C. At higher temperatures, strain rate and temperature depen- dent steady-state flow occurs.

It is shown that for Carrara Marble, these characteristics are unaffected by the pres- ence of pore water in the temperature range 20-500°C. At room temperature, pore water weakens Solnhofen Limestone, but although the interpretation of the experimental re- sults for this rock tested wet was complicated by the effects of elevated pore pressures produced by compaction, it is argued that water weakening is much less significant at higher temperatures.

From the experimental data, a method is proposed for estimating the probable strength of calcite rocks under geological conditions.

INTRODUCTION

The experiments described in this paper are a continuation of a series of tests on Solnhofen Limestone and Carrara Marble reported earlier (Rutter, 197213). In the latter article, the effects of temperature, confining pressure and the presence of interstitial water on the mechanical behaviour of these rocks deformed at a constant strain rate were described. This paper extends the previous work, and describes the effects of strain rate and temperature variations at a constant effective confining pressure.

The results of the experiments on dry samples of the two rock types are compared with previously published data obtained from experiments on dry Yule Marble (Heard and Raleigh, 1972). It is shown that all three rock types exhibit similar rheological characteristics, which reflect the fact that they are all calcite rocks, but also significant differences, which are attributable to

312

textural and microstructural differences. Geologists interested in making quantitative models to describe the mechanics of formation of structures involving calcite rocks will find this comparative treatment of value.

It is shown that in the temperature range studied, ZO-5OO”C, interstitial water can only affect the behaviour of the relatively coarse-grained Carrara Marble through the mechanical effects of the pressure it exertsThe much finer grained Solnhofen Limestone is weakened by the action of water at grain boundaries at low temperatures. The interpretation of the high- temperature data for this rock was complicated because high pore fluid pressures tended to be generated through pore compaction, but it is argued that at high temperatures the physico-chemical weakening effect of water at grain boundaries is very slight. The rate of change of strength with strain rate for both rock types is not systematically affected by the presence of water at grain boundaries over the range of laboratory strain rates.

APPARATUS AND CHOICE OF EXPERIMENTAL CONDITIONS

The experiments were performed in six units of a triaxial deformation apparatus which has already been described (Rutter, 1972b). Specimen preparation methods and experimental procedures were as outlined in the latter paper. For most of the experiments, samples 0.375 inch (0.95 cm) in diameter, and 0.75 inch (1.9 cm) long were used. For tests lasting more than two hours at 5OO”C, samples 0.25 inch (0.635 cm) in diameter and 0.5 inch (1.27 cm) long were employed. With these relatively strong calcite rocks, the forces supported by samples of the larger size produced creep of the internal force gauge column at 500” C during experiments of long duration. All of the experiments reported in this paper were performed in compression. Petro- graphic descriptions of the rock types used have been given in Rutter (1972b).

The full ranges of strain rate and temperature permitted by the apparatus were used for the experiments. Both rocks were tested at 2O”C, 2OO”C, 400” C and 500” C at strain rates ranging from 6 s 1U4 set-’ to 3 * 1U8 set-’ . In addition, experiments on Solnhofen Limestone were performed at 300°C and 380°C.

In nature, the effective normal stress components on an element of rock (the difference between pore fluid pressure and the normal stress transmitted from grain to grain in the rock) probably vary from about six tenths of the overburden pressure, through zero, to small values of effective tensile stress (Price, 1970; Price and Hancock, 1972). The former condition inhibits intergranular movements, thus permitting ductile flow by intracrystalline processes or pressure solution. The latter conditions favour either the forma- tion of through going fractures or cataclastic flow, but do not necessarily preclude intracrystalline processes or pressure solution. The experiments reported here were designed to explore behaviour towards one end of the effective pressure spectrum - a moderate compressive effective pressure such that macroscopically brittle behaviour would be suppressed.

The effective pressure chosen for these tests was 1.5 kbar. This is a conve- nient pressure for use with compression tests on this type of machine, and does not produce excessive force on the loading screw when the differential pressure for quite strong rocks at room temperature is added to it. An effective pressure of 1.5 kbar is sufficient to suppress cataclastic deformation in calcite rocks at and above 300°C but not at lower temperatures. It was shown by Rutter (197213) that the component of cataclasis which is charac- teristic of deformation at low temperatures produces pore space dilation which tends to reduce any pore fluid pressure, thereby increasing the effec- tive confining pressure and hence the strength of the rock (dilatancy harden- ing of Brace and Martin, 1968).

At 200°C in Solnhofen Limestone, pore dilation gives way to compaction., which tends to raise the pore pressure. In experiments designed to isolate the influence of pore fluids on mechanical behaviour due to action at grain boundaries, the influence of dilatancy or compaction on the magnitude of effective confining pressure must be minimised as far as possible. Thus most of the experiments on wet rock were run with the total confining pressure at, 1.65 kbar and the pore pressure at 0.15 kbar, a nominal pore pressure intended solely to keep the specimen wet. Further, compressed air was used to pressurise the pore water, so that the fluid contents of the pore pressure system would be highly compressible. For comparison, some of the wet tests were run with a total confining pressure of 3.0 kbar, X = 0.5 (where X is the ratio of the pore pressure to the total confining pressure), and also with a total confining pressure of 1.65 kbar, pore pressure = 0.15 kbar. In each of the latter two groups of experiments, the pore pressure system was liquid filled, so that the influence of compaction on pore pressure would be more marked than in the case of a gas backed pore fluid pressure system.

EXPERIMENTAL RESULTS

A standard stress/strain curve was obtained for each test performed. The force data of each run were corrected for the effects of pressure and temper- ature on the stiffness of the internal force gauge, the stiffness of the loading system, increase in cross-sectional area of the specimen with shortening (as- suming homogeneous deformation of the test piece without volume changes), and for the load supported by the annealed copper jacket.

Experiments on dry rock (Tables I and II)

From the stress/strain curves of Figs. 1, 2 and 3, and the synoptic dia- grams of Figs. 4 and 5, which show stress at 10% strain plotted against -log,, strain rate, the following points may be noted:

(1) At all temperatures, for both rocks, the general level of the stress/ strain curve is lowered as the strain rate is decreased, the effect being more pronounced at high temperatures.

(2) Steady-state flow is achieved at 500” C and at 400” C at low strain rates.

314

TABLE I

Results of experiments on dry Solnhofen Limestone

-_- --- --.- _.._ ___ _-.._.. --

Test Machine Temper- Strain rate Nr. ature

CC) (set-’ )

Differential stress (bars) ----.. .._ - -

5% 10% strain strain

128 1 20 3.0.10-4

123 2 20 4.3.10~’

319 2 20 5.5.10-5

125 2 20 3.0.10-6 315 2 20 5.9.10-7

115 1 200 2.7.10-4 27 1 200 2.1.10-5 30 1 200 2.1.10+ 32 1 200 1.9.10~” 31 3 200 2.1 .10-s

106 1 200 3.1.10-* 246 3 200 3.1 .lOP

22 1 200 1.9.10-6 120 3 200 3.0.10-6 124 3 200 3.0.10-7 129 3 200 4.3.10-s

26 2 200 3.o.1o-s 316 6 300 3.2.10-4

25 1 300 1.3.10~’ 34 I. 300 2.1 .1o-s

318 5 300 3.0.10-6

296 3 300 3.2.10-7

329 4 300 5.9.10-8 117 1 400 3.1 .lo-4

121 2 400 4.5.1o-s

323 6 400 3.2.16” 122 3 400 3.1 *1o-6 118 3 400 3.1.10-7

294 3 400 3.3‘100

307 6 400 4.0.16* 126 1 500 3.1 .10-4

349A 5 500 4.3.10-4

231A 3 500 4.2.10-5

230 3 500 1.6.10-” 354 5 500 1.3.1o-5 353 5 500 9.0.1d6 156 1 500 4.3.10-6 231 3 600 4.2.10-7

338 5 500 4.4.16’ 349 5 500 1.8.10-7 351 5 500 1.5.10-7

4325 4170 4170 4200 4050 3620 3520 3550 3580 3510 3470 3410 3450 3580 3350 3220 3400 3620 3520 3460 3480 3610

3300 3250 3200

3180 3080 2880 2770 2750 2870 - -

2870 2850 2900 2850 2500 2570 2000 1970

4700 4530 4450 4590 4400

4120 3930 3980 4050 3960 3860 3900 4000 4080 3820 3800 3900*’ 4100 3870 3860 3900 4000 3700 3610 3460 3500 3430 3200 2830 2820 3180

3300*2 3130 3030 2900 3030 2900*3 2600*4 2650 2250 2210

*1 *2 Extrapolated from 7% strain. *3 Extrapolated from 6.4% strain. *4 Extrapoiated from 9% strain.

Extrapolated from 11% strain.

315

TABLE II

Results of experiments on dry Carrara Marble

Machine

Nr.

Temper- ature

(OC)

122 6

13

17 24

132 28 25 11 10

131 128A

23 12

121 15

139 16

126 19

110 120

26 27

31 29

141

2 20 1 20 2 20 2 20 2 20 3 20 1 200 1 200 1 200 3 200 2 200 3 200 2 200 3 200 6 200 1 400 6 400 1 400 6 400 1 400 6 400 5 400 1 500 1 500 3 500

3 500 5 500

*I *2 Extrapolated from 9.1% strain. *3 Extrapolated from 8.5% strain.

Extrapolated from 7.6% strain.

Strain rate (set-’ )

5.7 .lo-4 2.5.10-’

4.4 .lOP 4.1.10-6 4.3.10-7

8.3.10-* 2.2.10-4 2.4.10-4 2.2.10-4 1.5.10-5 3.2.10-5 3.2.16’ 4.2.10-6 1.5.10-7 4.6.10-* 2.5.10-4 4.7.1o-s 2.5.16’ 3.1 .lOP 2.5.10-6 4.2.10-7 4.2.10-* 2.2.10-4 3.2.10-5 4.5.10-6 4.3.10-7 1.2.10-7

Differential stress (bars)

5% 10%

strain strain

3525 3795

3350 3870

3250 3750

3170 3750

3130 3700 2830 3210 2225 2900 2330 2970 2330 2970 2450 3200*’ 2410 3190 2600 3250 2340 2980 2880 3070 2275 2940 2350 2850 2050 2555 2050 2560 2090 2510 2005 2420 1950 2180 1730 1900** 1870 2160 1740 1910

1660 1780 1420 1420 1200 1200*3

(3) The general level of the stress / -log,, strain rate isotherms is higher for Solnhofen Limestone than for Carrara Marble. This is in accordance with the general tendency for fine-grained aggregates of a crystalline material to be stronger than coarser grained aggregates.

(4) The general temperature and strain rate characteristics of these rocks are closely similar to those described for Yule Marble by Heard (1963). Yule marble is weaker than Carrara marble (see Fig. 8).

Experiments on wet rock (Tables III and IV)

Figs. 1, 2 and 3 show stress/strain curves obtained at various strain rates

“

1 !

128 3.0 x10-b A 228 Mx10d 3.

B 31, 6.0X IO.5

c 310 5.9 x10-6

2. 0 312 5.9 x 10-7

I ): 3L6 3.0 I lo-6

20’% Dry 2tR wet 1.

A= 0

1

A 115 2.7X10-&

0 2 6 8 to I? 0 2 L 0 I to 12

s 7 RAIN tPERCEHT1

Fig. 1. StreseJrtrain curves for Solnhofen Lime&tone tested both wet and dry at 2O”C, 200” C and 300°C. Strain rates (set-’ ) are given with each curve.

326 6.1 x iC-‘

341 mxKl-5

330 34 x 10‘6

331 3.0 x 10‘7

303 3~0x10’6

k 20.1

2 I 6 8 10 x? 0 2 4 6 8 10 12

STRAIN (PERCENT)

Fig. 2. Stress/strain curves for Solnhofen Limestone tested both wet and dry at 400” C and 500°C. Strain rates (set-‘) are given with each curve.

and temperatures for Solnhofen Limestone and Carrara Marble deformed wet, with an effective confining pressure of 1.5 kbar in all cases. Stress at 10% strain is plotted against -log 1o strain rate in Figs. 5, 6 and 7 for wet Solnhofen Limestone and wet Carrara Marble, and compared with the corresponding data for the dry rocks.

In the case of Carrara Marble, it is evident from Fig. 5 and from the comparison of the stress/strain curves for the wet and dry rock that there is no significant weakening or decrease in the rate of work hardening on wetting. This behaviour is in strong contrast to what appears to be the case

0,

3.

2.

0,

t

2oooc Dry

IS 2.5x10”

Fig. 3.Stremletrain curves for Carmra llkbb tarred both wet and dry at ZO“C, 200” C, 400” C and BOO’C. Strain ratea (~6’ ) are pjven with each curve.

313

” 300%

. 400°C

A 500%

3 L 5 6 7 8 -log,,Strain rate (set-‘1

Fig. 4. Synoptic diagram for dry Solnhofen Limestone, showing stress supported at 10% strain against --log1 0 strain rate (set-’ ) at various temperatures. Dashed lines show trends in data. Solid lines are best fits by multiple regression to data points from experiments exhibiting the beginnings of steady-state flow. The regression uses the logarithmic form of eq. 1 with the exponential stress function.

. -. ‘e--;--a~--z

- A-“,

I

3 L 5 6 7 8 - loglo Strain rate (WC-‘)

Fig. 5. Synoptic diagram for dry and wet Carrara Marble (solid and open symbols respec- tively), showing stress supported at 10% total strain against -1ogr e strain rate (see-‘) at various temperatures. Dashed lines show trends in data. Solid lines are best fits by multi- ple regression to data points from experiments exhibiting the beginnings of steady-state flow. The regression uses the logarithmic form of eq. 1 with the exponential stress func- tion, and applies only to data for the dry rock.

TABLE III

Results of experiments on wet Solnhofen Limestone

_I.--___ .-...- --.-_- . ..-. ~~ -_ ~_..._.__ .._ _.____~. __-.-__.~~_-_ ____..____. _ Test Ma-

chine Nr.

228 2 20 3.0 *0.5 1.6.10-4 311 2 20 1.5 0 6.0.15~’ 310 2 25 1.5 0 5.9 .10-6 306 6 20 1.65 0.1 3.3 .10-7 312 2 20 1.5 0 5.9.10-7 346 6 20 1.5 0 3.0.10s 320 2 200 1.65 0.1 5.9-10-4 313 2 200 1.65 0.1 6.2.10-’ 314 2 200 1.65 0.1 6.2 *lo-6 317 2 200 1.65 0.1 5.9.10-7 337 2 200 1.65 0.1 7.0.10-s 344 6 305 1.65 0.1 3.1 .ld4 229 3 300 3.0 “0.5 4.3 .10-s 234 3 300 2.2 *0.32 4.o.1o-5 327 2 300 1.65 0.1 5.7 *lo-+ 235 3 300 3.0 0.5 1.9.10-s 335 2 300 1.65 0.1 3.5 -15-6 339 6 300 1.65 0.1 3.2.15-7 258 3 300 1.65 *0.1 5.5.10-s 345A 6 380 1.65 0.1 3.1 .ld4 321 2 380 1.65 0.1 5.7.10-4 322 2 380 1.65 0.1 5.7 .ld4 325 2 380 1.65 0.1 5.8*10-s 345 6 380 1.65 0.1 3.1 .10-6 324 2 380 1.65 0.1 5.8.18’ 326 6 400 1.65 0.1 6.1 .ld4 341 6 400 1.65 0.1 3.0.10-” 330 6 450 1.65 0.1 3.4 .lo-6 331 6 400 1.65 0.1 3.0.10-7 303 6 400 1.65 0.1 3.0.10-* 224 3 400 2.60 *0.6 1.6.1d4 174 2 400 3.0 *0.5 1.5 .1o-5 257 3 400 1.65 *0.1 7.6.1d6 225 3 400 2.90 *0.4 4.5.16” 232 3 400 2.68 *0.56 4.5 .lo-7 308A 5 500 1.65 0.1 4.4.10-4 309 5 500 1.65 0.1 3.0.10-4 348A 5 500 1.65 0.1 4.8.10-* 350A 5 500 1.65 0.1 4.3.10-5 334 5 500 1.65 0.1 2.6.10~’ 248 3 500 1.65 *0.1 3.3 *lo+ 343 5 550 1.65 0.1 4.5.10-s 259 3 500 1.65 *0.1 5.8.10-e 308 5 500 1.65 0.1 4.4.16? 348 5 500 1.65 0.1 4.8 .10-7 350 5 500 1.65 0.1 1.6.10-7

Temp.

t*C)

Confining X Pressure (kbar)

__.~___

Strai; rate

(set )

Differential stress (bars) ~-_-... __ .._..._._

5% 10% strain strain

-.-._l___

*I *z Extrapolated from 8.0% strain. *3 Extrapolated from 8.0% strain. *4 Extrapolated from 13.0% strain.

Extrapolated from 11.0% strain.

*s *s *l *

3850 3890 3820 3825 3710 3490 2930 2930 2830 2780 3000 3070 2950 3000 3500 2700 2575 2530 2100 -

3300 3300 3200 3020 2900 3230 2880 2520 2310 1870 2750 2950 2500 2270 2025

2760

-

2725 2240 2270 2150 1750 1820 2030

4135 4150 4240 4220 4150 3950 3175 3050 3070 3250 3690 3380 3570 3150 3960 3000 2980 2840 2600 3800 3780 3780 3630 3345** 3075 3580 3360 2770 2445 1900*2 2930 2850 2640 2270 2025 2550*3 3050 2900*4 275O*s 2950 2270e6 2570 2200*7 1750 1820 2220

-- -. -.._

Extrapolated from 11.3% strain. Extrapolated from 6.0% strain. Extrapolated from 7.5% strain. Liauid-backed nom oressure svstem used

321

TABLE IV

Results of experiments on wet Carrara Marble

Test Machine Nr.

Temper- ature

(OC)

-

117 5 20 142 5 20 123 2 20 124 2 20 116 2 20 138 3 20 129 6 200 125 3 200 130 6 200 127 3 200 140 2 200 111 5 400 119 5 400 114 6 400 118 5 400 112 6 400 137A 5 500 133 5 500 134 5 500 136 5 500 137 5 500

- *1 *2 Extrapolated from 5.2% strain. *3 Extrapolated from 8.3% strain.

Extrapolated from 8.5% strain.

Strain rate

(se<‘)

3.0.10-4 4.6 .lO-’

5.5.10-6

3.5.10-7 5.8.10-s 34.10+

2.9.10-4 3.1 .1o-5 2.9.10-6 2.1 .lo-7 3.5.10@ 2.7.10-4 3.o.1o-s 3.0.10-6 3.0.10-7 3.o.1o-s 4.0.10-4 3.0.10-4 3.1 .lo-s

Differential stress (bars, __-_

5% strain

3460 3270 3150

3060 3070 2790 2450

2260 2240 2205 2390 2130 2050 1950 1850 1680

1790 1630 1610 1550

10% strain

3760

3660 3680 3525

3650

3300 3060 2910 2900 3880*’ 2990 2770 2600 2275 2000 1880*? 2200 2200 1925 1825*s 1575

for Solnhofen Limestone. It may be argued that because of the low porosity (0.28%) and, presumably, low permeability of Carrara Marble, water did not surround all of the grain boundaries. However, it was shown by Rutter (197213) that at room temperature this rock obeys the law of effective stress, from which it may be argued that water was present around a significant proportion of the grain surfaces. In a later experiment, water was pumped into the pores of a sample of rock at 400°C until the pore water pressure was equal to the confining pressure. The sample was then retrieved, and it was noted that it could easily be disaggregated along every grain boundary. Thus it is almost certain that in the wet experiments described in this paper, all of the grain boundaries were wetted.

Compared with Carrara Marble, the presence of pore water produced complex effects in Solnhofen Limestone. These effects will be described in detail as they are interpreted in a later section.

322

- log,Strain rateisec-‘1

Fig. 6. Synoptic diagrams comparing rtreeo support.4 at 10% strain at various strain rates for dry (solid eymbole) and wet (open symboh) Solnbofen Limeatone at 2O”C, 200°C and 300” C. Dashed lines show trends in data.

DISCUSSION OF RESULTS

High- tempem ture data for dry rock

At temperatures at and above about half of the abeolute melting tempera- ture for short-term experiments, intracryatalhne flow is predominantly ther- mally activated, and is described (Dorn, 1967) by the equation of state:

i = A exp (--H/RZ’) f, (u) f2 (S) (1) where 6 is the strain rate at differential stress <I and absolute temperature T. A is a constant, R is the gas constant and H is the activation energy for flow. The function f2 (S) deecribee those structutrtl features of the material which influence strain rate. Steady4at.e flow at con&ant strain rate takes place at con&ant temperature, constrrnt s&e88 and con&&ant structure.

The initial period of work hardening (equivalent to transient creep) observed during high-temperature deformation of calcite rocks represents the initial structural modification, and this indude the genemtion of any preferred orientation of cry&a&tea. AccoPdirsg to the high temperature transient creep theory of Mott (19&l), the transient creep rate at a particular

323

LI ’ 1

3-

n

0

22. " v

‘Vo, 'v

360”~ and LOOOC A-<-_

\ -3

‘AA --p.,

\ v\-\e

\ \ \

21 \ v\ ' '0 A\ '0

\ '1

\ LOOT h=O.l ‘",

LOOOC AzO.1 & 0.5 q '\ O\

(liquid backed) ‘\ \

q \ \

380°C h.0.1 ‘\

,” I I

u 3 L 5 6 I 8

Ci -0. 5o0°c

m _ l . . JK

.- 3 . . . z

>

? --A.

a e,.,

- _% \

t _ .I. . . il ‘* % WA

.A. ‘1 D 0

c. h zO.1 0 --i-:2;, \

2- ‘A.\ . 0 A = 0.1 (liquid backed) \

DLY %

. 1.5 kb confining pressure

A 1.0 bar (unconfined 1 1

3 L 5 6 I 0 -log,, Strain rate (set-‘1

Fig. 7. Synoptic diagrams comparing stress supported at 10% strain at various strain rates for dry (solid symbols) and wet (open symbols) Solnhofen Limestone at 400” C and 500” C. Additional data points obtained at 380” C (wet) and 500” C (dry, unconfined) are shown for comparison. Dashed lines show trends in data. All of the tests on wet samples were performed with a compressed air-backed pore water pressure, unless otherwise indicated.

level of strain and the steady-state creep rate are related. It was shown by Misra and Murrell (1965) that the structural modifications necessary for steady state creep are complete by about 10% strain. It may be noted that eq. 1 is valid even during transient creep, provided that fi (S) is allowed to take the value appropriate to the particular level of strain.

The representation of the stress function, f 1 (a), by either:

fl (0) = B exp (Co) (2)

or: fl (u) = D u” (i3) where B, C, D and n are empirical constants, has been discussed by Heard and Raleigh (1972) with reference to Yule Marble. They showed that eq. 3 described flow by diffusion-controlled polygonisation at stress levels below about 800 bars, where it = 8. This “power law” has been found to describe polygonisation in various metals, rocks and ice, with n-values ranging from 2.5 to 8, at relatively low stress levels (brief review by Heard and Raleigh,

324

1972). The latter authors also point out that the “exponential law” (eq. 2) describes the stress-dependence of strain rate in the same temperature range at high stress levels.

Stress levels at 10% strain from the 400” C and 500” C stress/strain curves which show the beginnings of steady-state flow for dry Carrara Marble and Solnhofen Limestone were fitted to eq. 1 by multiple linear regression, using both the exponential and power functions of stress. For comparison, the same analysis was carried out on the data of Heard and Raleigh (1972) which covered a similar range of strain rate and temperature for Yule Marble 1 and T orientations. The results of the analyses are shown in Table V. By taking stress levels at 10% strain for these analyses, it was assumed that structure depends only on strain over limited ranges of stress and temperature. Experi- mental support for this assumption has been obtained by Rutter and Schmid (in preparation) from experiments on Solnhofen Limestone.

As will be seen from Table V, the exponential description of the stress- dependence on strain rate gives a marginally better fit than the power func- tion. Further, the high values of the stress exponent, n, argue against disloca- tion climb being the deformation rate controlling process. In contrast to this, there are remarkable similarities in the value of the slope, C, for all three rock types.

The data and the best-fit lines are shown graphically in Fig. 8 for all three rock types. By plotting -log,, d + H(l/T - l/773)/~ against differential stress, these data can all be referred to 500°C. For Yule Marble, the transi- tion to power law creep is clearly seen at about 800 bars differential stress. There is no such indication of curvature in the plots of Solnhofen Limestone or Carrara’Marble data, neither was there any evidence of polygonisation

TABLE V

MuItiple regression analyses

Solnhofen Carrara Limestone Marble

Yule &idle 1 cylinders

Yule h&&le T cylinders

Exponential

Lo& oA -0.12 5.77 7.84 6.97

*(kcal+mol&‘) 47.1 + 4.5 62.1 i: 5.8 62.0 + 3.8 56.6 + 2.6

‘(kbar-’ loglo(sec-’ )) 2.71 * 0.26 3.80 t 0.25 4.75 f 0.20 3.14 f 0.10

Power

Logi OD -0.28 7.28 11.08 9.60

H( kca! ~male”’ ) 44.9 F 5.3 57.0 + 9.5 56.7 I!z 10 53.8 f 7.0

n 16.6 + 1.9 15.8 + 1.8 10.0 f 1.2 9.2 + 0.8

Confidence limits at one standard deviation.

355

l Solnhofen limestone.LOOO& 500°C

o Solnhokn Ist..un!ax~al , SOO’C

. Carrara marble , LOO’& 500°C

Fig. 8. Synoptic diagram showing the available data for three calcite rocks tested dry. Al. points represent the steady-state or near steady-state flow stress measured at 10% strain, plotted against -log1 & + H( 1 /T - I /773)/R to refer to 500” C for easy comparison between rock types. The points for Yule Marble are replotted from Heard and Raleigh (1972). Solid lines represent best fits to the data points by multiple regression, using the logarithmic form of eq. 1 with the exponential stress function.

found in a limited microscopic study of deformed samples of these rocks. Linear arrays of etch pits were seen on lightly etched polished sections of Carrara Marble deformed at 400°C and 500°C. No evidence of significant recrystallisation and grain growth was found in either rock.

It is suggested that at differential stress levels above about 800 bars, a slope C in the range 3-4 kbar-” log, ,(sec-’ ) may be characteristic of the thermally activated deformation of calcite rocks by intracrystalline slip. The slope obtained for Solnhofen Limestone from triaxial tests is probably too low, because data from experiments performed under uniaxial (unconfined) conditions at strain rates approaching 109 set-l (points plotted on Fig. 8, from Rutter and Schmid, in preparation) set a lower limit for strength which would not be consistent with the triaxial data extrapolated using C = 2.71 kbar-‘log, o(secW’ ).

Attention is drawn to the broad similarity in the figures for activation energy for flow for all three calcite rocks (Table V). Although not demon- strated here, these figures are virtually independent of the level of strain at which the determination is made. The activation energy for flow of Soln- hofen Limestone (47.1 kcal*mole-” f is significantly lower than for the two marbles. This may be due to a relatively high concentration of point defects in the calcite of Solnhofen Limestone, perhaps resulting from grown-in monovalent or trivalent impurities. The activation energy for the formation of point defects would therefore not have to be supplied by thermal fluctua-

326

tions until a higher temperature was reached. For deformation whose rate is controlled predominantly by the motion of thermally produced point defects, the activation energy for flow would be the sum of the activation energies for the formation and motion of point defects. Thus 47.1 kcal- mole-’ may be the activation energy for the motion alone of point defects in calcite, provided that point defect motion is deformation rate controlling in these experiments.

Low-tempemture data for dry rock

At temperatures below 400°C there is only a slight reduction in the strength of these calcite rocks with variations in strain rate over a large range (Figs. 1, 2, 4 and 5). There is now a considerable amount of data available on behaviour in this regime, for example, Heard (1963) on Yule Marble; Serden- gecti and Boozer (1961) on Solnhofen Limestone; Boozer et al. (1963) on Indiana Limestone and Donath and Fruth (1971) on Beldens Marble and Solnhofen Limestone. With the possible exception of Indiana Limestone, extrapolation of data using either a best fit to observed data points, or by ~trapolation from high-tem~rat~e data (Heard, 1963) gives stress values at geological strain rates (of the order of lo-l4 see-’ , according to Heard, 1963) well in excess of 1.0 kbar, which is far higher than differential stresses likely to be encountered in the earth’s crust. Donath and Fruth (1971) have remarked on this point. From the results of earthquake studies, and from theoretical studies of the development of geologic structures, there is a broad consensus of opinion that differential stresses in tectonically active regions of the earth’s crust probably do not exceed 500 bars (Ambraseys, 1970; Brune, 1970; Wyss, 1970; Archambeau and Samnis, 1970; Healy et al., 1968; Price, 1970; Voight et al., 1969; De la Cruz and Raleigh, 1972). However, it is common in environments of low-grade metamorphism where calcite Eocks have been deformed, to find evidence of flow almost entirely by pressure solution (geometrically equivalent to flow by grain boundary diffusion, but at a relatively high rate) with no internal deformation of calcite crystals (Ramsay, 1967; Duney, 1972). It may be inferred that at low strain rates the laborato~-dete~in~ isotherms of stress against log strain rate, repre- senting deformation by a combination of cataclasis, twinning and work hardening intracrystalline slip, are intersected by pressure solution isotherms which carry the strength of the rock to low stress levels at a rapid rate.

Experiments on wet rock

In addition to the purely mechanical effects of pore fluid pressure, a polar fluid such as water adsorbed onto the grain surfaces produces a weakening of a polycrystalline solid. The effect is most significant under unconfined conditions. The frictional characteristics of brittle solids, which are responsi- ble for the increase in strength observed as confining pressure is increased, are unaffected by wetting {Colback and Wiid, 1966; Rutter, 1972b}. H.

327

Swolfs (personal communication, 1972) has also shown that ionic complexes dissolved in the pore fluid can further enhance such effects, which may be termed Rehbinder effects (Rehbinder and Lichtman, 1957).

Discussing these effects for rocks, Boozer et al. (1963) and Colback and Wiid (1965) have appealed to the lowering of grain surface energy as funda- mental to the mechanism of weakening. However, Westwood et al. (1967, 1968) and Westwood and Goldheim (1968) have suggested that charged point defects interacting with dislocations largely determine the mobility of dislocations during the plastic deformation of ionic crystals, and that the adsorbance of a polar fluid onto the crystal surface causes an alteration of the electron band structure associated with point and line defects, thereby modifying their interactive behaviour. They argue that this is not just a surface effect, like the alteration of the surface energy of the crystal, but one which penetrates up to 10 pm into the crystal. If this is correct, then the mechanical properties of the entire volume of a rock like Solnhofen Lime- stone (grain size = 10 pm) would be expected to be modified.

Whatever the explanation, it would be expected that the effect would diminish with increasing grain size in proportion to the grain surface area per unit volume of rock (specific grain surface area). This parameter is about 20 times greater for Solnhofen Limestone than for Carrara Marble (grain size = 200 pm). The room temperature experimental data for the two rocks are qu~itatively consistent with this suggestion. Figs. 1 and 6 show that the strength and work hardening rate of Solnhofen Limestone are lowered by wetting by an amount apparently independent of strain rate. At room temperature, the results are not complicated by pore compaction raising the pore fluid pressure, because it was shown by Rutter (1972b) and by Edmon(1 and Paterson (1972) that at this temperature pore dilation occurs during deformation.

It is reasonable to suppose that the magnitude of Rehbinder effects might be related to the concen~ation of water at grain surfaces. If the water is present as a vapour phase, the concentration is proportional to the partial pressure. Water remains liquid, and hence its concentration remains effective- ly constant, at the pore pressure used for these experiments up to 35O”C, and at all pressures above 220 bars up to 374°C (the critical temperature). At higher temperatures at constant pressure the density of water begins to decrease. Thus in the experiments reported in the temperature range 350- 5OO”C, there is a potential effect of variations in the concentration of water at grain boundaries, the importance of which it is impossible to evaluate from these tests. Similarly, it is impossible to evaluate the influence of any structural changes in the water at elevated temperatures, which might affect the mechanism of Rehbinder effects.

There is no evidence to suggest that hydrolytic weakening, facilitating either brittle or ductile deformation, as described for quartz by Griggs (1967), Martin (1972) and Scholz (1972), plays any role in the deformation of wet calcite rocks. Indeed, it is not to be expected that hydrolytic weaken- ing will be important in the deformation of ionic crystals.

Discussion of results for wet Soln~lofen Limestone at elevated temperatures

The data obtained from experiments conducted on dry samples at 200°C show a slight reduction of strength as the strain rate is lowered, but the corresponding isotherm for wet rock is substantially lower (Fig. 6). Refer- ence to Fig. 1 shows that the stress/strain curves for the wet rock at high strain rates have high, sharp yield points and low rates of work hardening characteristic of cataclastic flow with considerable dilatancy(Edmond and Paterson, 1972). As the strain rate is lowered, the yield point is lowered and the rate of work hardening increases, so that the differential stress supported at 10% strain increases as the strain rate is lowered (see also Donath and Fruth, 1971; and Rutter, 1972a, who describe similar behaviour of the same rock type at room temperature at various confining pressures). At the lowest strain rate, despite a complex initial straining history, the stress at 10% strain and the rate of work hardening are little different from those of the dry rock. The phenomena observed at high strain rates are probably those of “compaction softening” (Rutter, 1972b), giving way at lower strain rates to behaviour more likely to be typical of deformation at a true effective confin- ing pressure of 1.5 kbar. Thus it may be inferred that at 200°C Rehbinder effects are less significant than at room temperature.

The data obtained at 300°C may be interpreted in the same way. Experi- ment 335 in Fig. 1 has a stress/strain curve which shows a sharp kink at the point where the rock pores became cut off from the pore pressure system and the pore pressure began to rise, probably to a point where the effective confining pressure remained constant due to a balance established between cataclasis, producing dilatancy, and intracrystalline plasticity, producing compaction, resulting in deformation at constant volume. After several attempts, one experiment was performed (327, Table III) in which the rock behaved as if it were dry. Thus the available evidence permits us to infer that at 3OO”C, when the pore fluid is still liquid water, Rehbinder effects may be absent.

At 400°C the isotherm for the dry rock (Fig. 4) begins to show a greater rate of reduction of strength with decreasing strain rate, and this also appears to apply to the data for the wet rock (Fig. 7). At this temperature, experi- ments were performed with X = 0.1 with a gas backed pore water pressure, and at X-values ranging from 0.1 to 0.5 with a liquid-backed system. The isotherm for wet tests performed with a gas-backed pore pressure system was at a higher stress level than, but of approximately the same slope as, that for the tests performed with the liquid-backed system. It is believed that the stress level difference is due to a higher degree of elevation of the pore pressure by compaction in the latter instance.

The extent to which the wet, h = 0.1 isotherm is displaced to the left of the dry curve is a maximum measure of the importance of Rehbinder effects at this temperature. Because of the uncertainty of the actual pore pressure during these tests, it is impossible to draw con~~ions about the influence of water concen~ation on the m~itude of Rehbinder effects.

329

Similar conclusions may be drawn from the data obtained at 500” C. Some of the slower tests were continued from about 9% strain at the highest strain rate available, to compare with a complete test performed at the highest strain rate (308A and 348A, Table III). The results of experiments perform- ed at 500°C (plotted in Fig. 7) lie in a broad band of differential stress, but the apparent rate of work hardening is greater for those samples which appeared to be relatively strong (Fig. 2), as would be expected if compaction was cutting off the greater part of the pore volume of the sample in some (the weaker) samples and not (by chance) in others. It therefore seems reasonable to suppose that the upper and lower envelopes of these data points represent behaviour with high and low effective confining pressures respectively. Thus, comparing the upper envelope with the curve for the dry rock (Fig. 7), Rehbinder effects at 500°C are of minimal significance. In Fig. 7 stresses at 10% strain are also plotted for experiments performed under unconfined conditions (Rutter and Schmid, in preparation). It will be seen that the lower envelope for the wet data compares with the isotherm for the dry, unconfined rock, in a similar way to the relationship between the isotherm for the dry, confined rock, and the upper envelope of the points for the wet rock.

It is apparent that the interpretation of the experimental results for wet Solnhofen Limestone deformed at elevated temperatures is complicated by compaction softening. However, why were no such effects observed for Carrara Marble when deformed wet at high temperatures? It is suggested that the higher initial porosity of Solnhofen Limestone (5%) permitted a larger pore volume reduction, and hence pore pressure increase, due to initial compaction under the combined influence of confining pressure and differ- ential stress than in the case of Carrara Marble (initial porosity = 0.3%). Far higher stresses are required to reduce the size of small pores than large ones. It should be noted that the importance of Rehbinder effects in Solnhofen Limestone at high temperatures was overestimated by Rutter (1972b) because the data presented in that paper included experiments in which the maximum degree of compaction softening was produced.

It has been argued from the experimental data that Rehbinder effects become insi~ifi~~t at high temperatures, even in a fine-grained limestone. This is perhaps not surprising, for if fluid adsorbed on grain boundaries acts on point defects to produce weakening, it might be expected that the in- creased mobility of point defects at elevated temperatures would eventually override Rehbinder effects. If this is true, it therefore follows from eq. 1 th:at the importance of Rehbinder effects should also decrease as strain rate is decreased at constant temperature.

It is clear from the experimental data obtained at the slowest strain rates used, that syntectonic pore compaction of the initially porous Solnhofen Limestone severely reduces the rock’s permeability, so that the elevated pore pressures generated can persist for long periods of time. The generation and maintenance of pore fluid pressures greater than the least principal stress must be postulated to explain the genesis of extension cracks commonly

330

observed in terrains of low grade metamorphic rocks (Secor, 1968; Price, 1970; Price and Hancock, 1972). Although the cataclastic mechanisms experimen~lly observed in the moderately low temperature deformation of limestones in compression seem to require stresses so high that they are geologically untenable, processes of fracture and cataclastic flow can be postulated, which are not thermally activated, and which might occur at very low differential stresses provided that one of the principal stresses is tensile. The latter condition can only be brought about at depth in the earth’s crust when the pore fluid pressure exceeds the least principal stress.

EXTRAPOLATION OF HIGH-TEMPERATURE DATA TO GEOLOGICAL STRAIN

RATES

It has been shown for Carrara Marb;ie, and argued from the experimental data for Solnhofen Limestone, that Rehbinder effects do not seriously modify the strength and rate of change of strength with strain rate for these rocks under moderate effective confining pressures and particularly at high temperatures. It is reasonable to suppose that the same will be true for other calcite rocks too, for example, for Yule Marble. Thus we may infer that predictions of the behaviour of the latter rock under geological conditions which were made by Heard and Raleigh (1972) would be equally valid if the rock had been tested wet.

When extrapolating the results of laboratory experiments to geological conditions, it is necessary to be able to extrapolate to large strains in addi- tion to low strain rates, and this can only be done with confidence in the steady-state flow regime. The samples of Soinhofen Limestone and Garrara Marble deformed at low temperatures exhibited considerable work harden- ing, so that estimates of the stress supported at a particular level of strain in the observed strain range are all that can be obtained from extrapolation to low strain rates. However, from a geologicat standpoint this is not a serious problem, for as was shown earlier, the mech~~sms of deformation observed in the low-temperature laboratory experiments at moderate effective confin- ing pressures are unlikely to obtain under geological conditions because of the high stress levels required to operate them.

The beginnings of steady-state flow were detected in the high temperature experiments in this series, and as has been shown, the behaviour of Carrara Marble and Solnhofen Limestone in this regime is very similar to Yule Marble under comparable conditions. However, Yule Marble has been tested by Heard and Raleigh (1972) over a much wider range of temperature than has yet been possible for Solnhofen Limestone and Carrara Marble, and a transition in the flow law to “power law” creep at differential stresses below 800 bars was detected (Fig. 8). Therefore it is reasonable to suppose that the presently available data for So~hofen Limestone and Carrara Marble do not by themselves provide an adequate basis for extrapolation to geological periods of time.

There are several instances where geologists have attempted to use presently

3ti1

available experimental data to make semi-quantitative models for the devel- opment of certain geologic structures, for example Hsii (1969), Price (1970), Kehle (1970), Rutter and Schmid (in preparation). Bearing in mind the close similarities in the mechanical behaviour of three calcite rocks already demon- strated, it is suggested that the following be used as an interim basis for mod-, elling the steady-state flow behaviour of calcite rocks:

(1) A slope of 3.5 kbar-’ log, ,,(sec-’ ) using the “exponential” creep law, giving way to a “power” creep law, where IZ = 8, at stresses below 800 bars.

(2) An activation energy for flow of 60 kcal*mole-’ above 500°C and 47 kcal*mole-’ at lower temperatures.

Values of the constant, A, in eq. 1 reflect the comparative ‘“strengths” of different calcite rocks, all other factors being constant. The data shown in Fig. 8 probably reflect the greater part of the strength range of most calcite rocks.

Heard and Raleigh (1972) have presented an argument from which it follows that Nabarro-Herring creep, characterised by a linear stress/strain- rate relationship, is unlikely to be of significance in calcite rocks over the greater part of the temperature range representing common metamorphic conditions.

Strictly, most of the experiments from which stress measured at 10% strain has been taken to represent the steady-state flow stress still exhibit some work h~dening at that level of strain. However, bearing in mind the u~ce~inties and necessary approximations with which geologists must contend in trying to make semi-quantitative models of geological processes, it is believed that the degree of work hardening in these high-temperature experiments will not seriously invalidate the proposed basis for extrapolation of laboratory data to geological periods of time.

Example of extrapolation based on the proposed model

Using the model suggested above, experimental data taken at a strain rate of 1c5 set-’ at 500°C have been graphically extrapolated to a strain rate of 3 l 10-l 4sec-i. The validity of the extrapolation depends on structure rem~ning constant. Stress levels of 600 bars, 180 bars and 94 bars were obtained for Solnhofen Limestone, Carrara Marble and Yule Marble, respec- tively.

Stress levels obtained for the two marbles are within the range considered likely to develop during orogenesis, but the 600 bars differential stress predicted for Solnhofen Limestone is a rather high stress to be supported, especially at 500°C. Wenk et al. (1973) have shown that syntectonic grain growth, resulting in a polygonal texture with grains of the order of 100 pm in diameter, begins in Solnhofen Limestone at 800-900°C at a strain rate of 1c4 see-’ . The increase in grain size is likely to result in considerable weak- ening of the rock, Assuming an activation energy of ca. 60 kcal* mole-’ for the process, grain growth will begin at about 350°C at a strain rate of 3 + lt.7’ 4sec-i. Thus above 35O”C, the extrapolation suggested above is likely to be invalidated through structural changes. However, at slightly

332

lower temperatures at such strain rates, too low for grain growth yet high enough for recovery creep, we must conclude that such creep in very fine grained limestones requires differential stresses too high compared with natural stress levels. Frequently observed evidence of deformation by pres- sure solution at the expense of intracrystalline processes in natural fine- grained limestones which have been subjected to conditions of low-grade metamorphism is consistent with these deductions made from the experi- mental data.

CONCLUSIONS

(1) Dry samples of three calcite rocks exhibit broadly similar stress/strain rate/temperature characteristics. At low temperatures deformation takes place by a combination of work hardening intracrystalline slip, and cataclasis depending on the confining pressure, and the strength is largely independent of strain rate. At 400°C at laboratory strain rates the transition to tempera- ture and strain rate dependent recovery creep begins. At stress levels above 800 bars, the flow stress is related to the strain rate by an exponential law, and at lower stress levels by a power law. These together can be used as a basis for extrapolation to geological conditions. It is concluded, on the basis of a consideration of stress levels required for intracrystalline flow, that a temperature in the region of 400°C over geological periods of time separates the low-temperature regime of deformation dominated by pressure solution from the high-temperature regime dominated by intracrystalline processes.

(2) The presence of water around Gain boundaries does not significantly affect the rheological behaviour of coarse-grained calcite rocks at any tem- perature in the range 20-500°C. At low temperatures water weakens the very fine grained Solnhofen Limestone, but the effect becomes progressively less important as the temperature is raised. The presence of water at grain boundaries probably does not affect the validity of the proposed basis for extrapolation of laboratory data on calcite rocks to geological strain rates.

Syntectonic compaction of initially porous limestones represents a power- ful method of elevating pore fluid pressures to high levels. This would assist in the formation of mineral&d extension fractures, such as are very com- mon in terrains of low-grade metamorphic rocks.

ACKNOWLEDGEMENTS

The apparatus used for these experiments was built with the aid of a generous grant from the Natural Environment Research Council. During part of the time that this work was carried out, the writer was the holder of an N.E.R.C. Research Studentship, under the supervision of Dr. N.J. Price.

The writer is grateful to Prof. J.G. Ramsay, Dr. N.J. Price and Dr. B.K. Atkinson for critical reading of the manuscript and for much helpful discus- sion. Some of the experiments were performed in collaboration with Dr. J.E. Matthews.

333

The advice and assistance of experimental officer Mr. R.F. Holloway in the construction of the apparatus and in the carrying out of the majority of the experiments is gratefully acknowledged.

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