Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. 17, pp. 225 to 229 Pergamon Press Ltd 1980. Printed in Great Britain

Effect of Confining Pressure on the Fracture Behaviour of a Porous Rock T. N. GOWD* F. R U M M E L t

Triaxial compression tests were carried out on a porous sandstone from SW-Germany. The confining pressures ranged up to 200 MPa. Direct volu- metric strain measurements indicated that pre-peak microfracturing is a pre- cursory deformation process to the development of macroscopic shear faults in intact porous rock at low confining pressures. Post-peak dilation at low press- ures is due to fault dilation. At high pressures multiple shear fractures develop with progressively less dilation. Transition from brittle to ductile deformation takes place at a confining pressure of lO0 MPa. Ductile shear at high pressure occurs without any dilation, and leads to progressive compaction and homo- geneous shear throughout the rock specimen.

Applied to earthquake precursory phenomena this implies that dilatancy effects in low porosity fault zones may only exist at shallow depths. At greater depth compaction will dominate over dilation.

INTRODUCTION

A basic understanding of fracture phenomena is of cen- tral importance in rock mechanics, whether it is the aim to prevent collapse of rock engineering structures or to promote fracturing as in drilling, blasting, mining, or in hydraulic fracturing for oil and gas well stimulation, stress measurements or to create heat exchange surfaces for future hot dry rock geothermal energy exploitation. In addition, studies of fracture processes are urgently needed in the field of earthquake source physics for earthquake prediction and earthquake hazard reduc- tion research.

Due to its complexity a precise theoretical formula- tion of rock fracture is not possible, and may even be difficult for specific simple situations such as the propa- gation of tensile fractures induced by hydraulic fractur- ing. In this respect, controlled laboratory fracture ex- periments are still of great interest, particularly for cases where rock fracture occurs under compression such as assumed in earthquake focal regions. During the past decade numerous experimental studies have successfully contributed to this subject. They have demonstrated that fracture in rocks under compression consists of a sequence of fracture processes. Dilatancy is one facet within this sequence which characterizes the initiation and propagation of microfracturing which precedes the final stage macroscopic shear fracture de-

* National Geophysical Research Institute, Hyderabad--500 007, India.

I" Institut fiir Geophysik, Ruhr-University, 4630 Boehum, West Germany.

velopment. Although dilatancy in crystalline rock has attracted considerable attention [e.g. 1,2,3,4], little effort has been spent in studying dilatancy in porous sedimentary rocks [5,6,7,8]. Further, rock dilatancy has been mostly investigated in the brittle field at press- ures much lower than those required to cause brittle to ductile transition. Whether or not dilatancy exists in rocks at high pressures where deformation is ductile, is essential knowledge for the formulation of earthquake source models [e.g. 9], the search for earthquake pre- cursors [4,10] and earthquake prediction research.

From this point of view, fracture experiments were carried out on a low strength rock which could be readily subjected to pressures under which transition from brittle to ductile deformation occurs. The rock selected was a medium grain-sized Buntsandstone from SW-Germany with subangular to round quartz grains bedded within a clayey matrix. Its initial porosity was 15~o, the initial permeability was 50/~ darcy.

EXPERIMENTAL TECHNIQUE

The tests were conducted on cylindrical rock speci- mens 6 cm long and 3 cm in dia. Axial compressive stress, trx, was applied by a closed-loop electro- hydraulic servo-controlled loading system [e.g. 6] using a constant displacement rate of the axial loading piston (10 mm per hr). Axial strain of the specimen, Ex, was calculated from piston displacement during compres- sion. Confining pressure tra was applied to the speci- mens by a 2 kbar capacity triaxial fluid pressure vessel and was carefully maintained constant throughout each

225

226 T.N. Gowd and F. Rummel

Initiot Compensating Pressure

J =============================================================================== ::::::::::::::::::::::::::

Displacement Tronsducer ~ ~

To Reguloting Volve

Fig. 1. Pressure compensating unit to measure radial expansion of the rock specimen in the pressure vessel. Confining pressure aa is held constant by a regulating valve. Resulting piston displacement is measured by an inductive displacement

transducer.

test, Since the diameter of the axial loading piston within the pressure vessel was equal to the specimen diameter, axial piston advancement and axial specimen shortening during axial compression have no effect on the initially applied fluid pressure within the vessel (neglecting the small effect caused by radial elastic expansion of the hardened steel piston due to its axial compression). Thus, any fluid pressure increase in the vessel is due only to radial expansion of the rock speci- men, which may consist of both elastic expansion due to axial compression as well as expansion due to micro- fracture development. Thus, the fluid volume dV to be extracted from the pressure vessel to keep the con- fining pressure constant during the test is a measure of the radial volumetric expansion of the specimen, dV ~ 2Vodr/ro, where Vo is the initial volume, r0 the initial radius and dr the mean increase in radius of the rock specimen. Therefore, the total volumetric strain 0 of the rock can be determined by measuring the axial strain ~ and the radial expansion dV:

O ~ e t +dV/Vo

i /(~3 : 200 NPQ 600, /

• ~ - ~ ~o

LLI fJP'~--'---'--- 90 LU o: 1 ¢ . " . ~ 80 p_

' °

,~ / / l , ~ ' ~ - - ' - - 3o

1 ~ ' - - ~ " ~° ~×~ ~ T ~ 0 0 . (b)

0 1 2 3 t. 5 6.10-" AXIAL STRAIN £1

(o)

Fig. 2. (a) Axial stress versus axial strain curves (at vs El) of Bunt- sandstone at constant confining pressures a3 up to 200 MPa. (b) Defi- nition of yield strength ~r peak strength or,, and residual strength at.

dV was measured by a pressure compensating unit (Fig. 1) which permitted the controlled extraction of pressure fluid from the vessel in order to maintain the initially applied confining pressure, 0 3 . The unit essen- tially consists of a servo-controUed hydraulic cylinder (fluid pressure control), where dV is given by the dis- placement of its piston. The piston displacement was accurately monitored by an inductive displacement transducer. All experimental variables were continu- ously plotted during each test.

EXPERIMENTAL RESULTS

The complete axial stress versus axial strain curves (crL vs e l )of the rock at constant confining pressures up to 200 MPa are presented in Fig. 2. The rock deforms linearly and elastically at axial stresses below a critical value, trl < try. The value of try, which is called the yield strength in the following, is dependent on the confining pressure, a3. Further compression leads to inelastic deformation. At low confining pressures, tr3 < 90 MPa, the curves show a defined peak strength, am, and a gradual strength decrease in the so-called post-failure region until final deformation occurs at about constant axial stress trr, referred to as the residual strength. As revealed by visual analysis, inelastic deformation of the rock in this case consisted of brittle micro-fracturing during pre-peak deformation, the development of a macroscopic shear zone at decreasing strength and macroscopic shear at constant residual strength. At higher confining pressures, 0" 3 >/ 100MPa, the rock exhibits work-hardening without the development of macroscopic singular shear fractures. Multiple shear fractures develop at confining pressures between 100 and 130 MPa, and the rock exhibits prominent bulging only at a confining pressure of 200 MPa.

Axial stress versus volumetric strain curves (trl vs 0) of the rock under confining pressures up to 100 MPa are given in Fig. 3. The elastic deformation of the rock is characterized by the linear decrease of volumetric strain with increasing axial compression try. The onset of dilation occurs at trl = tr,, which therefore is called the dilatancy strength. In contrast to the yield strength,

Confining Pressure on the Fracture Behaviour of a Porous Rock 227

~o

~00 t rY / ~ 0" 3 = loo MPQ

l 90n / _

00t I 60&)'/ ~ 1 \

/ I

(b) 15.10 -3 10 5 0 -5 -10 -15.10 -3

I nc rease VOLUMETRIC STRAIN 0 Decrease

(o) Fig. 3. (a) Axial stress versus volumetric strain curves (a I vs 0) of Buntsandstonc at constant confining pressures Ga up to 100 MPa. (b) Definit ion of dilatancy strength 0", volumetric strain 0,, at 0",., volumetric strain 0, at 0-r. Pre-peak di lat ion:

0,, - 0~, post-peak di lat ion: 0r -- 0,,.

% (Fig. 2), the onset of dilation can easily be defined from the measurement of volumetric strain.

Dilation of the rock is significant at low confining pressures, aa < 10 MPa, and leads to a considerable permanent volume increase (0 ~ 1%) of the rock speci- mens compared to their initial volume. Most of this volume increase occurs in the post-failure region. It is caused by the development of macroscopic shear faults at decreasing strength and by the dilation of fault seg- ments during frictional sliding at about constant re- sidual strength. Pre-peak dilation is about 2.5%o and is due to brittle microfracturing of the rock matrix. At higher confining pressures dilation progressively de- creases and is zero at aa _> 100 MPa.

In order to particularly investigate the two stages of pre-peak microfracturing and the development of shear faults, the values of pre-peak dilation, 0 ~ - 0v, and post-peak dilation, 0 r - 0m, are plotted separately

15

Z

tY p . t/1

~10- W

|

• post-fai lure dilation Or Om o p r e - p e a k d i la t ion ( ~ - Or

', \x

wz ~s . \ .

~ ~ ~°--O--o X,~,~

50 CONFINING PRESSURE. MRa

Fig. 4. Pre-pcak dilation 0, - 0, and post-failure dilation 0~ - 0= as a function of confining pressure o"a-

against a 3 in Fig. 4. The plot shows that pre-peak dila- tion is about constant at confining pressures of up to 40 MP a and is negligible at higher pressures. Post-peak dilation drastically decreases in the low pressure range, a3 < 20 MPa, and is progressively inhibited at higher pressures. This demonstrates that pre-peak brittle microfracturing is a precursory deformation process to the development of macroscopic shear faults. Multiple shear faults which develop at intermediate pressures, 40 < a3 < 90, still exhibit dilation but are preceded by only minor microfracturing. The formation of shear fractures at higher confining pressures, o-a > 100 MPa, occurs without any dilation. Thus, transition from brittle fracturing to pure ductile shear deformation in the Buntsandstone tested takes place at a pressure of about 100 MP&

Similar conclusions may be derived from the strength data of the rock. Numerical values of the peak strength am, dilatancy strength av and the residual strength ar are listed in Table 1. Since at transition the differ-

TABLE 1. STRENGTH DATA OF BUNT- SANDSTONE (0" 3 confining pressure, 0". peak strength, a, dilatancy strength, a, residual strength, 0"y yield strength;

all data in MPa)

0"3 0-m 0-y O'v 0-r

0 60 48 -- 10 5 100 75 57 46

10 122 90 72 81 20 154 125 106 105 30 193 150 150 139 40 221 180 167 180 50 253 220 230 212 60 275 200 264 239 70 310 250 -- 272 80 323 260 -- 310 90 346 280 331 332

1 0 0 361 280 - - - -

130 - - 350 -- - - 150 - - 400 -- - - 200 -- 500 -- - -

LMWS 17/4~D

228 T.N. Gowd and F. Rummel

i

d

b I

I IX IX •

Ix Ix-~

I

I

O" m -O"v 2 \

• \ \ • . \

\

i i i i i i | i 9

50 I~ CONFINING PRESSURE.M~

Fig. 5. Stress drop (a,. - a,) and pre-peak dilation range (tr,, - a,) as a function of confining pressure o 3.

portion of the 0 vs al curve may be represented by

O= A + B o " 1

with

A = 2tr3(1 - 2v)/E

B = (1 - 2v)/E

where E is Young's modulus, and v is Poisson's ratio. With K = E/3(1 - 2v) we obtain

K = 1/3B.

Using Fig. 3 we then obtain 104 < K < 1.3 x 104 MPa, independent of the confining pressure applied to the specimens for a3 < 100 MPa. The individual data are included in Table 2.

ent strength values should be equal, the differences (0-,, - av) and (0-" - 0-,) are plotted in Fig. 5 as func- tions of the confining pressure. The plot again indicates that transition from brittle to ductile deformation in the rock occurs at 0 3 ,~ 100 MPa. The values of the stress- drops, (tr,, - 0",), diminish gradually with 0"3, while the values for (0",,- 0"0 significantly decrease at much lower pressures. Since (0",.- 0"0 corresponds to pre- peak dilation this again demonstrates that brittle crack- ing is suppressed during deformation at intermediate pressures where during post-peak deformation still dila- tant fault formation is active.

The experimental results may be described in terms of shear and ,nor~a.1. stresses by_the following empirical relations:

(a) Failure at peak strength 0",,: log z: = 2 + 0.55 log 0": for 50 < aa < 100 MPa or for 0": < 240 MPa

(b) Onset of dilation at 0"v:

log Zd = 10 + 0.73 aa for < 0" 3 50 MPa or 0-d < 100 MPa

Here, z:, ca, 0-: and 0-a are the shear and normal stresses at peak failure (f) and at the onset of dilation (d).

Finally, from the linear portion of the volumetric strain versus axial stress curve (Fig. 3) it is possible to determine the value of the bulk modulus K. The linear

TABLE 2. D I L A T A N C Y D A T A A N D B U L K

M O D U L U S K O F B U N T S A N D S T O N E (0v volu- metric strain at onset of dilation, 0,, volu- metric strain at am, 0, volumetric strain at

begin of fault shear)

a3 0v 0,1 0r K MPa % %0 % 104MPa

0 . . . .

5 - 1.7 0.5 16.5 1.28 10 - 2.0 0.5 10.2 1.30 20 - 3 . 2 - 0 . 8 2.7 1.26 30 - 4.7 - 2.4 2.4 1.06 40 - 4.7 - 1.9 2.3 1.26 50 - 4 . 7 - 7 . 0 - 5 . 3 1:04 60 - 8.4 - 7.4 - 6.0 1,05 90 - 10.4 -10 .3 - 1 0 . 0 1,05

CONCLUSIONS

Transition from brittle to ductile deformation in porous sandstone is characterized by an abrupt change from dilational behaviour at low pressures to compac- tion during inelastic axial strain at high pressures. This is in contrast to observations on Carrara marble with only 1% porosity where dilatancy persists well into the ductile field, but is comparable to results obtained for a sandstone with similar high pordsity [5]. Compaction during ductile deformation in sandstones presumably consists of a collapse of pore space and a subsequent readjustment of quartz grains into a denser packing which obviously explains the significant strain harden- ing effect. Compaction is not preceded by dilation and follows directly after linear elastic compression. Dila- tion in sandstones at lower pressures is certainly due to both fracturing along grain boundaries and microfrac- turing of grains as well as to relative movements of grains and their fragments, whereas intracrystalline plasticity may be neglected. During pre-peak dilation, fracturing dominates over frictional sliding, which mainly controls post-peak deformation and leads to macroscopic shear plane formation.

The experimental results may have various impli- cations to high porosity rock material such as myllo- nites in active fault zones. Earthquake precursory phenomena such as a decrease of seismic velocities may only be expected in such rock material at very shallow depths (0-3 "~ 100 MPa), while transition to ductile deformation inhibits dilatancy-induced precursors at greater depth. However, compaction of high porosity rock at greater depth should result in an increase of seismic velocities and also an increase of pore pressure if the rock permeabili, ty is small compared to the rate of compaction. The latter will cause a decrease of the effective normal stress acting on a potential fault plane and may thus lead to unstable sliding. Any significant build-up of pore-pressure in active fault zones therefore may be due to the presence of high porosity sedimen- tary rock at depth.

Acknowledgemeal~--The experimental work was carried out by T. N. Gowd as DAAD (German Academic Exchange Service) research fel-

Confining Pressure on the Fracture Behaviour of a Porous Rock 229

low at the Institute of Geophysics, Ruhr-University Bochum. The paper was written by F. Rummei during a visit to NGRI in Hydera- bad, India. The authors wish to thank DAAD and CSIR India for making the exchange .visits possible. Financial support of the experi- mental work was provided by the German Science Foundation (SFB 77, A.9).

Received 17 May 1979; in revised form 29 February 1980.

REFERENCES

1. Brace W. F., Paulding B. & Scholz C. H. Dilatancy in the fracture of crystalline rocks. J. geophys. Res. 71, 3939-3954 (1966).

2. Hadley K. Azimuthal variation of dilatancy. J. geophys. Res. 80, 4845--4850 (1975).

3. Rummel F., Alheid H. J. & Frohn C. Dilatancy and fracture

induced velocity changes in rock and their relation to frictional sliding PAGEOPH 116, 743-764 (1978).

4. Sobolev G., Spetzler H. & Salov B. Precursors to failure in rocks while undergoing anelastic deformation. J. geophys. Res. 83, 1775-1784 (1978).

5. Edmond J. M. & Paterson M. S. Volume changes during deformation of rocks at high pressure. Int. J. Rock. Mech. Min. Sci. 9, 161-182 (1972).

6. Rummel F. Experimentelle Untersuchungen zum Bruchvorgang in Gesteinen. Ber. Inst. Geophysik, Ruhr-Univ., Bochum, No. 4 (1975).

7. Zoback M. D. & Byerlee J. D. Permeability and effective stress. Bull. Am. Ass. Petrol. Geol. 59, 154-158 (1975).

8. Logan J. M. Brittle phenomen& Rev. Geophys. Space Phys. 17, 1121-1132 (1979).

9. Miachkin V., Brace W. F., Sobolev G. & Dieterich J. H. Two models for earthquake forerunners. PAGEOPH 113, 169-181 (1975).

10. Rummel F. Laboratory fracture mechanics related to earthquake source physics. A review. Chron. J.U.G.G. 131, 18-21 (1979).