Chapter 8
Fractured rock stress–permeability relationships from in situ data and effects of temperature and chemical–mechanical couplings

Jonny Rutqvist

Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA, USA

Introduction

Coupled thermal–hydrological–mechanical–chemical 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 hydromechanical 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 is discussed in this chapter, it is crucial that site-specific in situ 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. 8.1). 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 chapter is the back analysis of stress–permeability relationships by model calibration against field data of stress-induced changes in rock-mass permeability (illustrated by Path 2 in Fig. 8.1). Unrepresentative sampling of a rock fracture is illustrated in Figure 8.2. 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.

Schematic diagram of two alternative ways (Path 1 and Path 2) for deriving a stress–permeability relationship of a fractured rock unit. — **Fig. 8.1** 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. (*See color plate section for the color representation of this figure*.)

Image described by caption and surrounding text. — **Fig. 8.2** Schematic showing the effects of unrepresentative sampling through a fracture. (A) The *in situ* fracture and (B) 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 that would indicate a smaller aperture and higher stiffness than for the original larger scale fracture.

(Adapted from Wei & Hudson 1988.)

Model calibration according to Path 2 in Figure 8.1 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 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 carbon sequestration (Taron & Elsworth 2009; Rutqvist 2012; Rutqvist & Tsang 2012).

The objective of this chapter is to (i) review field data on stress-induced permeability changes in fractured rock; (ii) describe the back analysis of rock-mass stress–permeability relationships through model calibration against such field data; and (iii) discuss the 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, excavation-induced 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 the so-called thermal overclosure or chemically mediated mechanical changes are discussed.

Fractured rock stress–permeability relation and sample size effect

Figure 8.3, from a review by Rutqvist & Stephansson (2003) on hydromechanical coupling in fractured rocks, presents “typical” hydromechanical behavior of single rock fractures as known from several decades of experimental and theoretical studies. In Figure 8.3A, a size dependency on fracture normal closure is indicated as an increased maximum closure, δ_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 8.3B 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 is discussed in the following section. Such a correlation between fracture stiffness (or fracture compliance) and permeability is also being used to develop scaling relationships aiming at new methods for seismic (nonintrusive) evaluation of fractured rock permeability (Petrovitch et al. 2013). The effect of sample size on fracture shear behavior (Fig. 8.3C,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.

Four plots marked (A), (B), (C), and (D) of Two alternative ways (Path 1 and Path 2) for deriving a stress–permeability relationship of a fractured rock unit. — **Fig. 8.3** 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-m² size).

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. 8.3D). 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 shear-induced 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 8.4 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, that is, 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 Figure 8.4 might also depend on the model size, with free moving boundaries around the 5 × 5 m model domain. Indeed, the same fracture network was used in a different study, but considering a larger 20 × 20 m model, and as a result, much less shear-induced permeability increase occurred (Rutqvist et al. 2013a).

“A plot of Simulation of the horizontal permeability evolution of an intensely fractured rock mass subject to increasing shear stress ratio. Three schematic diagrams are inset with arrows pointing to Kx MC model and Kx elastic plotted points in different lines.” — **Fig. 8.4** Simulation of the horizontal permeability evolution of an intensely fractured rock mass subject to increasing shear stress (*σ_x*/*σ_Y*) ratio (results from Min *et al.* 2004). Elastic simulation results are compared with that of elastoplastic using Mohr–Coulomb failure along fractures to investigate the effect of shear dilation on horizontal permeability.

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 8.5 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 8.5A compares results from several experiments from the 1970s (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 Figure 8.5B,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 8.5D presents results from an in situ block experiment at the Stripa Mine in Sweden exhibiting different behaviors (Makurat et al. 1990a). 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. 1990a).

Figure 8.6 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 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. 8.6B). 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 8.6E 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 Figure 8.6C,D, the shear and normal stresses 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 8.6E 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 flows, possibly related to differences between hydraulically conducting and mechanical apertures. Nevertheless, the overall response resembles that of the numerical simulations in Figure 8.4. Moreover, the mechanical behavior of fracture D follows in general that of generic curves in Figure 8.3 for 1 m² 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 shear-induced 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 Figures 8.5 and 8.6 show the important effects of sample size and fracture filling, effects that can lead to very different permeability evolution with stress – which would be difficult to predict from tests on small-scale core samples of the same fractures. Moreover, the large core experiment in Figure 8.6 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 following section, one type of such in situ tests is described.

Borehole injection tests

Hydraulic jacking test (or step-rate test) is a type of borehole injection test that has 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. 8.7). 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. 8.7A). 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. 8.7B). Such numerical modeling of injection tests are also presented in Preisig et al. (2015), using a discrete fracture model, and indicating the potential for more complex responses, including shear slip.

Figure 8.7C shows one example of a pressure-versus-flow-rate 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 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 8.8A 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. 8.8B). The stress–permeability behavior of these fractures resembles that of the large fracture-scale experimental data in Figure 8.5, 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. (1990a) in situ block test shown in Figure 8.5D. 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 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 the estimates of storativity and reduces nonuniqueness during the evaluation of hydraulic well tests. The most recent development of this concept involves a three-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 carbon sequestration sites and for assessing the potential for fault activation and leakage during shale-gas hydraulic fracturing operations (Rutqvist 2012; Rutqvist et al. 2013b).

Model calibration against excavation-induced permeability changes

Stress-induced changes in permeability around excavations, including the excavation disturbed zone, have been studied since the early 1980s at many sites with various rock types (Bäckblom & Martin 1999; Tsang et al. 2005; Blümling et al. 2007). The excavation disturbed zone 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 in Manitoba, Canada, and another from an intensely fractured rock site at Yucca Mountain, Nevada.

The Manitoba underground rock laboratory TSX tunnel experiment

The TSX tunnel (Room 425) at the Manitoba underground rock laboratory (Martino & Chandler 2004) was one of several experimental tunnels at the underground rock laboratory dedicated to studying the excavation disturbed zone. To minimize the excavation disturbed zone, the TSX tunnel was excavated using smooth drill-and-blast techniques in an elliptical cross-section 3.5 m high and 4.375 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 excavation disturbed zone was characterized by a variety of methods, including the microvelocity probe method for measuring changes in 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 underground rock laboratory 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, σ′_m, and deviatoric stress, σ_d, according to (Rutqvist et al. 2009b):

8.1

where k_r is residual (or irreducible) permeability at high compressive mean stress, Δk_max, β₁, and γ are fitting constants, and Δσ_d is the change in deviatoric stress relative to a critical deviatoric stress for onset of shear-induced permeability.

Figure 8.9 compares simulated and measured permeability changes for β₁ = 4 × 10⁻⁷ Pa⁻¹, k_r = 2 × 10⁻²¹ m², Δk_max =8 × 10⁻¹⁷ m², γ = 3 × 10⁻⁷ 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 Figure 8.10. 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 Manitoba underground rock laboratory 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 several-orders-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. 8.1, 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.

$Two plots of Permeability versus radius along (A) a horizontal profile from the side of the tunnel and (B) a vertical profile from the top of the tunnel. Two digital images are inset and lines point to areas in the plots marking Field data from SEPPI, Simulated, and Permeability increases by macrofracturing.$

Fig. 8.10 Calibrated stress-versus-permeability relationship according to Eq. 8.1, with β₁ = 4 × 10⁻⁷ Pa⁻¹, k_r = 2 × 10⁻²¹ m², Δk_max = 8 × 10⁻¹⁷ m², γ = 3 × 10⁻⁷ 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.)

The Yucca Mountain niche excavations

Figure 8.11 presents the measurements of excavation-induced changes in permeability above a niche excavated off a tunnel 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 0.65–1 m above the niche, supposedly outside the damaged zone (Fig. 8.11). The results in Figure 8.11 for one niche show that the pre-/postpermeability ratio ranges between a factor of 1 and 400, with a trend of relatively stronger permeability increase for those sections where the initial permeability is smaller.

A plot with Log change ratio on the vertical axis, Log initial permeability on the horizontal axis, and UL, UM, and UR plotted in diamond, square, and triangle respectively. A schematic diagram is inset with UL, UM, and UR marked. — **Fig. 8.11** Results of pre- to postexcavation 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). (*See color plate section for the color representation of this figure*.)

Figure 8.12 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. 8.12). However, the wide range of permeability changes (from 1 to 400) observed in the field (Fig. 8.11) 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.

A plot with Log change ratio on the vertical axis, Log initial permeability on the horizontal axis, and Measured geometric mean, Measured mean – Stdv, Measured mean + Std, and Simulated geometric mean plotted in different shapes. — **Fig. 8.12** Measured and calculated mean values of pre- to postpermeability change ratio at three niches (Niche 3107, 3560, and 4788).

(Rutqvist 2004.)

Figure 8.13 presents the stress–aperture relationship used for the best match solution. In this relationship, the aperture b depends on the effective normal stress σ′_n according to (Rutqvist & Tsang 2003):

8.2

where b_r is the irreducible aperture, and b_max and α are fitting parameters used to match measured and calculated permeability responses. In this case, b_max = 200 µm and α = 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. 8.2 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).

Two plots marked (A) exponential stress–aperture relationship and (B) corresponding stress–transmissivity relationship with Effective normal stress (MPa) on the horizontal axis, Aperture on the vertical axis, and different curves plotted. — **Fig. 8.13** Fracture stress–transmissivity behavior of fractures back-calculated from permeability measurements during excavation of niches: (A) exponential stress–aperture relationship and (B) corresponding stress–transmissivity relationship.

The functions in Figure 8.13 display some resemblance to the results of the in situ block and ultra-large core tests shown in Figure 8.5. 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. 8.8). 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. 8.2 would be expected to be valid at relatively low stress, since 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 allow 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 as fracture frequency, connectivity, infilling by mineral precipitation, and history. For example, Figure 8.14 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 Gideå, 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 six 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 2015). One general observation from Figure 8.14, and from many fractured crystalline rock sites, is that a more pronounced depth dependency can be found in the upper 100–300 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 (1968a), who used detailed pumping tests and fracture statistics to determine fracture apertures at numerous dam foundations.

A plot with Depth (m) on the vertical axis, Permeability on the horizontal axis, and dotted lines and circles plotted with arrows and descriptive text pointing to areas in the plot. — **Fig. 8.14** 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 Gideå, 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.

The minimum values of permeability on the left-hand side of Figure 8.14 represent the permeability of the rock matrix, implying that either 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 Figure 8.14 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 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 allow substantial shear dislocation and extension of oblique fractures (National Research Council 1996). Interestingly, in Figure 8.14, the maximum permeability values of about k = 1 × 10⁻¹³ m² below a few 100 m depth correspond quite accurately to the transmissivity value for of the most transmissive fracture in Figure 8.8. That is, for a packer spacing of b = 3 m, k = 1 × 10⁻¹³ m² corresponds to a transmissivity of about T = (k × b × ρ × g)/μ ≈ (1 × 10⁻¹³ × 3 × 1000 × 10)/1 × 10⁻³ =3 × 10⁻⁶ m² s⁻¹, which is very similar to the transmissivity of the fracture at 315 m in Figure 8.8. The “average” permeability at depth in Figure 8.14 is about 1 × 10⁻¹⁶ to 1 × 10⁻¹⁵ m² and this corresponds to a transmissivity of about 3 × 10⁻⁹ to 3 × 10⁻⁸ m² s⁻¹, which is similar to the transmissivity of the fractures at 266 and 267 m in Figure 8.8.

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. (2010b). 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 groundwater table at 600 m depth (Fig. 8.15). Figure 8.15A shows that the permeability varies by about two orders of magnitude, that is, much less than the six-order variation for the crystalline rock site in Figure 8.14. 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 8.15B shows that the fracture frequency ranges from 0.1 to 5 fractures per meter, with some tendency toward higher permeability in layers with higher fracture frequency. Finally, Figure 8.15C 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)

8.3

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. 8.3 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. 8.3 is relatively accurate. At other sparsely fractured rock sites, such as the aforementioned Gideå crystalline rock sites, Eq. 8.3 is likely not appropriate.

The subparallel curved lines in Figure 8.15C 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. 8.2 with b_max = 200 µm and α = 0.8 MPa⁻¹. Both permeability and frequency vary 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 Gideå crystalline rock site shown in Figure 8.14. Again, the aperture is relatively constant for stresses above 5 MPa, indicating that the fracture aperture approaches an irreducible value.

The stress–aperture functions matched to field data in Figure 8.15C, 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 collapse under ambient stress. As is 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 100,000 m³ of intensely fractured volcanic tuff was heated for 4 years, including several tens of thousands of cubic meters heated to above-boiling temperature (Fig. 8.16). This massive heating induced strongly coupled thermal–hydrological–mechanical–chemical changes that were continuously monitored by thousands of sensors embedded in the fractured rock mass. Among the monitoring data were periodic active pneumatic (air-injection) measurements that were used to track changes in air permeability within the variably saturated fracture system around the heated drift. Air-injection testing was conducted in 44 several-meter-long packed-off sections in hydrological boreholes, located in three clusters forming vertical fans that bracketed the heated drift (Fig. 8.16).

Thermally induced permeability changes at the Yucca Mountain drift scale test were analyzed using coupled thermal–hydrological–mechanical 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 moisture-induced changes (Fig. 8.17). The modeling reproduced the average permeability evolution using the stress–permeability function shown in Figure 8.18A, which is based on the exponential stress–aperture function in Eq. 8.2. 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 thermohydroelastic solution (Fig. 8.17). 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).

Two plots with Normal stress (MPa) on the horizontal axis. The vertical axis is Fracture permeability in (A) and Conducting aperture in (B). Lines with descriptive text point to areas on the plotted curve in (B). — **Fig. 8.18** Fracture stress-versus-permeability behavior back-calculated from air-permeability measurements at the Yucca Mountain drift scale test: (A) fractured rock permeability versus stress along one set of fractures and (B) corresponding aperture-versus-stress relationship for two assumptions regarding the spacing of dominant fractures.

Whereas the stress–permeability relationship shown in Figure 8.18A provides a good match to the measured average permeability responses, the underlying aperture-versus-stress relationship depends on the spacing of active (or dominant) fractures. Therefore, two alternative functions are presented in Figure 8.18B. Note that the aperture-versus-stress relationships shown in Figure 8.18B are quite different from those that were back-calculated from the niche-excavation experiments (Fig. 8.13A). 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 overclosure and/or chemically mediated changes that resulted in additional fracture closure during heating at the drift scale test. This possibility is further discussed in the following section.

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 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 thermal–hydrological–mechanical 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, was formed at variously elevated temperatures. They were thereby given a primeval “fingerprint” of three-dimensional 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 thermal–hydrological–mechanical–chemical 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. 8.19). 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 8.19B shows that the agreement between modeling (lines) and observations (filled circles) is excellent for all loading stages except for the end point, that is, 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 preheating 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.

Schematic diagram of Perspective of the Terra Tek in situ block experiment. — **Fig. 8.19** (A) Perspective of the Terra Tek *in situ* block experiment (Adapted from Hardin *et al*. 1982 and (B) 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.

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. 8.20) (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 8.20B 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 stress–aperture function resembles that back-calculated from the niche experiments (Fig. 8.13A) and other large-scale fracture experiments on clean open fractures (Fig. 8.5A–C). That is, the fracture appears to reach an irreducible aperture at stresses above 5 MPa. Figure 8.20B also shows a marked reduction in aperture after heating and a relatively modest temperature increase, from the ambient 19 °C to about 40 °C. This heating appears to have caused an irreversible decrease in hydraulic conducting aperture.

Schematic diagram with parts marked for perspective of G-tunnel heated block experiment. — **Fig. 8.20** (A) Perspective of G-tunnel heated block experiment (Adapted from Zimmerman *et al*. 1985) and (B) 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) are separated in the sequential steps showing additional fracture closure as a result of heating.

(Rutqvist & Tsang 2012.) (*See color plate section for the color representation of this figure*.)

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 Figures 8.13A and 8.18B: 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 Figure 8.18B may implicitly include additional fracture closure caused by thermally and chemically mediated changes. This possibility is illustrated in Figure 8.21, which presents aperture-versus-stress functions back-calculated from both field experiments. In Figure 8.21, 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 closures may have been the result of pressure solution and compaction of stressed fracture surface asperities, or so-called thermal overclosure.

A plot with Normal stress (MPa) on the horizontal axis, Conducting aperture (μm) on the vertical axis, and different lines plotted with arrows and descriptive text marked pointing to areas in the plot. — **Fig. 8.21** Comparison of stress-versus-aperture relationships derived by model calibration from Yucca Mountain niche-excavation experiments (dashed curve) and the drift scale test (solid curve) and possible chemically mediated fracture closure as a result of rock-mass heating during the drift scale test.

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 thermal–hydrological–mechanical behavior associated with geoengineering activities, such as geologic nuclear waste disposal, geothermal energy extraction, hydrocarbon production, and geologic carbon 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 back analysis from underground Yucca Mountain experiments described in Sections “The Manitoba underground rock laboratory 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 analysis 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 Manitoba underground rock laboratory TSX tunnel experiment” was applied in a forward analysis related to the excavation disturbed zone 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 carbon 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 the attempts of sequestering carbon in deep sedimentary formations (Rutqvist 2012; Rinaldi et al. 2013). Related to geothermal energy extraction, enhanced geothermal systems involve stimulation of a rock volume to enhance permeability for an economic energy production (Tester 2006). The approach favored in current enhanced geothermal system projects is the so-called hydroshearing involving the injection of water to cause existing fractures to shear and dilate. In such a case, the injection pressure is kept below the fracturing pressure but sufficiently high to cause fractures to fail in shear. Hydroshearing can permanently enhance the permeability of natural fractures that, in theory, should remain open because of fracture self-propping (due to surface roughness) even after the stimulation period ends and fluid pressure is reduced. In this context, the borehole hydraulic jacking described in Section “Borehole injection tests” can be used to test the rock mass for potential permeability increase that can be achieved on individual fractures. During the actual stimulation an increase in permeability might be achieved similar to that shown in Figure 8.4 and will depend on the initial permeability as observed in Figure 8.12. The potential permeability increase that can be achieved can also be inferred from Figure 8.14, where the permeability values to the left represent intact rock or a rock mass with completely closed fractures, whereas the highest permeabilities to the right represent highly conductive fractures that might have been propped open by shear dilation. If the initial average permeability is somewhere around 1 × 10⁻¹⁵ m², and if the maximum permeability is about 1 × 10⁻¹³ m² (as shown in Figure 8.14), then at best a two orders of magnitude increase is feasible.

Finally, the review presented in this chapter on in situ stress–permeability relations as well as effects of thermal and chemical coupling may be relevant to crustal permeability distribution with depth. Figure 8.22 shows a compilation of permeability data from crystalline bedrock to a depth of 7000 m (Juhlin et al. 1998). At shallow depth, the variability of permeability shown in Figure 8.22 is similar to that of Figure 8.14, that is, about six orders of magnitude. Such variability in permeability is also observed in a recent comprehensive compilation of permeability data by Ranjram et al. (2015). Again, in Figure 8.22, the minimum permeability values to the left are similar to stress–permeability functions for intact rock (e.g., Rutqvist & Stephansson 2003), whereas maximum permeability values to the right correspond to highly transmissive fractures that could be propped open by shear dilation. Figure 8.22 displays few data at the greatest depths, but those available show decreasing permeability with depth toward intact rock permeability. At 7000 m depth, the lithostatic stress would be about 200 MPa, that is, on the order of the uniaxial compressive strength of granite. Large voids may not stay open; that is, an open void in a fracture as shown in Figure 8.2 is likely to collapse under high ambient stress. However, laboratory experiments by Durham & Bonner (1994) on a fracture in granite propped open by slight shear offset showed that the fracture remained open and conductive even at a very high normal stress of 160 MPa. This indicates that fractures could stay open even at great depths, leading to permeability higher than that of the intact rock. However, at these great depths, high temperatures and stress may affect the long-term behavior, and chemically mediated mechanical processes such as pressure solution and associated creep could further compact fractures. Still, significant permeability can persist at very great depths, as inferred from hydrothermal modeling and the progress of metamorphic reactions (Ingebritsen & Manning 2010), and from seismicity (Townend & Zoback 2000).

Concluding remarks

A number of field observations and experiments on stress-induced permeability changes in fractured rock are reviewed here to summarize our general understanding of the relationship between stress and permeability in fractured rock, and to describe the use of such field data and model calibration to back-calculate the stress–permeability functions for fractured rock units. Data presented show how the stress–permeability relationship depends strongly on local in situ conditions such as shear offset or fracture fillings. The various model calibrations presented here suggest that while coupled hydromechanical behavior in fractured rock is very complex and cannot be predicted in detail at every location of the rock mass, the overall rock-mass stress–permeability relationship can be estimated and bounded. Model calibration of the stress–permeability relationship against field data of stress-induced permeability changes has the advantage of eliminating issues related to unrepresentative sampling and sample disturbance, issues usually associated with laboratory testing on drill cores.

However, as highlighted in this chapter, model calibration of stress–permeability relationships against field experiments involving simultaneous stress and temperature changes may be affected by additional fracture closure, a phenomenon that has been described as thermal overclosure, due to thermal–mechanical changes in the fracture surface geometry and/or to chemically mediated fracture closure as a result of the pressure solution of stressed fracture surface asperities. Model calibration against field experiments may implicitly account for such effects, but the relative contribution of purely mechanical versus thermal or chemically mediated mechanical changes is difficult to isolate. It may well be that the observed temperature-dependent fracture closure results from a combination of the two proposed mechanisms. Therefore, 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 chemically mediated mechanical changes on the long-term evolution of fractured rock permeability. Such thermal–hydrological–mechanical–chemical effects on permeability are important to consider when estimating the long-term permeability evolution associated with geoengineering activities, such as geologic nuclear waste disposal, and can also explain crustal permeability distribution with depth.

Acknowledgments

This chapter was prepared with funds from the Swedish Radiation Safety Authority (SSM) to the Lawrence Berkeley National Laboratory through the US Department of Energy Contract No. DE-AC02-05CH11231. Technical review comments of the initial manuscript by Victor Vilarrasa and editorial review by Dan Hawkes of the Lawrence Berkeley National Laboratory are greatly appreciated. Technical and editorial reviews for the journal publication by Steven Micklethwaite, University of Western Australia, and by Steven Ingebritsen, U.S. Geological Survey, substantially improved the manuscript and are greatly appreciated by the author.