Fractured rock stress-permeability relationships from in situ data and effects of temperature and chemical-mechanical couplings

Transcription

1 Geofluids (2015) 15, doi: /gfl Fractured rock stress-permeability relationships from in situ data and effects of temperature and chemical-mechanical couplings J. RUTQVIST Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA, USA ABSTRACT The purpose of this paper is to (i) review field data on stress-induced permeability changes in fractured rock; (ii) describe estimation of fractured rock stress-permeability relationships through model calibration against such field data; and (iii) discuss observations of temperature and chemically mediated fracture closure and its effect on fractured rock permeability. The field data that are reviewed include in situ block experiments, excavation-induced changes in permeability around tunnels, borehole injection experiments, depth (and stress) dependent permeability, and permeability changes associated with a large-scale rock-mass heating experiment. Data show how the stresspermeability relationship of fractured rock very much depends on local in situ conditions, such as fracture shear offset and fracture infilling by mineral precipitation. Field and laboratory experiments involving temperature have shown significant temperature-driven fracture closure even under constant stress. Such temperature-driven fracture closure has been described as thermal overclosure and relates to better fitting of opposing fracture surfaces at high temperatures, or is attributed to chemically mediated fracture closure related to pressure solution (and compaction) of stressed fracture surface asperities. Back-calculated stress-permeability relationships from field data may implicitly account for such effects, but the relative contribution of purely thermal-mechanical and chemically mediated changes is difficult to isolate. Therefore, it is concluded that further laboratory and in situ experiments are needed to increase the knowledge of the true mechanisms behind thermally driven fracture closure, and to further assess the importance of chemical-mechanical coupling for the long-term evolution of fractured rock permeability. Key words: chemical and mechanical coupling, fractured rock, in situ experiments, permeabilty and stress, temperature Received 15 January 2014; accepted 22 May 2014 Corresponding author: Jonny Rutqvist, Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA 94720, USA. Jrutqvist@lbl.gov. Tel: Fax: Geofluids (2015) 15, INTRODUCTION Coupled thermal-hydrological-mechanical-chemical (THMC) processes are critically important for many geological engineering practices, including geological disposal of nuclear waste, geothermal energy extraction, and underground carbon sequestration (Tsang 1991, 1999; Rutqvist & Stephansson 2003; Rutqvist 2012; Rutqvist & Tsang 2012). Results from the international DECOVALEX project on modeling of coupled processes associated with nuclear waste disposal have shown that some processes, such as thermal and thermal-mechanical processes, can be predicted with a relatively high confidence level, whereas other processes are much more difficult to predict (Rutqvist et al. 2005, 2009a). In particular, coupled hydro-mechanical processes, including the effects of stress and deformation on rock-mass permeability, are notoriously difficult to predict in complex fractured rock masses (Rutqvist & Stephansson 2003; Rutqvist et al. 2013a). This difficulty arises because mechanically induced changes in rock-mass permeability depend on site-specific hydraulic and mechanical interactions within a heterogeneous fracture network which are very sensitive to small changes in fracture aperture and fracture connectivity (Min et al. 2004; Baghbanan & Jing 2008; Koh et al. 2011; Zhao et al. 2013). As a result, for a given rock mass, it is not easy to confidently predict how permeability might change under different mechanical forcing without observations from actual site-specific field experiments. Thus, as will be shown in this paper, it is crucial that site-specific in situ Ltd This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

2 In-situ stress-permeability relationships 49 experiments are undertaken at the appropriate scale (or across multiple scales), to avoid misleading results. In theory, a relationship between stress and permeability may be derived using laboratory testing on single fractures and an effective medium theory (see Path 1 in Fig. 1). However, owing to issues related to unrepresentative sampling and sampling disturbances, it is difficult to upscale reliable stress-permeability relationships (Rutqvist & Stephansson 2003). An alternative approach described in this paper is the back-analysis of stress-permeability relationships by model calibration against field data of stressinduced changes in rock-mass permeability (illustrated by Path 2 in Fig. 1). Unrepresentative sampling of a rock fracture is illustrated in Fig. 2. It shows how rock fractures in the field might contain large voids as a result of large shear offset and waviness along fracture surfaces. Using data from laboratory experiments on rock cores sampled from such a fracture could likely result in underestimation of aperture and permeability, whereas fracture normal stiffness would likely be overestimated. Model calibration according to Path 2 in Fig. 1 eliminates difficulties related to unrepresentative sampling and sample disturbances. However, model calibration against field data may be less controlled in terms of boundary conditions, and involves a number of underlying processes not directly related to stress that affect the overall permeability evolution. For example, field experiments involving elevated temperature may be strongly affected by additional temperature-dependent fracture closure. Such a temperature-driven fracture closure has been observed both in laboratory experiments and field tests, and has been described as thermal overclosure related to better fitting of opposing fracture surfaces at high temperatures (Barton 2007). Similar phenomenon has also been described as chemically Fig. 2. Schematic showing the effects of unrepresentative sampling through a fracture. Upper part shows the in situ fracture and the lower part potential core samples if drilled through the fracture. The large void under in situ conditions may not be captured in laboratory experiment on core samples which would indicate a smaller aperture and higher stiffness than for the original larger scale fracture (Modified from Wei & Hudson 1988). mediated fracture closure attributed to pressure solution (and compaction) of stressed fracture surface asperities (Yasuhara et al. 2004, 2011; Min et al. 2009). Such chemical-mechanical coupling and its impact on permeability has received renewed attention, especially related to long-term evolution of rock-mass permeability associated with nuclear waste disposal, geothermal energy extraction, and even geologic CO 2 sequestration (Taron & Elsworth 2009; Rutqvist 2012; Rutqvist & Tsang 2012). The objective of this paper is to (i) review field data on stress-induced permeability changes in fractured rock; (ii) describe back-analysis of rock-mass stress-permeability relationships through model calibration against such field data; and (iii) discuss observations of temperature and chemically mediated fracture closure and its effect on fractured rock permeability. Reviewed field data include in situ block experiments, borehole injection experiments, excavationinduced changes in permeability around tunnels, depth (and stress) dependent permeability, and permeability changes associated with a large-scale rock-mass heating experiment. Back-analyses of stress-permeability relationships against such field data are presented, including one case involving a large-scale rock-mass heating experiment. Finally, observations of additional temperature-dependent fracture closure as a result of so-called thermal overclosure or chemically mediated mechanical changes are discussed. Fig. 1. Two alternative ways (Path 1 and Path 2) for deriving a stress-permeability relationship of a fractured rock unit. Path 1 involves laboratory testing on single fractures and an effective medium theory, whereas Path 2 involves back-analysis by model calibration against field data. FRACTURED ROCK STRESS-PERMEABILITY RELATION AND SAMPLE SIZE EFFECT Figure 3, from a review by Rutqvist & Stephansson (2003) on hydromechanical coupling in fractured rocks, presents

3 50 J. RUTQVIST typical hydromechanical behavior of single rock fractures as known from several decades of experimental and theoretical studies. In Fig. 3A, a size dependency on fracture normal closure is indicated as an increased maximum closure, d max, with increased sample size. Such a sample size effect on fracture normal stiffness was observed by Yoshinaka et al. (1993) and through systematic experiments on concrete replica of rock fractures by Fardin (2003), as well as in a recent comprehensive review of joint stiffness data by Zangerl et al. (2008). Similar reduction in fracture normal stiffness with sample size has also been observed from seismic wave propagation through fractured rocks (Worthington & Lubbe 2007; Hobday & Worthington 2012). Figure 3B shows a corresponding increase in hydraulic conducting fracture aperture with sample size, which has been observed by comparing the hydromechanical behavior of different sized rock fractures, including in situ block and ultra-large core experiments that will be discussed in the next section. Such correlation between fracture stiffness (or fracture compliance) and permeability is also being used to develop scaling relationships aiming at new methods for seismic (non-intrusive) evaluation of fractured rock permeability (Petrovitch et al. 2013). The effect of sample size on fracture shear behavior (Fig. 3C,D) was quantified in the late 1970s by Barton & Choubey (1977), with conclusive experiments by Bandis et al. (1983). For a larger fractured sample, the peak shear stress is smaller and takes place after a larger shear displacement magnitude and the onset of shear dilation is delayed. In fractured rock, a change in the stress field may mechanically reactivate fractures, either as a result of changes in effective normal stress (normal stress reactivation) or shear stress (shear stress reactivation). Such reactivation may be triggered by fluid injection and associated increase in fluid pressure that reduces the effective normal stress and thereby also reduces the shear resistance (shear strength) of the fracture. Permeability change by effective normal stress reactivation is related to changes in the local stress field across fractures and occurs to some degree even for small and elastic mechanical responses. Substantial permeability changes by shear reactivation generally require shear failure and a shear displacement of several millimeters (Fig. 3D). However, the magnitude of shear displacement along a fracture is limited by its length and the elastic properties of the surrounding rock mass (Dieterich 1992; Rutqvist et al. 2013a). To allow for substantial shearinduced permeability changes, fractures must be sufficiently long or located near a free surface, such as the ground surface or a tunnel wall, or within a fracture zone of highly fractured rocks. Figure 4 shows an example of calculated stress-induced permeability changes for a fractured rock mass as a combination of elastic fracture normal closure and shear dilation (Min et al. 2004). For the assumed Mohr-Coulomb mechanical properties, shear dilations were initiated at a stress ratio of 3, i.e., a maximum compressive stress magnitude three times the minimum compressive stress magnitude. A substantial shear dilation occurred because the rock mass was assumed to be intensely fractured, and shearing was localized along multiple aligned fractures. Moreover, it appears that the substantial shearing observed in Fig. 4 might also depend on the model size, with free moving boundaries around the m model domain. Indeed, the same fracture network was used in a different study, but considering a larger m model, and as a result, much less shear-induced permeability increase occurred (Rutqvist et al. 2013a). IN SITU BLOCK AND ULTRA-LARGE CORE EXPERIMENTS In situ block and ultra-large core experiments enable controlled studies of coupled hydraulic and mechanical behavior of fractured rocks and rock fractures at meter scale. Figure 5 presents the results of a number of such in situ block and ultra-large core experiments conducted in the 1970s and 1980s. In situ block experiments are typically loaded with flat jacks a thin envelope-like bladder that may be pressurized with hydraulic oil in slots around the block, whereas ultra-large core experiments involve collecting a large core (including fractures) and then loading the core in a laboratory. Figure 5a compares results from several 1970s experiments (Iwai 1976; Pratt et al. 1977; Witherspoon et al. 1979). From these data, Witherspoon et al. (1979) identified an apparent dependency of fracture permeability on sample size. According to their findings, for the maximum stress level that could be attained, the minimum values of fracture hydraulic conductivity increased with specimen size. Similar behavior for a high minimum fracture hydraulic conductivity is observed in Figs. 5B,C for two other large-scale experiments (Hardin et al. 1982; Sundaram et al. 1987). In these experiments, aperture and permeability change rapidly at low stress, but for stress increases above 5 MPa, aperture and permeability do not change as rapidly and reach irreducible (or residual) values. Figure 5D presents results from an in situ block experiment at the Stripa Mine in Sweden exhibiting different behavior (Makurat et al. 1990). In this in situ block experiment, the fracture permeability goes to zero when the normal stress exceeds about 5 MPa. This was attributed to soft fracture infilling of precipitated minerals that completely clogs the fracture at high stress (Makurat et al. 1990). Figure 6 presents another unique experimental result of a uniaxial compression test conducted at the Lawrence Berkeley National Laboratory on a large core sample (about 1 m high and 1 m diameter) of fractured granite from the Stripa Mine (Thorpe et al. 1982). The fractured

4 In-situ stress-permeability relationships 51 (C) (D) Fig. 3. Typical hydromechanical behavior of rock fractures during normal (A, B) and shear (C, D) deformation (Rutqvist & Stephansson 2003). Effects of sample size is indicated with the laboratory sample response (dashed lines) compared with in-situ fracture response (1-m 2 size). Fig. 4. Simulation of the horizontal permeability evolution of an intensely fractured rock mass subject to increasing shear stress (r X /r Y ) ratio (results from Min et al. 2004). Elastic simulation results are compared to that of elasto-plastic using Mohr-Coulomb failure along fractures to investigate the effect of shear dilation on horizontal permeability. sample was loaded in unconfined compression (axial load) until shear failure was initiated, with shear in some existing subvertical fractures and creation of some new fractures. Fluid flow from an internal borehole was used to evaluate changes in transmissivity with axial loading. Before the actual compression test, a seepage test was conducted showing that the fluid flow was dominated by flow through the subhorizontal Fracture B and a steeply dipping Fracture D (Fig. 6B). Fracture B was inadvertently opened during the sample preparation, which may explain its dominance. At the intersection between fractures D and B, an offset of 1 2 cm was observed, indicating previous shear in Fracture D. Figure 6E shows the flow rate versus axial load, with initial decreasing flow until shear failure is initiated at an axial load of about 6 MPa. Thereafter, the flow increases with the additional axial load. In Fig. 6C,D, the shear and normal stress have been estimated (with great uncertainty) by projection from the axial load normal and along the steeply dipping fracture plane. The initial flow decrease is caused by fracture normal compression under increasing normal stress, whereas the subsequent flow increase is caused by shear dilation once shear failure occurs. Figure 6E shows measured total outflow as well as calculated outflow from fractures B and D using measurements of aperture changes (from strain measurements). There are discrepancies between calculated and observed flow, possibly related to differences between hydraulically conducting and mechanical aperture. Nevertheless, the overall response resembles that of the numerical simulations in Fig. 4. Moreover, the mechanical behavior of Fracture D follows in general that of generic curves in Fig. 3 for 1 m 2 sample size. That is, an initial (elastic) shear displacement of about 1 mm, followed by a shear failure without a pronounced peak shear stress. Then, during an additional 1 mm shearing, a shear dilation of about 0.3 mm was observed, resulting in an increased permeability when the axial load was increased up to 7.5 MPa. Further shearinduced permeability increases would be expected if the loading had been continued. In summary, the large-scale in situ block and ultra-large core experiments in Figs 5 and 6 show the important effects of sample size and fracture filling, effects that can lead to very different permeability evolution with stress

5 52 J. RUTQVIST (C) (D) Fig. 5. Hydromechanical behavior of fractures from in situ block and ultra-large core experiments: fracture conductivity (in cm sec 1 ) as a function of normal stress for several experiments of different sample sizes compared in (Witherspoon et al. 1979), unit flow rate (in cm 3 sec 1 MPa 1 ) as a function of normal stress for a fractured ultra-large core specimen (Sundaram et al. 1987), (C) unit flow rate (in cm 3 sec 1 MPa 1 ) as function of normal stress for an in situ block experiment (Hardin et al. 1982), (D) stress-versus-hydraulic conducting aperture from an in situ block experiment, including a mineral filled fracture (Makurat et al. 1990). which would be difficult to predict from tests on smallscale core samples of the same fractures. Moreover, the large core experiment in Fig. 6 shows the heterogeneous nature of the flow, with flow focused in a few open fractures and their intersections, and heterogeneously distributed along fracture planes. In this large core experiment, the flow response to loading was complex, but demonstrated theoretically predicted behavior, with compression and shear dilation according to the loading on the dominant fractures. Nevertheless, at a fractured rock site, it would be difficult to predict the magnitude of these changes, as well as the initial permeability, without actual site-specific in situ testing. In the next section, one type of such in situ tests is described. BOREHOLE INJECTION TESTS Hydraulic jacking tests (or step-rate tests) is a type of borehole injection test that have been used to investigate pressure-sensitive permeability within dam foundations (Louis et al. 1977) and also used in association with hydraulic fracturing stress measurements (Doe & Korbin 1987; Rutqvist & Stephansson 1996). Rutqvist (1995) and Rutqvist et al. (1997) applied hydraulic jacking tests combined with coupled numerical modeling to determine the in situ hydromechanical properties of fractures at two crystalline rock sites in Sweden (Fig. 7). Hydraulic jacking tests were conducted by a step-wise increase in fluid pressure. At each step, the well pressure was kept constant for a few minutes until the flow was steady (Fig. 7A). Numerical analysis of these injection tests showed that the flow rate at each pressure step is strongly dependent on the aperture and normal stiffness of the fracture in the vicinity of the borehole, where the flow resistance and pressure gradient are the highest (Fig. 7B). Such numerical modeling of injection tests are also presented in Preisig et al. (2014), using a discrete fracture model, and indicating the potential for more complex responses, including shear slip. Figure 7C shows one example of a pressure-versus-flowrate response from a hydraulic jacking test at 267 m depth in a borehole at the Laxemar crystalline rock site in Southeastern Sweden (Rutqvist et al. 1997). At the first cycle of step-wise increasing pressures, the flow rate increased as a nonlinear function of pressure. A temporal peak-pressure was obtained at a flow rate of 1.3 l min 1, and thereafter the pressure began to decrease with increasing flow rate. A shear-slip analysis of the particular fracture, which was inclined to the principal in situ stresses, indicated that

6 In-situ stress-permeability relationships 53 (C) (D) (E) Fig. 6. Uniaxial compression on a ultra-large core of fractured Stripa Granite conducted at the Lawrence Berkeley National Laboratory (Thorpe et al. 1982). Schematic of test arrangement, fracture mapping and seepage during a hydraulic test conducted before the unixial compression test, (C) shear stress versus shear displacement, (D) normal stress versus normal displacement, and (E) flow versus axial stress (modified from Thorpe et al. 1982). these irreversible fracture responses could be caused by shear slip, because the increasing fluid pressure reduces fracture shear strength. The subsequent step-pressure cycle took a different path because of the change in hydromechanical properties, possibly as a result of shearing or break-up of fracture filling. Figure 8A presents the back-calculated relationships between fracture transmissivity and effective normal stress for several fractures at depths ranging from 266 to 338 m. Results showed that the transmissivity of the most conductive fractures is relatively insensitive to stress. From borehole images, these fractures appeared to be open fractures that were incompletely cemented, suggesting flow channels in a fracture that appears to be locked open (e.g., fractures at about 338 m shown in Fig. 8B). The stress-permeability behavior of these fractures resembles that of the large fracture-scale-experimental data in Fig. 5, such as that of Witherspoon et al. (1979). That is, permeability changes rapidly at low stress, but for stress increases above 5 MPa aperture and permeability do not change as rapidly and reach irreducible (or residual) values. The back-calculated stress-versus-transmissivity relationships for fractures at 316 and 336 m resemble that of the Makurat et al. (1990) in situ block test shown in Fig. 5D. That is, soft mineral filling is postulated to have a strong effect, making transmissivity of these fractures extremely stress-dependent, clogging the fractures completely for fluid flow when the stress normal to the fracture exceeds a certain threshold. Recently, specialized borehole testing tools enabling simultaneous measurements of hydraulic and mechanical fracture responses have been developed, both at Clemson University in South Carolina (Schweisinger et al. 2007; Svenson et al. 2008) and at Geosciences Azur at University of Nice and Marseille, France (Cappa et al. 2006a,b; Guglielmi et al. 2014). This kind of specialized equipment has been used to evaluate in situ properties such as fracture

7 54 J. RUTQVIST normal stiffness and storativity during various types of injection tests, including step-rate and pulse tests. As described in Schweisinger et al. (2009), and further developed in Schweisinger et al. (2011), Murdoch & Germanovich (2012), and Slack et al. (2013) the use of simultaneous pressure and deformation measurements improves estimates of storativity and reduces non-uniqueness during the evaluation of hydraulic well tests. The most recent development of this concept involves a 3-component borehole deformation sensor that enables simultaneous measurements of fracture normal and shear displacement during a borehole injection test (Guglielmi et al., 2014). The equipment has been tested for measurements of injection-induced shear deformation in fractured carbonate rock (Derode et al. 2013). Moreover, the use of this equipment has been qualified as an International Society of Rock Mechanics Suggested Method, denoted Step-Rate Injection Method for Fracture In-Situ Properties (Guglielmi et al. 2014). Future applications of this equipment will include in situ measurements of coupled hydromechanical responses during reactivation of faults in shale. These measurements will help to constrain model parameters for permeability change during reactivation of minor faults in shales, which is relevant for assessing caprock sealing performance at geologic CO 2 sequestration sites and for assessing the potential for fault activation and leakage during shale-gas hydraulic fracturing operations (Rutqvist 2012; Rutqvist et al. 2013b). (C) Fig. 7. In situ determination of stress-transmissivity relationships, using a combination of pulse, constant head, and hydraulic jacking tests. Schematic representation of pressure and flow versus time, the radius of influence in each test, and (C) results of a hydraulic jacking test at 267 m depth (Rutqvist et al. 1997). MODEL CALIBRATION AGAINST EXCAVATION-INDUCED PERMEABILITY CHANGES Stress-induced changes in permeability around excavations, including the Excavation Disturbed Zone (EDZ), have been studied since the early 1980s at many sites with various rock types (B ackblom & Martin 1999; Tsang et al. 2005; Bl umling et al. 2007). The EDZ includes a damage zone of induced rock failure and fracturing by the excavation process, a zone with altered stress distribution around an excavation and a zone of reduced fluid pressure. Permeability measurements in the zone of altered stress around an excavation may be utilized for model calibration of stress-permeability relationships. Here, two examples are presented, one from a sparsely fractured rock site at the underground rock laboratory (URL) in Manitoba, Canada, and another from an intensely fractured rock site at Yucca Mountain, Nevada. The Manitoba URL TSX tunnel experiment The TSX tunnel (Room 425) at the Manitoba URL, Canada (Martino & Chandler 2004) was one of several experimental tunnels at the URL dedicated to studying the EDZ. To minimize the EDZ, the TSX tunnel was excavated using smooth drill-and-blast techniques in an elliptical cross section 3.5 m high and m wide (a horizontal to vertical aspect ratio of 1.25). At the depth of the TSX tunnel (420 m), the principal stresses were estimated to be 60 MPa (maximum stress), 45 MPa (intermediate stress), and 11 MPa (minimum stress), with the maximum principal stress parallel with the tunnel axis and the minimum principal stress subvertical. During excavation, the occurrence and location of microseismic events were monitored. After excavation, the resulting EDZ was characterized by a variety of methods, including the microvelocity probe (MVP) method for measuring changes in

8 In-situ stress-permeability relationships 55 Fig. 8. Back-calculated hydromechanical properties of fractures intersecting a borehole at a crystalline rock site in Sweden (Rutqvist et al. 1997): Fracture transmissivity versus effective normal stress for fractures at depths between m (solid lines) with comparison to results from in situ block experiment by Makurat et al. (1990) and ultra-large core experiment by Witherspoon et al. (1979) (dashed lines), borehole image indicating open fractures at about 338 m depth. sonic velocities, and the SEPPI, which is a borehole pressure pulse probe for measuring changes in permeability. The results of the SEPPI permeability measurements were used for model calibration of a stress-permeability relationship (Rutqvist et al. 2009b). The excavation-induced permeability changes at the TSX tunnel were simulated using a simplified but practical model that could be both implemented in the numerical simulator at hand and capture reasonably well the observed damage and permeability changes at the URL field experiments (Rutqvist et al. 2009b). Using recommended in situ rock-strength parameters (corresponding to an in situ strength about 50 60% of short-term laboratory strength) the simulation resulted in a limited mechanical failure at the crown of the tunnel, in agreement with observed increased macroscopic fracturing. This is the region where the highest shear stress occurs and most microseismic events were clustered. The permeability around the tunnel was simulated using an empirical stress-permeability relationship in which permeability is a function of effective mean stress, r 0 m, and deviatoric stress, r d, according to (Rutqvist et al. 2009b): k½k r þ Dk max expðb 1 r 0 m ÞŠ expðcdr dþ ð1þ where k r is residual (or irreducible) permeability at high compressive mean stress, Dk max, b 1 and c are fitting constants, and Dr d is the change in deviatoric stress relative to a critical deviatoric stress for onset of shear-induced permeability. Figure 9 compares simulated and measured permeability changes for b 1 = Pa 1, k r = m 2, Dk max = m 2, c = Pa 1, and with the critical deviatoric stress for onset of shear-induced permeability set to 55 MPa. The 55 MPa critical deviatoric stress roughly coincides with the extent of the observed cluster of microseismic events at the top of the tunnel and to about 0.3 of the instantaneous uniaxial compressive stress of small-scale core samples, which is consistent with the stress level at which crack initiation has been observed in studies of Lac du Bonnet granitic samples Martin & Chandler (1994). Thus, at least part of the observed permeability increase above the tunnel is caused by microfracturing under high compression, whereas permeability increase off to the side of the tunnel is caused by opening of existing microfractures as a result of decreased mean stress. The back-calculated stress-permeability relationship is presented in Fig. 10. Having determined this relationship by in situ calibration at the scale of the tunnel, one can implicitly take into account scale and time-dependent strength degradation. Studies at the URL have indicated that strength reduction of the granitic rock around open tunnels reaches a steady state at 50 60% of the short-term strength within a few weeks. It is possible that the severalorders-of-magnitude increase in permeability measured at the top of the tunnel was caused by macroscopic fracturing that was indeed observed in the boreholes. The macrofracturing implies that a simple relationship between mean and deviatoric stress, as defined in Eq. 1, may no longer be valid. Instead, the permeability may be governed by fracture permeability as a function of stress normal to the created fracture planes. The Yucca Mountain niche excavations Figure 11 presents measurements of excavation-induced changes in permeability above a niche excavated off a tun-

9 56 J. RUTQVIST Fig. 9. Calculated and measured permeability changes around the TSX tunnel (Rutqvist et al. 2009b). Permeability versus radius along a horizontal profile from the side of the tunnel and a vertical profile from the top of the tunnel. Fig. 10. Calibrated stress-versus-permeability relationship according to Eq. 1, with b 1 = Pa 1, k r = m 2, Dk max = m 2, c = Pa 1, and the critical deviatoric stress for onset of shear induced permeability is set to 55 MPa. MEQ refers to microearthqaukes which were also triggered in areas around the tunnel where deviatoric stress exceeded 55 MPa (Rutqvist et al. 2009b). nel in unsaturated fractured tuff at Yucca Mountain, Nevada (Wang et al. 2001; Rutqvist & Stephansson 2003; Rutqvist & Tsang 2012). The complete data set involved measurements of air permeability at four niches excavated by a mechanical (alpine mining) method. Permeability was measured before and after excavation in 30 cm packed-off sections along 10 m long boreholes located about m above the niche, supposedly outside the damaged zone (Fig. 11). The results in Fig. 11 for one niche show that the pre/post permeability ratio ranges between a factor of 1 400, with a trend of relatively stronger permeability increase for those sections where the initial permeability is smaller. Figure 12 presents the best match of calculated and measured geometric mean permeability change ratio for data from two welded tuff units, denoted Tptpmn and Tptpll. The calculation was conducted assuming three orthogonal fracture sets (consistent with fracture mapping at the site), with permeability depending on the stress normal to each fracture set (Rutqvist 2004; Rutqvist & Tsang 2012). The calculated geometric mean permeability matches the measured geometric mean change (Fig. 12). However, the wide range of permeability changes (from 1 to 400) observed in the field (Fig. 11) may be related to opening of fractures with different orientation relative to the niche. It is likely that pressure-flow response in each section is determined by flow into a few dominant fractures, and that their mechanical response upon excavation depends on their orientation. Figure 13 presents the stress-aperture relationship used for the best match solution. In this relationship, the aperture b depends on the effective normal stress r 0 n according to (Rutqvist & Tsang 2003): b ¼ b r þ b max expðar 0 n Þ ð2þ where b r is the irreducible aperture and b max and a are fitting parameters used to match measured and calculated permeability responses. In this case, b max = 200 lm and a = 0.8 MPa 1. The irreducible aperture, b r, varies with initial permeability, which explains the trend of stronger permeability increase at lower initial permeability. The stress-versus-aperture function defined by Eq. 2 was developed and applied as an empirical function for matching the permeability changes observed in the intensely fractured tuff units. However, such an exponential function was later derived by a closed form solution and verified using a number of data sets in the literature for fracture closure versus stress (Liu et al. 2013). The functions in Fig. 13 display some resemblance to the results of the in situ block and ultra-large core tests shown in Fig. 5. In essence, permeability is very stress-sensitive at low stress, but for normal stresses above 5 MPa, the permeability is relatively insensitive to stress and approaches an irreducible permeability. Moreover, the tendency for stronger permeability change in fractures with smaller initial aperture is consistent with observations at the borehole injection tests at the Swedish crystalline rock site (Fig. 8). This behavior could be related to the notion that fractures with high initial aperture might have been locked open by shearing offset between rough fracture surfaces (Rutqvist & Stephansson 2003). However, Eq. 2 would be expected to be valid at relatively low stress, since

10 In-situ stress-permeability relationships 57 Fig. 11. Results of pre- to post excavation air-permeability tests above a niche in fractured unsaturated tuff. The results shown are for a niche with three boreholes (UL, UM and UR) located above niche 3560 (Wang et al. 2001). Fig. 13. Fracture stress-transmissivity behavior of fractures back-calculated from permeability measurements during excavation of niches: exponential stress-aperture relationship and corresponding stress-transmissivity relationship. Fig. 12. Measured and calculated mean values of pre- to post permeability change ratio at three niches (Niche 3107, 3560, and 4788) (Rutqvist 2004). ultimately, at very high stresses, fractures are not expected to stay open at such a high residual aperture. The exponential function in Liu et al. (2013) contains additional terms that allows for gradual fracture closure at very high stress. DEPTH DEPENDENT PERMEABILITY OF SHALLOW BEDROCK Measurements of permeability in vertical boreholes and their variations with depth (and stress) might be used to calibrate in situ stress-permeability relationships. However, one has to consider that rock-mass permeability is strongly affected by other parameters or factors, such a fracture frequency, connectivity, infilling by mineral precipitation and history. For example, Fig. 14 presents a schematic by Rutqvist & Stephansson (2003) based on a vertical permeability profile of short-interval (3-m packer separation) well tests performed in crystalline rock at Gidea, Sweden. The figure shows a general decrease in permeability with depth; however, the depth dependency is obscured by a very large permeability variation at any given depth (up to 6 orders of magnitude). This large variability may also be affected by difficulties in evaluating appropriate permeability from transmissivity values obtained from well tests (Stober & Bucher 2014). One general observation from Fig. 14, and from many fractured crystalline rock sites, is that a more pronounced depth dependency can be found in the upper m of the bedrock. The more pronounced depth dependency in shallow areas can be explained by the nonlinear normal stress-aperture relationship of single extension joints. Such a decrease in hydraulic aperture with depth was observed in the 1960s by Snow (1968), who used detailed pumping tests and fracture statistics to determine fracture apertures at numerous dam foundations. The minimum values of permeability on the left-hand side of Fig. 14 represent the permeability of the rock matrix, implying either that no fracture intersected the 3- m long test interval, or if fractures were intersecting the interval, they are either completely cemented with minerals or isolated from a conducting fracture network. The maximum permeability values on the right-hand side of Fig. 14 represent the transmissivity of at least one intersecting fracture which is highly conductive and connected to a larger network of conducting fractures. It is likely that these

11 58 J. RUTQVIST Fig. 14. Depth-dependent permeability in fractured rock obscured by chemical and mechanical processes (Rutqvist & Stephansson 2003). Permeability was measured in short-interval well tests in fractured crystalline rocks at Gidea, Sweden (data points from Wladis et al. 1997). Schematic of effects of shear dislocation and mineral precipitation/dissolution processes that obscure the dependency of permeability on depth (stress). The permeability values on the left-hand side represent intact rock granite, whereas the permeability values on the right-hand side represent highly conductive fractures. highly conductive fractures are locked open either by bridges of hard mineral filling or by large shear dislocation. In crystalline rock, the locked open fracture category could comprise mineral-filled or shear dislocated fractures throughout the rock mass; however, large channels are more likely to occur in fault zones where large movements allows substantial shear dislocation and extension of oblique fractures (National Research Council 1996). Interestingly, in Fig. 14, the maximum permeability values of about k = m 2 below a few 100 m depth correspond quite accurately to the transmissivity value for of the most transmissive fracture in Fig. 8. That is, for a packer spacing of b = 3m, k = m 2, correspond to a transmissivity of about T = (k 9 b 9 q 9 g)/l ( ) / = m 2 sec 1, which is very similar to the transmissivity of the fracture at 315 m in Fig. 8. The average permeability at depth in Fig. 14 is about to m 2 and this correspond to a transmissivity of about to m 2 sec 1, which is similar to the transmissivity of the fractures at 266 and 267 m in Fig. 8. When properly considering the many processes that could impact the depth-dependent permeability, such data could be useful for bounding and/or validating stress-permeability relationships at a fractured rock site. An example of such development applied to fractured sandstone is presented in Jiang et al. (2009) and for granite and shale in Jiang et al. (2010). Here, a practical example from Yucca Mountain is presented, in which the fracture permeability and fracture frequency have been carefully characterized for different layers of a sequence of welded and unwelded tuff units, from the ground surface of the mountain down to the ground water table at 600 m depth (Fig. 15). Figure 15A shows that the permeability varies by about two orders of magnitude, i.e., much less than the 6-order variation for the crystalline rock site in Fig. 14. The permeability was evaluated from air-injection tests in packed-off sections of vertical boreholes (with 3 m packer separation) and with one average permeability value assigned to the entire thickness of each geological unit. Figure 15B shows that the fracture frequency ranges from 0.1 to 5 fractures per meter, with some tendency towards higher permeability in layers with higher fracture frequency. Finally, Fig. 15C (red line) presents the equivalent hydraulic conducting aperture, b h, calculated from the permeability, k, and fracture frequency, f, using the cubic relation between equivalent fractured rock permeability and aperture according to Rutqvist & Stephansson (2003) p b h ¼ ffiffiffiffiffiffiffiffiffiffi 3 6k=f ð3þ assuming a fractured medium with three orthogonal sets of fractures and with uniform fracture spacing, s = 1/f. The uniform fracture spacing assumption in Eq. 3 is certainly a simplification that results in an average b h for the particular rock unit. At the Yucca Mountain, the rock units are intensely fractured with three orthogonal fracture sets and therefore Eq. 3 is relatively accurate. At other sparsely fractured rock sites, such as the aforementioned Gidea crystalline rock sites, Eq. 3 is likely not appropriate. The blue lines in Fig. 15C represent the stress-aperture function that was back-calculated from the aforementioned niche-excavation experiments; that is, the exponential function of stress according to Eq. 2 with b max = 200 lm and a = 0.8 MPa 1. Both permeability and frequency varies substantially between different rock units, whereas the back-calculated hydraulically conducting aperture is quite consistent around the average stress-aperture function. Note that the rock mass at Yucca Mountain has a dense, well-connected fracture network, which also explains why permeability does not vary as much as in a sparsely fractured rock site such as the Gidea crystalline rock site in Fig. 14. Again, the aperture is relatively constant for stresses above 5 MPa, indicating that the fractures aperture approaches an irreducible value. The stress-aperture functions matched to field data in Fig. 15C, with a residual aperture, could be expected to be valid for the shallow Earth crust, where stresses are much lower than the uniaxial compressive rock strength. Going much deeper, large voids created by fracture shear dislocation may not be kept open, but would be expected to

12 In-situ stress-permeability relationships 59 Fig. 15. Field data of fractured rock permeability, fracture frequency and calculated hydraulic conducting aperture through a vertical sequence of fractured volcanic rock units at Yucca Mountain, Nevada (Rutqvist 2004). Blue lines in the right figure correspond to the exponential stress-aperture function for various residual apertures. collapse under ambient stress. As will be further discussed in Section Application to geoengineering activities and potential implications for crustal permeability, such collapse of larger voids at depth may have important implications for crustal permeability-depth distribution. MODEL CALIBRATION AGAINST THE YUCCA MOUNTAIN DRIFT SCALE TEST The Yucca Mountain Drift Scale Test provides perhaps the most comprehensive data set of thermally induced changes in fractured rock permeability during rock-mass heating and cooling (Rutqvist et al. 2008). During the experiment, a volume of over m 3 of intensely fractured volcanic tuff was heated for 4 years, including several tens of thousands of cubic meters heated to above-boiling temperature (Fig. 16). This massive heating induced strongly coupled thermal-hydrological-mechanical-chemical (THMC) changes that were continuously monitored by thousands of sensors embedded in the fractured rock mass. Among the monitoring data was periodic active pneumatic (air-injection) measurements used to track changes in air permeability within the variably saturated fracture system around the heated drift. Airinjection testing was conducted in 44 several-meters-long packed-off sections in hydrological boreholes, located in three clusters forming vertical fans that bracketed the heated drift (Fig. 16). Thermally induced permeability changes at the Yucca Mountain Drift Scale Test were analyzed using coupled THM modeling (Rutqvist et al. 2008). The analysis showed that observed changes in air permeability at the site can be explained by a combination of thermal-mechanically-induced changes in fracture aperture and moistureinduced changes (Fig. 17). The modeling reproduced the average permeability evolution using the stress-permeability function shown in Fig. 18A, which is based on the exponential stress-aperture function in Eq. 2. Moreover, a better match between calculated and measured responses was achieved when assuming that the measured permeability was dominated by air flow into the dominant vertical fracture set oriented normal to the subhorizontal boreholes. However, the analysis also indicated irreversible permeability changes that significantly deviated from the reversible thermo-hydro-elastic solution (Fig. 17). The identified irreversible permeability changes may be attributed to inelastic thermal-mechanical processes consistent with either inelastic fracture shear dilation (where permeability increased) or inelastic fracture surface asperity shortening (where permeability decreased). Whereas the stress-permeability relationship shown in Fig. 18A provides a good match to the measured average permeability responses, the underlying aperture-versusstress relationship depends on the spacing of active (or dominant) fractures. Therefore, two alternative functions are presented in Fig. 18B. Note that the aperture-versusstress relationships shown in Fig. 18B are quite different from those that were back-calculated from the niche excavation experiments (Fig. 13A). A possible explanation for this apparent inconsistency in the stress-aperture relationships derived from the two different field experiments in the same rock unit may be related to thermal over-closure and/or chemically mediated changes that resulted in additional fracture closure during heating at the Drift Scale Test. This possibility will be further discussed in the next section.

13 60 J. RUTQVIST Fig. 16. Three-dimensional view of the Yucca Mountain Drift Scale Test. The color-coded lines indicate boreholes for various measurements of thermally driven THMC responses (Tsang et al. 2009; Rutqvist & Tsang 2012). Fig. 17. Schematic of the range of measurements of air permeability at the Yucca Mountain Drift Scale Test. Details of calculated and measured responses in all 44 measurement intervals can be found in (Rutqvist et al. 2008). THERMAL AND CHEMICALLY MEDIATED MECHANICAL CHANGES Chemically mediated changes in fracture permeability received renewed attention after a series of laboratory experiments conducted at the Penn State University (Polak et al. 2003; Yasuhara et al. 2004). For example, experiments conducted on single fractures in Arkansas Novaculite (essentially pure quartz) show that fracture permeability decreases with increasing temperature up to 150 C, even under a constant stress. During these experiments, the chemical composition of the fluid flowing through the fracture was carefully monitored. Minerals were dissolved as the permeability decreased, indicating fracture closure as a result of pressure solution of fracture asperities. Similar behavior has been observed in laboratory experiments on fractures in samples of volcanic tuff (Lin & Daily 1990) and in granite (Yasuhara et al. 2011). The effect of temperature on fracture permeability under constant normal stress has also been observed during previously reported in situ block heater tests. For example, during the Terra Tek in situ heated block tests in gneiss (Hardin et al. 1982), aperture magnitude was reduced by more than three times as the temperature increased from 12 C to 74 C under constant stress. These results and other field observations were reviewed by Barton (2007), who emphasized that these effects, although known from experiments for almost 40 years, appear to have been ignored in the analysis of coupled THM processes of fractured rock. The explanation for this phenomenon, which Barton (2007) described as thermal overclosure, is that the joint in question, and perhaps the huge majority of joints developed in the crust, were formed at variously elevated temperatures. They were thereby given a primeval fingerprint of 3D roughness influenced by all the minerals (or grains) forming the joint walls. When cooled, various subtle changes would occur, causing reduced fit (Barton 2007) as a result of thermal-mechanical changes in the fracture surface geometry, rather than chemically mediated mechanical changes. Min et al. (2009) developed a THMC model of fracture permeability, including dissolution-like compaction of the fracture surfaces, based on the experimental results for Arkansas Novaculite. They applied the model to explain the effects of temperature on permeability observed during the Terra Tek in situ heated block experiment (Fig. 19). The model did not explicitly include the time-dependent pressure solution process, but instead considered the steady-state aperture value achieved for a given load and temperature (Min et al. 2009). The model explains the additional temperature-dependent permeability reduction as being caused by pressure solution of highly stressed surface asperities, causing additional irreversible fracture closure. Figure 19B shows that the agreement between modeling (lines) and observations (filled circles) is excellent

14 In-situ stress-permeability relationships 61 Fig. 18. Fracture stress-versus-permeability behavior back-calculated from air-permeability measurements at the Yucca Mountain Drift Scale Test: fractured rock permeability versus stress along one set of fractures and corresponding aperture-versus-stress relationship for two assumptions regarding the spacing of dominant fractures. for all loading stages except for the end point, i.e. point 6. The modeling shows irreversible fracture closure as a result of shortening of fracture surface asperities by pressure solution, while the experiments indicate that the fracture rebounds to the pre-heating conditions. This might be a result of the fact that the in situ block was fixed to underlying rock at the bottom, which was not considered in the modeling. The G-tunnel in situ heated block experiment conducted in welded fractured tuff close to Yucca Mountain, Nevada, provides another example of temperature-dependent fracture closure (Fig. 20) (Zimmerman et al. 1985). Fracture flow testing was first conducted under a number of isothermal stress cycles, and then the block was exposed to heat. Figure 20B presents the interpreted hydraulic conducting aperture (estimated from the flow rate) versus effective normal stress from the flat-jack loading of the block. For loading under isothermal conditions, the stressaperture function resembles that back-calculated from the Niche experiments (Fig. 13A) and other large-scale fracture experiments on clean open fractures (Fig. 5A C). That is, the fracture appears to reach an irreducible aperture at stresses above 5 MPa. Figure 20B also shows a marked reduction in aperture after heating and a relatively modest temperature increase, from the ambient 19 C to Fig. 19. Perspective of the Terra Tek in situ block experiment (modified from Hardin et al. 1982) and comparison of calculated (lines) and measured (filled circles) evolution of hydraulic conducting fracture aperture with stress and temperature at the Terra Tek in situ heated block experiment (Min et al. 2009). The calculated evolution shown by solid lines considers pressure solution of fracture surface asperities to be the mechanism causing fracture closure during temperature increase under constant stress.

15 62 J. RUTQVIST about 40 C. This heating appears to have caused an irreversible decrease in hydraulic conducting aperture. Considering the observations at the G-tunnel in situ block experiment, it is very likely that similar permeability reduction took place during the 4-year rock-mass heating at the Yucca Mountain Drift Scale Test. This may explain the differences in the back-calculated stress-aperture relationships in Figs 13A and 18B: At the Drift Scale Test, temperature and stress increased simultaneously, and it is difficult to separate the pure thermal-mechanical responses from chemically mediated thermal-mechanical responses. Therefore, the back-calculated stress-aperture function in Fig. 18B may implicitly include additional fracture closure caused by thermally and chemically mediated changes. This possibility is illustrated in Fig. 21, which presents apertureversus-stress functions back-calculated from both field experiments. In Fig. 21, the functions are plotted for vertical fractures at an equivalent initial normal stress and aperture, which illustrates how the temperature increase at the Drift Scale Test might have caused additional fracture closure. Such additional fracture closure may have been the result of pressure solution and compaction of stressed fracture surface asperities, or so-called thermal overclosure. APPLICATION TO GEOENGINEERING ACTIVITIES AND POTENTIAL IMPLICATIONS FOR CRUSTAL PERMEABILITY One important use of stress-permeability functions derived from field tests is to provide reliable input data to numerical models for predictions of THM behavior associated with geoengineering activities, such as geologic nuclear waste disposal, geothermal energy extraction, hydrocarbon production, and geologic CO 2 sequestration. For example, in the Yucca Mountain project for geologic nuclear waste disposal (Rutqvist & Tsang 2012), stress-permeability relationships for different rock units were determined by backanalysis from underground Yucca Mountain experiments described in Sections The URL TSX tunnel experiment and Model calibration against the yucca mountain drift scale test. These stress-permeability relations were then part of the input to a forward analyses for predicting the long-term behavior of a heat releasing nuclear waste repository (Rutqvist & Tsang 2003, 2012; Rutqvist 2004). Similarly, the stress-permeability function back-calculated from the TSX experiment described in Section The URL TSX tunnel experiment was applied in a forward analysis related to the EDZ evolution around a nuclear waste repository deposition tunnel (Nguyen et al. 2009). This approach could also be used for other applications, such as geologic sequestration of CO 2 and geothermal energy extraction. In situ data from experiments on faults would be particularly useful for predicting the potential for leakage along faults, which is an important issue related to Fig. 20. Perspective of G-tunnel heated block experiment (modified from Zimmerman et al. 1985), and hydraulic conducting aperture as a function of normal stress evaluated from the G-tunnel in situ block experiment. The data from Zimmerman et al. (1985) is separated in the sequential steps showing additional fracture closure as a result of heating (Rutqvist & Tsang 2012). Fig. 21. Comparison of stress-versus-aperture relationships derived by model calibration from Yucca Mountain niche excavation experiments (blue line) and the Drift Scale Test (red line) and possible chemically mediated fracture closure as a result of rock mass heating during the drift scale test.