東部南海トラフにおけるメタンハイドレート胚胎土の力学特性および弾粘塑性構成モデルに関する研究

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Mechanical characteristics and elasto-viscoplastic constitutive model for methane hydrate-bearing sediments in Eastern Nankai Trough

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1-9 1 Fujii et al., 2015

1-7 MH21 Research Consortium

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1-3 A 2L-38 Waite et al. 2009 B Waite et al. 2009 C Waite et al. 2009 D 2009 E MH21 Research Consortium

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1-11

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1.3

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1-14

MH21 Research Consortium, 2008

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1-16 MH21 Research Consortium

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(1) (2) (3) (4) (1) (1) (2)

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1.5

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1-23

Miyazaki et al., 2011

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1 2 3 4 5 6 1 2 3

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1-25 6 3 1 4 5

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(2) Chen, L., Yamada, H., Kanda, Y., Okajima, J., Komiya, A., Maruyama, S. : Investigation on the dissociation flow of methane hydrate cores: Numerical modeling and experimental verification. Chemical Engineering Science, 163, pp.31 43, 2017.

(3) Cyranoski, D. : Japanese test coaxes fire from ice. Nature, 496(7446), pp.409 409, 2013.

(4) Dai, S., Santamarina, J. C., Waite, W. F., Kneafsey, T. J. : Hydrate morphology: Physical properties of sands with patchy hydrate saturation. Journal of Geophysical Research B: Solid Earth, 117(11), 2012.

(5) Fujii, T. : Resource Assessment of Methane Hydrate by Applying a Probabilistic Approach in the Eastern Nankai Trough, Japan. Chigaku Zasshi (Jounal of Geography), 118(5), pp.814 834, 2009.

(6) Fujii, T., Suzuki, K., Takayama, T., Tamaki, M., Komatsu, Y., Konno, Y., Nagao, J. : Geological setting and characterization of a methane hydrate reservoir distributed at the first offshore production test site on the Daini-Atsumi Knoll in the eastern Nankai Trough, Japan. Marine and Petroleum Geology, 66, pp.310 322, 2015. (7) Hyodo, M., Yoneda, J., Yoshimoto, N., Nakata, Y. : Mechanical and dissociation properties of methane

hydrate-bearing sand in deep seabed. Soils and Foundations, 53(2), pp.299 314, 2013. (8)

(9) Jung, J. W., Jang, J., Santamarina, J. C., Tsouris, C., Phelps, T. J., Rawn, C. J. : Gas production from hydrate-bearing sediments: The role of fine particles. Energy and Fuels, 26(1), pp.480 487, 2012.

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Artificial Gas Hydrate Bearing Sediments. International Conference on Gas Hydrates (ICGH), pp.6 13, 2008. (23) Matsumoto, R. : Methane Hydrate as an Unconventional Natural Gas Resource, Shigen-to-Sozai (Journal of

Mining and Materials), 108(7), pp.511 520, 1992.

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(29) Miyazaki, K., Masui, A., Sakamoto, Y., Haneda, H., Ogata, Y., Aoki, K., Yamaguchi, T., Okubo, S. : Strain Rate Dependency of Sediment Containing Synthetic Methane Hydrate in Triaxial Compression Test. Journal of MMIJ, 123(11), pp.537 544, 2007.

(30) Miyazaki, K., Masui, A., Yamaguchi, T., Sakamoto, Y., Haneda, H., Ogata, Y., Aoki K., Okubo, S. : Strain Rate Dependency of Peak and Residual Strength of Sediment Containing Synthetic Methane Hydrate. Journal of MMIJ, 124(10/11), pp.619 625, 2008.

(31) Miyazaki, K., Masui, A., Haneda, H., Ogata, Y., Aoki, K., Yamaguchi, T. : Variable-Compliance-Type Constitutive Model for Methane Hydrate Bearing Sediment. Proceedings of the 6th International Conference on Gas Hydrates (ICGH 2008), Vancouver, British Columbia, Canada, 2008.

(32) Miyazaki, K., Yamaguchi, T., Sakamoto, Y., Haneda, H., Ogata, Y., Aoki, K., Okubo, S. : Creep of Sediment Containing Synthetic Methane Hydrate. Journal of MMIJ, 125(4), pp.156 164, 2009.

(33) Miyazaki, K., Yamaguchi, T., Sakamoto, Y., Tenma, N., Ogata, Y., Aoki, K. : Effect of Confining Pressure on Mechanical Properties of Sediment Containing Synthetic Methane Hydrate. Journal of MMIJ, 126(7), pp.408 417, 2010.

(34) Miyazaki, K., Sakamoto, Y., Kakumoto, M., Tenma, N., Aoki, K., Yamaguchi, T. : Triaxial Compressive Properties of Artificial Methane-Hydrate-Bearing Sediments Containing Fine Fraction. Journal of MMIJ, 127(9), pp.565 576, 2011.

(35) Miyazaki, K., Yamaguchi, T., Sakamoto, Y., Aoki, K. : Time-dependent behaviors of methane-hydrate bearing sediments in triaxial compression test. International Journal of the JCRM, 7(1), pp.43 48, 2011.

(36) Miyazaki, K., Tenma, N., Aoki, K., Yamaguchi, T. : A nonlinear elastic model for triaxial compressive properties of artificial methane-hydrate-bearing sediment samples. Energies, 5(10), pp.4057 4075, 2012. (37) Miyazaki, K., Endo, Y., Tenma, N., Yamaguchi, T. : Constitutive Equation for Triaxial Compression Creep of

Artificial Methane-Hydrate-Bearing Sand by. Journal of MMIJ, 131(2), pp.47 55, 2015. (38)

Chigaku Zasshi (Jounal of Geography), 118(5), pp.758 775, 2009.

(39) Nakamizu, M., Namikawa, T., Ochiai, K., Tsuji, Y. : Efforts heading for production of methane from methane hydrate resources

-and development plan-. Journal of the Japanese Association for Petroleum Technology, 69(2), pp.214 221, 2004.

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status and perspectives. Energy & Environmental Science, 5(5), pp.6779-6795, 2012.

(41) Nixon, M. F., Grozic, J. L. : Submarine slope failure due to gas hydrate dissociation: a preliminary quantification. Canadian Geotechnical Journal, 44(3), pp.314 325, 2007.

(42) Pinkert, S., Grozic, J. L. H. : Prediction of the mechanical response of hydrate-bearing sands, Journal of 119, pp.4695 4707, 2014.

(43) Pinkert, S., Grozic, J. L. H., Priest, J. A. : Strain-Softening Model for Hydrate-Bearing Sands, International Journal of Geomechanics, 15(6), pp.1 6, 2015.

(44) Roscoe, K. H., A. N. Schofield, C. P. Wroth : On the yielding of soils, Geotechnique, 8(1), 22 53, 1958. (45) Roscoe, K. H., and J. B. Burland : On the Generalized Stress- Cambridge Univ.

Press, Cambridge, U. K., 1968.

(46) Sato, M., Maekawa, T., Okuda, Y. : Estimation of amount of methane and resources of natural gas hydrates in the world and around Japan. Journal of Geological Society of Japan, 102(11), pp.959 971, 1996.

(47) Sloan D.E. : Clathrate Hydrate of Natural Gases, Marcel Dekker, Inc., New York, p.641, 1990. (48) Sultan, N., Garziglia, S. : Geomechanical Constitutive Modeling of Gas-hydrate-bearing Sediments,

Proceeding of the 7th International on Gas Hydrate (ICGH 2011), Edinburgh, Scotland, United Kingdom, 2011.

(49) Suzuki, K., Ebinuma, T., Narita, H. : Features of Methane Hydrate-bearing Sandy-sediments of the Forearc Basin along the Nankai Trough: Effect on Methane Hydrate-Accumulating Mechanism in Turbidite, Chigaku Zasshi (Jounal of Geography), 118(5), pp.899 912, 2009.

(50) Takahashi, H., Yonezawa, T., Takedomi, Y. : Exploration for natural hydrate in Nankai-Trough wells offshore Japan. Journal of the Japanese Association for Petroleum Technology, 66(6), pp.652 665, 2001.

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(52) Tsuji, Y., Ishida, H., Nakamizu, M., Matsumoto, R., Shimizu, S. : Overview of the MITI Nankai Trough wells: A milestone in the evaluation of methane hydrate resources, Resource Geology, 54(1), pp.3 10, 2004. (53) Uchida, T., Hirano, T., Mae, S., Narita, H. : Raman spectroscopic analysis on artificial methane hydrates,

Journal of Geological Society of Japan, 102(11), pp.983 988, 1996.

(54) Uchida, T., Lu, H., Tomaru, H., Matsumoto, R., Senoh, O., Oda, H., Okada, S., Delwiche., M., Dallimore, S. R. : Subsurface occurrence of natural gas hydrate in the Nankai Trough area: Implication for gas hydrate concentration. Resource Geology, 54(1), pp.35 44, 2004.

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(55) Uchida, S., Soga, K., Yamamoto, K. : Critical state soil constitutive model for methane hydrate soil. Journal of Geophysical Research: Solid Earth, 117(3), 2012.

(56) Uchida, S., Xie, X. G., Leung, Y. F. : Role of critical state framework in understanding geomechanical behavior of methane hydrate-bearing sediments. Journal of Geophysical Research: Solid Earth, 121(8), pp.5580 5595, 2016.

(57) Waite, W. F., Winters, W. J., Mason, D. H. : Methane hydrate formation in partially water-satulated Ottawa sand. American Mineralogist, 89, pp.1202 1207, 2004.

(58) Waite, W. F., Santamarina, J. C., Cortes, D. D., Dugan, B., Espinoza, D. N., Germaine, J., Jang, J., Jung, J.W., Kneafsey, T. J., Shin, H., Soga, K., Winters, W. J., Yun, T.-S. : PHYSICAL PROPERTIES OF HYDRATE-BEARING SEDIMENTS. Review of Geophysics, 47, pp.1 38., 2009.

(59) Xu, W., Germanovich, L. N. : Excess pore pressure resulting from methane hydrate dissociation in marine sediments: A theoretical approach. Journal of Geophysical Research: Solid Earth, 111(1), pp.1 12, 2006. (60) Yamamoto, K. : Production Techniques for Methane Hydrate Resources and Field Test Programs. Chigaku

Zasshi (Jounal of Geography), 118, pp.913 934, 2009.

(61) Yamamoto, K. : Overview and introduction: Pressure core-sampling and analyses in the 2012-2013 MH21 offshore test of gas production from methane hydrates in the eastern Nankai Trough. Marine and Petroleum Geology, 66, pp.296 309, 2015.

(62) Yoneda, J., Hyodo, M., Nakata, Y., Yoshimoto, N. : Triaxial Shear Characteristics of Methane Hydrate-bearing Sediment in the Deep Seabed. Journal of Japan Society of Civil Engineers, 66(4), pp.742 756, 2010. (63) Yun, T. S., Santamarina, C. J., Ruppel, C. : Mechanical properties of sand, silt, and clay containing

tetrahydrofuran hydrate. Journal of Geophysical Research: Solid Earth, 112(4), pp.1 13, 2007. (64) (65) 4. 57(12) pp.50-57, 2009. (66) (67) (68) (69)

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(70) (71) , 50(5) pp.58 63 2015. (72) 5. 58(1) pp.118-124 2010. (73) (74) (75) (76) ô 63(2) pp.10 13 2015. (77)

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2-1 0.0010 0.01 0.1 1 20 40 60 80 100

Grain size (mm)

Methane hydrate concentrated zones Artificial sample Fc=8.9% Artificial sample Fc=10.6% Artificial sample Fc=22.9%

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2-1

(a) (b) Fc=8.9%

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(a) (b) (c) (d) (e) (f) (g) (h) (i) (j)

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(k) (l) (m) (n) (o) 3mm

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2-2

(c) (d)

(b) (a)

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100

MH MH V

V

S

V

100 100 MH V MH initial s S V w m

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PV

nRT

MH mes

V

V V

2-3 2010 2-4 -15 -10 -5 0 5 10 15 20 25 0 5 10 15 Temperature ( ) Methane hydrate phase boundary

(a) Frozen sand (d) Unsaturated MH-bearing sand

(b) Frozen sand + Methane gas

(c) Unsaturated sand +

Methane gas (e) Saturated MH-bearing sand

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2-5c F_c=22.9% 2-5b Fc=8.9% 2-5a 1 101 102 103 104 0 4 8 12 16 20 1 101 102 103 1040 4 8 12 16 20

Elapsed time (min)

Fc=8.9% Fc=10.6% Fc=22.9% p'-t v-t 1 101 ₁₀2 ₁₀3 ₁₀4 0 4 8 12 16 20 1 101 ₁₀2 ₁₀3 ₁₀40 4 8 12 16 20

Elapsed time (min)

Fc=8.9% (SM H=0%) Fc=8.9% (SM H=38.5%) Fc=8.9% (SM H=43.5%) p'-t v-t 1 101 102 103 104 0 4 8 12 16 20 1 101 102 103 1040 4 8 12 16 20

Elapsed time (min)

Fc=22.9% (SMH=0%)

Fc=22.9% (SMH=37.6%)

Fc=22.9% (SMH=51.3%)

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2-6c F_c=22.9% 2-6b Fc=8.9% 2-6a 0.01 0.1 1 10 100 0.5 0.6 0.7 0.8 0.9 1.0

Mean effective stress (MPa)

Fc=8.9% Fc=10.6% Fc=22.9% 0.01 0.1 1 10 100 0.5 0.6 0.7 0.8 0.9 1.0

Mean effective stress (MPa)

SM H=0% SM H=38.5% SM H=43.5% 0.01 0.1 1 10 100 0.5 0.6 0.7 0.8 0.9 1.0

Mean effective stress (MPa)

SM H=0%

SM H=37.6%

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2-7 2-8b Fc=22.9% 2-8a F_c=8.9% 0 10 20 30 40 50 60 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0 10 20 30 40 50 600.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

Methane hydrate saturation

MH

(%)

Compression index

Interpolation line for

Interpolation line for Swelling index 0 10 20 30 40 50 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0 10 20 30 40 500.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

Methane hydrate saturation

M H

(%)

Compression index

Interpolation line for Swelling index 0 5 10 15 20 25 30 35 40 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0 5 10 15 20 25 30 35 400.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

Fines content (%)

Compression index Swelling index Interpolation line for

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2-9a

(e) 10.0MPa

(a) 0.5MPa (b) 1.0MPa

(c) 3.0MPa (d) 6.0MPa (f) 13.0MPa (g) 16.0MPa (h) 20.0MPa 0.01 0.1 1 10 100 1.0 0.8 0.6 0.4 0.2 0.0

Elapsed time (min) Fc=8.9% Fc=10.6% Fc=22.9% 0.01 0.1 1 10 100 1.0 0.8 0.6 0.4 0.2 0.0

Elapsed time (min) Fc=8.9%

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2-9b Fc=8.9%

(e) 10.0MPa

(a) 0.5MPa (b) 1.0MPa

Elapsed time (min) Fc=8.9% (SMH=0%) Fc=8.9% (SMH=38.5%) Fc=8.9% (SMH=43.5%) 0.01 0.1 1 10 100 1.0 0.8 0.6 0.4 0.2 0.0

Elapsed time (min) Fc=8.9% (SMH=0%)

Fc=8.9% (SMH=38.5%)

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2-9c Fc=22.9%

(e) 10.0MPa

(a) 0.5MPa (b) 1.0MPa

Elapsed time (min) Fc=22.9% (SMH=0%) Fc=22.9% (SMH=37.6%) Fc=22.9% (SMH=51.3%) 0.01 0.1 1 10 100 1.0 0.8 0.6 0.4 0.2 0.0

Elapsed time (min) Fc=22.9% (SMH=0%)

Fc=22.9% (SMH=37.6%)

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2-11a 0 5 10 15 20 0 10 20 30 40 50 60

Mean effective stress (MPa)

Fc=8.9%

Fc=10.6%

Fc=22.9% 2-10

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2-11b Fc=8.9% 2-11c F_c=22.9% 0 5 10 15 20 0 10 20 30 40 50 60

Mean effective stress (MPa)

SM H=0% SM H=38.5% SM H=43.5% 0 5 10 15 20 0 10 20 30 40 50 60

Mean effective stress (MPa)

SM H=0%

SM H=37.6%

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0.0010 0.01 0.1 1 20 40 60 80 100

Grain size (mm)

SM H=0% (Before test) SM H=0% SM H=38.5% SM H=43.5% 2-12 F_c=8.9%

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ini

e e

e

MH sand NCL NCL NCL

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2-13a Fc=8.9% 2-13b Fc=22.9% 2-14 0.01 0.1 1 10 100 0.30 0.25 0.20 0.15 0.10 0.05 0.00

Mean effective stress (MPa)

SM H=0% SM H=38.5% SM H=43.5% NCL for SM H=0% NCL for SM H=38.5% NCL for SM H=43.5% 0.01 0.1 1 10 100 0.30 0.25 0.20 0.15 0.10 0.05 0.00

Mean effective stress (MPa)

SM H=0% SM H=37.6% SM H=51.3% NCL for SM H=0% NCL for SM H=37.6% NCL for SM H=51.3% 0 10 20 30 40 50 60 0.00 0.02 0.04 0.06 0.08 0.10

Methane hydrate saturation

M H

(%)

lnp' Interpolation line for Fc=22.9% Interpolation line for Fc=8.9% e eNCL NCL (with MH) NCL (without MH) Fc=8.9% Fc=22.9%

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(1) (2) (1) (2) (3) (1) (2) (3) (4) (5)

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(1) Nakamizu, M., Namikawa, T., Ochiai, K., Tsuji, Y. : Efforts heading for production of methane from methane hydrate resources

-and development plan-. Journal of the Japanese Association for Petroleum Technology, 69(2), pp.214 221, 2004.

(2) Suzuki, K., Ebinuma, T., Narita, H. : Features of Methane Hydrate-bearing Sandy-sediments of the Forearc Basin along the Nankai Trough: Effect on Methane Hydrate-Accumulating Mechanism in Turbidite, Chigaku Zasshi (Jounal of Geography), 118(5), pp.899 912, 2009.

(3) Takahashi, H., Yonezawa, T., Takedomi, Y. : Exploration for natural hydrate in Nankai-Trough wells offshore Japan. Journal of the Japanese Association for Petroleum Technology, 66(6), pp.652 665, 2001.

(4) Tsuji, Y., Ishida, H., Nakamizu, M., Matsumoto, R., Shimizu, S. : Overview of the MITI Nankai Trough wells: A milestone in the evaluation of methane hydrate resources. Resource Geology, 54(1), pp.3 10, 2004. (5) Uchida, T., Takahashi, H., Mae, S., Narita, H. : Raman spectroscopic analysis on artificial methane hydrates.

Journal of Geological Society of Japan, 102(11), pp.983 988, 1996.

(6) Uchida, T., Lu, H., Tomaru, H., Matsumoto, R., Senoh, O., Oda, H., Okada, S., Delwiche., M., Dallimore, S. R. : Subsurface occurrence of natural gas hydrate in the Nankai Trough area: Implication for gas hydrate concentration. Resource Geology, 54(1), pp.35 44, 2004.

(7) Yoneda, J., Hyodo, M., Nakata, Y., Yoshimoto, N. : Triaxial Shear Characteristics of Methane Hydrate-bearing Sediment in the Deep Seabed. Journal of Japan Society of Civil Engineers, 66(4), pp.742 756, 2010. (8) Yoneda, J., Masui, A., Konno, Y., Jin, Y., Egawa, K., Kida, M., Ito, T., Nagao, J., Tenma, N. : Mechanical

properties of hydrate-bearing turbidite reservoir in the first gas production test site of the Eastern Nankai Trough. Marine and Petroleum Geology, 66, pp.471 486, 2015b.

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3-1 F_c=30.0% Yoneda et al., 2015b 3-1 Fc=30.0% 0.0010 0.01 0.1 1 20 40 60 80 100

Grain size (mm)

Methane hydrate concentrated zones Artificial sample Fc=30.0% AT1-C-8P AT1-C-8P AT1-C-10P-1(0-5)2-4 AT1-C-10P-1(12-18)2.5-4.5 AT1-C-12P-1(0-35.5) AT1-C cores Artificial sample Fc=30.0%

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3-2 -15 -10 -5 0 5 10 15 20 25 0 5 10 15 Temperature ( ) Methane hydrate phase boundary

(a) Frozen sand (d) Unsaturated MH-bearing sand

(b) Frozen sand + Methane gas

(c) Unsaturated sand +

Methane gas (e) Saturated MH-bearing sand (f) Test condition

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3-3a Fc=8.9% 3-3b F_c=10.6% 0 5 10 15 20 0 2 4 6 8 10 12 6 0 -6 -12 Axial strain a (%) SM H=0% SM H=31.4% SM H=47.4% 0 5 10 15 20 0 2 4 6 8 10 12 6 0 -6 -12 Axial strain a (%) SMH=0% SMH=24.4% SMH=40.3%

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3-3c F_c=22.9% 3-3d F_c=30.0% 0 5 10 15 20 0 2 4 6 8 10 12 6 0 -6 -12 Axial strain a (%) SM H=0% SM H=19.6% SM H=44.0% 0 5 10 15 20 0 2 4 6 8 10 12 6 0 -6 -12 Axial strain a (%) SMH=0% SMH=30.5% SMH=38.3%

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max 50 50 2 q E MH MH s S D S

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3-6 Yoneda et al., 2015b 3-5 Yoneda et al., 2015b 3-4 Fc=30.0% Yoneda et al., 2015b 0 5 10 15 20 0.0 0.6 1.2 1.8 12 6 0 -6 -12

Axial strain

a

(%)

Fc=30.0% SM H=38.3% Fc=30.0% SM H=0% AT1-C-8P SM H=38.0% AT1-C-8P SM H=0% (Reconstitute) 0 20 40 60 80 100 10 100 1000

Methane hydrate saturation

MH

(%)

Fc=8.9%

Fc=10.6%

Fc=22.9%

AT1-C Tokai-oki and Kumano-nada area

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3-7 Yoneda et al., 2015b 0 10 20 30 40 50 0.00 0.75 1.50 2.25 3.00

Methane hydrate saturation

M H

(%)

Empirical equation for natural core results Fc=8.9%

Fc=10.6%

Fc=22.9%

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3-8a SMH=0% 3-8b S_MH 20~30% 0 5 10 15 20 0 2 4 6 8 10 12 6 0 -6 -12 Axial strain a (%) Fc=8.9% Fc=10.6% Fc=22.9% Fc=30.0% 3-8c S_MH 40~50% 0 5 10 15 20 0 2 4 6 8 10 12 6 0 -6 -12 Axial strain a (%) Fc=8.9% SM H=31.4% Fc=10.6% SMH=24.4% Fc=22.9% SMH=19.6% Fc=30.0% SMH=30.5% 0 5 10 15 20 0 2 4 6 8 10 12 6 0 -6 -12 Axial strain a (%) Fc=8.9% SM H=47.4% Fc=10.6% SMH=40.3% Fc=22.9% SMH=44.0% Fc=30.0% SMH=38.3%

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3-9 3-10 0 8 16 24 32 40 0 140 280 420 560 700

Fines content (%)

SM H=0% SM H 20 30% SM H 40 50% SM H=0% SM H 40 50% SM H 20 30% 0 8 16 24 32 40 6 7 8 9 10

Fines content (%)

SMH=0% SMH 20 30% SMH 40 50% SMH=0% SMH 40 50% SMH 20 30%

(83)

(84)

3-12 3-13 0 10 20 30 40 50 60 0.00 0.25 0.50 0.75 1.00

Methane hydrate saturation

M H

(%)

Fc=8.9% Fc=10.6% Fc=22.9% Fc=30.0% 0 10 20 30 40 50 60 30 31 32 33 34 35

Methane hydrate saturation

M H

(%)

Fc=8.9%

Fc=10.6%

Fc=22.9%

(85)

tan

1.6 tan

MH f

c

S n

S

MH t n 0

1 sin

2 sin

MH MH MH S S

c

S

0 1 sin tan tan 2 sin MH MH f cS n cS SMH n 0 tan 1.6 tan MH MH MH f cS n S cS SMH t n SMH max pre q _q_maxexp max max 1 max

1

n pre exp i i exp i i

q

n

_q

(86)

3-14 (a) Fc=8.9% (b) F_c=10.6% (c) F_c=22.9% (d) F_c=30.0% 0 10 20 30 40 50 5 6 7 8 9 10

Methane hydrate saturation M H(%) Experiment Prediction Eq.(3-5) Prediction Eq.(3-6) 0 10 20 30 40 50 5 6 7 8 9 10

Methane hydrate saturation MH(%) Experiment Prediction Eq.(3-5) Prediction Eq.(3-6) 0 10 20 30 40 50 5 6 7 8 9 10

Methane hydrate saturation M H(%) Experiment Prediction Eq.(3-5) Prediction Eq.(3-6) 0 10 20 30 40 50 5 6 7 8 9 10

Methane hydrate saturation M H(%) Experiment

Prediction Eq.(3-5) Prediction Eq.(3-6)

(87)

int S_MH MH

p

S

3-15 Kasama et al., 2000 0 . 0 0 . 4 0 . 8 1 . 2 1 . 6 2 . 0 2 . 4 2 . 8 3 . 2 3 . 6 4 . 0 - 2 0 - 1 0 0 1 0 2 0 3 0 4 0 5 0

Deviator stress

Failure state line for host sand

1

Failure state line for MH-bearing sand

p

int

_{Mean stress}

(88)

3-16 3-17 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Methane hydrate saturation

M H

pint= SM H Fc=8.9% Fc=10.6% Fc=22.9% Fc=30.0% 0 5 10 15 20 25 30 35 40 0 2 4 6 8 10 0 2 4 6 8 10

Fines content

c

(%)

Parameter

Interpolation line for Parameter

(89)

2 2 p v p s C C d C d 2 2 p v p s

d

C

d

2 2 2 p v p s d d 2 2

2

p v p s

d

2

_*

2

*

p v p s

d

C

d

int

*

q

p p

(90)

(91)

3-18 (a) F_c=8.9% (b) F_c=10.6% (c) F_c=22.9% (d) F_c=30.0% -1.5 -1.0 -0.5 0.0 0.5 1.0 0.0 0.3 0.6 0.9 1.2 1.5 1.8 Dilatancy ratio - vp/ sp Modified stress ratio * SM H=0% SM H=31.4% SM H=47.4% c=1.69 Experiment Calculation =1.24 c=1.94 c=2.67 -1.5 -1.0 -0.5 0.0 0.5 1.0 0.0 0.3 0.6 0.9 1.2 1.5 1.8 Dilatancy ratio - vp/ sp Modified stress ratio * SMH=0% SMH=24.4% SMH=40.3% c=1.74 Experiment Calculation =1.27 c=2.22 c=2.78 -1.5 -1.0 -0.5 0.0 0.5 1.0 0.0 0.3 0.6 0.9 1.2 1.5 1.8 Dilatancy ratio - vp/ sp Modified stress ratio * SM H=0% SM H=19.6% SM H=44.0% c=1.96 Experiment Calculation =1.24 c=2.27 _c=4.07 -1.5 -1.0 -0.5 0.0 0.5 1.0 0.0 0.3 0.6 0.9 1.2 1.5 1.8 Dilatancy ratio - vp/ sp Modified stress ratio * SMH=0% SMH=30.0% SMH=38.3% c=1.99 Experiment Calculation =1.30 c=2.45 c=3.14 3-19 0 5 10 15 20 25 30 35 40 0 1 2 3 4 5

Fines content

c

(%)

SM H=0% SM H 20 30% SM H 40 50%

Modified Cam-clay model (C =2)

SM H=0%

SM H 20 30%

(92)

(93)

3-20 0.1 1 10 100 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mean effective stress ' (MPa)

After consolidation After shearing During shearing NCL for SMH=0% CSL for SMH=0% Consolidation line of SMH=0% (a) SMH=0% 0.1 1 10 100 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mean effective stress ' (MPa)

After consolidation After shearing During shearing NCL for SMH=38.5% CSL for SMH 30% Consolidation line of SMH=38.5% (b) SMH 30% 0.1 1 10 100 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mean effective stress ' (MPa)

After consolidation After shearing During shearing NCL for SMH=43.5% CSL for SMH 50% Consolidation line of SMH=43.5% (c) SMH 50%

(94)

3-21 q-p 3-22 e-lnp 3-23 0 2 4 6 8 10 12 0 3 6 9 12 15

Mean effective stress ' (MPa)

SMH=0% SMH 30% SMH 50% CSL for SM H=0% CSL for SM H 30% CSL for SM H 50% 0.1 1 10 100 0.5 0.6 0.7 0.8 0.9 1.0

Mean effective stress ' (MPa)

SMH=0% SMH 30% SMH 50% CSL for SMH=0% CSL for SMH 30% CSL for SMH 50% 0 10 20 30 40 50 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 0 10 20 30 40 500.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15

Methane hydrate saturation

MH

(%)

Intercept of CSL Interpolation line for

Slope of CSL *

(95)

3-24 0 10 20 30 40 50 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0 10 20 30 40 500.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15

Methane hydrate saturation

MH

(%)

Compression index

Slope of CSL *

(96)

(1) (2) (3) (1) (2) (3) (1) (2) (1) (2)

(97)

(1)

(98)

(1)

(2) Hyodo, M., Yoneda, J., Yoshimoto, N., Nakata, Y. : Mechanical and dissociation properties of methane hydrate-bearing sand in deep seabed. Soils and Foundations, 53(2), pp.299 314, 2013.

(3) Hyodo, M., Wu, Y., Nakashima, K., Kajiyama, S., Nakata, Y. : Influence of Fines Content on the Mechanical Behavior of Methane Hydrate-Bearing Sediments. Journal of Geophysical Research: Solid Earth, 122(10), pp.7511 7524, 2017.

(4) Jung, J. W., Santamarina, J. C. : Hydrate adhesive and tensile strengths. Geochemistry, Geophysics, Geosystems, 12(8), pp.1 9, 2011.

(5) Kajiyama, S., Hyodo, M., Nakata, Y., Yoshimoto, N., Wu, Y., Kato, A. : Shear behaviour of methane hydrate bearing sand with various particle characteristics and fines. Soils and Foundations, 57(2), 176 193, 2017. (6) Kasama, K., Ochiai, H., Yasufuku, N. : On the stress-strain behavior of lightly cemented clay based on an

extended critical state concept. Soils and Foundations, 40(5), pp.37 47, 2000.

(7) Kato, A., Nakata, Y., Hyodo, M., Yoshimoto, N. : Macro and micro behaviour of methane hydrate-bearing sand subjected to plane strain compression. Soils and Foundations, 56(5), 835 847, 2016.

(8)

Hydrate R & D Program Progresses to Phase 2. Fire in the Ice, 9(4), pp.1 28, 2018.

(9) Masui, A., Haneda, H., Ogata, Y., Aoki, K. : The effect of saturation degree of methane hydrate on the shear strength of synthetic methane hydrate sediments. Proc. of the 15th Int. Offshore and Polar Eng. Conf., pp.364-369. Seoul, 2005.

(10) Masui, A., Miyazaki, K., Haneda, H., Ogata, Y., Aoki, K. : Mechanical Characteristics of Natural and

Artificial Gas Hydrate Bearing Sediments. International Conference on Gas Hydrates (ICGH), pp.6 13, 2008. (11) Miyazaki, K., Yamaguchi, T., Sakamoto, Y., Tenma, N., Ogata, Y., Aoki, K. : Effect of Confining Pressure on

Mechanical Properties of Sediment Containing Synthetic Methane Hydrate. Journal of MMIJ, 126(7), pp.408 417, 2010.

(99)

Properties of Artificial Methane-Hydrate-Bearing Sediments Containing Fine Fraction. Journal of MMIJ, 127(9), pp.565 576, 2011.

(13) Miyazaki, K., Tenma, N., Aoki, K., Yamaguchi, T. : A nonlinear elastic model for triaxial compressive properties of artificial methane-hydrate-bearing sediment samples. Energies, 5(10), pp.4057 4075, 2012. (14) -Dilatancy Theory for Hydrate-Bearing Sand. International Journal of

Geomechanics, 17(1), 2017.

(15) Roscoe, K. H., Schofield, A. N., Worth, C. P. : On the yielding of soils, Geotechnique, 8(1), pp. 22-53, 1958. (16) Roscoe, K. H., and J. B. Burland : On the Generalized Stress- Cambridge Univ.

Press, Cambridge, U. K., 1968. (17)

(18) Waite, W. F., Santamarina, J. C., Cortes, D. D., Dugan, B., Espinoza, D. N., Germaine, J., Jang, J., Jung, J.W., Kneafsey, T. J., Shin, H., Soga, K., Winters, W. J., Yun, T.-S. : PHYSICAL PROPERTIES OF HYDRATE-BEARING SEDIMENTS. Review of Geophysics, 47, pp.1 38., 2009.

(19) Yasufuku, N., Murata, H., Hyodo, M. :

(20) Yasufuku, N., Murata, H., Hyodo, M., Adrian, F.L. H. : A stress-strain relationship for anisotropically consolidated sand over a wide stress region. Soils and Foundations, 31(4), pp.75 92, 1991.

(21) Yoneda, J., Hyodo, M., Nakata, Y., Yoshimoto, N. : Triaxial Shear Characteristics of Methane Hydrate-bearing Sediment in the Deep Seabed. Journal of Japan Society of Civil Engineers, 66(4), pp.742 756, 2010. (22) Yoneda, J., Hyodo, M., Yoshimoto, N., Nakata, Y., Kato, A. : Development of high-pressure low-temperature

plane strain testing apparatus for methane hydrate-bearing sand. Soils and Foundations, 53(5), pp.774 783, 2013.

(23) Yoneda, J., Masui, A., Konno, Y., Jin, Y., Egawa, K., Kida, M., Ito, T., Nagao, J., Tenma, N. : Mechanical behavior of hydrate-bearing pressure-core sediments visualized under triaxial compression. Marine and Petroleum Geology, 66, pp.451 459, 2015a.

(24) Yoneda, J., Masui, A., Konno, Y., Jin, Y., Egawa, K., Kida, M., Ito, T., Nagao, J., Tenma, N. : Mechanical properties of hydrate-bearing turbidite reservoir in the first gas production test site of the Eastern Nankai

(100)

Trough. Marine and Petroleum Geology, 66, pp.471 486, 2015b.

(25) Yoneda, J., Jin, Y., Katagiri, J., Tenma, N. : Strengthening mechanism of cemented hydrate-bearing sand at microscales. Geophysical Research Letters, 43(14), 7442 7450, 2016.

(26) Yoneda, J., Masui, A., Konno, Y., Jin, Y., Kida, M., Katagiri, J., Nagao, Jiro., Tenma, N. : Pressure-core-based reservoir characterization for geomechanics: Insights from gas hydrate drilling during 2012 2013 at the eastern Nankai Trough. Marine and Petroleum Geology, 86, pp.1 16, 2017.

(27) Yun, T. S., Santamarina, C. J., Ruppel, C. : Mechanical properties of sand, silt, and clay containing tetrahydrofuran hydrate. Journal of Geophysical Research: Solid Earth, 112(4), pp.1 13, 2007. (28)

(101)

ì

(1)

(102)

(103)

4-1

(104)

4-2b Fc=8.9% 0 5 10 15 20 0 2 4 6 8 10 12 6 0 -6 -12 Axial strain a (%) 0.1%/min 0.01%/min 1.0%/min 10%/min (a) SMH=0% 0 5 10 15 20 0 2 4 6 8 10 12 6 0 -6 -12 Axial strain a (%) 1.0%/min (SM H=51.6%) 0.1%/min (SM H=47.4%) 10%/min (SMH=43.4%) (b) SMH 50% 4-2a F_c=8.9%

(105)

4-3 Fc=22.9% 0 5 10 15 20 0 2 4 6 8 10 12 6 0 -6 -12 Axial strain a (%) 0.1%/min (SM H=44.0%) 1.0%/min (SM H=41.8%) 10%/min (SMH=40.7%)

(106)

a max m a

q

0.0010 0.01 0.1 1 10 100 2 4 6 8 10 12

Strain rate (%/min)

Fc=8.9% (Without MH)

Fc=8.9% (With MH)

Fc=22.9% (With MH)

Toyoura sand (Without MH) Toyoura sand (With MH) Miyazaki et al. (2011)

(107)

4-6 Fc=22.9% 4-5 Fc=8.9% 0 5 10 15 20 25 0 2 4 6 8 10 12 6 0 -6 -12 Axial strain a (%) cr=4.5MPa (SMH=43.0%) cr=7.0MPa (SMH=50.9%) 0.1%/min (SMH=47.4%) 0 5 10 15 20 25 0 2 4 6 8 10 12 6 0 -6 -12 Axial strain a (%) cr=4.5MPa (SMH=45.7%) cr=7.0MPa (SMH=47.5%) 0.1%/min (SMH=44.0%)

(108)

4-7 4-8 1 101 102 103 104 105 106 0 5 10 15 20 25

Elapsed time (s)

Fc=8.9% ( cr=4.5MPa) Fc=8.9% ( cr=7.0MPa) Fc=22.9% ( cr=4.5MPa) Fc=22.9% ( cr=7.0MPa) 1 101 ₁₀2 ₁₀3 ₁₀4 ₁₀5 ₁₀6 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0

Elapsed time (s)

Fc=8.9% ( cr=4.5MPa) Fc=8.9% ( cr=7.0MPa) Fc=22.9% ( cr=4.5MPa) Fc=22.9% ( cr=7.0MPa)

(109)

( 1)

c c

a a _t

(110)

4-9 4-10 1 101 ₁₀2 ₁₀3 ₁₀4 ₁₀5 ₁₀6 10-5 10-4 10-3 10-2 10-1

Elapsed time (s)

Fc=8.9% ( cr=4.5MPa) cr=4.5MPa cr=7.0MPa Fc=8.9% ( cr=7.0MPa) Fc=22.9% ( cr=4.5MPa) Fc=22.9% ( cr=7.0MPa) 1 101 ₁₀2 ₁₀3 ₁₀4 ₁₀5 ₁₀6 10-6 10-5 10-4 10-3 10-2

Elapsed time (s)

Fc=8.9% ( cr=4.5MPa) Fc=8.9% ( cr=7.0MPa) Fc=22.9% ( cr=4.5MPa) Fc=22.9% ( cr=7.0MPa)

(111)

(1) (2) (1) (2) (3) (4) (5) (6) (7) (8)

(112)

(1) Miyazaki, K., Masui, A., Sakamoto, Y., Haneda, H., Ogata, Y., Aoki, K., Yamaguchi, T., Okubo, S. : Strain Rate Dependency of Sediment Containing Synthetic Methane Hydrate in Triaxial Compression Test. Journal of MMIJ, 123(11), pp.537 544, 2007.

(2) Miyazaki, K., Masui, A., Yamaguchi, T., Sakamoto, Y., Haneda, H., Ogata, Y., Aoki K., Okubo, S. : Strain Rate Dependency of Peak and Residual Strength of Sediment Containing Synthetic Methane Hydrate. Journal of MMIJ, 124(10/11), pp.619 625, 2008.

(3) Miyazaki, K., Yamaguchi, T., Sakamoto, Y., Haneda, H., Ogata, Y., Aoki, K., Okubo, S. : Creep of Sediment Containing Synthetic Methane Hydrate. Journal of MMIJ, 125(4), pp.156 164, 2009.

(4) Miyazaki, K., Sakamoto, Y., Kakumoto, M., Tenma, N., Aoki, K., Yamaguchi, T. : Triaxial Compressive Properties of Artificial Methane-Hydrate-Bearing Sediments Containing Fine Fraction. Journal of MMIJ, 127(9), pp.565 576, 2011.

(5) Prameswaran, V. R. : Deformation Behaviour and Strength of Frozen Sand. Canadian Geotechnical Journal, 17(1), pp.74-88, 1980.

(6) Prameswaran, V. R., Jones, S.J. : Triaxial Testing of Frozen Sand. Journal of Glaciology, 27(95), pp.147-155, 1981.

(7) Prameswaran, V. R., Paradis, M., Handa, Y.P. : Strength of Frozen Sand Containing Tetrahydrofuran Hydrate, Canadian Geotechnical Journal, 26(3), pp.479-483, 1989.

(113)

(114)

(115)

1 ' ' 3 ij ij p 2 1

2

3

ij ij

S

q

2 1 2 3 ij ij d D De Dp e p ij ij ij

D

Maxwell Voigt 5-1 Maxwell Voigt Hashiguchi et al. (2000) Maxwell (5-5) 3 e p c ij ij ij ij

D

(116)

'

e e ij ij

d

D

11 11 22 22 33 33 12 12 23 ₂₃ 31 31 ' 1 / 0 0 0 ' 1 / 0 0 0 ' 1 / 0 0 0 ' 0 0 0 0 0 ' 0 0 0 0 0 0 0 0 0 0 ' e e e e e e D d D d d D d _D d _D d _D

1 1 2

E

ô

1

2 E

(117)

11 ₁₁ 22 ₂₂ 33 33 12 12 23 23 31 31 ' 1 0 0 0 ' 1 0 0 0 ' 1 0 0 0 1 ' 0 0 0 1 0 0 0 0 0 0 1 0 ' 0 0 0 0 0 1 ' e e e e e e D _d D d D d d E D d D d D 1 ' ' e ij ij kk ij D d d E E

3 1 2

E

K

11 22 33

'

_kk

3 '

'

d

dp

d

'

p ij ij

g

D

'

c c ij c ij

g

D

(118)

'

1

p v p s

d

dp

dq d

2 2 int ln 1 * ln ' . 2 1 C g C p Rp const C

Deviator stress

Mean effective stress '

Plastic potential g Volumetric strain d vp (d vp, d sp) Shear strain d sp dq dp'

(119)

5-4

Deviator stress

Mean effective stress

c=3.0%

1 2

Current stress state line d sp=d pcos d p d vp=d psin CSL c=1.5% 1 0

Deviator stress

Mean effective stress

c=3.0% c=2.5% c=2.0% c=1.5% CSL 1 pin t

(120)

*2 2 *

'

dq

N

dp

D

2 1 2 2 ₀ _int ₂ int int 2 int 1 ' ' ' 0 ' D D MH MH D p p F p p p p q p p N 2 int 2 2 0 int int ' exp ' 0 2 ' MH MH q F p p p p N p p 2 1 2 2 0 2 2

1 '

'

0 '

D D s s

D

p

F

p

q

p

N

2 0 2 2 'exp ' 0 2 ' s s q F p p N p 2 1 2 2 0 int 2 int int 2 int ' 1 ' ' 0 ' D D MH R p p D f p Rp p Rp q p Rp N 2 int 2 2 0 int int ' exp ' 0 2 ' MH q f p Rp R p p N p Rp

(121)

2 2 int ln 1 * ln ' . 2 1 c c c C g m C p p const C 5-5 3

Deviator stess

Mean effective stress

p'0 M H Rp'0 M H p'0 s Subloading surface f Plastic potential g & Creep potential gc

Normal yield surface for MH-bearing sand FMH

Normal yield surface for host sand Fs

1 1

-pi nt

pi nt

Internal stress

int

(122)

0 0

log

c c v v t

d

dt

t

0 0 c c v v t

d

t

dt

t

0 1 0 0 0 0 0

1

c v c t _t c v v t t

d

dt

d

t

dt

t

dt

t

11 22 33 11 22 33 ' ' ' ' c c c c c v c c c c v c c ij d g g g g D D D D tr dt 0 0

'

c v t c c ij

t

D

t

g

tr

0 0 ' ' c ij c c ij v t c ij g t D D g t _tr

(123)

11 11 0 0 11

'

c ij c c t c

g

t

D

g

t

(124)

' ' t p t ij ij ij g g dR U D U R ' ' t ij ij g g R U t R D

U

ln

R

U

u R

p D ij

U

D

ln

t p ij

U

u R

D

5-6 R U t _{Hashiguchi, 2000}

(125)

int p MH

p

W

S

1 int int int p p MH MH MH p MH p p dp dW dS dW S dS S W 2 ₂ 2 ' p p p p p in r v v s s r v dW p p d Xd d d p d C 2 * 2 2 2 2 int int ' p 2 * p p p c c p c in v v s s v c s v v dW p p d C d d d d m d p d d (a) (b) (c) 2 2 2 2 int 2 * p p p p p c c v v s s v c s dW p d C d d d d m d 1 1 2 2 2 2 2 2 2 2 1 int int 2 * ' ' ' c c c c MH MH g g g g g g dp p C m S dS p p q q p q 1

int int c intc MH MH

dp

p

S

dS

1 2 2 ₂ 2 int int _' 2 * _' g g g g p p C p p q q , 1 2 2 ₂ 2 intc int c_' c c g g p p m p q

(126)

0 ln ' ln ' ' exp i c i c s e e p p p 0 0

'

ln

'

s s i i

p

e

p

int int

p

e

p

0 0 0 0 ' ' ln ln ' ' MH MH s s p p e p p 5-7 e-lnp Mean effective stress ln ' NCL for MH-bearing sand Unloading line p'0M H p'0s p'c p'i ei ec e0s e0M H e 1 1 NCL for host sand Void ratio

(127)

int 0 0 int ' MH exp ln ' s p p p p 0 0 0 0 0 0 0 int 0 int 0 int 0 int ' ' ' 1 ' ' ' ' ' ' pc MH MH MH s MH MH s s v s s p p p e p dp dp dp p D dp p p p p ' pc p c c v v v v g D D D D p 0 0 int int ' ' T c MH MH v p dp k k D dp p 0 0 0 0 ' 1 ' ' ' MH s s s p e g k p p p 0 0 0 0

'

1 '

'

T MH s s s

p

e

k

p

(128)

'

e c ij ij ij ij

g

d

D

0 int 0 int ' ' 0 ' ' T ij MH ij MH f f f f df d dp dR dp p R p 0 int 0 int 1 int int int ' ' ' ' 0 T e c T c MH ij ij v ij ij MH c c MH MH p f g f f df D D k k D dp R p p R f p p S dS p D 1 0 int 0 int 0 int ' ' ' ' ' ' ' T T e T c MH e c ij v c c MH MH ij ij MH MH ij T e ij ij p f f f f f D k D p S dS D p p p p f g H D D D 0 int p R p

H H

H

0 0 0 0 0 0 0 ' 1 ' ' ' ' ' MH s p s s p e f f g H k p p p p p ' ' t R ij ij f f g g H R U R R int 2 2 2 0 0 int int

int 0 int int 0 int

' ' ₂ _* ' ' ' ' MH MH p MH MH p p f f f f g g g g H p p C p p p p p p p p q q

(129)

1 0 int 0 int 0 int ' ' ' ' ' ' ' ' ' T T e T c MH e c ij v c c MH MH ij ij MH MH ij e c ij ij T ij e ij ij ij p f _D f _{k D} f f _p _S _dS f _D p p p p g d D D f g H D D D D 1 0 int 0 int 0 ' ' ' ' ' ' ' ' ' ' ' ' T e e e MH e T c MH v ij ij ij MH ij MH e ij T ij T MH e e ij ij ij ij p g f g f f _S g f _{k D} p p p p d D dS f g f g H D H H D D D D D D 0 int int 0 int ' ' ' ' ' ' ' ' ' ' ' T e ij ij T e e e MH c c ij ij ij MH e c ij T T e e ij ij ij ij f g p g f g f f _p p p p D f g f g H D H D D D D D D 1 0 0 int 0 int int ' ' ' ' ' ' ' ' ' ' ' e T c e MH v MH ij MH ij MH ep ep c ij ij ij T T MH e e ij ij ij ij e ij p g f g f f k D S p p p p d D D dS f g f g H H g f f p p D D D D D D D 0 int 0 int ' ' ' ' MH c c MH T e ij ij p p p f g H D 1 0 0 int

int 0 int int 0 int

' ' ' ' ' ' ' ' ' ' ' ' e MH e MH MH c c ij MH ij MH ep c ij ij ij T MH T e e ij ij ij ij p p g f f g f f S p p p p p p p d D d dS f g f g H H D D D D D 0 ' ' ' ' ' e T c v ij MH c ep c ij ij T e ij ij g f k D p d D f g H D D D

(130)

'

_ij

'

_ij

'

_ij

g

p

g

q

p

q

'

_ij

'

_ij

'

_ij

f

p

f

q

p

q

ij ij

p

3

1 '

ij ij

q

1

2

3

2 2 2 2 int * ' 1 * ' g p C p p 2 2 int * ' 1 * ' g C q C p p 2 2 int 2 int 2 1 ' ' ' D f _p _Rp q p D p Rp 2 2 2 2 int int exp 1 ' 2 ' ' f q q p N p Rp N p Rp 2 2 D 1 f q q N 2 2 2 2 int int exp ' 2 ' f q q q _{N p Rp} N p Rp 2 0 int int 0 int ' 2 1 ' ' ' D D MH MH R p p D f R p Rp p D p Rp 0

'

_MH

f

R

p

(131)

2 2

0 int int

int int int

' 2 1 ' 1 ' ' D D MH R p p D f q R p Rp p D N p Rp p Rp 2 2 2 2 2 2

int _int _int

exp 1 2 ' ' f q q R R p _N _p _Rp _N _p _Rp 2 2 0 int

int ₂ 2 int 0 int

int int ' 2 1 ' 1 ' ' ' D D MH MH R p p D f q p Rp p R p p R D _N _p _Rp p Rp 2 2 int 0 int 2 2 2 2 int int exp 1 ' 2 ' 2 ' MH f q q p R p p R _N _p _Rp _N _p _Rp 0 int 0 0 int 0 0 0 ' 1 exp ln ' ' ' 1 ' ' MH s s s MH s p p p p p p p p 0 int 0 2

int int _int

0 2 int ' exp ln ' ' MH s MH p p p p p _p p p

(132)

(133)

1 1 exp 2 0 i c i e e e F e 1 1 exp 2 c 0 l l F 5-8 0.01 0.1 1 10 100 0.5 0.6 0.7 0.8 0.9 1.0 1.1

Mean effective stress (MPa)

Normally consolidation line

Over consolidation line 1

Isotropic consolidation line of Fc=8.9%

Simulation (u=71) pi=1MPa ei=1.00 py=5.86MPa 1

(134)

5-9 0 5 10 15 20 25 30 35 40 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

Fines content (%)

0 5 10 15 20 25 30 35 40 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0 5 10 15 20 25 30 35 400.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

Fines content (%)

Compression index Swelling index 5-10

(135)

1 1 ' ' e p v v v e p X d d d dp dp K K K ' e p x v _e _p _x K K K d dp K K K 0 1 ' e e K p ( ) 1 ' i iso p y e K R p

ln

'

x y

K

u

R p

' ln ' ' e p e p v e y v K K dp K K d u R p K d dp

max min max 1

(

)

n c n n c

F

u u

u

F

(136)

1 c 0

C c F

C

6 2.35 1

3.0 10

MH

0.015 c

S

5 2.65 0

4.5 10

MH

1.6 C

S

5-11 u 0 5 10 15 20 25 30 35 40 0 20 40 60 80 100

Fines content (%)

(137)

5-12 -1.5 -1.0 -0.5 0.0 0.5 1.0 0.0 0.3 0.6 0.9 1.2 1.5 1.8

Dilatancy ratio -

vp

/

sp

Modified stress ratio *

0 5 10 15 20 25 30 35 40 0 1 2 3 4 5

Fines content

c

(%)

SMH=0% SMH 20 30% SMH 40 50% SMH=0% SMH 20 30% SMH 40 50% 5-13

(138)

1 c 0

z F

1

1 exp

2 c 0

y

y F

5-14 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.2 0.4 0.6 0.8

Methane hydrate saturation MH

5-15 0 5 10 15 20 25 30 35 40 0 2 4 6 8 10 0 2 4 6 8 10

Fines content

c

(%)

Parameter Parameter

(139)

int int NCL

p

e

p

0

exp

b F

1 c 1 c 0

g F

0.0 0.1 0.2 0.3 0.4 0.5 0.00 0.02 0.04 0.06 0.08 0.10

Internal stress

i nt

(MPa)

5-16

(140)

0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 0 5 10 15 20 25

Fines content

c

(%)

Parameter Parameter 5-17

(141)

1 101 ₁₀2 ₁₀3 ₁₀4 ₁₀5 ₁₀6 10-5 10-4 10-3 10-2 10-1 Elapsed time (s) t0=1000s 1 D(t0 )c 5-18

(142)

5-19 5-20 5-3 0 5 10 15 20 0 2 4 6 8 10 12 6 0 -6 -12 Axial strain a (%) SMH=0% Exp. Sim . SMH=31.4% SMH=47.4% -1.5 -1.0 -0.5 0.0 0.5 1.0 0.0 0.3 0.6 0.9 1.2 1.5 1.8

Dilatancy ratio -

vp

/

sp

Modified stress ratio *

SM H=0%

SM H=31.4%

SM H=47.4%

(143)

5-21

-1 20

0 10

Deviator stress (MPa)

Mean effective stress (MPa)

Plastic potential

Initial

(a) SMH=0%

Critical Subloading surface

Normal yield surface for host sand

1 ₁

-1 20

0 10

Plastic potential

Initial

(b) SMH=31.4%

Normal yield surface for host sand Normal yield surface for MH-bearing sand

1 ₁

-1 20

0 10

Plastic potential

Initial

(c) SMH=47.4%

Normal yield surface for host sand Normal yield surface for MH-bearig sand