Aspects of rock permeability

Abstract

Effective evaluation of rock permeability is required in different energy, engineering and environmental projects. Although much research has been conducted on rock permeability, it is still one of the most difficult tasks for practicing rock engineers to accurately determine rock permeability. Based on a comprehensive literature review, this paper outlines the key aspects of rock permeability by presenting the representative values of the permeability of different rocks, describing the empirical and semi-empirical correlations for estimating the permeability of rocks, and discussing the main factors affecting the permeability of rocks. The factors discussed include stress, depth, temperature, and discontinuity intensity and aperture. This paper also highlights the scale effect on rock permeability, interconnectivity of discontinuities, and anisotropy of rock permeability. This paper provides the fundamental and essential information required for effective evaluation of rock permeability.

Keywords

rock / permeability / discontinuity / stress / temperature / scale effect / anisotropy

Introduction

Rock permeability is one of the most important parameters controlling project performance in energy, civil and environmental engineering. Effective characterization of fluid flow and chemical transport in rock requires accurate determination of permeability. Because of the presence of discontinuities in rock, the permeability of rock is controlled not only by the intact rock but also by the discontinuities separating the intact rock blocks. It has long been recognized that rock permeability is usually anisotropic and heterogeneous and affected by different factors such as the in situ stress and temperature [1-9]. Although much research has been conducted on rock permeability, it is still one of the most difficult tasks for practicing rock engineers to accurately determine rock permeability [2,8,10,11].

This paper reviews the results of previous research on rock permeability, focusing on the representative values of the permeability of different rocks and the main factors affecting the permeability of rocks. It also presents various empirical and semi-empirical correlations for estimating the permeability of rocks. The various test methods such as pumping tests and water injection tests for measuring rock permeability are outside the scope of this paper. The interested readers can refer to [2,12-14] for details on measuring rock permeability. This paper outlines the key aspects of rock permeability and provides the fundamental and essential information required for effective evaluation of rock permeability.

Fundamental definitions

The permeability of a rock is a measure of its capacity for transmitting a fluid. The coefficient of permeability (or hydraulic conductivity) is defined as the discharge velocity through a unit area under a unit hydraulic gradient and is dependent upon the properties of the medium, as well as the viscosity and density of the fluid. According to Darcy’s law, the quantity of flow through a cross-sectional area of rock can be calculated by

(1)q=KiA,

where q is the quantity of flow; K is the permeability coefficient of the rock, having the units of velocity; i is the hydraulic gradient (head loss divided by length over which the head loss occurs); and A is the cross-sectional area of flow.

The permeability coefficient of rock varies for different fluids depending on their density and viscosity as follows:

(2)K=k{\displaystyle \frac{\rho g}{\mu }}=k{\displaystyle \frac{g}{\nu }},

where k is the intrinsic (or specific) permeability of the rock, having the units of length squared; ρ, μ, and ν are, respectively, the density, viscosity and dynamic viscosity of the fluid; and g is the gravitational acceleration (9.81 m/s²). The intrinsic permeability k is independent of the properties of the fluid in the rock.

Very often water is the percolating fluid in rock. So in the following discussion, if not specifically mentioned, the fluid will be water. The general conclusions, however, will also be applicable to other types of fluids.

Permeability of intact rock

The permeability of an intact rock is usually referred to as the primary permeability. The intact rock permeability is governed by the porosity, which varies with factors like rock type, geological history and in situ stress conditions. Figures 1 and 2 are two examples of typical permeability k versus porosity n plots. The increase of permeability with growing porosity follows a quasi-linear log k – n relationship [15]:

(3)\log k=a_{\mathrm{1}}n+a_{\mathrm{2}},

where a₁ and a₂ are fitting constants. Since the porosity of intact rocks varies widely, 0.1 - 43% [16], the intact rock permeability varies in a great range – at least 8 orders of magnitude. Figure 3(a) shows the range of the intact rock permeability coefficient K for different rock types.

The permeability of intact rocks also varies with the grain size, increasing with larger grain size. Figure 4 shows a plot of permeability k versus grain size d. The trend of these data can be represented by

(4)\log k=\mathrm{2.221}\log d-\mathrm{2.101},

where k is in md (millidarcy ≈ 10^-15 m²) and d is in μm [17].

Theoretical and experimental data show that at a given porosity, pore size distributions of rocks are controlled in the first order by grain size [18-20]. At a given porosity, the pore size and thus the permeability decrease as the grain size decreases. Using clay content as a lithological or grain size descriptor, Yang and Aplin [20] derived the following expression relating permeability to both void ration (e = n/(1–n)) and clay content (CF) for mudstones:

(5)$$\begin{gathered} \log k=-\mathrm{69.59}-\mathrm{26.79}\cdot CF+\mathrm{44.07}\cdot C{F}^{\mathrm{0.5}}+(-\mathrm{53.61}-\mathrm{80.03}\cdot CF+\mathrm{132.78}\cdot C{F}^{\mathrm{0.5}})\cdot e \\ +(\mathrm{86.61}+\mathrm{81.91}\cdot CF-\mathrm{163.61}\cdot C{F}^{\mathrm{0.5}})\cdot e^{\mathrm{0.5}}, \end{gathered}$$

where k is in m² and CF in %.

Permeability of discontinuities

The flow of fluid through discontinuities in rock has been studied by different researchers [1,23-31]. If discontinuities are infilled, the permeability of a discontinuity is simply that of the infilling material. For unfilled discontinuities, by modeling the discontinuity as an equivalent parallel plate conductor, the permeability coefficient along the discontinuity can be determined for the laminar flow by

(6)K={\displaystyle \frac{g{e}^{\mathrm{2}}}{\mathrm{12}\nu C}},

where e is the aperture of the discontinuity; ν is the kinematic viscosity of the fluid (which for water can be taken as 1.0 × 10^-6 m²/s); and C is a correction factor representing the discrepancy between the actual physical aperture of the discontinuity and its equivalent hydraulic aperture.

If the equivalent hydraulic aperture is used, Eq. (6) can be rewritten as

(7)K={\displaystyle \frac{g{e}_h^{\mathrm{2}}}{\mathrm{12}\nu }},

where e_h is the equivalent hydraulic aperture of the discontinuity, which is related to its physical or mechanical aperture, e, as follows.

(8)e_h^{\mathrm{2}}={\displaystyle \frac{e^{\mathrm{2}}}{C}},

Owing to the wall friction and the tortuosity, the mechanical aperture e is generally larger than the hydraulic aperture e_h. Hakami [32] showed that the ratio of mechanical mean aperture to hydraulic aperture was 1.1-1.7 for discontinuities with a mean aperture of 100-500 μm. A study by Zimmerman and Bodvarsson [33] concluded that the mechanic aperture is larger than the hydraulic aperture by a factor that depends on the ratio of the mean value of the aperture to its standard deviation. Many researchers have evaluated the factor C, including Louis [26], Lomize [34], and Quadros [35]. Their findings can be summarized by the following expression:

(9)C=\mathrm{1}+m{\left({\displaystyle \frac{y}{\mathrm{2}e}}\right)}^{\mathrm{1.5}},

where m = 8.8 from Louis [26], m = 17 from Lomize [34], and m = 20.5 from Quadros [35]; and y is the magnitude of the discontinuity surface roughness. For a smooth parallel discontinuity, y becomes zero and thus C becomes one and e_h = e.

Barton et al. [36] related factor C to the joint roughness coefficient (JRC)

(10)C={\displaystyle \frac{{JRC}^{\mathrm{5}}}{e^{\mathrm{2}}}},

where e is in the unit of μm. The methods for determining JRC have been described in [37-39]. Combining Eq. (8) and (10) gives

(11)e_{\mathrm{h}}={\displaystyle \frac{e^{\mathrm{2}}}{{JRC}^{\mathrm{2.5}}}},

The background data for Eq. (10) and thus (11) mainly comes from normal deformation/fluid flow tests. Olsson and Barton [40] found that Eq. (11) only applies to the case that the shear displacement u_s does not exceed 75% of the peak shear displacement u_sp (the shear displacement at peak shear stress). After the peak shear stress (u_s≥u_sp), the hydraulic aperture e_h can be calculated from

(12)e_{\mathrm{h}}=e^{\mathrm{1}/\mathrm{2}}{JRC}_{mob}(u_{\mathrm{s}}\ge u_{\mathrm{s}\mathrm{p}}),

where JRC_mob is the mobilized value of JRC. In the phase of u_s≥u_sp, the geometry of the discontinuity wall changes with increasing shear displacement and thus JRC_mob should be used. The value of JRC_mob is dependent on the strength of the discontinuity wall, the applied normal stress and the magnitude of the shear displacement. It is also dependent on the size of the discontinuity plane and the residual friction angle of the discontinuity. For the calculation of u_sp and JRC_mob, the reader can refer to Olsson and Barton [40].

Since the intermediate phase (0.75u_sp<u_s<u_sp) is difficult to define, Olsson and Barton [40] recommended using a transition curve by connecting the two phases defined by Eqs. (11) and (12).

For a set of parallel discontinuities, the permeability coefficient parallel to the discontinuities can be determined by

(13)K={\displaystyle \frac{g{(e_{ave})}^{\mathrm{3}}}{\mathrm{12}\nu C_{ave}{s}_{ave}}},

where e_ave is the average of individual values of e for discontinuities in the set under consideration; s_ave is the average of individual spacing s between discontinuities; and C_ave is estimated from Eq. (9) using (y/e)_ave which is the average of the individual values of (y/e).

Figure 5 shows the variation of permeability coefficient K of a set of smooth parallel discontinuities with the discontinuity aperture and the discontinuity spacing, based on Eq. (13). The permeability coefficient is very sensitive to changes in aperture e.

Permeability of rock mass

For a rock mass containing a single set of continuous discontinuities, as illustrated in Fig. 6(a), the permeability coefficient of the rock mass in the direction of the discontinuities can be estimated as [41]

(14)K={\displaystyle \frac{g{e}_{\mathrm{1}}^{\mathrm{3}}}{\mathrm{12}\nu C_{\mathrm{1}}{s}_{\mathrm{1}}}}+K_i(\mathrm{1}-e_{\mathrm{1}}/s_{\mathrm{1}}),

where e₁, s₁ and C₁ are, respectively, the aperture, spacing and correction factor of discontinuity set 1; and K_i is the permeability coefficient of the intact rock.

The permeability coefficient of the rock mass in the direction perpendicular to the discontinuities can be simply taken as that of the intact rock.

As further discontinuity sets are added to produce an orthogonal array, the principal magnitudes of permeability coefficient remain coincident with the lines of intersection of the discontinuity sets. The permeability coefficient, K₁₁, in the x₁ direction of Fig. 6(b) can be estimated as [41]

(15)K_{\mathrm{11}}={\displaystyle \frac{g}{\mathrm{12}\nu }}\left({\displaystyle \frac{e_{\mathrm{2}}^{\mathrm{3}}}{C_{\mathrm{2}}{s}_{\mathrm{2}}}}+{\displaystyle \frac{e_{\mathrm{3}}^{\mathrm{3}}}{C_{\mathrm{3}}{s}_{\mathrm{3}}}}\right)+K_i(\mathrm{1}-e_{\mathrm{2}}/s_{\mathrm{2}})(\mathrm{1}-e_{\mathrm{3}}/s_{\mathrm{3}}),

The permeability coefficients in the two other orthogonal directions may be determined from Eq. (15) through appropriate permutation. Where discontinuity apertures and spacings between discontinuities differ for each of the sets, the permeability of the rock mass will be anisotropic. Commonly, the discontinuity permeability dominates over the intact rock permeability. Consequently, the second term of Eqs. (14) and (15) may often be neglected.

Researchers have related field measured rock mass permeability to rock mass quality indices such as rock quality designation (RQD) and rock mass rating (RMR) [42,43]. Figure 7 shows the measured permeability versus RQD data for the Cambrian sandstone rock mass in central Jordan. The following empirical relation between permeability and RQD can be derived using regression analysis [42]:

(16)\log K=\mathrm{2.249}-\mathrm{0.0157}\log RQD(r^2=\mathrm{0.}74),

where K is in the unit of LU ( = 1.30 × 10^-7 m/s). The permeability shows a progressive decrease with the increase of RQD. It needs to be noted that RQD does not include the information of discontinuity aperture. Since aperture is a main factor affecting the permeability of rock masses, caution should be taken when applying an empirical relation as Eq. (16) to a site different from the site where the empirical relation was derived.

Sen [44] derived analytical relations between rock permeability and RQD by considering the effect of discontinuity aperture. Figure 8 is the permeability-RQD-aperture chart produced based on the analytical relations. It clearly shows that the discontinuity aperture has a major effect on rock permeability.

Figure 3(b) illustrates the range of rock mass permeability coefficient for different rock types. It can be seen that the rock mass permeability coefficient varies in a very wide range – 11 orders of magnitude. This is mainly because rock discontinuities, which control the permeability of rock mass, are significantly variable in intensity and apertures.

Effect of stress on rock permeability

Stress has a great effect on the permeability of both intact rocks and rock masses. A number of studies on the variation of intact rock permeability with stress can be found in the literature [4-6,45-59]. Tiller [60] found an empirical power relationship between the permeability of intact rock and the effective pressure:

(17)K=A{\sigma }^{-m}(\sigma >{\sigma }_{threshold}),

where A and m are constants; and σ is the effective pressure (the difference between the exterior confining pressure and the pore-fluid pressure). Ghabezloo et al. [51] proposed the same type of relation between permeability and effective pressure based on constant head permeability tests on limestone in a triaxial cell with different conditions of confining pressure and pore pressure.

Louis et al. [61] presented the following negative exponential relationship between the permeability of intact rock and the effective pressure:

(18)K=K_{\mathrm{0}}{e}^{-\sigma },

where σ is the effective pressure (the difference between the exterior confining pressure and the pore-fluid pressure); and K₀ is the permeability at zero effective pressure.

Based on the Hertz theory of deformation of spheres, Gangi [46] derived the following expression illustrating the effect of confining pressure on the intact rock permeability:

(19)K=K_0{\left[\mathrm{1}-C_{\mathrm{0}}{\left({\displaystyle \frac{\sigma +{\sigma }_i}{p_{\mathrm{0}}}}\right)}^{\mathrm{2}/\mathrm{3}}\right]}^{\mathrm{4}},

where K₀ is the initial permeability of the loose-grain packing; C₀ is a constant depending on the packing and is of the order of 2; σ is the confining pressure; σ_i is the equivalent pressure due to the cementation and permanent deformation of the grains; and p₀ is the effective elastic modulus of the grains and is of the order of the grain material bulk modulus.

Figure 9 shows the variation of the intrinsic permeability of the intact Westerly granite rock with the confining pressure. The intact rock permeability decreases significantly when the confining pressure increases.

Stresses also affect the permeability of discontinuities and thus of rock masses. The effect of stresses on rock mass permeability depends on their direction with respect to the discontinuity orientation. According to Brace [62], a stress parallel to the discontinuities increases the permeability, while a stress perpendicular to the discontinuities decreases the permeability (Fig. 10).

Snow [24] presented the following empirical relation between the discontinuity permeability and the normal stress:

(20)K=K_0+k_n{\displaystyle \frac{g{e}_h^{\mathrm{2}}}{\nu s}}(\sigma -{\sigma }_{\mathrm{0}}),

where K is the discontinuity permeability at normal stress k_n; K₀ is the initial discontinuity permeability at initial normal stress σ₀; k_n is the normal stiffness of the discontinuity; ν is the dynamic viscosity of the fluid; g is the gravitational acceleration (9.81 m/s²); s is the discontinuity spacing; and e_h is the hydraulic aperture.

Based on the test results on carbonate rocks, Jones [63] proposed the following empirical relation between the discontinuity permeability and the confining pressure σ:

(21)K=c_0{\left[\log \left({\displaystyle \frac{{\sigma }_h}{\sigma }}\right)\right]}^{\mathrm{3}},

where σ_h is the confining pressure at which the permeability is zero; and c₀ is a constant that depends on the discontinuity surface and the initial aperture.

Using a “bed of nails” model for the asperities of a discontinuity, Gangi [46] derived the following relation between discontinuity permeability and effective confining stress σ:

(22)K=K_{\mathrm{0}}{\left[\mathrm{1}-{\left({\displaystyle \frac{\sigma }{p_{\mathrm{1}}}}\right)}^m\right]}^{\mathrm{3}},

where K₀ is the zero pressure permeability; m is a constant (0<m<1) which characterizes the distribution function of the asperity lengths; and p₁ is the effective modulus of the asperities and is of the order of one-tenth to one-hundredth of the asperity material bulk modulus.

Nelson [64] proposed the following general expression for the permeability of discontinuities:

(23)K=A+B{\sigma }^{-m},

where σ is the effective confining stress; and A, B and m are constants determined by regression analysis of test results. These constants vary with rock type, and even for the same rock type, change with the discontinuity surface.

Based on the simple model of Walsh and Grosenbaugh [65] for describing the deformation of discontinuities, Walsh [66] derived the following relation between permeability and confining pressure σ:

(24)K=K_{\mathrm{0}}{\left[\mathrm{1}-{\left(\mathrm{2}{\displaystyle \frac{h}{a_{\mathrm{0}}}}\ln {\displaystyle \frac{\sigma }{{\sigma }_{\mathrm{0}}}}\right)}^{\mathrm{0.5}}\right]}^{\mathrm{3}}\left[{\displaystyle \frac{\mathrm{1}-b(\sigma -u_w)}{\mathrm{1}+b(\sigma -u_w)}}\right],

where K₀ is the permeability at reference confining pressure σ₀; h is the root mean square value of the height distribution of the discontinuity surface; a₀ is the half aperture at the reference confining pressure; u_w is the pore fluid pressure; and

(25)b={\left[{\displaystyle \frac{\mathrm{3}\mathrm{\pi }f}{E(\mathrm{1}-{\nu }^{\mathrm{2}})h}}\right]}^{\mathrm{0.5}},

where f is the autocorrelation distance; E and ν are respectively the elastic modulus and Poisson’s ratio of the rock.

Variation of rock permeability with depth

Because in situ rock stress increases with depth, the permeability of field rock mass decreases with depth. Figures 11 and 12 show the variation of measured rock mass permeability with depth.

Based on field measurements, Louis [67] found that the rock mass permeability coefficient K decreases with depth z by a negative exponential formula:

(26)K=K_{\mathrm{0}}{e}^{-Az},

where K₀ is the surface rock permeability coefficient; and A is an empirical coefficient. For the Grand Maison dam site, he observed that K₀ varied between 10^-7 and 10^-6 m/s and A between 7.8 and 3.4 × 10^-3 m^-1. Meng et al. [68] applied the same form of expression as Eq. (26) to describe the variation of intrinsic permeability with depth in the Southern Qinshui coalbed reservoir.

Based on the data given by Snow [24,25] about the variation of the permeability coefficient of fractured crystalline rocks with depth, Carlsson and Ollsson [69] proposed the following relation between permeability coefficient K and depth z:

(27)K={\mathrm{10}}^{-(\mathrm{1.6}\log z+\mathrm{4})},

where K and z are, respectively, in the units of m/s and m.

Strack [70] proposed the following relation between permeability coefficient K and depth z for modeling purposes in crystalline rock masses:

(28)K=K_{\mathrm{0}}{\left(\mathrm{1}-{\displaystyle \frac{z}{\mu }}\right)}^{\beta },

where K₀ is the initial rock mass permeability coefficient at the surface; and β and μ are constants.

A numerical study conducted by Wei and others based on rock discontinuity network simulation [71,72] suggested the following relation between rock mass permeability coefficient K and depth z:

(29)K=K_{\mathrm{0}}{\left(\mathrm{1}-{\displaystyle \frac{z}{\mathrm{58.0}+\mathrm{1.02}z}}\right)}^{\mathrm{3}},

where K₀ is the rock mass permeability coefficient at initial stage where normal stress approaches to zero.

Based on the measurements in Sweden, Burgess [73] presented the following empirical relation between the mean horizontal permeability coefficient K and depth z:

(30)\log K=\mathrm{5.57}+\mathrm{0.352}\log z-\mathrm{0.978}{(\log z)}^{\mathrm{2}}+\mathrm{0.167}{(\log z)}^{\mathrm{3}},

where K and z are, respectively, in the units of m/s and m.

The effective vertical in situ rock stress due to the weight of the overburden can be simply estimated by :

(31)\sigma =\gamma z,

where γ′ is the effective unit weight of the overlying rock mass; and z is the depth below surface. Combining Eqs. (23) and (31) yields the following general relation between rock mass permeability coefficient K and depth z:

(32)K=A+C{z}^{-m},

where A, C ( = Bγ^-m), and m are constants.

The decrease of rock mass permeability with depth is mainly due to the decrease of discontinuity aperture with depth. Figure 13 shows the variation of discontinuity aperture with depth based on the data of Snow [24,25].

Effect of temperature on rock permeability

Changes in temperature also affect the rock permeability. An increase in temperature will cause a volumetric expansion of the rock material leading to reduction in discontinuity aperture and thus an overall reduction in the rock mass permeability. Mineral dissolution and precipitation due to increased temperature will also cause redistribution of minerals in the rock, such that asperities are chemically removed while pores and discontinuities are filled leading to reduction of the rock mass permeability [76-78]. Figure 14 shows the reduction of hydraulic aperture of a natural discontinuity in novaculite due to temperature increase, under a constant effective stress of 3.5 MPa. The hydraulic aperture decreased from above 12 μm to 2.7 μm as temperature was increased from 20°C to 150°C over a period of 900 h. Figure 15 shows the variation of the permeability of tuff as temperature was increased from below 30°C to 150°C and then decreased back to below 30°C. The permeability decreased with higher temperature and then increased with lower temperature [79].

Studies in the Stripa Iron Ore Mine, Sweden demonstrated a decrease of permeability coefficient for granites from 4±0.8 × 10^-11 m/s to 1.8±0.3 × 10^-11 m/s when temperature was increased by 25°C by circulating warm water. Considering the change in viscosity of the permeant at the higher temperatures, the intrinsic permeability of the rock mass had been reduced by a factor of approximately four [80].

Barton and Lingle [81] presented the results of tests made in situ on fractured gneiss. The permeability of fractured gneiss was decreased 10-fold with a temperature increase of 74°C.

Scale effect on rock permeability

Research results have shown that the rock mass permeability is strongly scale dependent. As illustrated in Fig. 16, the permeability of rock will vary as the problem domain enlarges. For domain A, water can flow only through the intact rock and the rock mass permeability is simply the intact rock permeability. For domain B, water can flow vertically through the intact rock and along a single discontinuity and thus the rock mass permeability in the vertical direction is the sum of the intact rock permeability and the permeability of that single discontinuity. In the lateral direction, however, the water can flow only through the intact rock and thus the rock mass permeability is simply the intact rock mass permeability. As the domain enlarges to C, water will flow through the intact rock and along discontinuities in both the vertical and lateral directions. Therefore, the rock mass permeability in both the vertical and lateral directions will be the sum of the intact rock permeability and the permeability of the corresponding discontinuities. As the domain further enlarges and thus the number of discontinuities in it increases, water will flow along more discontinuities in both the vertical and lateral directions. When the domain enlarges to a certain volume, called “representative elementary volume” (REV), the rock mass permeability will reach a steady magnitude.

The concept of REV is illustrated in Fig. 17. The rock mass permeability will become constant after REV is reached if the discontinuity occurrence is statistically homogeneous in the region considered. If the discontinuity occurrence is inhomogeneous, the permeability may show further oscillations in the trace or steady increases or decreases.

The REV increases in size with larger discontinuity spacing [82]. Figure 18 illustrates how discontinuities affect REV. In rocks without discontinuities, small REV can be representative of the rock mass [Fig. 18(a)]. In rock masses containing discontinuities, REV should be large enough to include sufficient discontinuity intersections to represent the flow domain [Fig. 18(b)]. The size of REV will be large compared to the discontinuity lengths in order to provide a good statistical sample of the discontinuity population. In the case of large scale discontinuities, such as faults and dykes, REV may not be feasible as it will be too large an area [Fig. 18(c)]. So the REV concept may not be satisfied for every rock mass. The only way to define REV for a rock mass is to investigate in detail the discontinuity geometry.

Interconnectivity of discontinuities

Another important point that can be seen from Fig. 16 is the interconnection of discontinuities. For example, there are 8 discontinuities included in domain C; but only 5 of them are interconnected and may act as flow path for the lateral and vertical water flow (see Fig. 19). Interconnectivity of discontinuities is one of the most important factors affecting the permeability of rock masses. Since all discontinuities are of finite length, a discontinuity can act as a flow path only when it extends completely across the zone interested or is connected to other conductive discontinuities. McCrae [84] estimated that only about 20% of discontinuities encountered during construction of the Muna highway tunnels, Saudi Arabia, were potential water conduits, of which only about 25% had positive evidence of being so. Andersson et al. [85] found that only 10-40% of discontinuities in the Brandan aream, Finnsjon, Sweden were conductive. Of the 11,000 discontinuities documented throughout the Äspö Hard Rock Laboratory in Sweden, only 8% were wet when they were excavated [86].

Anisotropy of rock permeability

Like mechanical properties, the permeability of rocks also shows appreciable anisotropy [3,7,87-92]. The anisotropy of intact rock permeability is primarily a function of the preferred orientation of mineral particles and micro-discontinuities. The permeability of intact rock parallel to the bedding is usually larger than that perpendicular to it. Table 1 lists the ratios of the permeability parallel to bedding to that perpendicular to bedding for different rocks.

Because of the discontinuities, the degree of permeability anisotropy for jointed rock masses may be much higher than that for intact rock. The ratio K_h/K_v may vary from 10^-2 for rock masses whose discontinuities are mainly vertical to 10³ for rock masses containing bedding planes. The contribution of discontinuities to the permeability of a rock mass can be estimated using the methods presented in Section 4.

Changes in pore pressure can affect the degree of permeability anisotropy. For example, in cases with both significant intact rock and discontinuity permeability where there is only one dominant discontinuity set, an increase in pore pressure will lower the effective stress. This leads to an increase in anisotropy by opening the discontinuities, thus increasing the permeability parallel to the discontinuity orientation. Where there is more than one discontinuity set, the nature of anisotropy change with stress would depend on which of the sets are more deformable. In a poorly connected discontinuity network, a decrease in pore pressure could theoretically make the rock more isotropic.

Summary and conclusions

This paper reviewed the research on rock permeability and outlined the key aspects of rock permeability. The conclusions are as follows:

1) The permeability of different intact rocks varies in a great range – at least 8 orders of magnitude. Because of the presence of discontinuities, the permeability of rock masses varies in an even wider range – 11 orders of magnitude.

2) For the evaluation of rock permeability, the geometric properties of discontinuities, such as intensity, aperture and interconnectivity, should be properly considered. Usually only a small portion of the discontinuities are conductive and contribute to the permeability. The hydraulic aperture instead of the physical or mechanical aperture should be used when evaluating the rock mass permeability, the former being smaller than the later.

3) Stress has a great effect on rock permeability and should be considered when evaluating rock permeability. A stress acting perpendicular to discontinuities decreases the permeability, while a stress parallel to discontinuities may increase the permeability. Field measured rock permeability decreases with depth because in situ rock stress increases with depth.

4) Changes in temperature also affect rock permeability, higher temperature leading to lower permeability.

5) Rock permeability is strongly scale dependent. It is important to investigate the discontinuity geometry in detail when applying the representative elementary volume (REV) concept to rock permeability evaluation.

6) Rock permeability usually shows strong anisotropy. The permeability of intact rock parallel to bedding is usually larger than that perpendicular to bedding. The degree of permeability anisotropy for jointed rock masses depends on the distribution of discontinuities and may be much higher than that for intact rock.

7) For effective evaluation of rock permeability, it is important to consider all of the key aspects outlined in this paper.

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