The relations between mean rock stress and fluid flow in the crust

Ore Geology Reviews, 8 (1993) 23-37 23 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

The relations between mean rock stress and fluid flow in the crust: With reference to vein- and lode-style gold deposits

John Ridley Key Centre for Strategic Mineral Deposits, Department of Geology, The University of Western Australia, Nedlands, WA 6009,

Australia

(Received November 13, 1991; revised version accepted September 2, 1992)

ABSTRACT

Ridley, J., 1993. The relations between mean rock stress and fluid flow in the crust: With reference to vein- and lode-style gold deposits. In: D.I. Groves and J.M. Bennett (Editors), Structural Setting and Controls on Mineral Deposits. Ore Geol. Rev., 8: 23-37.

Fluid movement in the crust at the typical depths of formation of vein- and lode-style gold deposits will be dominated by upward flow. Focussing of upward flow into discrete channelways, as required to form gold deposits, is due to lateral gradients in fluid pressure. Fluid channelways should have lower fluid pressures than surrounding rock, if lateral gradients are induced by variations in permeability. This is, however, at variance with inferences from quartz-vein structures of high relative fluid pressures during the formation of gold deposits. Focussing into zones of low mean rock stress will, in contrast, be associated with high relative fluid pressures in the zone of focussed fluid flow. Variations in mean rock stress are a direct consequence of a regional deviatoric stress acting on an inhomogeneous rock sequence. Analysis of stress fields shows a wide variety of potential sites of low mean stress, dependent on the geometry of rock units, and on patterns of faults, fractures or shear zones. A model of fluid focussing in the crust due to variations in mean stress is thus consistent with the large variety of structural setting of vein- and lode-gold deposits observed in nature. Use of the model, through the technology of 'stress-mapping', has the potential to generate viable exploration targets.

Introduction

Considerations of mass balance of ore components emphasise the importance of focussing and channeling of hydrothermal fluid flow in the localisation of vein- and lode-style gold deposits. Large gold deposits require large volumes of hydrothermal fluid. This fluid needs to be 'collected', either from a volume of rock from which the gold has been leached, or from a magma undergoing crystallisation.

Indications of the size and nature of fluid focussing and channeling in the formation of

Correspondence to: J. Ridley, Key Centre for Strategic Mineral Deposits, Depar tment of Geology, The Univer- sity of Western Australia, Nedlands, WA 6009, Australia.

mesothermal deposits have been given by geo- chemical studies. The size of systems is indicated from isotopic and trace-element data which show that mineralising fluids have sam- pled source rocks other than the immediately adjacent country rocks, including the lower- crust (Kerrich et al., 1987; Golding et al., 1989; King and Kerrich, 1989). Large distances of fluid transport are also implied by recent ge- netic models which regard deposits across a wide range of metamorphic settings as having formed from a fluid of uniform source (Groves et al., 1992). That fluid-focussing systems at gold deposits are long-lasting, is indicated from radiogenic-isotope data and dating studies which show that many lode systems have been open with respect to episodic or continuous

0169-1368/93/$6.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.

24 J. RIDLEY

throughflow of fluids for tens or hundreds of million years (e.g., Browning et al., 1987 ).

Estimates of fluid volume involved in the formation of a deposit can be made from consideration of the solubility of ore and gangue components. Kerrich ( 1986 ) considers quartz precipitation, and estimates a minimum fluid volume for mineralisation in the entire Tim- mins (Porcupine) Camp in Canada to be 65 km 3. Similar estimates are obtained from consideration of the volume of source rock required to provide an ore component through leaching, and the potential volume of fluid derived from such a source rock. The calculations of Phillips et al. (1987) imply fluid flux through the Kalgoorlie lode system equivalent

' hannelway

/~fluid focussina

Fig. 1. Conceptual model of fluid focussing required to form a mesothermal gold deposit. The dimensions of source rock volume are the minimum required for formation of a large (hundreds of ton Au) deposit.

to that derivable from 100-300 km 3 of green- stones undergoing metamorphic dehydration reactions. These estimates of source rock and of fluid volumes indicate that the collection distances over which fluid is focussed into a large ore system are of the order of several kilometres (Fig. 1 ).

Most recent studies have argued for a role of faults or shear zones in controlling the move- m e n t of hydrothermal fluids associated with lode-type and vein-hosted gold deposits, though there is disagreement over whether the role of faults is dominantly passive (as high- permeability channelways), or active, involv- ing the creation of transient high permeability during episodes of fault movement (Phillips, 1972; Guha et al., 1983; Cox et al., 1986; Sib- son, 1987; Sibson et al., 1988). Little consideration has been given, however, to the requirements for fluid focussing on the scale required for the formation of a large gold deposit. The causes of, and constraints on, this scale of fluid focussing in the crust are considered in this paper.

An approach to understanding the controls on such large-scale fluid movement has been suggested by Oliver et al. (1990) and Holy- land (1990a,b,c), who investigate the control of stress fields on fluid flow, particularly variations in the mean stress. This paper expands on this suggestion. The relations between fluid flow, fluid pressure and stress fields are first examined. From these it is shown that fluid focussing is expected towards zones of low mean rock stress, and that the fluid-pressure regime

Dr. John Ridley obtained his Ph.D. from Edinburgh University in 1982. He has sub- sequently worked at ETH-Ziirich, and The University of Zimbabwe, and is currently a lecturer at the Key Centre for Strategic Mineral Deposits, The University of Western Australia, with major research interests in the structural and metamorphic setting of Ar- chean lode-gold deposits.

MEAN ROCK STRESS AND FLUID FLOW IN THE CRUST: VEIN- AND LODE-STYLE GOLD DEPOSITS 25

predicted in zones of low mean rock stress is consistent with important aspects of deposit structure. The distribution of mean stress in simplified rock geometries is discussed with reference to example deposits, mainly from the Yilgarn Block, Western Australia.

Fluid pressure and fluid flow in the crust

Summary o f fundamental relationships

The equations governing fluid flow in rock have been summarized by Baer (1972) and Dullien (1979). Fluid flow is driven by gradients in the hydraulic head (Hf), defined by:

ef H f = z + - - (1)

g P f

where: z is the height above an arbitrary datum, Pf fluid pressure, g gravitational acceler- ation, and 10f the average fluid density. Because it is the differences in head that drive fluid flow, the position of the datum is not important. The velocity of fluid flow, v, is governed by Darcy's law, expressed in scalar form for direction x, by:

k OPf v= (2a)

It Ox

where: k is permeability, It fluid viscosity. Equation 2a can be written in terms of hydraulic head as:

kgpf OHf v= (2b)

It Ox

Darcy's law equations determine the velocity and direction of fluid flow, and are fundamental to the discussion in this paper. Fluid viscosity can be considered approximately constant under crustal conditions. The controls on permeability and fluid pressure are discussed separately below.

Changes in fluid pressure, at constant volume of rock, will be related to the mass balance of fluid influx or outflow through the rock storage capacity. In the simplest form, for the case

of no fluid production or absorption and no externally imposed volume changes, the change in fluid pressure with time, t, can be related to the fluid pressure gradient through:

ffsp Oef OzPf k Ot - Ox 2 (3)

where ffs is the storage capacity per unit volume, defined as the volume of fluid injected into a unit volume of rock so as to produce unit change in fluid pressure. As the storage capacity is always positive, fluid influx into a volume of rock will cause increasing fluid pressure.

The ratio of fluid pressure to rock (lithostatic) pressure (P~) is measured using the pore- pressure factor 2 f, given by:

2f--~--~f (4)

Fluid pressure may be described as 'lithostatic' (2f~ 1.0), if controlled by rock pressure, or 'hydrostatic' (2f~0.4), if controlled by a hypothetical column of water. In a deviatoric stress field, the rock pressure can be considered to be the mean of the principal stresses [eL = (r= ~ (ff~ + a2 + 0"3 ) ], and will be referred to as the 'mean stress' in this paper. The mean stress at a depth, z, is given approximately by the overburden (#=p~gz, where p~ is the average rock density, and z the depth).

Controls on permeability

Permeability of crustal rocks is known to range over several orders of magnitude and be dominated by fractures at depths of more than a few kilometres (e.g., Brace, 1980). In the consideration of large-scale focussing of fluid flow, it is the bulk permeability of a body of rock that is important. Permeability associated with individual fractures, or anisotropic permeability due, for instance, to a preferen- tial orientation of fractures, may be important on a local scale, but it is probable that, on a scale of hundreds of metres to kilometres, all rock can be considered to be fractured,

26 J. RIDLEY

and permeability independent of local inhomogeneities.

Available data does not allow the definition of a 'characteristic' value of bulk permeability at the depths of formation of mesothermal gold deposits. In the context of this paper, however, the controls of fluid pressure on permeability are important. Permeability will be a function of effective mean stress, Pc: given to a first approximation by PI-Pf , that is, rock mean stress minus fluid pressure (Paterson, 1978; Ber- nabe, 1987; Fischer and Paterson, 1989). Available experimental data show a rapid increase of permeability in all rock types as effective mean stress is reduced. Fischer (1987) shows typically an increase in permeability of an order of magnitude on reduction of effective mean stress from 1.5 to 0.5 kbar. Walsh (1981 ), through fitting experimental data to theoretical models, derives a general law of the form:

k l / 3 ~ A - B l n P e (5)

where A and B are constants. Equation 5 suggests a dramatic effect on permeability as effective mean stress approaches zero.

Fluid pressure in the middle and lower crust

Fluid pressures at depth in the crust will be controlled by interrelations between a number of factors: ( 1 ) Fluid buoyancy - Fluids are me- chanically unstable at depth in the crust if fluid pressures are greater than 'hydrostatic': there will be a buoyancy force promoting upward movement . (2) Pore-space collapse - - Any pore space with an internal fluid pressure less than lithostatic pressure will tend to close up (densify) to equilibrate the pressure difference (Raj, 1982; Walder and Nur, 1984).(3) Fluid production and absorption in metamorphic reactions, or through magmatic processes. (4) Changing rock volume through deformation-induced dilatancy, metamorphic reactions, and thermal contraction or expansion.

Consideration of the relations between mean stress and permeability (Eq. 5 ) show that the combined effects of fluid buoyancy and pore- space collapse are likely to buffer fluid pressure towards an 'equilibrium' state, for which upward fluid loss is balanced by the rate of pore-space reduction. High effective pressures will be associated with low permeabilities and will cause rapid pore-space collapse, hence increasing fluid pressures. Low effective pressures will be associated with relatively high permeabilities, allowing rapid drainage of fluid, hence decreasing fluid pressures. The rate of pore-space reduction will be dependent on rock rheology, hence on temperature and the absolute pressure difference between pore fluid and rock. Raj ( 1982 ) defines a 'rock densification rate' analogous to strain rate. This analogy between pore-space collapse and ductile deformation allows estimation of the maximum sustainable effective pressure, and hence of the 'equilibrium' fluid pressure. Using the equations of Raj (1982) and the deformation mechanism maps for quartz of Rutter ( 1976 ), a rock densification rate of greater than 10- ~ 2 (a geologically rapid strain rate) is predicted for effective pressures of 200 bars at 400°C, and higher rates at higher effective pressures or temperatures. The effect of such a densification rate on fluid pressure through pore-space reduction is dependent on porosity and mean rock stress, but calculations for likely values of these parameters show that effective mean stresses of greater than about a hundred bars could not be maintained for periods of more than about a thousand years in rocks at middle-greenschist-facies temperatures or higher, and that 'equilibrium' values of pore pressure at these temperatures are likely to be 'slightly less' than lithostatic. This inference is consistent with a number of petrological lines of evidence that show that fluid pressures were close to lithostatic pressures during active low- and medium-grade metamorphism (see summar- ies by Etheridge et al., 1983; Wood and Walther, 1986).


Fluid flow in the middle and lower crust

The prediction of fluid pressure close to mean rock stress in the middle and lower crust suggests overall upward movement of fluid at these levels (c.f., Wood and Walther, 1986; Yardley, 1986). The buoyancy force on fluids at near-lithostatic pressures is expressed through the vertical hydraulic head gradient -dHf/Oz=(pl-pf)/pf. The development of fluid convection cells would be possible in a lithostatic fluid-pressure regime in 'cells' in which the fluid-pressure gradient is hydrostatic (Etheridge et al., 1983; Cox et al., 1991 ). These are, however, unlikely to develop in rocks in which pore-space collapse is rapid. In this paper it is assumed that fluid flow is per- vasively upwards at the depth of formation of lode-style gold deposits.

Focussing of upward-directed fluid flow

The prediction of pervasive upward flow under 'near-lithostatic' fluid pressures places

zone of focussed 1

f flow

~" \ "~" % hydraulic depth - - ~ head

/ t

x

Fig. 2. Schematic cross-section through a segment of the crust, showing variation of fluid pressure that would give rise to fluid focussing in a 'lithostatic' fluid pressure regime - - in which there is pervasive upward fluid movement. Focussing is through lateral gradients in hydraulic head at any depth. Fluid flow directions are shown by ar- rows. They are drawn assuming isotropic permeability and are, hence, perpendicular to contours of hydraulic head. The zone of relatively low, fluid pressure becomes a zone of fluid focussing.

different constraints on possible mechanisms of focussing of fluid flow than those operative in near-surface hydrothermal regimes (see, for example, Nesbitt, 1990). In a regime of pervasive upward flow, focussing will occur where lateral hydraulic-head gradients are superim- posed on the vertical hydraulic-head gradient, such that flow is both upward and laterally toward zones of lower fluid pressure (Fig. 2). In rock with isotropic permeability, fluid flux will be perpendicular to contours of hydraulic head. Possible causes of lateral variations in fluid pressure considered here are: lateral variations in permeability, and lateral variations in rock mean stress.

Variations in permeability Variations in permeability will affect fluid

pressures through the efficiency of upward drainage of fluid produced or present at depth (Fig. 3 ). A zone of relatively high permeability will be a zone of relatively low fluid pressure, if it forms an effectively continuous channelway allowing upward fluid drainage. Faults, fractures, and shear zones are possible sites of long-lasting high permeability. Studies of fluid flow in metamorphic terrains have

high permeability channelway

/ ~ / / / fluid pressure - Pf

I ~ \ fluid pressures i \ ~ \ \ \

/ / . . , / J / J / ~ ~=0.4 iJ\channelway"~ \

hydrostatic \,

Fig. 3. Fluid flow into a high permeability channelway, and schematic fluid-pressure - depth profiles for the channelway and surrounding rock. Fluid is focussed into the high-permeability channelway because it is a zone of lowered fluid pressure, as a result of more rapid upward drainage of fluid within it.

28 J. RIDLEY

shown that individual rock units may act as fluid channelways (Yardley et al., 1991 ). This may be indicating differences in permeability between lithologies (see Thompson and Con- nolly, 1990), or, alternatively, may reflect stress-field effects as discussed in the following section.

Variations in rock pressure Variations of mean stress are expected in an

inhomogeneous rock sequence in an imposed regional deviatoric stress field, due to stress- guide and stress-refraction effects (e.g., Esh- elby, 1957; Jaeger and Cook, 1979; Dewers and Ortoleva, 1989). Variations in mean stress may develop on all scales, corresponding to the scale of inhomogeneity. Variations on a kilometre scale will be related to the gross geometry of rock units and major fractures in an area. A site of low mean stress will be a dilatant site as, through the bulk compressibility, there will be a volume increase during deformation. Dila- tion may also be inelastic and involve porosity increase (cf., Fischer and Paterson, 1989 ) and hence a low mean-stress site may be a 'dilatant site' in the sense normally used in the mining literature, as a synonym for sites of 'opening'

zone of low mean stress

t

J ,I ]

]"

1.i depth

fluid pressure - Pr

~ \ fluid pressures

\\ \x \ ~ regional stress

hydrostatic ~,2 = "1.0

low mean stress

Fig. 4. Fluid flow into a zone of low, mean rock stress, and schematic fluid-pressure - depth profiles for within and outside the low mean-stress zone. If fluid pressures are buffered to 'slightly less' than lithostatic pressures, fluid pressures will be lower within the zone of low mean stress than in surrounding rock, and, hence, fluid will be focussed into it.

(cf., McKinstry, 1948, p 318). If fluid pressures are buffered close to lithostatic values (see discussion under 'Fluid pressures in the middle and lower crust'), then variations in mean stress at any depth will be mirrored by variations in fluid pressure (Fig. 4), and there will be a tendency for fluid flow toward zones of low mean stress.

Which fluid-focussing mechanism is applicable to lode-style gold deposits? If fluid-focussing results from variations in

permeability, then zones of high fluid flow will have lower fluid pressures and higher effective mean stress than surrounding rock (Fig. 3). However, extension veins indicative of near- lithostatic or supralithostatic fluid pressures are present throughout mesothermal gold systems

At any depth

a) initial

fluid flow PI

x- ) b) after finite fluid flow

i

low or negative effective pressure (Pe)

x--)

Fig. 5. Profiles of rock mean stress and fluid pressure at a specific depth across a low mean stress zone. The ' initial ' profile (a) would be that on imposit ion of variable mean stress (assumed instantaneous). After finite fluid flow into the zone of low mean stress, fluid pressure is increased in this zone, and reduced in surrounding rock (b), inducing low or negative effective mean stress in the zone of low mean rock stress.


(e.g., Phillips, 1972; Sibson et al., 1988). These veins are often restricted to the deposit and immediate surroundings, hence suggesting lower effective mean stress in the channelway than in surrounding rock. The association of extension veins and mineralisation implies, therefore, that variations in permeability are unlikely to be the major cause of fluid focussing in gold deposits.

The potential effects of variations in mean stress on fluid pressure can be seen by considering the relations between rock mean stress and fluid pressure (Fig. 5). Finite fluid flow down a fluid pressure gradient will cause increasing fluid pressures in the zone of initially lower pressure (Eq. 3), and decreasing fluid pressure where it was initially higher, hence changing 2f (Eq. 4). The low mean stress zone will become a zone of relatively low, potentially negative, effective mean stress (Fig. 5b ), but still maintain lower absolute fluid pressures lower than surrounding rock. If this lateral focussing through variations in mean rock stress operates in an overall vertical hydraulic- head gradient, through the relations between permeability and effective pressure (Eq. 5 ), a balance would be expected to develop between the focussing of fluid into a zone of low mean stress, and increased fluid flux upwards through the zone. Sites of low mean stress can, therefore, be simultaneously sites of fluid focussing and of low, effective mean stress. This is consistent with the low effective stresses and supralithostatic fluid pressures inferred at gold deposits.

Examples of sites of low mean stress

Possible low mean stress sites can be divided into those resulting predominantly from discontinuities (fractures, faults, shear zones), and those related to differences in the rheology of adjacent rock units.

Low mean stress associated with discontinuities

Stress fields around simple fractures have been analysed by Pollard and Segall (1987). Low mean stress is developed adjacent to fractures in tension, and at the termination of fractures along which there is a component of shear. The position of dilatant, low mean stress sites associated with irregularities along faults or with complex fault zones have been discussed by Sibson ( 1987 ) and Hodgson ( 1989 ), and include dilational jogs, releasing bends, tension gashes and Riedel shears. Hronsky et al. ( 1991 ) show that variations in orientation along a shear zone required to give significant variations in mean stress can be relatively sub- tle, potentially only a few degrees. The importance of fault intersections as preferentially mineralised sites has been recognised for a long time (e.g., McKinstry, 1948, p. 324), and is presumably related in many instances to dilation associated with compatibility problems where two active faults intersect (see Hodg- son, 1989).

Low mean stress associated with contrasting rheologies

Rigid bodies The stress field around circular or spherical

rigid bodies and boudins in an elastic deform- able matrix has been analysed by Strrmg~rd ( 1973 ). Figure 6 shows the broad geometrical features of the stress field. These are independent of the exact shape of the rigid body. If the matrix is homogeneous, low mean stress oc- curs adjacent to the faces of the rigid body that are perpendicular to the minimum principal stress (a3) - - the pressure - shadow position.

The stress field about a rigid body may be significantly different if the matrix is inhomogeneous. The presence of a shear zone or a weak horizon wrapping around the rigid body is a common situation. Such a shear zone may be an pre-existing feature, or be formed as a result

30 J. RIDLEY

P3 .[-

0.2 ~ .25 P1 P1

P3 T

Fig. 6. Stress field about a rigid circular inclusion in a homogeneous elastic matrix in a regional stress field P~ - P3 (after Strrmg&rd, 1973). Contours of mean stress indicate ~(r, given by:

,8d= [ ½ (o', +¢r3)--½(P, +P3)]/(P,-Ps)

the difference in mean stress relative to the average (regional) mean stress ( ½ (P~ +/ '3) ), in units of the far-field deviatoric stress (P~- t'3). Negative values indicate reduced mean stress.

of high shear stress along the margins of the rigid body, as predicted in the stress-field models of Strrmg&rd ( 1973 ). Where one side of the rigid body is wrapped by a shear zone, opposing senses of movement along differ- ently orientated segments of the zone may in- duce low mean stress adjacent to the face of the rigid body perpendicular to the maximum principal stress (tr~) (Fig. 7 ).

Layered sequences Aspects of stress fields associated with layers

of contrasting competence have been examined in the studies of Strrmghrd (1973 ), Ste- phansson (1974), Robin (1979) and Casey (1980). There are systematic differences in the stress fields dependent on the orientation of the layering with respect to the principal stress directions (Casey, 1980). These can be under-

Pt

P3 $

%

convergent flow I H + + + 1 x ' , , ~ -

divergent ~ ' ~ % ~ divergent

flow ~ L \,/ rigid block '~ ," ",fl°w --) \ - t l L ~ ~-- + + +\ . P,

convergent flow I H / "/./" ~ +

P3 I"

Fig. 7. Displacements about a rigid inclusion in an inhomogeneous matrix (with visco-plastic rheology) which includes a zone of easy slip wrapping one side of the inclusion (modified from Holyland, 1990b). The position of low, and high, mean stress zones are reversed with respect to the imposed stress compared to the case of a rigid inclusion in a homogeneous matrix (Fig. 6), because of divergent slip along the two oblique-orientated segments of the easy-slip zone.

stood through consideration of stress and strain continuity across layer boundaries (Fig. 8 ).

If the imposed stress is such that strain includes a component of extension parallel to the layering, then relatively competent layers will have a lower mean rock stress. Fluid focussing will be toward more competent layers in the sequence.

Where the imposed stress is such that strain involves a component of compression parallel to the layering, the least competent layers will have the lowest mean rock stress and be loci of fluid focussing.

Where the principal stress directions are at 45 ° to the layering (the case of simple shear parallel to the layering), for a rock rheology for which volume changes during deformation are small, minimal variations in mean stress are


"~ Pz

v v I" v cx,1 <-- (I11)

V V V ~L v v v

" ~ --~ 1" ~X,2 ~ (T12) ~'~ PX $

v v I" v (~x,1 ~-- ( r l l ) --~v v v .~ v v

I" az

?

Fig. 8. Stress field in a sequence of alternating layers of differing viscosity (r/l > r/2) in a regional stress field Px-Pz. If deformation is pure shear with shortening or extension parallel to the layering, strain compatibi l i ty between layers requires el = e2. Assuming a viscous rheology, we can, therefore, write:

trx.l -tr=,l =~h "e

and similarly for layer 2. Stress compatibi l i ty across inter- faces requires balanced normal stresses:

a~.l =az,2

hence, the deviatoric stress and the mean stress [½ (ax +a=) ] must be different in the two layers. Whether the competent of incompetent layers have the lower mean stress depends on whether Px or Pz is the maximum principal stress. Mean stress wi l l be lower in the incompetent layers i f compression is parallel to the layering, and lower in the competent layers i f there is layer-parallel extension.

predicted in a layered sequence, whatever the variations in competency between layers.

Scale and efficiency of fluid focussing into sites of low mean stress

It has been argued above that tectonically induced variations in mean rock stress are the dominant cause of fluid focussing at the depth of formation of mesothermal gold deposits. To show that this mechanism of focussing would be effective in producing large gold deposits, the scale of focussing, its time span, and its efficiency, need be sufficient to focus the volumes of fluid inferred to have passed through a large lode-style deposit.

Scale and time dependence of stress fields

Stress fields, as discussed above, are dependent dominantly on the geometry of rock units and the imposed regional stress. The stress- field geometries are scale-independent, and will reflect the scale of lithological inhomogeneity in the rock sequence. They will also be largely independent of individual seismic events and of fault motion, so long as this does not significantly alter the rock geometry, and thus form potentially long-lived sites of fluid focussing.

Magnitudes of variations of mean stress and the efficiency of fluid focussing

The magnitude of mean stress variations may be calculated for the simple geometries discussed above. These calculations are used to give an estimate of the order of magnitude of the mean-stress variations that are likely to occur in nature. Str/Smg~rd's (1973) calculations for stress around a circular rigid body show a range of mean stress of two times the far field deviatoric stress (P1 -P3 ) (Fig. 6). As the calculations assume a perfectly rigid body, this is the maximum possible stress difference for this geometry. A similar variation of mean stress is calculated for stress fields around fractures in an elastic medium (Pollard and Segall, 1987), though more extreme variations are predicted within restricted volumes of rock around the crack tips. Mean stress variations in layered sequences depend on the relative layer thicknesses as well as relative competencies (Str/Smg~rd, 1973 ). In a sequence of equal- thickness weak and strong layers, the maximum possible variation in mean stress will be equal to the deviatoric stress. Larger variations are possible if thin competent layers occur in a relatively incompetent matrix.

The range of mean stress, and hence the efficiency of mean stress variations as a mechanism of fluid focussing, is dependent, therefore, on the magnitude of the regional deviatoric stress, and on relative competencies

32 J. RIDLEY

of rock units. Published measurements and estimates of rock viscosity show variations of several orders of magnitude (e.g., Kusznir and Park, 1986), hence results for perfectly rigid bodies are taken as a valid approximation of likely stress fields. Estimates of crustal stress suggest regional deviatoric stresses associated with active faulting of 100-500 bars (Hanks and Raleigh, 1980 ). For large-scale focussing, lateral gradients in mean stress must be effective over distances of a few kilometres. Assum- ing a regional deviatoric stress of 200 bars, possible variations of mean stress are about 300 bars, which over a 2-km gradient would give a lateral gradient of hydraulic head of 1.5 m/re . Vertical hydraulic-head gradients in the lithostatic regime are given by (Pl--Pf)/Pf, about 1.7 m/m. If permeability is isotropic, the overall gradient in hydraulic head would give rise to fluid flow at about 45 ° to the vertical, toward the zone of low mean stress. The parameters used in this calculation are considered typical of an efficient focussing system, and the direction of flow inferred is, therefore, the maximum likely large-scale deviation from vertical flow in the lithostatic fluid pressure regime. The calculation confirms the potential effectiveness of mean stress variations in focussing fluid flow, but also indicates that focussing to create a large deposit, requires fluid movement over several kilometres, vertically as well as laterally.

Significant vertical fluid travel may not be required for focussing, if the mineralising fluid was derived from crystallising magma (e.g., Burrows and Spooner, 1987). The physical controls on magma movement in the crust are similar to those on fluid movement (e.g., Spera, 1987), and the stress-field principles outlined above will apply to magma migration. Whether as discrete intrusions, or as late-stage melts within plutonic systems, magma will move down pressure gradients towards sites of low mean stress (Cooper, 1990), which are likely to be favoured sites of magma crystallisation, and hence of fluid exsolution in the crust.

Discussion

Application to example gold deposits

The geometries discussed above of sites of low mean stress are compared with known sites of mineralisation, though no rigourous computation of stress fields has been undertaken to confirm the applicability of the model suggested in each case.

Given the proposed E-W compression in the Yilgarn Craton of Western Australia during the last phases of Archean deformation and mineralisation (Holyland, 1990c), there are a number of examples of gold deposits whose sitings are within possible pressure shadow zones of granite masses, e.g., Nevoria, South- ern Cross Belt (Cullen et al., 1990), Mount Pleasant; 25 km NNW of Kalgoorlie, Eastern Goldfields Province. In contrast, the modelled stress field around a rigid body in an inhomogeneous matrix (Fig. 7 ) compares well with the siting of early mineralisation at the Granny Smith deposit, 20 km south of Laverton, NE Goldfields (Holyland, 1990b).

A possible example of fluid focussing caused by mean-stress variations in a layered sequence is the localisation of mineralisation at Mount Charlotte in the Golden Mile Dolerite, Kalgoorlie, within the granophyric 'unit 8' of this 600 - 900 m thick differentiated mafic sill (Clark, 1980; Clout et al., 1990). The coarse grain size of this unit and its high feldspar con- tent are consistent with relatively high competency under the greenschist-facies conditions prevailing during mineralisation. An example of the converse case, of focussing into incompetent layers in compression, may be the formation of early (pre- or early-folding) layer- parallel veins in the shale units of saddle-reef deposits in greywacke sequences (Cox et al., 1991 ). The lack of mean-stress variations in a sequence undergoing simple shear parallel to the layering, is a possible explanation of the observation that major shear zones in Archean cratons are largely devoid of mineralisation


(cf., Eisenlohr et al., 1989). Variations in mean stress will only develop where there are irregularities in the shear zone, for instance, at the lensing out of a unit.

Depth distribution of deposits

The calculations of the fluid-focussing power of mean-stress variations have consequences for the depth distribution of deposits. Resis- tance to deformation varies with temperature and confining pressure. Maximum shear resis- tance in rock, and hence maximum deviatoric stresses, will generally occur at the base of the seismogenic zone, around the frictional - quasi- plastic transition, at levels at which temperatures are 300°-350°C (e.g., Turcotte et al., 1980; Sibson, 1983, 1990). It has been noted by a number of authors that the majority of large gold deposits formed under greenschist- facies conditions (Kerrich, 1986; Groves et al., 1989). Sibson (1990) and Cox et al. (1991) suggested that this dominance is related to an enhancement of gold deposition during fluid- pressure fluctuations resulting from episodic fault movement. Fluid-pressure fluctuations in faults are predicted to be largest at the base of the seismogenic zone. As variations in mean stress vary linearly with deviatoric stress, the strength of fluid focussing, due to mean-stress variations at this level, is an alternative factor that would favour the formation of large deposits.

The role of faulting and shear zones in the localisation of gold deposits

Large-scale fluid focussing resulting from mean rock stress variations is independent of the mechanisms and direct effects of slip or movement along faults or shear zones. Fluid focussing is toward sites of low mean stress in an inhomogeneous rock pile in a regional stress field. The variations in mean stress result from interaction between the imposed regional stress with the overall geometry of fractures, faults,

and rock units within the terrain. Most lode- type gold deposits are, however, located along faults or shear zones, for which there is generally evidence that mineralisation was syn- chronous with part of the deformation. In ad- dition, the nature of alteration haloes around lodes implies a fluid-dominated regime (high fluid:rock ratio) in the lode zone or vein, and a rock-dominated regime (low fluid:rock ratio) in the distal alteration zones, and indicates, therefore, strong channeling of fluid flow along structures within a deposit, both along specific structures, and within specific segments of structures (McKinstry, 1948; Hodg- son, 1989; Hronsky et al., 1991 ).

It is suggested that the observed important role of faults and shear zones in localising fluid flow on a deposit scale can be understood by considering their control on fluid movement within a low mean stress domain, both through the role of transient deformation-induced dilatancy, and through the behaviour of faults and shear zones as mechanical discontinuities. The latter point can be understood through consideration of the Mohr-Coulomb criteria for failure under conditions of low, or negative effective mean stress. With progressively decreasing effective mean stress, any discontinu- ity, a fault, or particularly a segment of a fault in an orientation of low, resolved normal stress, will be favoured sites of hydrofracturing (Fig. 9), because of its lower cohesion and tensile strength relative to intact rock. Analysis of the positions of lodes or ore shoots within gold deposits has shown the importance of dilatant sites, particularly sites of low, resolved normal stress, along a single fault or shear zone as loci of relatively high fluid flux (O'Driscoll, 1953; Harley and Charlesworth, 1990; Hronsky et al., 199 l; Hagemann et al., 1992 ).

The possible role of transient dilation along active faults, and resulting fluid-pressure fluc- tuation, in promoting gold deposition has been mentioned above. The formation of alteration haloes around lodes requires fluid advection into wallrock around the ore zone. This advec-

34 J. RIDLEY

inta.ct

1 / ~ pre-existing

Fig. 9, Mohr-circle construction showing the effect of decreasing effective mean stress (increasing fluid pressure) on failure in a rock containing pre-existing fractures or planes of weakness. Stress state 'a' is stable whatever the orientation of fractures in the rock. For stress state 'b', tensile failure will occur along pre-existing fractures perpendicular to tr3, and shear failure along a range of orien- tations of pre-existing fractures. Stress state 'c' is con- structed such that intact rock is just stable, and shows that tensile or mixed extensional-shear failure would have oc- curred along fractures orientated at up to 45 ° from perpendicular to tr3. If tensile or mixed extensional-shear failure releases excess fluid pressure, this stress state is unlikely to be attained, as fluid pressure would have been released by hydrofracturing along pre-existing planes of weakness before reaching the level indicated.

tion may be promoted by fluid-pressure fluctuations within active faults (Cox et at., 1991 ). Guha et al. (1991 ) has shown that fluid im- miscibility, which may be promoted by fluid- pressure fluctuations in active faults, can be an important fluid process associated with gold deposition in quartz veins.

Summary

Large-scale fluid focussing is required to produce significant lode-gold deposits; focussing over a few kilometres lateral distance for bigger deposits. Fluid pressures at the depths of formation of most mesothermal deposits are likely to be close to 'lithostatic', and fluid flow

in the formation of these deposits is thus con- strained to be generally upward. Fluid focussing will occur where there are lateral gradients in hydraulic head at any depth.

Possible causes of lateral gradients in hydraulic head are: (a) spatial variations in permeability, and (b) spatial variations in mean rock stress. Variations in permeability are unlikely to be the cause of fluid focussing in mesothermal gold deposits. Fluid channelways in this case will have lower fluid pressures and higher effective mean stresses than surrounding rock, at variance with the observation of widespread dilational veining in deposits. Variations in mean stress are a general consequence of tectonic stresses acting on an inhomogeneous rock sequence. Fluid focussing will be into zones of relatively low mean rock stress. These will become zones of relatively low effective mean stress.

The calculation of stress fields is a tool for targeting potential sites of mineralisation, in that it provides a prediction of sites of en- hanced fluid flow. Sites of low mean stress have a wide range of possible origins and geometries, and fluid focussing through variations in mean stress allows, therefore, for the observed variety in the structural setting of mesothermal gold deposits. In a layered sequence, for instance, the lowest mean stress will develop in either the most competent or the least competent layers, depending on the orientation of the layering relative to the principal stress axes. In areas of complex geology, stress fields will be influenced by interplay between different rock types, and faults and fractures, and may not be amenable to analysis using the results pre- sented here. Numerical computation methods are available for calculating stress fields in inhomogeneous material, and have been adapted to geological situations in 'Stress-Mapping' technology, as described by Holyland (1990a,b), who shows its applicability to the calculation of stress fields in particular geological terrains.

MEAN ROCK STRESS AND F L U I D FLOW IN THE CRUST: VEIN- AND LODE-STYLE G O L D DEPOSITS 35

Nomenclature

b

g k t v

x , Z

A , B Hf PI, P2, P3

Po Pr 1", B~

2f # P~, Pf O"

o"1, o'2~ 0" 3

ax, trz O'xA 0"

strain rate = (Ol/l) ( 1 / 0 t), where I is any length marker gravitational constant permeability time fluid velocity coordinate axes, x: horizontal, z vertical empirical constants hydraulic head maximum, intermediate, and minimum principal regional stress effective pressure fluid pressure lithostatic (rock) pressure rock storage capacity rock viscosity pore-pressure factor fluid viscosity rock, and fluid density stress at a point maximum, intermediate, and minimum principal stress at a point stress in the x, z direction stress in the x direction in unit 1 mean stress

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Documents

The relations between mean rock stress and fluid flow in the crust