A coupled hydromechanical system defined through rock mass classification schemes

*Correspondence to: J. Liu, Environmental Engineering Research Group, CSIRO Exploration & Mining, Private Bag,PO Wembely WA 6014, Australia.tFormerly at Department of Civil Engineering, The University of Western Australia, Nedlands, WA 6907.sResubmitted to International Journal for Numerical and Analytical Methods in Geomechanics by Jishan Liu in October1998.

Contract grant sponsor: Australian Research Council; contract grant number: A89600730

CCC 0363}9061/99/151945}16$17.50 Received 26 May 1998Copyright ( 1999 John Wiley & Sons, Ltd. Revised 5 February 1999

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS

Int. J. Numer. Anal. Meth. Geomech., 23, 1945}1960 (1999)

A COUPLED HYDROMECHANICAL SYSTEM DEFINEDTHROUGH ROCK MASS CLASSIFICATION SCHEMESs

J. LIU1,*,t, D. ELSWORTH2 AND B. H. BRADY3

1Environmental Engineering Research Group, CSIRO Exploration & Mining, Private Bag, PO Wembely WA 6014, Australia.2Department of Energy and Geo-Environmental Engineering, The Pennsylvania State University, University Park, PA

18602-5000, USA3Faculty of Engineering and Mathematical Sciences, The University of Western Australia, Nedlands, WA 6907, Australia

SUMMARY

Changes in the hydraulic conductivity "eld, resulting from the redistribution of stresses in fractured rockmasses, are di$cult to characterize due to complex nature of the coupled hydromechanical processes.A methodology is developed to predict the distributed hydraulic conductivity "eld based on the originalundisturbed parameters of hydraulic conductivity, Rock Mass Rating (RMR), Rock Quality Designation(RQD), and additionally the induced strains. The most obvious advantage of the methodology is that theserequired parameters are minimal and are readily available in practice. The incorporation of RMR and RQD,both of which have been applied to design in rock engineering for decades, enables the stress-dependenthydraulic conductivity "eld to be represented for a whole spectrum of rock masses. Knowledge of the RQD,together with the original hydraulic conductivity, is applied to determine the e!ective porosity for thefractured media. When RQD approaches zero, the rock mass is highly fractured, and fracture permeabilitywill be relatively high. When RQD approaches 100, the degree of fracturing is minimal, and secondaryporosity and secondary permeability will be low. These values bound the possible ranges in hydraulicbehaviour of the secondary porosity within the system. RMR may also be applied to determine the scalee!ect of elastic modulus. As RMR approaches 100, the &softening' e!ect of fractures is a minimum andresults in the smallest strain-induced change in the hydraulic conductivity because the induced strainis uniformly distributed between fractures and matrix. When RMR approaches zero, the laboratorymodulus must be reduced signi"cantly in order to represent the rock mass. This results in the largest possiblechange in the hydraulic conductivity because the induced strain is applied entirely to the fracture system.These values of RMR bound the possible ranges in mechanical behaviour of the system. The mechanicalsystem is coupled with the hydraulic system by two empirical parameters, RQD and RMR. Themethodology has been applied to a circular underground excavation and to qualitatively explainthe in situ experimental results of the macropermeability test in the drift at Stripa. Copyright ( 1999John Wiley & Sons, Ltd.

KEY WORDS: permeability; e!ective porosity: fractured media; strains; RMR; RQD

1. INTRODUCTION

A knowledge of changes in hydraulic conductivity due to the redistribution of stresses or strains iscrucially important in many engineering "elds. Changes in hydraulic conductivity, as a result ofthermoporomechanical coupling in a radioactive waste repository may impact the spread ofaqeuous and colloidal contaminants.1~3 Changes in hydraulic conductivity due to undergroundexcavation may a!ect groundwater in#ow into a tunnel, and create di$cult tunnelling conditionsand a slow rate of advance.4~6 Changes in hydraulic conductivity due to the redistribution ofstresses within a coal seam may a!ect the di!usion and #ow of methane, thus in#uencing the rateof emission of coal-bed methane into both underground mine workings and to the environmentas a greenhouse gas.2,7,8 Underground mining potentially induces large strains in the overlyingstrata that in turn may result in a strongly heterogeneous and anisotropic hydraulic conductivity"eld. This strain-dependent conductivity "eld is of special importance in evaluating the potentialimpact of underground mining on ground water resources.9~12 Consequently, the local groundwater system may be appreciably altered.13~16 Changes in hydraulic conductivity around a wellmay a!ect its productivity, with applications in the petroleum or mining industries. The impactsof this behaviour are clearly widespread.

Rock masses typically have a complex internal structure and stress state, both of which are, inlarge part, unknown and perhaps unknowable. This would appear to make solutions for thestress-dependent hydraulic conductivity "eld intractable. However, understanding of the control-ling processes has been improved by recent studies. The long-range transport of gas and waterthrough coal seams has been investigated2 and changes in porosity and permeability resultingfrom additional microfracturing in the yielded zone have been calculated based on a model ofyielding in metal sheets. The method in the study2 does not include the e!ects of pre-existingfractures on porosity and permeability. Changes in stress and corresponding changes in rockmass hydraulic conductivity have been analysed for a circular shaft using simpli"ed assumptionsregarding fracture geometry and initial stress state17 and the results subsequently applied toexplain the in situ experimental results of the macropermeability test at Stripa.1 The model in thestudy2 does not evaluate the stress-dependent e!ective porosity, which is important in evaluatingthe transport of contaminants, although it does incorporate the e!ects of pre-existing fractures onthe hydraulic conductivity. Several other studies document the interaction between deformationof overlying strata and its in#uence on ground water #ow.18~22 These studies have reported thee!ects of longwall mining on the post-mining hydraulic conductivity "eld and on the post-mininggroundwater #ow. This study represents a new methodology to predict the hydraulic conductiv-ity "eld based on the original undistributed parameters of hydraulic conductivity, Rock MassRating (RMR), Rock Quality Designation (RQD), and additionally the induced strains. Theimportance of this study is that the mechanical system is coupled with the hydraulic system bytwo empirical parameters, RQD and RMR, both of which are rock mass classi"cation parametersand have been applied to design in rock engineering for decades.

2. SCIENTIFIC RATIONALE

From the assumptions that rock blocks are functionally impermeable, and that #uid #owsdominantly within the fractures, the transmissive capacity of the fractured rock mass can becharacterized by the e!ective porosity, /

&. The e!ective porosity of a fractured porous medium is

de"ned as the volumetric fraction of connected pores per unit volume of the medium. It is

1946 J. LIU E¹ A¸.

Copyright ( 1999 John Wiley & Sons, Ltd. Int. J. Numer. Anal. Meth. Geomech., 23, 1945}1960 (1999)

apparent, based on the de"nition of e!ective porosity, that /&is a measure of the rock mass

hydraulic conductivity "eld. A theoretical relation between e!ective porosity and hydraulicconductivity for fractured rock masses is developed based on the equivalence theory, presented inthe following.

2.1. Equivalence theory

Assuming that a rock mass consists of n families of plane, parallel and constant width fractureswith di!erent orientations and density, Castillo23 theoretically proved that a fractured mediumwith two orthogonal sets of fractures may be replaced by an isotropic porous medium, and viceversa. This conclusion is also demonstrated numerically by Panda and Kulatilake.24 By applyingMonte Carlo methods, Snow25 concluded that two orthogonal sets of fractures with equalproperties have the anisotropic permeability of a prolate spheroid, with maximum parallel to theintersection of the sets twice that on an isotropic plane normal to both sets, and that there equalorthogonal sets are statistically isotropic. Assuming the dominant #uid #ow within the fracturescan be de"ned by an equivalent parallel plate model,26 Liu27 developed the relations between thehydraulic conductivities, K

x, K

y, and K

z, and the equivalent fracture apertures, b

x, b

y, and b

z, in

the x-, y- and z-directions as

Kx"

gb3y

12ks#

gb3z

12ks(1)

Ky"

gb3x

12ks#

gb3z

12ks(2)

Kz"

gb3x

12ks#

gb3y

12ks(3)

respectively. By solving equations (1)}(3), bx, b

y, and b

z, are obtained as

bx"C

6ks

g(K

y#K

z!K

x)D

1@3(4)

by"C

6ks

g(K

x#K

z!K

y)D

1@3(5)

bz"C

6ks

g(K

x#K

y!K

z)D

1@3(6)

respectively. In this, s is the equivalent fracture spacing, g is gravitational acceleration, and k isdynamic viscosity. The e!ective porosity is de"ned as

/&"

(bx#s) (b

y#s) (b

z#s)!s3

(bx#s) (b

y#s) (b

z#s)

(7)

Substituting equations (4)}(6) into (7) gives

/&"C

6kgs2

(Ky#K

z!K

x)D

1@3

C6kgs2

(Kx#K

z!K

y)D

1@3

C6kgs2

(Kx#K

y!K

z)D

1@3(8)

COUPLED HYDROMECHANICAL SYSTEM 1947


Figure 1. Relations between fracture spacing, s(m), and e!ective porosity, /&, under di!erent isotropic hydraulic

conductivities, K0

(m/s)

Assuming the original porous medium is isotropic, substituting Kx"K

y"K

z"K

0and

bx"b

y"b

z"b

0into equations (1)}(8) yields the equivalent hydraulic conductivity "eld, fracture

aperture and e!ective porosity for the isotropic case as

Kx"K

y"K

z"

gb30

6ks(9)

bx"b

y"b

z"A

6ks

gK

0B1@3

(10)

/&"3A

6kK0

gs2 B1@3

(11)

respectively. Equation (11) may be interpreted as a microscale model, assuming the material ismade of cubes and s is the side length of cubes. When s is small, it represents that the medium ismade of very "ne grains such as soil. When s is large, it represents that the medium is made of big&grains' or rock blocks. Therefore, soils have much higher intergranular e!ective porosity thanrock masses. This conclusion is consistent with observational data. As illustrated in Figure 1,e!ective porosity decreases as the value of s increases.

2.2. Strain-dependent hydraulic conductivity xeld

Fracture apertures, as shown in equation (4)}(6) or (10), may be changed due to the redistribu-tion of stresses. As a result of changes in fracture apertures, the originally isotropic hydraulicconductivity "eld may become highly anisotropic. It is assumed that fracture and matrixdeformations are both linear, and that deformations in normal closure or extension are the

1948 J. LIU E¹ A¸.


predominant conductivity-enhancing mode. Deformations are fully recoverable in this mode,with strains de"ned positive in extension. Conductivity changes in compression are typicallytruncated by a lower threshold de"ning the limits of conductivity reduction. Strains are par-titioned between fracture and matrix as de"ned by the modulus reduction ratio, R

.. Additionally,

fracture spacing, s, does not change due to the redistribution of stresses. Under these assumptions,the strain-dependent hydraulic conductivities, K

x, K

y, and K

z, are de"ned for the two-dimen-

sional case as [28]

Kx"K

0C1#2(1!R

.)

/&

*eyD

3(12)

Ky"K

0C1#2(1!R

.)

/&

*exD

3(13)

and for the three-dimensional case as

Kx"

K0

2 C1#3(1!R

.)

/&

*eyD

3#

K0

2 C1#3(1!R

.)

/&

*ezD

3(14)

Ky"

K0

2 C1#3(1!R

.)

/&

*exD

3#

K0

2 C1#3(1!R

.)

/&

*ezD

3(15)

Kz"

K0

2 C1#3(1!R

.)

/&

*exD

3#

K0

2 C1#3(1!R

.)

/&

*eyD .

3(16)

Equations (12)}(16) can be used to evaluate the strain-dependent hydraulic conductivities of theoriginal isotropic porous medium. As shown in equations (12)}(16), relations between hydraulicconductivities, K

x, K

y, and K

z, and induced strains, *e

x, *e

y, and *e

z, are primarily determined

by the three parameters: modulus reduction factor, R., e!ective porosity, /

&, and the original

hydraulic conductivity, K0. In the following analysis, the "rst two parameters are linked to the

rock mass classi"cation parameters, RMR and RQD respectively.

2.3. Determination of modulus reduction ratio, R.

The modulus reduction ratio, R.

is de"ned as the ratio of the elastic modulus of the rock massto that of the intact rock. Actually, it is a measure of scale e!ect which is de"ned as the variation oftest results with specimen sizes. It is apparent that for the application to "eld problems,laboratory values of deformation moduli should be reduced.29,30 According to a variety ofresults,29 R

.is de"ned as a function of RMR:

R."0)000028RMR2#0)009eRMR@22>82 (17)

where RMR is de"ned as rock mass rating.31 This rock mass classi"cation utilizes the followingsix parameters, all of which are measurable in the "eld and can also be obtained from boreholedata: 1. unaxial compressive strength of intact rock material; 2. rock quality designation (RQD);3. spacing of discontinuities; 4. condition of discontinuities; 5. groundwater conditions; and 6.orientation of discontinuities. The classi"cation scheme quanti"ed rock mass conditions accord-ing to a scale varying from 0 to 100, as illustrate in Figure 2. Highly fractured (crushed) rockapproaches an RMR value of zero while intact rock approaches 100. It is the empirical parameter,



Figure 2. Relation between modulus reduction factor R.

and RMR

RMR, that determines the hydraulic response of a fractured medium to induced deformations, aspresented in the following sections.

2.4. Determination of ewective porosity

As shown in equation (11), the e!ective porosity of rock masses is a function of hydraulicconductivity, K

0, and the equivalent fracture spacing, s. The hydraulic conductivity can be

determined in in situ hydraulic tests. The equivalent fracture spacing is determined by anempirical rock classi"cation index, RQD, de"ned as32,33

RQD"100n+i/1

Xi

¸

(18)

where n is the number of intact lengths greater than 10 cm, ¸ is the length of a drill hole orscanline, and X

iis the intact length. Based on the value of RQD, rock masses are classi"ed into

"ve categories, namely: excellent (90(RQD(100); very good (75(RQD(90); fair(50(RQD(75); poor (25(RQD(50); and very poor (0(RQD(25). Assuming that thefractures occur randomly in nature and that the number of fractures along a borehole follows thePoisson process so that the intact lengths have a negative exponential distribution, Priest andHudson34 derived the following relation:

RQD"100(1#0)1j)e~0>1j (19)

where j is the average number of fractures per meter. Substituting s"1/j into equation (19) gives

RQD"100A1#1

10sBe~1@10s (20)

1950 J. LIU E¹ A¸.


Figure 4. Relation between hydraulic conductivity, K0

(m/s), and e!ective porosity, /&, under di!erent values of RQD

Figure 3. Relation between RQD and equivalent fracture spacing, s(m)

where s is the equivalent fracture spacing. Equation (20) is graphically illustrated in Figure. 3. Thee!ective porosity can be obtained from Figure 4 if the hydraulic conductivity and the value ofRQD for a speci"c rock mass are known. The incorporation of RQD into the determination ofe!ective porosity makes it possible to link the e!ective porosity to empirical geotechnicalparameters that are readily available in practice. When RQD approaches zero, the rock mass is



Figure 5. Simpli"ed representation for a circular excavation made within a biaxial stressed medium. The far-"eld biaxialstresses are equal to p

1and p

2, respectively. q is the #uid pressure in the circular opening

highly fractured, and fracture permeability will be relatively high. When RQD approaches 100,the degree of fracturing is minimal, and secondary porosity and secondary permeability will below. These values bound the possible ranges in hydraulic behaviour of the secondary porositywithin the system.

3. ANALYTICAL SOLUTIONS FOR A CIRCULAR OPENING

The methodology, developed above, is applied to a two-dimensional case, as illustrated inFigure 5. The circular opening may represent a vertical well that pierces a petroleum reservoir, ora horizontal tunnel. p

1and p

2represent the far-"eld stresses that are de"ned positive in extension.

q represents the injection pressure in the circular opening.

3.1. Deformation analysis

The stress "eld resulting from a circular excavation within the biaxially stressed medium can bede"ned as35

pr"

p1#p

22 A1!

a2

r2 B#p1!p

22 A1#

3a4

r4!

4a2

r2 B cos 2h#a2

r2q (21)

ph"p1#p

22 A1#

a2

r2 B!p1!p

22 A1#

3a4

r4 B cos 2h!a2

r2q (22)

qrh"!

p1!p

22 A1!

3a4

r4#

2a2

r2 B sin 2h (23)

where pr, ph , and q

rh are stress components, p1

and p2

are far "eld stresses, de"ned positive inextension, q is injection pressure in the opening, a is radius of the opening, and r and h are polarco-ordinates. As shown in equations (12)}(16), post-excavation hydraulic conductivities arede"ned as a function of only normal strains, assuming deformations in normal closure orextension are the predominant hydraulic conductivity-enhancing model. Therefore, the equation

1952 J. LIU E¹ A¸.


of shear stress as shown in equation (23) is neglected in the following derivation. The excavation-induced stress "eld is de"ned as

*pr"p

r!p

r(a"0) (24)

*ph"ph!ph (a"0) (25)

where *prand *ph are excavation induced stresses. Substituting equations (21) and (22) into (24)

and (25) yields

*pr"!

(p1#p

2)a2

2r2#

(p1!p

2)a2 cos 2h

2r2 A3a2

r2!4B#

a2

r2q (26)

*ph"(p

1#p

2)a2

2r2!

3(p1!p

2)a4cos 2h

2r4!

a2

r2q. (27)

The constitutive equations are de"ned as

*er"

1!l2E A*p

r!

l1!l

*phB (28)

*eh"1!l2

E A*ph!l

1!l*p

rB (29)

*crh"

2(1#l)E

*qrh (30)

where *er, *eh and *c

rh are components of the induced strain, E is elastic modulus of the rockmass, and l is Poisson ratio. Substituting equations (26) and (27) into (28) and (29), excavation-induced strains are de"ned as

*er"

1!l2E C

3(p1!p

2)a4 cos 2h

2(1!l)r4!

(p1#p

2)a2

2(1!l)r2!

2(p1!p

2)a2 cos 2h

r2 D#(1#l)a2

Er2q (31)

*eh"1!l2

E C3(p

1!p

2)a4 cos 2h

2(1!l)r4!

(p1#p

2)a2

2(1!l)r2!

4l (p1!p

2)a2 cos 2h

(1!l)r2 D!(1#l)a2

Er2q (32)

where *erand *eh are components of the induced strain in the r and h-directions, respectively.

They are used to evaluate the post-excavation hydraulic conductivity "eld, as discussed in thefollowing.

3.2. Post-excavation conductivity analysis

Substituting equations (31) and (32) into (12) and (13), hydraulic conductivity ratios are de"nedas

Kr

K0

"G1#b1!l2

E C!3(p

1!p

2)a4 cos2h

2(1!l)r4#

(p1#p

2)a2

2(1!l)r2#

4l(p1!p

2)a2 cos2h

(1!l)r2 D!b(1#l)a2

Er2qH

3

(33)



KhK

0

"G1#b1!l2

E C3(p

1!p

2)a4 cos 2h

2(1!l)r4!

(p1#p

2)a2

2(1!l)r2!

2(p1!p

2)a2 cos 2h

r2 D#b(1#l)a2

Er2qH

3

(34)

where the parameters, b, is de"ned as

b"2(1!R

.)

/&

(35)

where the e!ective porosity, /&, and the modulus reduction factor, R

., are de"ned by equations

(11) and (17), respectively. Equations (33) and (34) are rewritten as

Kr

K0

"G1#bepC!3(a!1)a4 cos 2h

2r4#

(a#1)a2

2r2#

4l (a!1)a2 cos 2hr2 D!beq

a2

r2 H3

(36)

KhK

0

"G1#bepC#3(a!1)a4 cos 2h

2r4!

(a#1)a2

2r2!

2(a!1) (1!l)a2 cos 2hr2 D#beq

a2

r2 H3

(37)

where a, ep and eq are de"ned as

a"p1

p2

(38)

ep"(1#l)p

2E

(39)

eq"(1#l)q

E(40)

respectively. These relations are rigorously correct for h"03 and 903, as the fractures arehorizontal and vertical. Alternatively, the expressions are rigorously correct if the fracture systemis considered radial and concentric, and centered on the tunnel center. Although approximate inrepresenting the rock mass geometry, results are representative of behaviour around the tunnelperiphery.

Assuming b"1000, a"2, ep"!0)001, eq"!0)005, and l"0)25, equations (36) and (37) aregraphically illustrated in Figures 6 and 7. Conductivity changes in compression are truncated bya threshold of K

r/K

0"0)2 de"ning the limits of conductivity reduction, as shown in Figure 6. It is

clear that a &skin e!ect' exists in both the horizontal (h"03) and the vertical (h"903) directions.Furthermore, changes in the tangential hydraulic conductivity and the radial hydraulic conduct-ivity are more dramatic in the horizontal direction than in the vertical direction, as illustratedin Figure 7. This is because the horizontal far-"eld stress (p

1) is double the vertical far-"eld

stress (p2).

When a"1 and p1"p

2"p, equations (36) and (37) are simpli"ed as

Kr

K0

"G1#b(ep!eq)a2

r2 H3

(41)

KhK

0

"G1!b(ep!eq)a2

r2 H3

(42)

1954 J. LIU E¹ A¸.


Figure 6. Variation in hydraulic conductivity ratios of Kr/K

0with the distance away from the excavation centre, r. Where

a is the radium of a underground circular excavation, made in a biaxial stressed medium (p1/p

2"2)

Figure 7. Variation in hydraulic conductivity ratios of Kh/K0with direction. Where a is the radium of a underground

circular excavation, made in a biaxial stressed medium (p1/p

2"2), and r is the distance away from the excavation centre

Equations (41) and (42) are graphically shown in Figure 8 under di!erent conditions. Tangentialhydraulic conductivity, Kh , increases dramatically after the excavation while the radial hydraulicconductivity, K

r, decreases signi"cantly. Magnitudes of the tangential hydraulic conductivity

enhancement or the radial hydraulic conductivity degradation are regulated by the parameter, b,



Figure 8. Distribution of hydraulic conductivity ratios around a circular underground excavation made in a hydrostaticstressed medium. Negative numbers represent compressive strains

as illustrated in Figure 8(a) and (b), and by ep and eq, as illustrated in Figure 8(c) and (d). Fora particular loading condition, the magnitudes of change in hydraulic conductivity are regulatedby the parameter, b, which is a function of the e!ective porosity and the modulus reduction ratiofor the original rock mass. For a particular rock mass, the magnitudes of change in hydraulicconductivity are regulated by strains on the excavation surface, ep and eq, which are a function ofexternal loads and the elastic modulus of the rock mass.

4. APPLICATIONS

The Bu!er Mass Test was conducted in the Stripa mine over the period 1981}1985.1,17 This testwas designed to measure the permeability of a large volume of low-permeability fractured rock bymonitoring water #ow into a 33m long section of a tunnel. The radius of the tunnel is about2)5 m. Two major sets of fractures strike obliquely to the tunnel. The radius of the tunnel is about2)5 m. Two major sets of fractures strike obliquely to the tunnel axis, as illustrated in Figure 9(a).Fracture frequency measured in holes drilled from the tunnel was on average 4)5 joints/m ininclined holes and 2)9 joints/m in vertical holes.17 The initial stress "eld is anisotropic with a highhorizontal stress component and the conductivity of the virgin rock is about 10~10 m/s. Theexcavation of the test drift produced a dramatic increase in axial hydraulic conductivity ina narrow zone adjacent to the periphery of the drift. The conductivity increase is estimated to be

1956 J. LIU E¹ A¸.


Figure 9. Hypothetical stress-induced alteration of granitic fracture geometry. Notice expansion and generation ofsubhorizontal fractures and closure of steeply oriented fractures at crown and #oor

of the order of 1000 times. It is observed that the piezometric head is 40}90 m of water at abouta 2 m distance from the periphery of the drift and 80}130 m at 10 m distance. The hydraulicgradient is approximately 5. It was concluded from the pressure gradient that a &skin' of lowerradial permeability surrounds the drift. The skin e!ect determines that water #owing towards thedrift may be e!ectively discharged through the rock in the axial direction of the drift. It isbelieved1 that there are considerable e!ects of the excavation-induced stress changes on thewater-bearing capacity of pre-existing fractures which will be widened, compressed, extended orshortened depending on their orientation as well as on the prevailing stress "eld, as illustrated inFigure 9(b).

Assuming that 1. A statistically uniform aperture and spacing distribution exists prior toexcavation; 2. fracture spacing and continuity are not altered by the excavation; 3. stress changesmay be adequately calculated by elastic theory; and 4. water-bearing capacity of individualfractures are determined by the normal stress; the stress-dependent hydraulic conductivity "eld isevaluated by the method developed in this study. The experimental hydraulic conductivity for thevirgin rock is taken as K

0"10~10 m/s. The observed fracture spacings are averaged as

s"0)27 m. The far-"eld stress is taken as p1"20 MPa, and p

2"10 MPa. The elastic modulus

and Poisson ratio are assumed as 3)75]105 MPa and 0)25, respectively. The value of RMR istaken as 70. Substituting these numbers into equations (36) and (37) yields

Kr

K0

"A1#12)495a4

r4cos 2h!

8)33a2

r2!

8)33a2 cos 2hr2 B

3(43)

KhK

0

"A1!12)495a4

r4cos 2h!

8)33a2

r2#

12)495a2 cos 2hr2 B

3(44)

Equations (43) and (44) are graphically shown in Figure 10. Assuming h"03 and 903, thedistribution of hydraulic conductivity ratios around the circular tunnel is shown in Figure 10. It isapparent that these theoretical results are consistent with the experimental results reported forthe bu+er mass test at Stripa. Furthermore, both the tangential hydraulic conductivity andthe radial hydraulic conductivity doubles in the horizontal direction than in the verticaldirection. This is because the horizontal far-"eld stress (p

1) is twice higher than the vertical

far-"eld stress (p2).



Figure 10. Distribution of hydraulic conductivity ratios around a circular underground excavation made in a biaxialstressed medium (p

1"20 MPa, p

2"10 MPa). Where a is the radius of the excavation and r is the distance away from the

excavation centre

5. CONCLUSIONS

Changes in the hydraulic conductivity "eld can be quantitatively evaluated through the methodo-logy, developed in this study. The most obvious advantage of this methodology is that onlya minimal set of rock mass parameters, commonly available in practice, are required. Theseparameters include hydraulic conductivity, Rock Mass Rating (RMR), Rock Quality Designa-tion, (RQD), and additionally the induced strains. The incorporation of RMR and RQD, both ofwhich are valuable rock mass classi"cation parameters, enables the stress-dependent hydraulicconductivity "eld and excavation-induced porosity "elds to be represented for a whole spectrumof rock masses. When RQD approaches zero, the rock mass is highly fractured, and fracturepermeability will be relatively high. When RQD approaches 100, the degree of fracturing isminimal, and secondary porosity and secondary permeability will be low. These values bound thepossible ranges in hydraulic behaviour of the secondary porosity within the system. RMR isapplied to determine the scale e!ect of elastic modulus. When RMR approaches 100, thelaboratory modulus can be used to directly represent rock mass without any reduction. Thisresults in the smallest change in the hydraulic conductivity because the induced strain isuniformly distributed between fractures and matrix. When RMR approaches zero, the laboratorymodulus must be reduced signi"cantly in order to represent the rock mass. This results in thelargest possible change in the hydraulic conductivity because the induced strain is applied entirelyto the fracture system. These values of RMR bound the possible ranges in mechanical behaviourof the system. The mechanical system is coupled with the hydraulic system by two empiricalparameters, RQD and RMR.

The methodology has been applied to a circular underground excavation and to qualitativelyexplain the in situ experimental results of the macropermeability tests in the drift at Stripa. It isconcluded that the tangential hydraulic conductivity increases dramatically after the excavationwhile the radial hydraulic conductivity decreases signi"cantly. The magnitudes of the tangentialhydraulic conductivity enhancement or the radial hydraulic conductivity degradation are regu-lated both by parameters for the original undisturbed rock mass and by external loads such asfar-"eld stresses and injection pressures. For a particular loading condition, the magnitudes of

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change in hydraulic conductivity are regulated by the parameters for the undisturbed rock masssuch as RQD and RMR. For a particular rock mass, the magnitudes of change in hydraulicconductivity are regulated by strains induced around the excavation periphery, which aredetermined by external loads and the elastic modulus of the rock mass.

ACKNOWLEDGEMENTS

The work reported in this paper was supported by the Australian Research Council under LargeGrant No. A89600730. Two reviewers' constructive comments are gratefully acknowledged.

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A coupled hydromechanical system defined through rock mass classification schemes

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