- Email: [email protected]
Fundamentals of the hydro-mechanical behaviour of rock fractures: roughness characterization and experimental aspects
Paper 1A 26 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
FUNDAMENTALS OF THE HYDRO-MECHANICAL BEHAVIOUR OF ROCK FRACTURES: ROUGHNESS CHARACTERIZATION AND EXPERIMENTAL ASPECTS L. Jing¹ , J. A. Hudson² 1)
Royal Institute of Technology (KTH), S-100 44 Stockholm, Sweden 2)
Rock Engineering Consultants, Herts, UK
Abstract: The coupled hydro-mechanical behaviour of rock fractures plays an important role in design, performance and safety assessments of rock engineering projects. However, due to the complexity in the mathematical representation of the fracture surface geometry and its effects on the stress-flow behaviour of the fractures, and the limitations in the test conditions in laboratories, significant lack of knowledge still exists in testing and modelling approaches regarding rock fractures. Based on a general review of the roughness characterization and shear-flow testing of rock fractures, this paper presents the definition of the stationarity threshold of roughness, and a combined experimental-numerical approach for simulating rock fracture testing conditions for more general fluid flow behaviour of the rock fractures. The conclusions are that fracture roughness characterization must be conducted and represented in three-dimensions and the more general fluid flow behaviour cannot be observed with conventional parallel shear-flow tests or compressionradial flow tests. Numerical simulations are needed to reveal more general behaviour of stress-flow processes of rock fractures with boundary and loading conditions that are difficult or impractical in laboratory tests. Keywords: Rock fractures, roughness characterization, stationarity threshold, fracture testing, shear-flow coupling, numerical modelling.
1. INTRODUCTION The understanding of the coupled hydromechanical behaviour of rock fractures is of utmost importance for the characterization and modelling of fractured rock masses for rock engineering design and performance/safety assessments. The main method to obtain first hand information about fracture behaviour in practice is laboratory tests. Field tests can also be performed to obtain knowledge about the fracture behaviour at specific sites, but are rarely adopted in practice due to higher economic costs and limitations in defining the test conditions. A typical procedure for testing a rock fracture includes three steps (besides sample preparation): roughness characterization, test design and implementation, and results evaluation and/or model development, with the determination of the involved physical processes beforehand. Major assumptions have to be made at each of the above steps to make the tests practically applicable under laboratory conditions, considering mainly the sample sizes, dimensional effects and loading conditions.
In this paper, following a brief discussion on the conventional methods for fracture roughness characterization, the concept of the stationarity threshold for the scale dependence of the fracture roughness is presented, followed by three examples for its existence with real rock fracture samples. Numerical simulations of different testing conditions for coupled shear-flow tests are then performed to investigate the effects of roughness and aperture evolution on the fluid flow behaviour, which cannot be observed during the conventional parallel shear-flow tests of rock fractures. The results show that current practice of compressionradial flow and parallel shear-flow tests cannot reveal important flow mechanisms under more general translational and rotational modes of fracture displacements, and numerical modelling is an necessary complementary tool to partially overcome this difficulty. Due to the ever-growing literature and interests in the experimental study of rock fractures, the review on literatures has to be very limited due to the space limit.
1
Paper 1A 26 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
2. CHARACTERIZATION OF FRACTURE ROUGHNESS A rock fracture is composed of two opposite surfaces of usually very complex topography due to numerous asperities of different sizes and shapes. This morphological feature is called the roughness of the rock fracture and is the major reason behind the complexity in mechanical and hydraulic behaviour of the rock fractures. The characterization of the surface roughness remains one of the most important and challenging aspects in the study of rock fractures.
2.1 Roughness Measurement and Stationarity Threshold In practice, the roughness of rock fractures is measured by means of line profilometry, compass and disc clinometry, photogrammetry and laser scanners at laboratory and/or in-situ scales. In line profilometry, the roughness of rock fractures is represented by a slope angle, whose value is different at different scales. The ‘waviness’ of lower frequencies becomes more dominant with the increase of the fracture size while the significance of the ‘roughness’ of higher frequencies decreases. When the fracture size is large enough, its surface may be regarded as statistically pseudo-planar (although not smooth). We called such fracture surfaces stationary surfaces. The minimum size of the fracture at which its surface roughness becomes statistically stationary is called its stationarity threshold. For real rock fractures of larger sizes, the stationarity value may not be a constant but changes with multiple values with increasing fracture sizes. In view of statistics, the definition of the stationarity threshold is equivalent to the Representative Elementary Volume (REV) of a fractured rock, at which the representative geometrical properties may be established for the fracture surfaces as a whole at large scale. In theory, the representative geometrical and hydromechanical behaviour of the fractures can only be obtained with testing results measured with fracture samples of sizes equal or larger than its stationarity threshold. Results with sample sizes less than the stationarity threshold will have larger effects of local effects of fracture surface geometry and cannot be applied to represent fracture behaviour at field scales. Roughness of rock fractures is also generally anisotropic, i.e. values of the slope angles are different in different directions. Conventional line profilometry with a limited numbers of profiling
cross-sections are generally not adequate to represent the roughness anisotropy realistically. Scale-dependency and anisotropy of the roughness are the major contributors to the scale effects and anisotropy of the hydro-mechanical properties of rock fractures, for example, the shear strength and hydraulic aperture. This fact requires that the roughness measurements should be conducted in three-dimensions with sample size not less than its stationarity threshold.
2.2 Roughness Characterization The most widely used measure to quantitatively characterize the fracture roughness is perhaps the JRC (Fracture Roughness Coefficient) with special consideration for scale effect (Barton et al., 1985), given by
JRC 0 =
φt − φr Log10 JCS 0 / σ n0
[
]
(1)
where JRC 0 and JCS 0 are the JRC of the fracture samples at laboratory scale and the wall strength of rock materials of the fractures, respectively. The symbol σ0n represents the normal stress exerted on the fracture by the self weight of the upper half of the fracture sample during tilting tests and φt and φr are the inclination angle of the upper half of the sample when slipping occurs during tilting test and the residual friction angle of the joint sample, respectively. The scale effect of the roughness is considered by an empirical model where JRC n is the roughness of the fracture at field scale of length Ln and L0 is the length of the fracture sample at laboratory scale with a JRC value of JRC 0 from tilting tests, written as
L JRC n = JRC 0 n L0
−a
(2)
where the exponent a is an experimental constant and a value of a = 0.02 JRC 0 was specified in Barton et al. (1985). Different correlation models between JRC and other roughness measures such as fractal dimension, spectral analysis and statistical indices of asperity heights were proposed to characterize the roughness of rock fractures, as reviewed in Jing and Stephansson (1995).
2
Paper 1A 26 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
The concept of JRC has the advantages of being in a simple form, easy to perform the necessary tilting tests in laboratory for small samples and explicit consideration of the scale effect. However, the empirical relation for scale effect is valid only at scales that can be covered in laboratory tests, and for fractures at field scales beyond the laboratory limit the validity of the extrapolated empirical constant in the model cannot be realistically estimated. In addition, the approach has experimental difficulties for representing roughness anisotropy. The empirical constants in the correlation models relating to JRC values were derived from laboratory measurements and may not be valid for rock fractures at different field scales. The fractal approach is a widely used in practice. The precondition to use fractal approach is that the topographical pattern of the rough surface is self-affine, which may or may not be satisfied by rock fractures, especially at large scales. The approach is a special case of spectral analysis using a general power law with its exponent as a constant so that the log-log curves of the comparing parameters can be fitted by linear functions. The approach has the merits of being of a simple and compact mathematical form for scale effects with two main properties (fractal dimension D and amplitude A), for either two or threedimensions. However, the representation of the anisotropy of the roughness using fractal approach is not straightforward. A common problem for the above mentioned method for roughness characterization is the uniqueness. Due to the randomness of the asperity distributions and the uncertainties in the measurement, a value of JRC or D may correspond to different fracture surfaces whose morphological patterns are statistically equivalent, but may have different physical properties. The roughness of rock fractures also varies during a deformation process because of the accumulated damage on the asperities. Therefore, the roughness depends also on the stresses and the history of fracture deformation.
2.3 Examples for existence of roughness stationarity Figure 1a shows a 3D laser scanner at KTH with a capability of scanning fracture samples up to 1 m × 1.4 m in size. Figure 1b shows the scanned surface geometry of a fracture replica (1 m × 1 m in size) from a rock fracture surface at the Äspö Hard Rock Laboratory (HRL) in Southern Sweden.
a)
b)
c)
d) Figure 1. A 3D laser scanner at KTH (a), the scanned surface geometry of a fracture replica of 1 m × 1 m in size (b), a planar fracture surface of schist (c) and a nonstationary fracture sample of gneiss (d). Figures 1c and 1d show fracture surfaces examples scanned using the device. Figure 1c shows a planar surface of a schist rock and Fig. 1d shows the two opposite surfaces of a fracture of a gneiss rock. Different characterization techniques were applied to examine the existence of the stationarity thresholds of the samples, the spectral analysis using the height of asperities and the fractal approach. Figure 2 shows the variation of the fractal dimension D and the amplitude A with the sampling size of the large fracture replica,
3
Paper 1A 26 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
defining the existence of a stationarity threshold of 500 mm. Figure 3a shows the standard deviation of the asperity height of the planar schist surface (in Fig. 1c), defining a stationarity threshold of 20 mm. For the gneiss fracture shown in Fig. 1d, however, a stationarity threshold cannot be defined due to the structural non-stationary effects of the large waviness of the surfaces. This is a clear example of the effects of the sampling technique for fracture characterization and testing. With such non-stationary fractures, the testing results for stresses, strength or fluid flow are valid only for the sample itself, not for the parent fracture in the field.
3. NUMERICAL SIMULATION OF FRACTURE TEST CONDITIONS Figure 2. The variation of the fractal dimension (D) and amplitude A with sampling size for the fracture replica in Fig. 1b. (Fardin et al., 2001).
Figure 3. The variation of the asperity heights with sampling size for the fracture samples of planar schist surface (Sample A) and non-stationary gneiss fracture (Sample B) shown in Fig. 1c and 1d. (Lanaro et al., 1999).
Rock fractures in 3D have six degrees of freedom for relative motion/deformation. Four of them (one opening/compression, two in-plane translational shears and one in-plane rotational shear) are important for the fracture behaviour. All four mechanisms will induce changes in stresses, strengths and apertures of the fractures and should be considered in both testing and modelling. Both translational and rotary shear tests of rock fractures have been performed in the past. However, due to limitations of laboratory testing conditions, most of the tests were basically 2D with one-directional compression-shear tests or rotary shear tests with hollow-cylinder samples, and the parallel shear-flow tests with the same flow and shear directions, although truly 3D mechanical shear test technique is also available and used. These test techniques may be adequate for understanding the basics of mechanical behaviour of rock fractures. However, they have significant shortcomings when coupled shear-flow tests are needed to observe more general fluid flow behaviours under field conditions that are different and more general than these simplified test conditions. In reality, relative displacements of fractures can be contributed from a combination of all four mechanisms, and cause aperture variations in different directions by their combined effects. In practice of fracture testing, it is very difficult or impractical to perform coupled shear-flow tests with the mixed modes of all four mechanisms. To partially overcome this difficulty and examine the directional effects of the shear displacement on flow patterns in fractures, an algorithm for deriving the evolutions of fracture apertures using the numerically simulated shear
4
Paper 1A 26 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
displacement processes of the digitalized rough fracture surface images (Fardin et al., 2004). FEM simulations of water flows are then performed (assuming steady state Darcy flows using the Cubic law). The advantage is that such numerical simulations will not have the limitations in testing conditions as in the laboratory tests, and therefore effects of more general boundary conditions can be tested.
No flow
0.4
H=0 No flow
H=1m
0.5
a)
H=1m H=0
b)
No flow
Figure 4 illustrates results from such numerical tests. For a fracture (250 mm × 250 mm in size represented with 6400 FEM elements) with the aperture and transmissivity changes by numerically simulated linear and rotary shear displacements (Fardin et al., 2004; Koyama et al., 2004). Figure 4a show the contour map of the water head corresponding to a conventional parallel shearlinear flow test with a 1.0 m hydraulic gradient and a 5.0 mm shear displacement. The test produced a heterogeneous flow field as widely reported in literature. Figure 4b shows a shear-flow test with shear direction perpendicular to the flow direction, also with a 1.0 m hydraulic gradient and 5.0 mm shear displacement. This test condition, however, produced a more uniform flow pattern but a higher flow rate, due to a uniform increase of aperture in the flow direction. Figure 4c shows a rotary shear test coupled with a radial fluid flow from a central hole, with a hydraulic gradient of 1.0 m from the centre outwards for a rotation angle of 5 degrees. A very isotropic flow pattern with a high flow rate was induced, despite the heterogeneous initial aperture field. The test conditions in Figure 4b and 4c have not been tried in fracture testing practice and show totally different flow behaviours compared with the one commonly tested in practice as shown in Figure 4a. Using current practice, the derived transmissivity of the fracture using the parallel shear-flow test will produce a transmissivity value much lower than that using the other two. The simulations clearly identified the shortcomings of the currently adopted shear-flow test conditions.
4. CONCLUSIONS
c) Shear direction Flow direction H= 0.9m H=0.7m H=0.5m H=0.3m H=0.1m Figure 4. Different flow patterns produced by a) a parallel shear-flow test, b) a perpendicular shear-flow test, and c) a rotary shear-radial flow test.
All experimental findings clearly indicate that the roughness is the decisive factor for all aspects of hydro-mechanical behaviour of rock fractures. Despite the accumulated achievements, the unique and quantitative characterization of fracture surfaces roughness, and its definitive correlations with hydro-mechanical properties of fractures remains a great challenge. The conventional parallel shear-flow tests are not adequate to represent the general stress-flow behaviour of rock fractures. Totally different flow patterns can be observed when perpendicular shearflow and rotary shear-radial flow tests are performed, with different induced fracture transmissivity values. The numerical examples show clearly that the hydro-mechanical properties of the rock fractures are both stress- and (shear)
5
Paper 1A 26 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
path-dependent, due to the effects of anisotropic roughness on aperture/transmissivity evolutions. The existence of the stationarity threshold of surface roughness poses a serious problem for fracture characterization and testing: how to estimate fracture properties when in most cases in practice the sizes of the fracture samples are much less than their corresponding stationarity thresholds? This is similar to the question of how to evaluate the properties of fractured rocks with samples much less than their REVs. There are no ready solutions to this difficulty and much research is needed in this direction.
single rock fracture during shear. Manuscript submitted to Int. J. Rock Mech. Min. Sci. Koyama T, Fardin N and Jing L. 2004. Shear induced anisotropy and heterogeneity of fluid flow in a single rock fracture by translational and rotary shear displacements – a numerical study. (Accepted for Int. Conf. of SINOROCK, May 2004, China).
5. ACKNOWLEDGEMENT The work presented in this paper is a part of an in-depth review of the coupled THMC processes of rock fractures, and the authors like to express their appreciation of the works performed by Flavio Lanaro, Nader Fardin and Tomofumi Koyama in the field of fracture roughness characterization and shear-flow testing under supervision of the first author at KTH.
6. REFERENCES Barton N, Bandis S and Bakhtar K. 1985. Strength, deformation and conductivity coupling of rock joints. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 22(3), 121-140. Fardin N, Stephansson O and Jing L. 2001. The scale dependence of rock joint surface roughness. Int. J. Rock Mech. Min. Sci., 38(01), 659-669. Lanaro F. 2001. Geometry, mechanics and transmissivity of rock fractures. Ph. D. Thesis. Royal Institute of Technology, Stockholm, Sweden. Lanaro F, Jing L and Stephanss O. 1999. Scale dependency of roughness and staionarity of rock joints. Proc. Of the 9th Cong. Of ISRM, Paris 25-28 1999. Vouille G and Berest P (eds.), Balkema, 1391-1395. Jing L and Stepahnsson O. 1995. Mechanics of rock joints: experimental aspects. In: Mechanics of Geomaterial interfaces (eds. Selvadurai & Boulon), Elsevier, Amsterdam, pp.317 – 342. Fardin N, Koyama T, Jing L and Stephansson O. 2004. Experimental and numerical studies on aperture evolution and fluid flow through a
6
FUNDAMENTALS OF THE HYDRO-MECHANICAL BEHAVIOUR OF ROCK FRACTURES: ROUGHNESS CHARACTERIZATION AND EXPERIMENTAL ASPECTS L. Jing¹ , J. A. Hudson² 1)
Royal Institute of Technology (KTH), S-100 44 Stockholm, Sweden 2)
Rock Engineering Consultants, Herts, UK
Abstract: The coupled hydro-mechanical behaviour of rock fractures plays an important role in design, performance and safety assessments of rock engineering projects. However, due to the complexity in the mathematical representation of the fracture surface geometry and its effects on the stress-flow behaviour of the fractures, and the limitations in the test conditions in laboratories, significant lack of knowledge still exists in testing and modelling approaches regarding rock fractures. Based on a general review of the roughness characterization and shear-flow testing of rock fractures, this paper presents the definition of the stationarity threshold of roughness, and a combined experimental-numerical approach for simulating rock fracture testing conditions for more general fluid flow behaviour of the rock fractures. The conclusions are that fracture roughness characterization must be conducted and represented in three-dimensions and the more general fluid flow behaviour cannot be observed with conventional parallel shear-flow tests or compressionradial flow tests. Numerical simulations are needed to reveal more general behaviour of stress-flow processes of rock fractures with boundary and loading conditions that are difficult or impractical in laboratory tests. Keywords: Rock fractures, roughness characterization, stationarity threshold, fracture testing, shear-flow coupling, numerical modelling.
1. INTRODUCTION The understanding of the coupled hydromechanical behaviour of rock fractures is of utmost importance for the characterization and modelling of fractured rock masses for rock engineering design and performance/safety assessments. The main method to obtain first hand information about fracture behaviour in practice is laboratory tests. Field tests can also be performed to obtain knowledge about the fracture behaviour at specific sites, but are rarely adopted in practice due to higher economic costs and limitations in defining the test conditions. A typical procedure for testing a rock fracture includes three steps (besides sample preparation): roughness characterization, test design and implementation, and results evaluation and/or model development, with the determination of the involved physical processes beforehand. Major assumptions have to be made at each of the above steps to make the tests practically applicable under laboratory conditions, considering mainly the sample sizes, dimensional effects and loading conditions.
In this paper, following a brief discussion on the conventional methods for fracture roughness characterization, the concept of the stationarity threshold for the scale dependence of the fracture roughness is presented, followed by three examples for its existence with real rock fracture samples. Numerical simulations of different testing conditions for coupled shear-flow tests are then performed to investigate the effects of roughness and aperture evolution on the fluid flow behaviour, which cannot be observed during the conventional parallel shear-flow tests of rock fractures. The results show that current practice of compressionradial flow and parallel shear-flow tests cannot reveal important flow mechanisms under more general translational and rotational modes of fracture displacements, and numerical modelling is an necessary complementary tool to partially overcome this difficulty. Due to the ever-growing literature and interests in the experimental study of rock fractures, the review on literatures has to be very limited due to the space limit.
1
Paper 1A 26 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
2. CHARACTERIZATION OF FRACTURE ROUGHNESS A rock fracture is composed of two opposite surfaces of usually very complex topography due to numerous asperities of different sizes and shapes. This morphological feature is called the roughness of the rock fracture and is the major reason behind the complexity in mechanical and hydraulic behaviour of the rock fractures. The characterization of the surface roughness remains one of the most important and challenging aspects in the study of rock fractures.
2.1 Roughness Measurement and Stationarity Threshold In practice, the roughness of rock fractures is measured by means of line profilometry, compass and disc clinometry, photogrammetry and laser scanners at laboratory and/or in-situ scales. In line profilometry, the roughness of rock fractures is represented by a slope angle, whose value is different at different scales. The ‘waviness’ of lower frequencies becomes more dominant with the increase of the fracture size while the significance of the ‘roughness’ of higher frequencies decreases. When the fracture size is large enough, its surface may be regarded as statistically pseudo-planar (although not smooth). We called such fracture surfaces stationary surfaces. The minimum size of the fracture at which its surface roughness becomes statistically stationary is called its stationarity threshold. For real rock fractures of larger sizes, the stationarity value may not be a constant but changes with multiple values with increasing fracture sizes. In view of statistics, the definition of the stationarity threshold is equivalent to the Representative Elementary Volume (REV) of a fractured rock, at which the representative geometrical properties may be established for the fracture surfaces as a whole at large scale. In theory, the representative geometrical and hydromechanical behaviour of the fractures can only be obtained with testing results measured with fracture samples of sizes equal or larger than its stationarity threshold. Results with sample sizes less than the stationarity threshold will have larger effects of local effects of fracture surface geometry and cannot be applied to represent fracture behaviour at field scales. Roughness of rock fractures is also generally anisotropic, i.e. values of the slope angles are different in different directions. Conventional line profilometry with a limited numbers of profiling
cross-sections are generally not adequate to represent the roughness anisotropy realistically. Scale-dependency and anisotropy of the roughness are the major contributors to the scale effects and anisotropy of the hydro-mechanical properties of rock fractures, for example, the shear strength and hydraulic aperture. This fact requires that the roughness measurements should be conducted in three-dimensions with sample size not less than its stationarity threshold.
2.2 Roughness Characterization The most widely used measure to quantitatively characterize the fracture roughness is perhaps the JRC (Fracture Roughness Coefficient) with special consideration for scale effect (Barton et al., 1985), given by
JRC 0 =
φt − φr Log10 JCS 0 / σ n0
[
]
(1)
where JRC 0 and JCS 0 are the JRC of the fracture samples at laboratory scale and the wall strength of rock materials of the fractures, respectively. The symbol σ0n represents the normal stress exerted on the fracture by the self weight of the upper half of the fracture sample during tilting tests and φt and φr are the inclination angle of the upper half of the sample when slipping occurs during tilting test and the residual friction angle of the joint sample, respectively. The scale effect of the roughness is considered by an empirical model where JRC n is the roughness of the fracture at field scale of length Ln and L0 is the length of the fracture sample at laboratory scale with a JRC value of JRC 0 from tilting tests, written as
L JRC n = JRC 0 n L0
−a
(2)
where the exponent a is an experimental constant and a value of a = 0.02 JRC 0 was specified in Barton et al. (1985). Different correlation models between JRC and other roughness measures such as fractal dimension, spectral analysis and statistical indices of asperity heights were proposed to characterize the roughness of rock fractures, as reviewed in Jing and Stephansson (1995).
2
Paper 1A 26 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
The concept of JRC has the advantages of being in a simple form, easy to perform the necessary tilting tests in laboratory for small samples and explicit consideration of the scale effect. However, the empirical relation for scale effect is valid only at scales that can be covered in laboratory tests, and for fractures at field scales beyond the laboratory limit the validity of the extrapolated empirical constant in the model cannot be realistically estimated. In addition, the approach has experimental difficulties for representing roughness anisotropy. The empirical constants in the correlation models relating to JRC values were derived from laboratory measurements and may not be valid for rock fractures at different field scales. The fractal approach is a widely used in practice. The precondition to use fractal approach is that the topographical pattern of the rough surface is self-affine, which may or may not be satisfied by rock fractures, especially at large scales. The approach is a special case of spectral analysis using a general power law with its exponent as a constant so that the log-log curves of the comparing parameters can be fitted by linear functions. The approach has the merits of being of a simple and compact mathematical form for scale effects with two main properties (fractal dimension D and amplitude A), for either two or threedimensions. However, the representation of the anisotropy of the roughness using fractal approach is not straightforward. A common problem for the above mentioned method for roughness characterization is the uniqueness. Due to the randomness of the asperity distributions and the uncertainties in the measurement, a value of JRC or D may correspond to different fracture surfaces whose morphological patterns are statistically equivalent, but may have different physical properties. The roughness of rock fractures also varies during a deformation process because of the accumulated damage on the asperities. Therefore, the roughness depends also on the stresses and the history of fracture deformation.
2.3 Examples for existence of roughness stationarity Figure 1a shows a 3D laser scanner at KTH with a capability of scanning fracture samples up to 1 m × 1.4 m in size. Figure 1b shows the scanned surface geometry of a fracture replica (1 m × 1 m in size) from a rock fracture surface at the Äspö Hard Rock Laboratory (HRL) in Southern Sweden.
a)
b)
c)
d) Figure 1. A 3D laser scanner at KTH (a), the scanned surface geometry of a fracture replica of 1 m × 1 m in size (b), a planar fracture surface of schist (c) and a nonstationary fracture sample of gneiss (d). Figures 1c and 1d show fracture surfaces examples scanned using the device. Figure 1c shows a planar surface of a schist rock and Fig. 1d shows the two opposite surfaces of a fracture of a gneiss rock. Different characterization techniques were applied to examine the existence of the stationarity thresholds of the samples, the spectral analysis using the height of asperities and the fractal approach. Figure 2 shows the variation of the fractal dimension D and the amplitude A with the sampling size of the large fracture replica,
3
Paper 1A 26 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
defining the existence of a stationarity threshold of 500 mm. Figure 3a shows the standard deviation of the asperity height of the planar schist surface (in Fig. 1c), defining a stationarity threshold of 20 mm. For the gneiss fracture shown in Fig. 1d, however, a stationarity threshold cannot be defined due to the structural non-stationary effects of the large waviness of the surfaces. This is a clear example of the effects of the sampling technique for fracture characterization and testing. With such non-stationary fractures, the testing results for stresses, strength or fluid flow are valid only for the sample itself, not for the parent fracture in the field.
3. NUMERICAL SIMULATION OF FRACTURE TEST CONDITIONS Figure 2. The variation of the fractal dimension (D) and amplitude A with sampling size for the fracture replica in Fig. 1b. (Fardin et al., 2001).
Figure 3. The variation of the asperity heights with sampling size for the fracture samples of planar schist surface (Sample A) and non-stationary gneiss fracture (Sample B) shown in Fig. 1c and 1d. (Lanaro et al., 1999).
Rock fractures in 3D have six degrees of freedom for relative motion/deformation. Four of them (one opening/compression, two in-plane translational shears and one in-plane rotational shear) are important for the fracture behaviour. All four mechanisms will induce changes in stresses, strengths and apertures of the fractures and should be considered in both testing and modelling. Both translational and rotary shear tests of rock fractures have been performed in the past. However, due to limitations of laboratory testing conditions, most of the tests were basically 2D with one-directional compression-shear tests or rotary shear tests with hollow-cylinder samples, and the parallel shear-flow tests with the same flow and shear directions, although truly 3D mechanical shear test technique is also available and used. These test techniques may be adequate for understanding the basics of mechanical behaviour of rock fractures. However, they have significant shortcomings when coupled shear-flow tests are needed to observe more general fluid flow behaviours under field conditions that are different and more general than these simplified test conditions. In reality, relative displacements of fractures can be contributed from a combination of all four mechanisms, and cause aperture variations in different directions by their combined effects. In practice of fracture testing, it is very difficult or impractical to perform coupled shear-flow tests with the mixed modes of all four mechanisms. To partially overcome this difficulty and examine the directional effects of the shear displacement on flow patterns in fractures, an algorithm for deriving the evolutions of fracture apertures using the numerically simulated shear
4
Paper 1A 26 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
displacement processes of the digitalized rough fracture surface images (Fardin et al., 2004). FEM simulations of water flows are then performed (assuming steady state Darcy flows using the Cubic law). The advantage is that such numerical simulations will not have the limitations in testing conditions as in the laboratory tests, and therefore effects of more general boundary conditions can be tested.
No flow
0.4
H=0 No flow
H=1m
0.5
a)
H=1m H=0
b)
No flow
Figure 4 illustrates results from such numerical tests. For a fracture (250 mm × 250 mm in size represented with 6400 FEM elements) with the aperture and transmissivity changes by numerically simulated linear and rotary shear displacements (Fardin et al., 2004; Koyama et al., 2004). Figure 4a show the contour map of the water head corresponding to a conventional parallel shearlinear flow test with a 1.0 m hydraulic gradient and a 5.0 mm shear displacement. The test produced a heterogeneous flow field as widely reported in literature. Figure 4b shows a shear-flow test with shear direction perpendicular to the flow direction, also with a 1.0 m hydraulic gradient and 5.0 mm shear displacement. This test condition, however, produced a more uniform flow pattern but a higher flow rate, due to a uniform increase of aperture in the flow direction. Figure 4c shows a rotary shear test coupled with a radial fluid flow from a central hole, with a hydraulic gradient of 1.0 m from the centre outwards for a rotation angle of 5 degrees. A very isotropic flow pattern with a high flow rate was induced, despite the heterogeneous initial aperture field. The test conditions in Figure 4b and 4c have not been tried in fracture testing practice and show totally different flow behaviours compared with the one commonly tested in practice as shown in Figure 4a. Using current practice, the derived transmissivity of the fracture using the parallel shear-flow test will produce a transmissivity value much lower than that using the other two. The simulations clearly identified the shortcomings of the currently adopted shear-flow test conditions.
4. CONCLUSIONS
c) Shear direction Flow direction H= 0.9m H=0.7m H=0.5m H=0.3m H=0.1m Figure 4. Different flow patterns produced by a) a parallel shear-flow test, b) a perpendicular shear-flow test, and c) a rotary shear-radial flow test.
All experimental findings clearly indicate that the roughness is the decisive factor for all aspects of hydro-mechanical behaviour of rock fractures. Despite the accumulated achievements, the unique and quantitative characterization of fracture surfaces roughness, and its definitive correlations with hydro-mechanical properties of fractures remains a great challenge. The conventional parallel shear-flow tests are not adequate to represent the general stress-flow behaviour of rock fractures. Totally different flow patterns can be observed when perpendicular shearflow and rotary shear-radial flow tests are performed, with different induced fracture transmissivity values. The numerical examples show clearly that the hydro-mechanical properties of the rock fractures are both stress- and (shear)
5
Paper 1A 26 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
path-dependent, due to the effects of anisotropic roughness on aperture/transmissivity evolutions. The existence of the stationarity threshold of surface roughness poses a serious problem for fracture characterization and testing: how to estimate fracture properties when in most cases in practice the sizes of the fracture samples are much less than their corresponding stationarity thresholds? This is similar to the question of how to evaluate the properties of fractured rocks with samples much less than their REVs. There are no ready solutions to this difficulty and much research is needed in this direction.
single rock fracture during shear. Manuscript submitted to Int. J. Rock Mech. Min. Sci. Koyama T, Fardin N and Jing L. 2004. Shear induced anisotropy and heterogeneity of fluid flow in a single rock fracture by translational and rotary shear displacements – a numerical study. (Accepted for Int. Conf. of SINOROCK, May 2004, China).
5. ACKNOWLEDGEMENT The work presented in this paper is a part of an in-depth review of the coupled THMC processes of rock fractures, and the authors like to express their appreciation of the works performed by Flavio Lanaro, Nader Fardin and Tomofumi Koyama in the field of fracture roughness characterization and shear-flow testing under supervision of the first author at KTH.
6. REFERENCES Barton N, Bandis S and Bakhtar K. 1985. Strength, deformation and conductivity coupling of rock joints. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 22(3), 121-140. Fardin N, Stephansson O and Jing L. 2001. The scale dependence of rock joint surface roughness. Int. J. Rock Mech. Min. Sci., 38(01), 659-669. Lanaro F. 2001. Geometry, mechanics and transmissivity of rock fractures. Ph. D. Thesis. Royal Institute of Technology, Stockholm, Sweden. Lanaro F, Jing L and Stephanss O. 1999. Scale dependency of roughness and staionarity of rock joints. Proc. Of the 9th Cong. Of ISRM, Paris 25-28 1999. Vouille G and Berest P (eds.), Balkema, 1391-1395. Jing L and Stepahnsson O. 1995. Mechanics of rock joints: experimental aspects. In: Mechanics of Geomaterial interfaces (eds. Selvadurai & Boulon), Elsevier, Amsterdam, pp.317 – 342. Fardin N, Koyama T, Jing L and Stephansson O. 2004. Experimental and numerical studies on aperture evolution and fluid flow through a
6