Fluid overpressure and flow in fault zones: field measurements and models

Tectonophysics 336 (2001) 183±197

www.elsevier.com/locate/tecto

Fluid overpressure and ¯ow in fault zones: ®eld measurements and models A. Gudmundsson* Geological Institute, University of Bergen, Allegt. 41, N-5007 Bergen, Norway

Abstract Field studies of small normal faults (throws of metres to tens of metres) show that their fault cores consist of breccias that vary in thickness along the fault plane. Commonly, the down-dip variation in the breccia thickness is 0±1 m with a wavelength of 5±10 m. The breccia acts mechanically as an inclusion; soft, ductile and sometimes creeping when the fault zone is active, but stiff and brittle when the fault zone is inactive. During interseismic periods, and when the fault has become inactive, the breccia behaves as a very dense, low-permeability material that is a barrier to transverse ¯ow of groundwater. The breccia barrier thus collects water and channels it downdip or updip along the contact between the fault core and the damage zone. For a typical 1-m-thick interseismic breccia, the maximum transmissivity is estimated at Tp , 10 210 m 2 s 21. The ®eld data, however, indicate that during the high strain rates associated with faulting, seismogenic slip may occur either along the breccia, or along its contacts with the damage zone. The resulting fractures with apertures of ,0.3 cm may temporarily increase the transmissivity of the fault core by at least 8 orders of a magnitude, to as much as Tf , 10 22 m 2 s 21. It is suggested that slip of faults of this type is commonly associated with the ¯ow of overpressured water into the fault plane. High water pressure lowers the critical driving shear stress needed for fault slip and may greatly increase the aperture, hence the ¯uid transport, of the slipping fracture. Theoretical considerations indicate that, other things being equal, ¯uid ¯ow along strike±slip faults is favoured over ¯ow along dip±slip faults and that, generally, the steeper the dip of the fault, the more effective it is for ¯uid transport. q 2001 Elsevier Science B.V. All rights reserved. Keywords: ¯uid overpressure; fault zones; hydrogeology; Norway

1. Introduction The association of groundwater and fractures is well established. In solid rock where the rock-matrix hydraulic conductivity is commonly very low, the main transport of water and other crustal ¯uids is through fractures. The fractured medium is modelled either using discrete models or continuum (equivalent porous) models, where one subgroup includes dual * Tel.: 147-5558-3521; fax: 147-5558-9416. E-mail address: [email protected] (A. Gudmundsson).

porosity models (Lee and Farmer, 1993; Smith and Schwartz, 1993). In recent models, the effects of fractal size distributions of various parameters associated with rock fractures (Odling, 1997; Odling et al., 1999) and ¯ow channelling (Tsang and Neretnieks, 1998) have been incorporated into models on ¯uid ¯ow in rock fractures. While groundwater ¯ow in rock fractures in general has received much attention, the physical parameters controlling the ¯ow along major and minor fault zones has received less attention from hydrogeologists. By contrast, ¯uid pressure in active fault zones has been of considerable interest to seismologists and structural

0040-1951/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0040-195 1(01)00101-9

184

A. Gudmundsson / Tectonophysics 336 (2001) 183±197

geologists specialising in the mechanical involvement of crustal ¯uids in seismogenic faulting (Nur and Booker, 1972; Nur, 1974; Knipe, 1993; Hickman et al., 1995). There is no doubt that many active fault zones receive and transport great volumes of groundwater, often under high ¯uid overpressure (Gudmundsson, 1999). This is, for example, indicated by the common occurrence of springs, both cold and geothermal, along fault zones (Umeda et al., 1996; Curewitz and Karson, 1997; Lee and Wolf, 1998; Leonardi et al., 1998; Melchiorre et al., 1999), and by the extensive sets of mineral-®lled veins that occur in many eroded fault zones (Gudmundsson, 1999). Nevertheless, the mechanisms of groundwater transport to and along fault zones are poorly understood. The principal aim of this paper is to provide simple conceptual and analytical models on ¯uid overpressure and ¯ow along fault zones and compare the model results with ®eld measurements. The ®eld data include some new structural data on small normal faults in Norway, brief summaries of similar data on normal faults in Iceland, and new results on mineral®lled veins associated with fault zones. In the conceptual model on the hydromechanical structure of normal faults, particular attention is made to the effect of the fault breccia in acting alternatively as a barrier and a conductor for groundwater ¯ow. In the analytical models, the focus is on the effects of ¯uid overpressure, fracture aperture, and fault dip on the ¯uid transport. 2. Field observations of faults zones A typical fault zone consists of two major hydromechanical units, a fault core and a fault mantle or damage zone (Bruhn et al., 1994; Caine et al., 1996; Seront et al., 1998). The fault core is the part where the main fault slip occurs. Its main characteristics are numerous subzones of breccia and cataclasis, commonly forming ellipsoidal bodies with a long axis parallel with the fault-slip direction, as well as fractures at various scales (Fig. 1). By contrast, the damage zone lacks extensive zones of cataclasis and breccia and is characterised by faults and fractures that in intensity exceed that of the adjacent host rock. On approaching the host rock, there is normally

Fig. 1. Schematic illustration of a fault zone (shaded) and the surrounding host rock (unshaded except for a marker horizon indicating the throw). Fault zones normally consist of two main hydromechanical units, a core and a damage zone, illustrated here for a normal fault. The damage zone consists primarily of numerous fracture and faults running parallel with the main fault (indicated), but also of subvertical fractures (Figs. 2±4) that may channel groundwater to the fault core. The fault core consists primarily of fault breccia (cataclastic rocks at greater depths). For the normal faults discussed in this paper, the breccia thickness varies downdip, and is absent from parts of the fault plane.

not a sharp boundary between the damage zone and the host rock, but rather a gradual decrease in fracture intensity and, sometimes, change in fracture strike. In major fault zones the fault core may be as thick as several tens of metres, occasionally one or two hundred metres (Bruhn et al., 1994; Gray et al., 1999), whereas that of the damage zone may be as thick as several hundred metres. Laboratory measurements of rocks from the core and damage zone of a major normal fault zone in Nevada (Seront et al., 1998) show that the inferred permeability of the damage zone is several orders of a magnitude higher than that of either the fault core or the host rock, and that the lowest permeability values are obtained from implosion breccias in the fault core. Also, drilling into fault zones in western Norway shows that the water yield is highest in the damage zone, and lowest in the fault core (Braathen et al., 1999). This suggests that the damage zone normally has the greatest hydraulic conductivity. The author's studies of normal faults show that the breccia thickness commonly varies along the fault

A. Gudmundsson / Tectonophysics 336 (2001) 183±197

185

Fig. 2. Small normal fault in gneiss on the west coast of Norway.View northeast, the fault is striking NE and dipping to the SE. The hanging wall is to the left, the footwall to the right. Notice many subvertical and oblique (antithetic) faults and fractures in the hanging wall that meet with the fault plane (and its associated breccia core) at an high angle. These fractures increase the vertical permeability of the hanging wall and channel water to the main fault plane (cf. Figs. 3±5). A backpack located on the fault plane in the central part of the picture provides a scale.

plane (Figs. 3 and 4). The wavelength of this variation in thickness depends on the size of fault and the associated displacement. It is well known that breccia thickness tends to increase with fault displacement up to a certain limit (Robertson, 1983; Scholz, 1987; Hull, 1988; Forslund and Gudmundsson, 1992). Thus, for large-displacement faults the breccia of the fault core is normally thick, and the wavelength of the breccia-thickness variation relatively large. The hydromechanical effects of breccia-thickness variation are, however, easier to study and understand in small-displacement faults (Fig. 2). A common observation in such small faults is that the ratio between the maximum thickness of a breccia unit and its down-dip wavelength is of the order of 0.1 (Figs. 3 and 5). The core is commonly composed of a very dense, low-permeability breccia (cataclastite at greater crustal depths). Most fractures in the damage zone

that meet the breccia at high angles do not propagate through it but become arrested at the core-damage zone boundary (Figs. 3 and 4). Consolidated breccia of the core may develop fracture systems, but normally individual fractures do not penetrate the whole thickness of the core (Fig. 4). In the normal fault in Figs. 3 and 4, there are three discontinuities associated with the breccia. Two are contacts with the damage zone, the third is a discontinuity inside the breccia itself (Figs. 3 and 4). The discontinuities at the contacts with the damage zone are presumably the effects of stress concentrations that, in turn, relate to the different mechanical properties of the breccia and the damage zone. The breccia zone acts mechanically as an inclusion (Eshelby, 1957; Lekhnitskii, 1968) that is soft and ductile when newly formed or reactivated, but stiff and brittle when consolidated. In this fault, the discontinuities at the contacts, as

186

A. Gudmundsson / Tectonophysics 336 (2001) 183±197

Fig. 3. View N808E, fault breccia in the core of a normal fault in Norway (cf. Fig. 2). The core and fault plane strike N528E and dip a ˆ 408SE. There are three discontinuities (fractures) associated with the breccia core. One is at its upper contact with the damage zone (top of the measuring tape), one along the lower central part of the breccia, and one at the lower contact between the breccia and the damage zone (bottom of the measuring tape). All these discontinuities have slickensides, indicating that they are fault planes. The breccia varies in thickness along the fault plane, from near zero in the upper right part of the photograph, to 1.5 m in the lower left part of the photograph. The measuring tape, 70 cm long, and a person provide a scale.

well as the discontinuity inside the breccia, are likely to act as slip planes during seismogenic faulting. For example, slickensides indicating faulting were observed at all the three discontinuities in Figs. 3 and 4. Although the breccia is likely to behave as

ductile and to creep at low to moderate strain rates, particularly when it is newly formed, it can fracture at the very high strain rates associated with seismogenic faulting. For example, in an active major fault zone in Iceland (Gudmundsson 1995; Rognvaldsson et al.,

A. Gudmundsson / Tectonophysics 336 (2001) 183±197

187

Fig. 4. Close-up of the breccia in Fig. 3. View NE, the breccia is consolidated and brittle, with numerous small cracks, some of which are conjugate. Most of these small cracks, however, do not cut through the whole breccia and do not form an interconnected pathway. In the damage zone in the hanging wall there are several subvertical fractures (also seen in Fig. 3) that meet with, and are arrested by, the fault core. These may transmit groundwater to the core where it would commonly (for low-permeability interseismic breccia) be transported along the uppermost discontinuity, at the contact between the damage zone and the breccia (where the notebook is located). The notebook, with a height of 15 cm, provides a scale.

1998), the core breccia, which is composed of unconsolidated material, is dissected by several discontinuities representing core-parallel faults. Such discontinuities along otherwise porous fault breccias are likely to greatly alter their transmissivities during periods of seismogenic faulting. 3. Fluid ¯ow in fault zones Here the focus is on conceptual and quantitative models of normal-fault zones located in rigid (nondeforming) host rocks (Fig. 1). The interseismic fault core is modelled as a porous medium and the damage zone is modelled as a fractured medium. Field observations show that discontinuities occur along parts of the fault core; thus, during

fault slip the core is modelled as a fractured medium. A common observation of normal-faults is that, in addition to fault-parallel fractures in the damage zone (Fig. 1), there are many fractures that meet the fault core at high angles (Figs. 3 and 4). Such fractures are particularly common in the hanging walls of many normal faults at shallow crustal depths. Some of these fractures are synthetic or antithetic faults, others are joints. These fractures increase the vertical hydraulic conductivity of the rock and channel water towards the fault core (Fig. 5). The general conceptual model of topographydriven groundwater ¯ow towards and along a normal fault in Fig. 5 is primarily derived from data on the small normal fault zones (throws of metres to tens of metres) observed in Iceland (Forslund and

188

A. Gudmundsson / Tectonophysics 336 (2001) 183±197

where the hydraulic conductivity of the porous medium, Kp, has the subscript p to distinguish it from that of fractured media, discussed below. In this equation, N is a dimensionless shape factor, r the density of the ¯uid, g the acceleration due to gravity, and m the dynamic (absolute) viscosity of the ¯uid. The property of the porous medium itself is given by its intrinsic permeability, k ˆ Nd 2, where: Kp ˆ

Fig. 5. Schematic model of groundwater circulation in the vicinity of a small normal fault zone (cf. Figs. 2±4). The water may be driven to the fault plane from above or below; here it migrates vertically down to the plane. In the hanging wall of the fault there are many subvertical fractures that help transporting water down to the low-permeability breccia core at the fault plane. There the water is channelled along the core to those parts of the plane where the breccia is missing and where water can migrate vertically to the footwall. The general effect of the breccia, with its low interseismic permeability and variations in thickness, is to collect and channel the groundwater, partly along the fault plane, partly into the footwall.

Gudmundsson, 1992; Gudmundsson, 1992) and Norway (Figs. 2±4). In this model, the breccia in the fault core is a low-permeability barrier to transverse groundwater ¯ow. Accordingly, the ¯ow is directed downdip along the damage zone parallel with the fault core. Where the breccia is missing from the fault plane, water can normally ¯ow through the fault plane to deeper crustal levels. For the interseismic porous-media behaviour of the breccia in the fault core, Darcy's law on ¯uid transport may be written as: Q ˆ 2KA7h

…1†

where the minus sign indicates that the ¯ow is in the direction of decreasing head. In this equation, Q is the volumetric ¯ow rate (volume of ¯ow in unit time), K is the hydraulic conductivity, A is the cross-sectional area normal to the ¯ow, and 7h is the hydraulic gradient, where 7 is the operator nabla. The hydraulic conductivity in a porous medium with a mean (or effective) grain diameter d is (Bear, 1972): Kp ˆ

N rgd2 m

…2†

k rg m

…3†

This equation, with g ˆ 9.8 ms 22, r ˆ 1000 kg m 23, and, from Giles (1977), m < (1.8±0.6) z 10 24 Pa s (for water at 0±508C, respectively), yields Kp ˆ (5.4 2 16) z 10 6k. For water at 218C, common in the upper crust, then m ˆ 9.8 z 10 24 Pa s and Kp , 10 7k. Laboratory tests of the permeability of fault±core materials from dip±slip fault zones give k , 10 217 ± 10 220 m 2 (Evans et al., 1997; Seront et al., 1998). Using the relation Kp , 10 7k, the corresponding hydraulic conductivity would be Kp ˆ (10 210 ±10 213) m s 21. These values are similar to the lowest in situ values from rock masses (Lee and Farmer, 1993) and support the suggestion that the fault core during interseismic periods is normally a barrier to groundwater ¯ow. The transmissivity of an aquifer is its hydraulic conductivity times its thickness. For the fault core the transmissivity of its porous breccia, Tp, is given by: Tp ˆ Kp bp

…4†

where Kp is the average hydraulic conductivity of the porous core breccia and bp its thickness. The thickness of the breccia in Figs. 3 and 4 varies from zero to a maximum of 1.5 m; its variation is indicated, schematically, in Fig. 5. For comparison, the average breccia thickness on normal faults in Iceland, with throws from a few metres up to 50 m, is from a few centimetres to ,2 m (Forslund and Gudmundsson, 1992; Gudmundsson, 1992). Because the transmissivity of the damage zone is generally much higher than that of the breccia, regions where the breccia thickness is near to, or quite, zero, would not act as barriers to along-fault transport of water. Consider the transmissivity of small normal faults, such as those in Figs. 2 and 3, with breccia thickness of 1 m. From Eq. (3) and common conditions in the

A. Gudmundsson / Tectonophysics 336 (2001) 183±197 210

213

upper part of the crust, we obtain Kp ˆ (10 ±10 ) m s 21. Then, with breccia thickness of bp ˆ 1 m, the transmissivity of the core of a the fault is, from Eq. (4), Tp ˆ (10 210 ±10 213) m 2 s 21. Consider next the temporary changes in transmissivity, of the same type and size of fault, as a result of fault slip. During seismogenic faulting any of the discontinuities commonly observed at the contacts of the breccia and the damage zone, or inside the breccia, can slip and thus act as a conduit for water. For example, if slip occurs along the breccia itself, its temporary hydraulic conductivity may increase. The three discontinuities in Figs. 3 and 4 were measured. The uppermost had an average aperture of 0.3 cm, the one inside the breccia also 0.3 cm, and the one at the lower contact an aperture of 0.2 cm. Although the discontinuities are essentially non-eroded, these may be the maximum apertures of these discontinuities because they are measured at the free surface. Nevertheless, the measurements are accurate and can be used when estimating the temporary effects of seismogenic slip along the breccia on the ¯uid transmissivity of the core. We model the observed discontinuity along the fault core as a single crack with an average hydraulic conductivity, Kc, given by: Kc ˆ

rgb2 12m

…5†

where, as before, r is the ¯uid density, g the acceleration due to gravity, b is the crack aperture, and m the dynamic (or absolute) viscosity of the ¯uid. The fracture transmissivity, Tf, of the discontinuity is equal to its hydraulic conductivity times its aperture; thus: Tf ˆ Kc b ˆ

rgb3 12m

…6†

Using g ˆ 9.8 ms 22, r ˆ 1000 kg m 23, b ˆ 0.003 m (3 mm) and m ˆ 9.8 z 10 24 Pa s (for water at 218C), from Eq. (6) we obtain the transmissivity of the discontinuity along the fault core as Tf ˆ 2.2 z 10 22 m 2 s 21. These very different results obtained for the transmissivity of the core during interseismic periods as compared with those during seismic periods have important implications for groundwater ¯ow. First,

189

they justify the conclusion that the interseismic core is a barrier to groundwater ¯ow; that it will normally collect groundwater and channel it along its contact with the damage zone. Part of this water, when it enters regions along the fault where the lowpermeability breccia of the core is missing, may be topographically driven to the footwall of the fault and, from there, to deeper crustal levels (Fig. 5). Alternatively, water coming to the fault zone from below, may be driven by ¯uid overpressure up along the fault plane towards the surface (Section 5). Second, the results show that the transmissivity of a core consisting of a porous material can increase enormously during faulting through that material. Following faulting along the core, its transmissivity may be as much as 10 8±11 times greater than that during the interseismic periods. There is wealth of data on increases in spring activity along faults following seismogenic faulting (Umeda et al., 1996; Lee and Wolf, 1998; Leonardi et al., 1998; Melchiorre et al., 1999). Although part of this increase is likely to be related to hydrofracturing, as discussed below, there is little doubt that much of it is attributable to the enormous fault±slip generated increase in the core transmissivity. The models in this section assume the fractures and faults to be self-supporting (in a rigid host rock) so that their shapes and apertures do not depend on the ¯uid pressure. This assumption, common in hydrogeology, may be fully justi®ed, especially at very shallow crustal depths. Generally, with increasing crustal depths and in the absence of ¯uid overpressure, fractures tend to close (Lee and Farmer, 1993), although some conduct water to depths of at least 9 km (Shapiro et al., 1997). Hydrofractures, however, are subject to water overpressure which may reach tens of mega-pascals (Gudmundsson, 1999). The overpressure has two main transient effects on the fault plane: making fault slip easier, and increasing the ¯uid transport. 4. Water overpressure and fault slip The driving shear stress that controls fault slip, Dt , may be de®ned as the difference between the remote applied shear stress, t , and the residual frictional strength on the fault after sliding. Commonly, the

190

A. Gudmundsson / Tectonophysics 336 (2001) 183±197

Fig. 6. Mineral-®lled veins are hydrofractures that normally propagate in the principal stress plane that contains the maximum and intermediate compressive principal stresses and is thus normal to the minimum principal stress. If the pathway of a hydrofracture is partly outside this principal stress plane, its ¯uid overpressure (with reference to the normal stress on the fracture) decreases, and the resulting mineral vein becomes thinner. This is seen here in the two main (1±2 cm) thick veins. Mineral veins, like dykes, are thus reliable paleostress indicators. These veins are a part of the network in Fig. 7. The host rock is basaltic lava in North Iceland. The pencil, 15 cm in length, provides a scale.

driving stress is also referred to as the nominal stress drop during earthquakes, partly because it is a measure of the drop or decrease in shear stress across the fault plane as a consequence of the slip. As measured from earthquakes, however, the stress drop is related to seismic ef®ciency, and thus to the total stresses. These cannot be determined from earthquakes alone, and it is widely considered that the stress drop is normally not exactly equal to the tectonic driving stress (Scholz, 1990; Engelder, 1993). In the Modi®ed Grif®th Criterion for fault slip in the compressive regime, fracture closure and associated friction is assumed to occur as soon as the normal stress exceeds a very low (essentially zero) value. This criterion may be presented by the following linear relationship between the principal stresses

at slip (Brace, 1960; Jaeger and Cook, 1969):

t ˆ 2T0 1 ms n

…7†

where T0 is the in situ tensile strength of the host rock and the residual frictional strength is considered equal to the coef®cient of sliding friction multiplied by the normal stress, that is, to the term m s n. If the fault plane is subject to so high water pressure during slip that the effective normal stress becomes zero or negative, then, in Eq. (7), we have m s n , 0. It follows that the total shear stress on it may relax, in which case t ˆ Dt . Then the criterion of Eq. (7) becomes:

t < 2T 0

…8†

Measurements of the in situ tensile strength of rocks, including jointed rocks, indicate that its normal range

A. Gudmundsson / Tectonophysics 336 (2001) 183±197

191

Fig. 7. View vertical, small-scale faults with mineral veins along the fault planes. The main faults are conjugate strike±slip faults with displacements of 1±2 cm. The circular white spots are amygdales. The host rock is basaltic lava. These veins (like those in Fig. 6) form a part of a network in a fault zone in North Iceland (Rognvaldsson et al., 1998; Gudmundsson et al., 2001) where the thickness of most of the veins is of the order of millimetres or less, but some reach centimetres (Fig. 6). The measuring tape, with a diameter of 6 cm, provides a scale.

is 0.2±6 MPa, the most common values being 2±3 MPa (Haimson and Rummel, 1982; Schultz, 1995). The tensile strength of an active fault zone is maintained by sealing and healing of fractures and other weaknesses in the fault rock (Olsen et al., 1998). These processes may operate quickly in comparison with the common lengths of the seismic cycles (Blanpied et al., 1992; Hickman et al., 1995; Olsen et al., 1998). Slip on pre-existing faults commonly occurs along a plane of maximum shear stress (Jaeger and Cook, 1969; Sibson, 1990). When the water overpressure on the slipping fault plane is great, so that formula (8) applies, then, from the de®nition of maximum shear stress, (s 1 2 s 3)/2 where s 1 is the maximum compressive principal stress and s 3 the minimum compressive (maximum tensile) principal stress, the difference between the principal (total) stresses,

ds ˆ s 1 2 s 3, when fault slip occurs, is: ds ˆ 2t ˆ 4T 0

…9†

This equation shows that the stress differences during fault slip under high water overpressure are very small. 5. Water overpressure and transport In the ®eld, paleohydrofractures are most easily recognised as mineral-®lled veins (Fig. 6). The great majority of the mineral veins propagate in a direction that is approximately perpendicular to the local minimum compressive principal stress in the area within which they form. This means that they are mode I (opening mode) cracks that propagate in a principal stress plane. For example, in a study of more than 800

192

A. Gudmundsson / Tectonophysics 336 (2001) 183±197

Fig. 8. Simpli®ed model of a self-supporting hydrofracture (located in a rigid host rock). The hydrofracture originates when its source, a water sill, becomes ruptured. The condition for rupture of the sill is that its excess ¯uid pressure, pe, reaches the tensile strength of the rock in the roof of the sill [Eq. (10)]. On these conditions, the volumetric rate of ¯uid ¯ow through the vertical hydrofracture is given, for a vertical fracture, by Eq. (11), and for a non-vertical fracture with dip a by Eq. (13).

mineral veins in North Iceland (Gudmundsson et al., 2001), nearly 80% were mode I cracks. When a mineral vein propagates in a plane that is oblique to the minimum compressive principal stress, its ¯uid overpressure, which is then referred to the normal stress on that plane, decreases and it normally becomes thinner (Fig. 6). Oblique planes such as these, by de®nition, are faults. Roughly 20% of the veins in North Iceland occupy faults (Fig. 7). Although commonly thinner than surrounding modeI veins, the veins that occupy faults in old geothermal areas are normally easily recognised (Fig. 7). In order to explore the effects of fracture attitude and host±rock behaviour on the volumetric rate of ¯uid ¯ow, we consider ®rst the condition for hydrofracture initiation. If a ¯uid-®lled source (say, a sill) is subject to internal ¯uid excess pressure pe (in excess of the lithostatic pressure in the roof of the source), it will rupture and initiate a hydrofracture

Fig. 9. Simpli®ed model of an elastic hydrofracture (located in an elastic host rock). The ¯uid excess pressure in the source is pe at the time of initiation of the hydrofracture, according to Eq. (10). For a vertical, elastic hydrofracture, the volumetric ¯ow rate is given by Eq. (12); for a non-vertical elastic hydrofracture with dip a , the volumetric ¯ow rate is given by Eq. (14).

when: pl 1 pe ˆ s 3 1 T 0

…10†

where p1 is the lithostatic stress at the depth of the source; pe ˆ pf 2 p1 is the excess ¯uid pressure, that is, the difference between the ¯uid pressure, pf, in the source at the time of its rupture and the lithostatic pressure; and s 3 and T0 are the minimum principal stress and the in situ tensile strength, respectively, in the roof of the source. If the host rock behaves as rigid, we refer to the resulting hydrofractures as self-supporting (Fig. 8); alternatively, if the hydrofracture deforms as the ¯uid pressure inside it changes, the host rock is assumed to behave as elastic (Fig. 9) and the fracture is referred to as elastic. For water ¯ow in a vertical self-supporting fracture, an assumption frequently made in considering groundwater transport in hydrogeology (Fig. 8), it follows from the Navier±Stokes equations (Lamb, 1932; de Marsily, 1986) that the volumetric ¯ow rate, Q zs , is given by:   b3 W 2pe s Qz ˆ r g2 …11† 12m w 2z

A. Gudmundsson / Tectonophysics 336 (2001) 183±197

where b is the aperture (opening) of the fracture, W its width in a direction that is perpendicular to the ¯ow direction (the fracture cross-sectional area perpendicular to the ¯ow is thus A ˆ bW), r w is the density of the water (here we use a subscript to indicate that the ¯uid is water and to distinguish it from the rock density), g the acceleration due to gravity, m is the dynamic (absolute) viscosity of the water, and 2pe/2z is the pressure gradient in the direction of the ¯ow. The z-axis is positive upwards, which explains why the ®rst term on the right side of the equation is positive, despite the ¯ow being in the direction of decreasing pressure, and the second term negative. Because the ¯ow is always in the direction of decreasing pressure, the gradient 2pe/2z is negative. This means that during calculations, the term 22pe/2z in Eq. (11) becomes positive and is added to the term r wg. If the walls are free to deform as the ¯uid is transported from the sill and up through the vertical fracture (Fig. 9), the weight of the rock above the sill must be supported by its internal ¯uid pressure. Because of the density of the host rock, r r, is different from that of the water, r w, a buoyancy term must be added to the pressure gradient, so that for an elastic hydrofracture Eq. (11) becomes:   b3 W 2p Qez ˆ …rr 2 rw †g 2 e …12† 12m 2z In this equation, the ¯uid driving pressure (the term in the brackets) is with reference to the vertical stress. Again, the gradient 2pe/2z is negative; in calculations the term 22pe/2z is thus positive and added to the driving pressure due to buoyancy. Eqs. (11) and (12) apply to vertical fractures such as many mode I cracks and strike±slip faults but are easily extended to water ¯ow in non-vertical fractures such as dip±slip faults (Figs. 1±3). If we denote the dip of the fault by a , then the component of gravity in the direction of the fault becomes gsina . If the water ¯ows along the length dL of the dip-dimension of the fault, and is driven by pressure difference dp, the volumetric rate QsL of ¯uid ¯ow along a self-supporting fault, from Eq. (11), is:   b3 W 2p rw gsina 2 e QsL ˆ …13† 12m 2L Similarly, from Eq. (12), the volumetric ¯ow rate QeL

193

along an elastic dip±slip fault is: QeL

  b3 W 2pe ˆ …rr 2 rw †gsina 2 12m 2L

…14†

where all the symbols have been de®ned above. The special case of ¯ow along a horizontal fracture is also easily obtained from Eqs. (11) and (12). For example, consider a self-supporting fracture in the horizontal x±y plane, with aperture b, width W (measured along the y-axis) and length L measured along the x-axis. We substitute 2x for 2L, use the fault dip a ˆ 08, so that sina ˆ 0, and, from Eq. (13), get: Qsx ˆ 2

b3 W 2pe 12m 2x

…15†

Here the excess pressure, pe ˆ pf 2 p1, refers either to that of a sill propagating horizontally in its own plane, or to that at the junction between a horizontal hydrofracture and the vertical hydrofracture that supplies the ¯uid. Consider now the effects of water overpressure on the hydraulic transmissivity of a fault zone using the model of a circular, interior hydrofracture, such as might propagate along the fault plane in Fig. 3 and the small faults in Fig. 7. For a uniform water overpressure, Dp, with reference to the normal stress on the fault plane, the aperture b of the fracture is given by (Sneddon and Lowengrub, 1969): bˆ

8Dp…1 2 n2 †R pE

…16†

where n is Poisson's ratio and E Young's modulus of the host rock (damage zone), and R is the radius of the crack. Because the crack is circular, R can represent either half its dip dimension or half its strike dimension. This equation shows that the aperture, b, of the fracture is directly proportional to its controlling dimension, 2R, and to the water overpressure Dp at the time of fracture propagation. Similar equations can be derived for restricted hydrofractures (Sneddon and Lowengrub, 1969; Tada et al., 1973). For a hydrofracture modelled as a through-crack with a dip dimension L smaller than its strike dimension (L thus being the controlling dimension), the fracture aperture b is related to the

194

A. Gudmundsson / Tectonophysics 336 (2001) 183±197

aperture as a function of the water overpressure:

water overpressure Dp through the equation: bˆ

2Dp…1 2 n2 †L E

…17†

where, as before, E is Young's modulus of the rock and n its Poisson's ratio. 6. Application 6.1. Overpressure and fault slip When the water overpressure on a seismogenic fault plane is great, it follows from formula (8) that the driving shear stress is ,2T0. Consequently, when the common in situ tensile strength is 2±3 MPa, the stress drop, under conditions of high water pressure on the fault plane, would be expected to be 4±6 MPa. These results are very similar to those estimated from earthquake stress drops, where the most common values are 3±6 MPa (Kanamori and Anderson 1975; Scholz, 1990). One implication is that under conditions of high water pressure measured earthquake stress drops and estimated driving stresses may be roughly equal. 6.2. Overpressure and aperture For the normal fault in Figs. 2 and 3, the apertures of the contact discontinuities are 0.2±0.3 cm, whereas the common wavelength of the breccia, and thus the possible length of a fracture resulting from stress concentration at breccia-damage zone contacts, is 5±10 m (Fig. 5). The strike dimensions of these fractures are not known; they may be similar to the dip dimensions (Nicol et al., 1996), in which case Eq. (16) should be used, or different, in which case Eq. (17) should be used. Here we consider both cases. The host rock is gneiss (Figs. 2 and 3). We estimate its in situ Poisson's ratio as ,0.25 and its situ Young's modulus as ,20 GPa. These values are obtained by extrapolating laboratory values (Jumikis, 1979) to in situ, static conditions, in a manner analogous to that used previously to obtain these moduli for the basaltic crust of Iceland (Gudmundsson, 1988). Substituting these values in Eqs. (16) and (17), and using the wavelength of the breccia, 10 m, as the diameter of the fracture in Eq. (16) and as its length in Eq. (17), we obtain the following approximate formula for the

b < …6 2 9†´1024 Dp

…18†

In this formula, the aperture is in metres, the water overpressure in mega-pascals, and the numerical value 6 corresponds to circular crack, Eq. (16), and the value 9 to a through-crack, Eq. (17). Clearly, for hydrofractures to propagate along the fault plane, the water overpressure with reference to the normal stress on the fault plane must exceed the average in situ tensile strength of the damage zone, previously estimated at ,3 MPa. Thus, for a water overpressure of 3 MPa, formula (18) gives the fracture aperture as ,0.2±0.3 cm, the same as the currently measured apertures. By contrast, if the average water overpressure was 10 MPa, half the estimated average value from mineral veins in Iceland (Gudmundsson, 1999), the corresponding aperture, from formula (18), would be 0.6±0.9 cm. These values are three-times the currently measured apertures and equal to commonly observed mineral-vein thicknesses (Figs. 6 and 7). From Eq. (6) it follows that, other things being equal, increasing the fracture aperture temporarily by a factor of 3 would increase the water transmissivity along the fault zone by a factor of 27. 6.3. Fault attitude and ¯uid transport Consider again a normal fault with a maximum aperture of 0.3 cm and a controlling dimension of 10 m (Figs. 3±4). We assume that the water is transported up along the fault plane through interconnected fractures, of the above dimensions, from a source depth of 2 km to the surface. For convenience, we take the water temperature to be 218C, as in Section 3, in which case its dynamic viscosity is m ˆ 9.8 z 10 24 Pa s and its density r w ˆ 1000 kg m 23. We use the excess ¯uid pressure in the source pe ˆ T0 ˆ 3 MPa and assume that it has the potential to drive the water to the surface where the excess pressure is assumed zero. The fault dip is 408 (Fig. 3) and the vertical depth to the source is 2 km. For a horizontal surface and a horizontal source roof, we then have 2L ˆ 2z/sin408 ù 3.1 km and the gradient 2pe/ 2L ù 2 970 Pa m 21. Using these values, and b ˆ 0.3 cm, W ˆ 10 m, and g ˆ 9.8 ms 22, from Eq. (13) we get, for a fault in a rigid host rock, QsL ù 0.17 m 3 s 21. For comparison, if the fault is

A. Gudmundsson / Tectonophysics 336 (2001) 183±197

located in an elastic host rock with an average density of 2600 kg m 23 for the uppermost 2 km (as is reasonable for the gneiss in Fig. 2), then QeL ù 0.25 m 3 s 21. Thus, when buoyancy contributes to the driving pressure, the volumetric ¯ow rate increases by a factor of roughly 1.5. Consider now ¯uid transport up the plane of a strike±slip fault, from a horizontal source at depth of 2 km to the surface. We use the same ®gures as for the normal fault, except that here the fault dip is a ˆ 908 so that sina ˆ 1 and the gradient 2pe/2L ˆ 2pe/2z ˆ 21500 Pa m 21. Thus, for a rigid host rock, Eqs. (11) and (13) yield Qsz ˆ QsL ù 0.26 m 3 s 21, and for an elastic host rock Qsz ˆ QsL ù 0.40 m 3 s 21. Thus, other things being equal, a vertical strike±slip fault, or any vertical fracture, would normally transport more ¯uid than an oblique fracture or a dip±slip fault. 7. Discussion The results presented in this paper indicate that fault zones can act either as barriers or as conduits to ¯ow of crustal ¯uids. Because they evolve through time, faults can act as barriers to groundwater ¯ow during certain periods of time, but as conduits during other periods. For dip±slip faults, the breccia associated with the fault core is normally the greatest barrier to vertical ¯ow of groundwater. However, the breccia thickness varies downdip along the fault and is commonly missing from parts of the fault plane. It follows that, although parts of an individual dip±slip fault may acts as barriers to vertical ¯ow of groundwater, other parts, where there is no breccia, may allow water ¯ow to deeper crustal levels. The conceptual and quantitative modelling here is mainly based on ®eld studies of normal faults in Iceland and Norway. Although these faults are from widely different tectonic regions, the west coast of Norway is a part of a continental shield whereas Iceland is a part of the rifting ocean-ridge system, the results are very consistent. However, all these normal faults are small, with throws ranging from several metres to several tens of metres. It remains to be seen how the model implications agree with observations of large faults. For example, the observed variation in breccia thickness is an important part of the conceptual model proposed in Fig. 5.

195

Although breccia thickness is also known to vary along large fault zones, this variation has not been explored in great detail. Based on the ®eld observations, subvertical, antithetic and synthetic fractures (Figs. 2±4) may channel water to the inclined fault plane. Such fractures are, of course, commonly observed in association with dip± slip faults, and are frequent in the hanging walls of many normal faults. The proposed channelling of water to the main fault plane may help build up high water pressure on the plane and thus contribute to the conditions of formula (8). However, so long as the breccia in the core acts as a barrier to vertical ¯ow of water, it will also tend to trap upward-migrating water that meets with the fault plane. Thus, water coming from deeper crustal levels that is temporarily trapped by low-permeability breccia on a dip±slip fault can also contribute to the condition of formula (8) being satis®ed. This is one aspect of the model that must be explored in more detail in a future work. One novel aspect of the analytical models on volumetric ¯ow rates presented here is that they predict that, normally, vertical fractures would be favoured over inclined fractures for ¯uid transport. In particular, the models indicate that, other things being equal, strike±slip faults are generally more effective than dip±slip faults as conductors of crustal ¯uids. These models obviously need to developed, where the associated crustal stress ®elds and host rock properties are explored in greater detail. Nevertheless, these conclusions may help explain the commonly observed differences in hydraulic effects of large active faults. Another novel feature of the model presented here is that the effects of the fault zone on the circulation of groundwater in its vicinity change during the development of the fault zone. The overall thickness of the breccia must change, and normally increase, with time (Robertson, 1983; Scholz, 1987; Hull, 1988; Forslund and Gudmundsson, 1992). These changes in thickness, however, are likely to ¯uctuate across the fault plane so that at any point on the fault plane periods of gradual increase in breccia thickness may alternate with periods of gradual decrease in breccia thickness. Because the groundwater circulation is partly controlled by the downdip and vertical channelling effects of the fault, these ¯uctuations in breccia thickness are likely to signi®cantly affect the

196

A. Gudmundsson / Tectonophysics 336 (2001) 183±197

overall groundwater system in the vicinity of the fault zone. Acknowledgements This work was supported by grants from the Research Council of Norway and by grants from the European Commission (contracts ENV4-CT96-0252 and EVR1-CT-1999-40002). References Bear, J., 1972. Dynamics of Fluids in Porous Media. Elsevier, New York, 764 pp. Blanpied, M.L., Lockner, D.A., Byerlee, J.D., 1992. An earthquake mechanism based on rapid sealing of faults. Nature 358, 574±576. Braathen, A., Berg, S., Storro, G., Jaeger, O., Henriksen, H., Gabrielsen, R., 1999. Fracture-zone geometry and groundwater ¯ow; results from fracture studies and test drilling in Sunnfjord. Geol. Surv. Norway, Report 99.017, 68 pp. (in Norwegian). Brace, W.F., 1960. An extension of the Grif®th theory of fracture to rocks. J. Geophys. Res. 65, 3477±3480. Bruhn, R.L., Parry, W.T., Yonkee, W.A., Thompson, T., 1994. Fracturing and hydrothermal alteration in normal fault zones. Pure Appl. Geophys. 142, 609±644. Caine, J.S., Evans, J.P., Forster, C.B., 1996. Fault zone architecture and permeability structure. Geology 24, 1025±1028. Curewitz, D., Karson, J.A., 1997. Structural settings of hydrothermal out¯ow: fracture permeability maintained by fault propagation and interaction. J. Volcanol. Geotherm. Res. 79, 149±168. De Marsily, G., 1986. Quantitative Hydrogeology. Academic Press, New York, 440 pp. Engelder, T., 1993. Stress Regimes in the Lithosphere. Princeton University Press, Princeton, 457 pp. Eshelby, J.D., 1957. The determination of the elastic ®eld of an inclusion and related problems. Proc. Roy. Soc. London A241, 376±396. Evans, J.P., Forster, C.B., Goddard, J.V., 1997. Permeability of fault-related rocks, and implications for hydraulic structure of fault zones. J. Struct. Geol. 19, 1393±1404. Forslund, T., Gudmundsson, A., 1992. Structure of Tertiary and Pleistocene normal faults in Iceland. Tectonics 11, 57±68. Giles, R.V., 1977. Fluid Mechanics and Hydraulics. McGraw-Hill, New York, 275 pp. Gray, D.R., Janssen, C., Vapnik, Y., 1999. Deformation character and palaeo-¯uid ¯ow across a wrench fault within a Palaeozoic subduction±accretion system: Waratah Fault Zone, southeastern Australia. J. Struct. Geol. 21, 191±214. Gudmundsson, A., 1988. Effect of tensile stress concentration around magma chambers on intrusion and extrusion frequencies. J. Volcanol. Geotherm. Res. 35, 179±194.

Gudmundsson, A., 1992. Formation and growth of normal faults at the divergent plate boundary in Iceland. Terra Nova 4, 464±471. Gudmundsson, A., 1995. Stress ®elds associated with oceanic transform faults. Earth Planet. Sci. Lett. 136, 603±614. Gudmundsson, A., 1999. Fluid overpressure and stress drop in fault zones. Geophys. Res. Lett. 26, 115±118. Gudmundsson, A., Berg, S.S., Lyslo, K.B., Skurtveit, E., 2001. Fracture networks and ¯uid transport in active fault zones. J. Struct. Geol. 23, 343±353. Haimson, B.C., Rummel, F., 1982. Hydrofracturing stress measurements in the Iceland research drilling project drill hole at Reydarfjordur, Iceland. J. Geophys. Res. 87, 6631±6649. Hickman, S., Sibson, R.H., Bruhn, R., 1995. Introduction to the special section: mechanical involvement of ¯uids in faulting. J. Geophys. Res. 199, 12831±12840. Hull, J., 1988. Thickness-displacement relationships for deformation zones. J. Struct. Geol. 10, 431±435. Jaeger, J.C., Cook, N.G.W., 1969. Fundamentals of Rock Mechanics. Chapman and Hall, New York, 515 pp. Jumikis, A.R., 1979. Rock Mechanics. Trans Tech Publications, Clausthal, 356 pp. Kanamori, H., Anderson, D.L., 1975. Theoretical basis of some empirical relations in seismology. Bull. Seismol. Soc. Am. 65, 1073±1095. Knipe, R.J., 1993. The in¯uence of fault-zone processes and diagenesis on ¯uid ¯ow. In: Horbury, A.D., Robinson, A. (Eds.), Diagenesis and Basin Development. Am. Ass. Petrol. Geol., pp. 135±151. Lamb, H., 1932. Hydrodynamics. Cambridge University Press, London, 738 pp. Lee, C.H., Farmer, I., 1993. Fluid Flow in Discontinuous Rocks. Chapman and Hall, London, 169 pp. Lee, M.K., Wolf, L.W., 1998. Analysis of ¯uid pressure propagation in heterogeneous rocks: Implications for hydraulically-induced earthquakes. Geophys. Res. Lett. 25, 2329±2332. Lekhnitskii, S.G., 1968. Anisotropic Plates. Gordon and Breach, New York, 534 pp. Leonardi, V., Arthaud, F., Tovmassian, A., Krakhanian, A., 1998. Tectonic and seismic conditions for changes in spring discharge along the Garni right lateral strike slip fault (Armenian Upland). Geodinamica Acta 11, 85±103. Melchiorre, E.B., Criss, R.E., Davisson, M.L., 1999. Relationship between seismicity and subsurface ¯uids, central Coast Ranges. California. J. Geophys. Res. 104, 921±939. Nicol, A., Watterson, J., Walsh, J.J., Childs, C., 1996. The shapes, major axis orientations and displacement pattern of fault surfaces. J. Struct. Geol. 18, 235±248. Nur, A., 1974. Tectonophysics: the study of relations between deformation and forces in the earth. In: Advances in Rock Mechancis, Vol. 1, Part A, U.S. National Committee for Rock Mechanics, National Academy of Sciences, Washington D.C., pp. 243±317. Nur, A., Booker, J.R., 1972. Aftershocks caused by pore ¯uid ¯ow? Science 175, 885±887. Odling, N.E., 1997. Scaling and connectivity of joint systems in sandstones from western Norway. J. Struct. Geol. 19, 1257± 1271.

A. Gudmundsson / Tectonophysics 336 (2001) 183±197 Odling, N.E., Gillespie, P., Bourgine, B., Castaing, C., Chiles, J.P., Christensen, N.P., Fillion, E., Genter, A., Olsen, C., Thrane, L., Trice, R., Aarseth, E., Walsh, J.J., Watterson, J., 1999. Variations in fracture system geometry and their implications for ¯uid ¯ow in fractured hydrocarbon reservoirs. Petrol. Geoscience 5, 373±384. Olsen, M.P., Scholz, C.H., Leger, A., 1998. Healing and sealing of simulated fault gouge under hydrothermal conditions: implications for fault healing. J. Geophys. Res. 103, 7421±7430. Robertson, E.C., 1983. Relationship of fault displacement to gouge and breccia thickness. Min. Engng. 35, 1426±1432. Rognvaldsson, S.T., Gudmundsson, A., Slunga, R., 1998. Seismotectonic analysis of the Tjornes Fracture Zone, an active transform fault in north Iceland. J. Geophys. Res. 103, 30117± 30129. Scholz, C.H., 1987. Wear and gouge formation in brittle faulting. Geology 15, 493±495. Scholz, C.H., 1990. The Mechanics of Earthquakes and Faulting. Cambridge University Press, Cambridge, 439 pp. Schultz, R.A., 1995. Limits on strength and deformation properties of jointed basaltic rock masses. Rock Mech. Rock Eng. 28, 1±15. Seront, B., Wong, T.F., Caine, J.S., Forster, C.B., Bruhn, R.L.,

197

1998. Laboratory characterisation of hydromechanical properties of a seismogenic normal fault system. J. Struct. Geol. 20, 865±881. Shapiro, S.A., Huenges, E., Borm, G., 1997. Estimating the crust permeability from ¯uid-injection-induced seismic emission at the KTB site. Geophys. J. Int. 131, F15±F18. Sibson, R.H., 1990. Rupture nucleation on unfavorably oriented faults. Bull. Seismol. Soc. Am., 1580±1604. Smith, L., Schwartz, F.W., 1993. Solute transport through fracture networks. In: Bear, J., Tsang, C.F., Marsily, G. (Eds.), Flow and Contaminant Transport in Fractured Rocks. Academic Press, New York, pp. 129±167. Sneddon, I.N., Lowengrub, M., 1969. Crack Problems in the Classical Theory of Elasticity. Wiley, London, 221 pp. Tada, H., Paris, P.C., Irwin, G.R., 1973. The Stress Analysis of Cracks Handbook. Del Research Corporation, Hellertown, Pennsyslvania. Tsang, C.F., Neretnieks, I., 1998. Flow channelling in heterogeneous fractured rocks. Rev. Geophys. 36, 275±298. Umeda, Y., Ito, K., Watanabe, H., 1996. Background ¯uid effect on the 1995 Hyogo-Ken Nanbu, Japan, earthquake. In: Thorkelsson, B. (Ed.), Seismology in Europe. European Seismological Commission, General Assembly 25. Icelandic Meteorological Of®ce, Reykjavik, pp. 282±287.