Laboratory Assessment of Fracture Permeability under Normal and Shear Stresses D. Phueakphum* and K. Fuenkajorn Geomechanics Research Unit, Suranaree University of Technology 111 University Avenue, Nakhon Ratchasima 30000, Thailand *E-mail: phueakphum@sut.ac.th Abstract Falling head flow tests have been performed to determine the hydraulic conductivity of tension-induced fractures while under normal and shear stresses for eight rock types. The joint roughness coefficients are determined and used to calculate the mechanical aperture. The shear stress is applied while the shear displacement and water head drop are monitored for every 0.5 mm interval of shear displacement. The fracture hydraulic conductivities decrease exponentially with increasing normal stresses. The physical and hydraulic apertures increase with shearing displacement, particularly under high normal stresses. The magnitudes of the fracture permeability under no shear and under peak shear stress are similar. For both peak and residual regions, the physical apertures are about 5 to 10 times greater than the hydraulic apertures. This is probably because the measured physical apertures do not consider the effect of fracture roughness that causes a longer flow path. The difference between the permeability under residual shear stress and that under peak stress becomes larger under higher normal stresses. The findings are useful to determine the rock mass permeability where the fractures are subject to changes of stress states induced by surface and underground excavations. Keywords: Flow test, Fracture roughness, Direct shear test, Fracture dilation 1. Introduction Understanding of groundwater flow in rock mass is one of the key factors governing the mechanical stability of engineering and geological applications, such as slope embankments, dam foundation, underground mines and tunnels. It is necessary to investigate the hydraulic properties of fractures under deformation as affected normal and shear stresses. The lack of proper understanding of the water pressure and flow characteristics in rock mass makes it difficult to predict the water inflow for underground mines and tunnels under complex hydro-geological environments. Unlike those in the soil mass, permeability of rock mass is path dependent, controlling mainly by the system of fractures as the permeability of the intact rocks is significantly lower (Lee et al. 2011; Bang et al., 2012). For undisturbed rock mass (before excavation) the joint characteristics that dictate the amount and direction of water flow, can be adequately determined by means of in-situ measurements, and sometimes assisted by numerical modeling. Slope or underground excavations disturb the surrounding rock mass, alter the stress states on the fracture planes, and often cause relative displacements of the fractures. The excavations usually increase the surrounding rock mass permeability, sometimes by several orders of magnitudes. Most past studies have estimated fracture permeability as a function of normal stress (e.g. Xiao et al. 1999; Pyrak-Nolte and Morrisa, 2000; Niemi et al., 1997; Indraratna and Ranjith,2001; Baghbanan and Jing, 2008) and very few as a function of shear stress (Bandis, et al., 1985; Yeo et al, 1998). Previous laboratory and field test results have revealed that the flow rate along the single fracture is highly sensitive to the change of joint aperture. Xiao et al. (1999), Pyrak-Nolte and Morrisa (2000), Niemi et al. (1997), Indraratna and Ranjith (2001) and Baghbanan and Jing (2008) conclude from their experimental results that fracture permeability exponentially decreases with increasing normal stresses. The apertures and permeability of rock fractures are also affected by the shearing displacement (Auradou et al., 2006). The flow testing results on fractures in granite and marble obtained by Lee and Cho (2002) indicate that the fracture permeability increases by up to two orders of magnitude as the shearing displacement increases. This finding is supported by the results of numerical simulations by Son et al. (2004).
The objectives of this study are to experimentally determine rock fracture permeability under normal and shear stresses. Falling head tests are performed to determine the permeability of tension-induced fractures in marble, granites and sandstones. The changes of the fracture apertures (physical and hydraulic), the water flow rates, and the applied shear stresses under each constant normal stress are monitored during the test and used to calculate the changes of the fracture permeability as a function of shear displacement. Empirical relations are developed to determine the fracture permeability as a function of the shear stresses and displacements. The findings are useful to determine the rock mass permeability where the fractures are subject to changes of stress states induced by surface and underground excavations. 2. Rock samples The rock samples are prepared from Saraburi marble (SBMB), Tak granite (TGR), Vietnamese granite (VGR) and Chinese granite (CGR), Phu Phan, Phra Wihan, Phu Kradung and Sao Kua Sandstones (PPSS, PWSS, PKSS, and SKSS). Petrographic analyses have been performed to determine their mineral compositions and textures. The results are summarized in Table 1. The fractures are artificially made in the laboratory by applying a line load to induce a splitting tensile crack in mid-length of 10 10 12 cm prismatic blocks (Figure 1). The water injection hole at the center of the lower block is 0.8 cm in diameter. It is connected to the hydraulic tube before casting the specimen in to the direct shear box. The surface roughness of the tension-induced fractures is characterized by laser profilometer (up to 0.01 mm resolution) to obtain three-dimensional images of the fracture surfaces. They are classified by comparing with a reference profiles (joint roughness coefficient JRC, Barton, 1973) and alternative method from measurements of surface roughness amplitude from straight edge (Barton and Bandis, 1982). The measurement points are taken with 1.0 mm spacing in x- and y-directions. Figure 2 shows an example of the strip profiles and the three-dimensional fracture surfaces. The JRC values of all rock types are ranging from 4 to 17. The JRC values obtained from the sandstones (4-10) are smaller than those obtained from me those obtained from marble (9-11) and granites (11-17). Table 1 Mineral compositions of tested sandstones obtained from X-ray diffraction. Rock Types Density (g/cc) Grain (Crystal) Size (mm) Metamorphic Rock SMB 2.58 4 8 (6) Igneous Rock TGR 2.62 4 8 (5) CGR 2.64 5 12 (7) VGR 2.62 2 10 (8) Sedimentary Rock PWSS 2.33 1.5 2.0 (1.6) Sorting - calcite 100% Mineral Compositions - plagioclase 40%, quartz 30%, orthoclase 5%, amphibole 3% and biotite 2% - plagioclase 70%, quartz 15%, orthoclase 7%, amphibole 5% and biotite 3% - orthoclase 75%, quartz 10%, plagioclase 10% and amphibole 7% well quartz 75%, feldspar 15%, mica 7%, and lithic fragment 3% PPSS 2.26 1.5 2.0 (1.8) PKSS 2.54 0.1 1.5 (1.0) SKSS 2.33 0.1 1.0 (0.5) well moderate poorly quartz 72%, feldspar 20%, rock fragment 3%, mica 3%, and other 2% lithic fragment 70%, quartz 18%, mica 7%, feldspar 3%, and other 2% feldspar 70%, quartz 18%, mica 7%, rock fragment 3%, and other 2%
Fig. 1. Some rock specimens prepared for falling head test under normal and shear stresses. Fig. 2. Example of three-dimensional scanned surface (a) and its strip profiles (b) for Phu Kradung sandstone.
3. Testing method Fig. 3 shows the laboratory arrangement of the falling head flow test while the fracture is subject to the direct shear test. The maximum water head above the tested fracture is taken as 1.23 m. The normal stresses are maintained constant at 0.69, 1.38, 2.76, 3.45 and 4.14 MPa for the sandstones and at 0.35, 1.03, and 3.10 MPa for the marble and granites. The shear stress is applied while the shear displacement and head drop are monitored for every 0.5 mm interval of the shear displacement. The maximum shear displacement is 5 mm. The (physical) fracture aperture is measured to the nearest 0.01 mm before and after normal and shear stress application. The fracture dilations are also monitored during the shear test. Fig. 3. Laboratory arrangement for falling head flow tests under normal and shear stresses. H 1 and t 1 representing pressure head and time at the beginning of test. H 2 and t 2 representing pressure and time at the end of test. 4. Permeability calculation The physical, mechanical and hydraulic apertures are used to calculate the hydraulic conductivity of the tested fractures. The physical aperture (e p ) is obtained from the actual measurements of the fractures dilation before and during normal and shear stress applications. The measurement points are at the four corners of the shear box. The physical aperture at each shear displacement is an average from the four measurements points. The mechanical aperture (e m ) or initial aperture under self-weight of sample (in mm) is calculated by (Barton and Bakhtar, 1983; Bandis et al., 1983, 1985): JRC c em 0.2 0. 1 (1) 5 JCS where c and JCS are the uniaxial compressive strength and joint compressive strength of the rock in MPa. Here c and JCS are assumed to be equal. The measured JRC values range from 4 through 17, which are classified as rough and undulating; bedding and tectonic joints; and relief joints, respectively (Zhao, 1998). From Eq. (1) the equivalent mechanical apertures for the above JRC values can be calculated as 80 to 340 micro-meters. These fractures can be classified as tight to partly open based on the classification of discontinuity aperture suggested by Zhao (1998). The equivalent hydraulic aperture (e h ) for the radial flow path is calculated here by (Maini, 1971): e h ln H1 / H t2 t 2 1 r 2 b R ln r 6 where γ is the unit weight of water (N/m 2 ), μ is the dynamic viscosity of water (N s/m 2 ), H 1 and H 2 are the water heads at t 1 and t 2, r b is the pipette radius (m), R is the radius of flow path (m), and r is the radius of the radius injection hole (m). 1 / 3 (2)
The fracture permeability is calculated by (Zeigler, 1976): e K (3) 12 where K represents hydraulic conductivity (m/s) between smooth and parallel plates and e is the parallel plate aperture (m). It is assumed here that the flow is uniform across the fracture plane, and that the intact rock is impermeable. Here the fracture conductivity is calculated from fracture apertures: e p, e m and e h, and differentiated by different symbols as K p physical, K m mechanical, and K h hydraulic conductivities. The joint shear stiffness for various normal stresses is calculated at the 50% peak stress using an equation (Indraratna and Ranjith, 2001): K s = s / s (4) where K s is the joint shear stiffness (MPa/m), s is the shear stress (MPa), s is the shear displacement (m). The normal stiffness of fractured is calculated by (Indraratna and Ranjith, 2001): 2 K n = σ n / n (5) where K n is the joint normal stiffness (MPa/m), n is the normal stress (MPa), n is the normal displacement (m). 5. Test results The peak and residual shear stresses as a function of normal stress are plotted and fitted with the Coulomb criterion in Fig. 4. The cohesions, friction angles and R-squared values of rock fractures are summarized in Table 2. Good correlations are obtained for all tested fractures. The values of peak and residual shear stress under various the normal stresses as plotted in Fig.4 for the determination of cohesion and friction angles are shown in Table 3. Fig. 4. Shear stresses ( ) plotted as a function of normal stresses ( n ).
Table 2 The cohesions, friction angles and R-squared values of rock fractures. Rock Types r (Degrees) c p (MPa) r (Degrees) R 2 () R 2 () SMB 46 1.4 51 0.6758 0.8261 TGR 42 1.4 52 0.5424 0.8810 CGR 46 1.2 53 0.9727 0.8660 VGR 39 1.1 40 0.6107 0.7875 PWSS 48 0.4 53 0.9620 0.9940 PPSS 42 0.8 51 0.9549 0.9640 PKSS 40 0.6 41 0.9255 0.9475 SKSS 39 0.6 42 0.9183 0.9680 Table 3 Shear stress, joint stiffness and hydraulic conductivity under various normal stresses. Rock Types SMB TGR CGR VGR PWSS PPSS PKSS SKSS n (MPa) 0.35 1.03 3.10 0.35 1.03 3.10 0.35 1.03 3.10 0.35 1.03 3.10 0.69 1.38 2.76 3.49 4.14 0.69 1.38 2.76 3.49 4.14 0.69 1.38 2.76 3.49 4.14 0.69 1.38 2.76 3.49 4.14 p (MPa) 1.08 3.45 4.53 4.92 1.08 3.23 4.53 4.96 1.08 3.23 4.53 4.96 0.86 2.59 3.23 3.45 1.50 2.20 2.97 4.10 5.20 6.01 2.41 2.97 4.07 5.47 5.99 1.16 1.81 2.37 2.80 3.02 4.31 1.55 1.64 2.37 2.93 3.88 4.53 r (MPa) 0.47 1.94 2.41 2.80 0.43 1.34 2.33 2.93 0.43 1.34 2.33 2.93 0.52 1.55 1.47 2.33 0.86 1.55 2.28 2.72 3.62 5.09 0.95 1.10 1.47 2.37 3.28 3.79 0.82 1.38 1.85 2.16 2.50 3.66 1.03 1.12 1.38 3.10 3.32 K s K n (GPa/m) (GPa/m) 2.87 5.60 5.77 2.68 14.92 2.72 14.92 7.09 4.06 12.58 11.54 17.92 7.19 14.39 14.68 18.81 4.40 7.00 7.33 8.60 12.50 13.33 14.29 15.38 16.67 18.18 5.26 6.67 8.70 10.00 11.76 14.29 4.65 5.40 9.09 12.50 16.67 18.18 5.00 7.14 10.00 12.50 16.67 18.18 4.00 2.35 7.53 4.00 0.39 2.75 3.57 2.76 0.69 3.32 2.76 6.08 1.86 4.18 4.27 8.36 4.42 4.16 5.31 6.57 4.81 10.13 6.07 8.72 3.14 3.23 3.87 4.80 7.35 6.49 1.15 3.29 7.53 6.42 7.35 7.02 Hydraulic Conductivity ( 10-3 m/sec) (K h,p ) (K h,r ) No Shear (K h,o ) 10.92 23.32 10.35 7.02 23.12 6.28 2.16 23.12 2.08 1.74 11.12 1.43 11.73 5.52 1.74 1.09 13.32 7.58 3.87 1.74 13.08 12.29 9.61 9.42 4.57 3.52 2.83 1.74 0.37 0.21 9.79 5.58 4.73 1.43 0.23 0.37 9.42 8.86 7.02 5.71 3.02 2.54 5.32 4.73 4.12 3.48 2.02 1.74 22.13 21.54 15.84 10.85 23.93 23.72 23.52 23.32 23.93 17.80 17.95 16.74 11.91 10.07 8.92 8.63 5.10 4.45 10.54 10.24 7.66 6.84 5.99 5.90 10.54 9.98 9.98 9.79 6.84 6.28 6.46 5.90 4.93 4.12 3.14 3.14 14.22 3.80 1.74 0.90 12.66 7.51 3.14 1.09 10.89 11.70 10.26 8.86 4.53 3.12 2.68 1.42 0.23 0.20 9.23 8.25 4.50 1.26 0.14 0.23 8.50 8.13 5.90 4.73 2.54 2.02 4.73 4.33 3.70 3.02 2.02 1.74
The fracture stiffness is calculated using Eqs (4) and (5) for all rock types (Table 3). The fracture stiffness determined here compare well with those obtained by Pyrak-Nolte et al. (2000). The joint stiffness tends to increase with the normal stresses. More discussion on the change of the joint stiffness with the normal stress and the influencing of joint stiffness on hydraulic conductivity of rock fracture will be presented in the next section. The fracture hydraulic conductivities (K p, K m and K h ) are calculated for the three aperture measurements (e p, e m and e h ) and plotted as a function of shear displacement ( s ) for normal stresses of 0.35, 1.03, and 3.10 MPa for the marble in Fig. 5. They are also compared with their corresponding shear stress-displacement diagram ( s - s ). Since the shear stresses after the peak value remain relatively constant through 5 mm of the displacement. The physical aperture, e p, tends to increase with the shearing displacement. Its value fluctuates before the peak and tends to be consistent in the residual stress region. The K p values calculated from e p subsequently show similar characteristics in the permeability-shear displacement diagram. The hydraulic aperture, e h, indirectly determined from the inflow rates also tends to increase with the shear displacement, particularly under high normal stresses. Even though the change of K p and K h values are similar in the permeability-shear displacement diagram, K p is always about an order of magnitude greater than K h, particularly in the residual region. Shear Stress, (MPa) Shear Stress, (MPa) Shear Stress, (MPa) Shear Stress, (MPa) 10 5 0 10 n = 1.03 MPa 5 n = 0.35 MPa 0 10 n = MPa 5 0 10 n = 3.10 MPa 5 0 Shear Displacement, s (mm) e (x10-6 m) e (x10-6 m) e (x10-6 m) e (x10-6 m) n = 0.35 MPa n = 1.03 MPa n = MPa n = 3.10 MPa Shear Displacement, s (mm) e p e m e h e p e m e h e p e m e h e p e m e h K (x10-3 m/s) K (x10-3 m/s) K (x10-3 m/s) K (x10-3 m/s) n = 0.35 MPa n = 1.03 MPa n = MPa n = 3.10 MPa Shear Displacement, s (mm) Fig. 5. Example test results for Saraburi marble. Shear stress ( ), fracture aperture (e p, e m and e h ) and hydraulic conductivity (K p, K m and K h ) plotted as a function of shear displacement ( s ) under normal stresses of 0.35, 1.03, and 3.10 MPa. K p K m K h K p K m K h K p K m K h K p K m K h
8th Asian Rock Mechanics Symposium ARMS8 Observations of the pre and post test fracture areas suggest that no significant change has occurred in terms of fracture roughness. Even though some portion of fracture is sheared off the JRC s remain roughly the same. This is primarily because the applied normal stresses used here are relatively low. The mechanical aperture, em before, during and after shearing remains constant during the shearing process. As a result the hydraulic conductivity Km calculated from em is independent of the shearing displacement. An example of the post test fracture for PW sandstone is shown in Fig. 6. Fig. 6. Example of post-test fracture surfaces in a Phra Wihan sandstone specimen. The sheared surfaces are indicated by white areas. 6. Effects of normal stresses on permeability Figs. 7 and 8 plot the hydraulic aperture (eh) and hydraulic conductivity (Kh) as a function of the normal stresses. They are calculated by using Eqs. (2) and (3). For all rock types the fracture hydraulic conductivities exponentially decrease with increasing the normal stresses. The fracture permeability values under no shear stress, immediately before the peak stress and under the residual shear stress are compared in Fig. 8. The fracture permeability under residual region is greater than those under no shear and immediately before peak stress. It decreases with increasing the normal stress. The magnitudes of fracture permeability under no shear and under peak stress are similar. Both tend to decrease exponentially with the normal stress. As a result the difference between the permeability under residual shear stress and that under peak stress becomes larger as the normal stress increases. The results agree reasonably well with those obtained by Lee and Cho (2002) and Son et al. (2004). 7. Effects of shear stresses on permeability Fig. 9 plots the fracture hydraulic conductivity (Kh) as a function of fractures shear strength. The fracture hydraulic conductivity decreases with increasing fracture shear strength. The decrease of fracture permeability under the peak shear strength (Kh,p) can be represented by an exponential equation: Kh,p = p exp ( p p) (6) where p and p are empirical constants. For the residual shear strength the change of fracture permeability under the residual shear strength (Kh,r) can be represented by Kh,r = r exp ( r r) (7) where r and r are empirical constants. The exponents p and r represent the reduction rate of the fracture permeability as the fracture shear strength increases. 8. Effects of joint stiffness and roughness on permeability Fig. 10 plots the fracture hydraulic conductivity (Kh) as a function of joint stiffness. The fracture hydraulic conductivity decreases with increasing joint stiffness. Fig. 11 plots the fracture hydraulic conductivity (Kh) as a function of joint roughness coefficient (JRC). The JRC values has significantly influenced on the fracture hydraulic conductivity during shear displacement. The fracture hydraulic conductivity increases with increasing joint stiffness.
Fig. 7. Hydraulic aperture (e h ) plotted as a function of normal stress ( n ). Fig. 8. Hydraulic conductivity (K h ) which determined from hydraulic aperture (e h ) plotted as a function of normal stress ( n ). - residual hydraulic conductivity, - peak hydraulic conductivity and - no shear hydraulic conductivity.
Kh (x10-3 m/sec) Kh (x10-3 m/sec) Kh (x10-3 m/sec) K h,p = 31.36exp(-0.6403 p) [R 2 = 0.9521] Tak Granite K h,r = 13.26exp(-0.2029 r) [R 2 = 0.7842] K h,p = 18.30exp(-0.4712 p) [R 2 = 0.8528] Phu Kradung Sandstone 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 K h,r = 30.37exp(-0.3552 r) [R 2 = 0.6795] Saraburi Marble K h,r = 29.02exp(-0.2142 r) [R 2 = 0.3529] K h,p = 21.93exp(-0.4784 p) [R 2 = 0.8541] K h,r = 11.81exp(-0.2018 r) [R 2 = 0.8692] K h,p = 76.60exp(-0.9707 p) [R 2 = 0.9606] Phu Phan Sandstone 0 2 4 6 8 0 2 4 6 8 K h,r = 24.04exp(-0.0100 r) [R 2 = 0.9909] K h,r = 15.06exp(-0.2502 r) [R 2 = 0.9319] Chinese Granite K h,p = 25.86exp(-0.4702 p) [R 2 = 0.8716] 0 2 4 6 8 Shear Strength, s (MPa) K h,p = 18.46exp(-0.7178 p) [R 2 = 0.9277] Phra Wihan Sandstone 0 2 4 6 8 Shear Strength, s (MPa) K h,r = 22.45exp(-0.2022 r) [R 2 = 0.8792] K h,p = 15.11exp(-0.1259 p) [R 2 = 0.7737] Vietnamese Granite Sao Kua Sandstone K h,r =8.11exp(-0.3011 r) [R 2 = 0.9588] K h,p = 9.51exp(-0.3770 p) [R 2 = 0.9744] 0 2 4 6 8 Shear Strength, s (MPa) Fig. 9. Hydraulic conductivity (K h ) plotted as a function of peak and residual shear strength ( p and r ). Fig. 10. Joint stiffness plotted as a function of hydraulic conductivity. Fig. 11. Joint roughness coefficient (JRC) plotted as a function of hydraulic conductivity.
9. Discussions and conclusions The physical aperture e p and hydraulic aperture e h increase with shearing displacement, particularly under high normal stresses. The magnitudes of fracture permeability under no shear and under peak shear stress are similar. For both peak and residual regions, the physical apertures are about 5 to 10 times greater than the hydraulic apertures, as a result the fracture hydraulic conductivity determined from the physical aperture are about one to two orders of magnitudes greater than these determined from the equivalent hydraulic apertures. The difference between the permeability under residual shear stress and that under peak stress becomes larger under higher normal stresses. The fracture hydraulic conductivities exponentially decrease with increasing the normal stresses. The fracture hydraulic conductivity determined here compares well with those obtained by Zhao (1998) and Chandra et al. (2008). The flow in fractures is sensitive to the normal and shear stiffness. The normal and shear stiffness tends to increase with increasing of normal stress on rock fracture. The fracture hydraulic conductivities exponentially decrease with increasing of joint stiffness. The range of normal stiffness is approximately from 1 to 18 GPa/m which is of the same order of magnitude with those obtained by Pyrak-Nolte et al. (2000). The findings are useful to determine the rock mass permeability where the fractures are subject to changes of stress states induced by surface and underground excavations. The hydraulic conductivity can be determined when the normal and shear stresses on rock fracture around the opening are calculated using the mathematical equations. Acknowledgements This study is funded by Suranaree University of Technology and by the Higher Education Promotion and National Research University of Thailand. Permission to publish this paper is gratefully acknowledged. References ASTM D5607-95, 1995, Standard test method for performing laboratory direct shear strength test of rock specimens under constant normal force. In: Annual Book of ASTM Standards, Vol. 04.08. West Conshohocken, PA: ASTM. Auradou, H., Drazer, G., Boschan, A., Hulin, J. and Koplik, J., 2006, Flow Channeling in a Single Fracture Induced by Shear Displacement, Geothermics, 35, 576 588. Baghbanan, A. and Jing, L., 2008, Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture, International Journal of Rock Mechanics & Mining Sciences, 45(8), 1320-1334. Bandis, S. C., Lumsden, A. C., and Barton, N.R., 1983, Fundamentals of Rock Joint Deformation, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 20(6), 249-268. Bandis, S.C., Makurat, A. and Vik, G., 1985, Predicted and Measured Hydraulic Conductivity of Rock Joints, Proceedings of the International Symposium on Fundamentals of Rock Joints, Björkliden, Sweden, 269 279. Bang, S.H., Jeon, S. and Kwon, S., 2012, Modeling the hydraulic characteristics of a fractured rock mass with correlated fracture length and aperture: application in the underground research tunnel at Kaeri, Nuclear Engineering and Technology, 24 (6), 639-652. Barton, N. and Bakhtar, K., 1983, Rock joint description and modeling for the hydrothermomechanical design of nuclear waste repositories (Contract Report, submitted to CANMET). Mining Research Laboratory, Ottawa, Parts 1-4: 270; Part 5: 105. Barton, N., 1973, Review of a new shear-strength criterion for rock joints. Engineering Geology, 7 (4), 287-332. Barton, N.R. and Bandis, S.C., 1982, Effects of block size on the shear behaviour of jointed rock, 23 rd U.S. symp. on rock mechanics, Berkeley, 739-760. Chandra, S., Ahmed, S., Ram, A. and Dewandel, B., 2008, Estimation of hard rock aquifers hydraulic conductivity from geoelectrical measurements : A theoretical development with field application, Journal of Hydrology, 357(3-4), 218-227. Fuenkajorn, K., 2005, Predictability of Barton s joint shear strength criterion using field-identification parameters. Suranaree Journal of Science and Technology, 12 (4), 296-308.
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