Title. Author(s)Akm Badrul, Alam; Fujii, Yoshiaki; Aramaki, Noritaka. CitationProceedings of Japan Symposium on Rock Mechanics, 14

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1 Title Water migration into underground cavern considering Author(s)Akm Badrul, Alam; Fujii, Yoshiaki; Aramaki, Noritaka CitationProceedings of Japan Symposium on Rock Mechanics, 4 Issue Date Doc URL Type proceedings (author version) Note 4th Japan Symposium on Rock Mechanics, January 0th File Information JSRM pdf Instructions for use Hokkaido University Collection of Scholarly and Aca

2 Proceedings of the 4 th Japan Rock Mechanics Symposium Japan Society for Rock Mechanics, January 207, Paper 047 Water migration into underground cavern considering stress and temperature dependent permeability of fractured rocks AKM Badrul ALAM *, Yoshiaki FUJII 2, Noritaka ARAMAKI & Katsuhiko KANEKO H-RISE, Northern Advancement Center for Science and Technology, 5-3, Sakae-machi, Horonobe-cho, Teshio-gun, Hokkaido , Japan 2 Rock Mechanics Laboratory, Faulty of Engineering, Hokkaido University, N3W8, Sapporo , Japan * badrul.alam@h-rise.jp ABSTRACT Water migration is an important factor in sealability of underground radioactive waste disposal (URWD) and is significantly controlled by permeability of rock. The permeability of rocks varies with various factors including stress and temperature. The rock stress changes by excavation of caverns for URWD and rock temperature changes by decay heat. The temperature change induces thermal stress. Water migration (flow in and out of URWD) should be therefore evaluated considering the effect of stress and temperature. In this regard, a series of triaxial compression tests was carried out under confining pressure between and 4 MPa at 295 K and 353 K, and the permeability under residual strength state was measured as input data for the water migration calculation with a 2-D elastic FEM for a simple URWD cavern in a fractured rock mass. Three rocks (Shikotsu welded tuff, Kimachi sandstone, Inada granite) are considered for the experiment to cover wide range of physical properties of rocks. Several new indices are also correlated with the post-compression permeability to show how well it can be predicted. The equations for the stress and temperature dependent permeability of fractured rocks are proposed. Fluid inflow was calculated with a 2-D elastic FEM for simple underground nuclear waste cavern with or without considering the stress and temperature dependency as an example to show the effect on water inflow. The results showed that water inflow became smaller considering the dependency. This could contribute for optimum design of underground cavern. The effects of temperature becomes slightly smaller by representing the permeability of fractured rock with indices than that of average effective stress (AES). Further consideration should be done because the effects of temperature can be clearly seen in the indices-permeability plots and the new indices were almost not effective to improve the approximation for the granite. Keywords: Post-compression, Rock-permeability, Water-migration, Stress and temperature. INTRODUCTION Water migration is an important factor in sealability of underground radioactive waste disposal (URWD) and is significantly controlled by permeability of rock. The permeability of rocks varies with various factors including stress and temperature. The rock stress changes by excavation of caverns for URWD and rock temperature changes by decay heat. The temperature change induces thermal stress. Water migration (flow in and out of URWD) should be therefore evaluated considering the effect of stress and temperature. In this regard, a series of triaxial compression tests was carried out under confining pressure between and 4 MPa at 295 K and 353 K, and the permeability under residual strength state was measured as input data for the water migration calculation with a 2-D elastic FEM for a simple URWD cavern in a fractured rock mass. Three rocks (Shikotsu welded tuff, Kimachi sandstone, Inada granite) are considered for the experiment to cover wide range of physical properties of rocks. Several new indices are also correlated with the post-compression permeability to show how well it can be predicted. The paper describe the equations which represent the post-compression permeability by average effective stress and temperature. The effect of stress and temperature on water migration into the underground cavern is explained based on 2-D FEM results. The results of permeability estimation by new indices are also shown. 2. EFFECTIVE STRESS DEPENDENCY OF PERMEABLITY The post compression permeability of Shikotsu welded tuff, Kimachi sandstone and Inada granite under confining pressure between and 4 MPa at 295K and 353K was measured for three kinds of rocks. The Shikotsu welded tuff is having higher effective porosity of 36.5% with uniaxial compressive strength in water saturated condition (UCS water-saturated ) of 3.53 MPa; Kimachi sandstone is having effective porosity of 8.54% with UCS water-saturated of 20.5 MPa, whereas the Inada granite is having effective porosity of

3 0.58% with UCSwater-saturated of 80.9 MPa. The experiment was on cylindrical cores with a diameter of 30 mm and a height of 60 mm, which were prepared from intact blocks. In this experiment, an ultra-compact triaxial cell, covered with a band-type heater with a controller (Alam et al. 205), a constant strain rate (0 5 s, i.e., mm/min)-controlled compression was applied until strain reached at stable residual strength state, measuring permeability (Figure ). The permeability of the Shikotsu welded tuff was measured by the constant flow method and, the permeability of Kimachi sandstone and Inada granite was measured by the transient pulse method (Alam et al. 205) with the approximate solution by Brace et. al In the experimental setup, a loading frame was used to apply the axial load and to maintain the confining pressure throughout the experiment a double ball plunger pump with a relief valve was connected to the ultra-compact triaxial cell. A pair of stainless steel attachments was attached to jacketed sample. Each attachment had a hole to allow the water flow and a pressure sensor was used to measure the pore pressure. In the constant flow method, the water flow path of the upper attachment was open to the atmosphere; a syringe pump was connected to the lower attachment and used to produce a constant flow of water. In the transient pulse method, an accumulator was connected to the upper attachment, which was upstream; the syringe pump was used to maintain the pore pressure and acted as a downstream accumulator. The average effective stress ( ) in the residual state was calculated from the residual strength ( ), confining pressure (P c ) and pore pressure (P p ) by Equation. 2P c Pp 3 The post-compression permeability showed negative correlation with average effective stress (Figure ). The post-compression permeability at 353 K (K 2 ) was lower than that at 295 K (K ) for Shikotsu welded tuff and for Inada granite. Whereas, the permeability was slightly lower at 353K than that at 295 K for Kimachi sandstone. The permeability is more stress dependent at 295 K than that at 353 K for tuff and granite whereas, the dependency is almost the same for the both temperature for sandstone. The relationship between the permeability and average stress for the rocks are represented as log K = A +B at T (2) () log K 2 = A 2 +B 2 at T 2 (3) A =log a (4) A 2 =log a 2 (5) where a i is the y intercept of the regression line and B i is the stress dependency at T i (Figure 3, Table ) 2. Stress and temperature dependency Considering the linear relationship between the permeability with, the stress and temperature dependent permeability at arbitrary and temperature can be calculated from the Equations 6 to 8 for the three types of rock. The differences between a (permeability at K under = 0) and a 2 (permeability at K 2 under = 0) or B and B 2 shows the temperature effects on permeability and it is much greater for granite and tuff than that for sandstone (Table ). K=0 A+B (6) T T A A A2 A T T (7) B B Stress and temperature dependent fluid flow 2.2. Model and properties T T B2 B T2 T The effect of temperature, stress, temperature-stress coupling effects to reveal fluid inflow amount of a radioactive Table. The permeability at 295 K (a ) and 353K (a 2 ), stress dependency at 295 K (B ) and at 353 K (B 2 ). Rock type a (m 2 ) a 2 (m 2 ) B (MPa - ) B 2 (MPa - ) Tuff 5.43E-5 4.9E Sandstone.25E E Granite.72E-5.22E (8) Figure. The correlation between post-compression permeability and effective average stress at 295 K and 353 K.

4 2.2.2 Stress around boundary of backfill The highest maximum effective principle stress at the tunnel edge was 36.0 to 43.2 MPa at 295 K (Figure 4). In the same condition at increased temperature of 353 K at the backfill boundary, the thermal stress appeared and the highest maximum principle stress was 64.0 to 72.0 MPa. Figure 2. The derivation of stress and temperature dependency of permeability. B Fluid inflow The fluid flow around the radioactive waste disposal site varied with temperature and stress dependent permeability (Figure 5). Fluid velocity became faster with approaching to the opening for the constant K because the area becomes narrower (Figure 5a). The velocity however becomes slower at the edge of the opening either by raised temperature for temperature dependent K or thermal stress for stress dependent K (Figure 5b, c). The velocity becomes even slower for the stress and temperature dependent K (Figure 5d). The inflow amount into the backfill significantly decreased (/50) considering temperature dependency of permeability and then stress dependency (/500) (Figure 6). Even more decreased inflow (/2000) appeared when stress and temperature dependency were considered together. v = h =3.5 MPa P p = 5 MPa = 8.5 MPa ux fixed uy fixed Force Node temp. Heat trans. 8 m Pore pres. 0 m 30 m 25 m Sig2 (MPa) Figure 3. The model of a radioactive waste disposal site, used for the inflow amount calculation. (a) 295 K waste disposal site in rock mass considering Inada granite at 500 m deep was calculated using a 2-D FEM (the model is in Figure 4). The mechanical properties of the rock mass was considered as tangent modulus GPa, Poisson s ratio 0.35, wet density 2700 kg/m 3 and the effective porosity of 0.58% (Alam et al. 204); and for the backfill the tangent modulus 6.94E-02 GPa, Poisson s ratio 0.22, wet density 200 kg/m 3 and effective porosity 0.80% (Kwon et al. 203). Considering the wet density up to the target depth, the vertical stress of 3.5 MPa was applied. The pore pressure was assumed as 5 MPa. The effective stress becomes 8.5 MPa. The post compression permeability shown above was used since the rock mass is fractured and the temperature of 295 K considered at the boundary and 353 K or 295 K at the edge of the backfill. Sig2 (MPa) (b) 353 K Figure 4. Maximum effective principle stress.

5 3. APPROXIMATION OF POST-COMPRESSION PERMEABILITY REGARDLESS OF TEMPERATURE 3. Average effective stress (AES) Considering the post-compression permeability at 295K and 353K together on log-log plots regardless of temperature, it showed negative correlation with average effective stress (AES) (Figure 6). The correlation coefficient for Kimachi sandstone was higher with 0.80 than that of Inada granite and Shikotsu welded tuff with 0.38 and 0.42 respectively. 3.2 New indices Different indices were considered by using the average effective stress and such mechanical properties as indirect tensile strength, uniaxial compressive strength and tangent modulus. The ductility (DUC) index, UCS index, TM index and TMi index were calculated from Equations 9, 0,, 2 respectively. The UCS and tangent modulus are from the experiment, and the indirect tensile strength from literature (Fujii et al. 998, Okumura et al. 990, Fujii & Uehara 2006). The UCS and unconfined tangent modulus were estimated from the linear relationship of effective peak stress and tangent modulus with confining pressure (Figure 8) are shown in Table 2. The indirect tensile strength was considered as 7 MPa for Inada granite (Fujii et al. 998), for Kimachi sandstone.64 MPa (Okumura et al. 990), for Tuff it was.27 MPa (Fujii & Uehara 2006).? i UCSindex UCS? i TMi index TM? i TM index TM i (9) (0) () (2) where is average effective stress; T 0 is indirect tensile strength; UCS estimated uniaxial compressive strength; TM estimated tangent modulus and TM i is tangent modulus at residual state of the i-th sample. For Shikotsu welded tuff in the log-log plot, the negative correlation of the post-compression permeability with the indexes is shown (Figure 9). The highest correlation value of 0.62 was for TM index, then for UCS index of 0.55, and almost same for DUC index and TMi index of 0.49 and 0.48 respectively. Table 2. Estimated uniaxial compressive strength and unconfined tangent modulus of the rocks. Rocks Estimated UCS (MPa) Estimated unconfined TM (GPa) 295K 353K 295K 353K Tuff Sandstone Granite E E E E E E E E E E E E E E E E E E E E-0 (a) Constant permeability (b) Temperature dependent permeability 3.227E E E E E-08.63E-08.29E E E E-09 (c) Stress dependent permeability.680e-09.52e e-09.76e e E E E E-0.680E-0 (d) Stress and temperature dependent permeability Figure 5. Fluid flow distribution around the radioactive waste disposal site considering stress and temperature dependent permeability.

6 The effects of temperature becomes slightly smaller by representing the permeability of fractured rock with indices than that of average effective stress (AES). Further consideration should be done because the effect of temperature can be clearly seen in the indices-permeability plots and the new indices were almost not effective to improve the approximation for the granite. Figure 6. Amount of inflow to the backfill (L/min/m). (a) Constant permeability, (b) Temperature dependent permeability, (c) Stress dependent permeability and (d) Stress and temperature dependent permeability. For Kimachi sandstone, highest correlation value was 0.82 for UCS index, 0.8 for TM index, 0.80 for DU index and 0.78 for TMi index (Figure 9) whereas, for average effective stress (AES) it was 0.42 (Figure 7). For Inada granite, the highest correlation value was 0.55 for TMi index, then for UCS index of The correlation value 0.39 for TM index and 0.38 for DUC index. The effect of temperature on permeability for AES (Figure 7) became relatively lower for the indexes (Figure 9) but can still be seen in the plot. It would be better to use AES for each temperature. 4. CONCLUSION (a) (b) (c) (d) The equations for the stress and temperature dependent permeability of fractured rocks are proposed. Fluid inflow was calculated with a 2-D elastic FEM for simple underground nuclear waste cavern with or without considering the stress and temperature dependency as an example to show the effect on water inflow. The results showed that water inflow became smaller considering the dependency. This could contribute for optimum design of underground cavern. REFERENCES Alam, B., Fujii, Y., Fukuda, D., Kodama, J. and Kaneko, K., 205. Fractured Rock Permeability as a Function of Temperature and Confining Pressure, Pure and Applied Geophysics, 72, pp Alam, B., Niioka, M., Fujii, Y., Fukuda, D and Kodama, J., 204. Effects of Confining Pressure on the Permeability of Three Rock Types under Compression, International Journal of Rock Mechanics and Mining Sciences, 65, pp Brace, WF., Walsh, JB., Frangos, WT., 968. Permeability of granite under high pressure, J. Geophysical Research 73, pp Fujii, Y. and Uehara Y., 2006 in Japanese. A Study on Deformation and Failure Behavior of Rock subjected to Axial Extension under Confining Pressure, Journal of MMIJ, 22 (nos 6/7), pp Fujii, Y., Kiyama, T., Ishijima, Y. and Kodama, J., 998. Examination of a Rock Failure Criterion Based on Circumferential Tensile Strain, Pure and Applied Geophysics, 52 (3), pp Kwon, S., Cho, WJ., and Lee JO., 203. An Analysis of the thermal and mechanical behavior of engineered barriers in a high-level radioactive waste repository, Nuclear engineering and technology, 45 () pp Okumura, K., Matsuki, K., Sukuki, K., and Mo-Shen C., 990. The Effects of Driving Pressure and Traverse Rate on the Depth of Cut for Slot Cutting in Rocks with High-speed Waterjets, Journal of MMIJ, 06 () pp Figure 7. Post-compression permeability under average effective stress. The broken lines shows the 95% confidence interval.

7 Tuff Sandstone Granite (a) Effective stress Tuff Sandstone Granite (b) Tangent modulus Figure 8. Estimation of effective peak stress and tangent modulus. (a) Tuff (b) Sandstone (c) Granite Figure 9. Correlation is between Index and permeability for tuff, sandstone and granite. The broken lines shows the 95% confidence interval.