Abstract
Creep properties of soft interlayers are key factors associated with the long-term stability of geological bodies. An experimental and theoretical study on the ring shear creep properties of soft interlayers collected from Esheng, Sichuan province, China are performed in this study. Ring shear creep tests of soft interlayers, which are remolded into over-consolidated samples having various water contents and the same initial dry density, are performed in laboratory, to analyze the creep deformation characteristics of samples in detail. The calculated long-term shear strength of samples is close to residual strength. By substituting the dashpot with a new unsteady fractal dashpot, a novel unsteady fractal derivative creep (UFDC) model, which can be defined in series with an improved Maxwell model and an improved viscoplastic model, is proposed based on theory of fractal derivative. The new model can efficiently explain the soft interlayers creep deformation. The results indicate that most model parameters are sensitive to the shear stress. However, at the accelerated creep stage, the fractional order of the second dashpot in the UFDC model has little effect on the fitting of experimental data.
Similar content being viewed by others
References
Arikoglu, A. (2014). “A new fractional derivative model for linearly viscoelastic materials and parameter identification via genetic algorithms.” Rheol. Acta., Vol. 53, No. 3, pp. 219–233, DOI: https://doi.org/10.1007/s00397-014-0758-2.
Bhat, D. R., Bhandary, N. P., Yatabe, R. C., and Tiwari, R. C. (2011). “Residual-state creep test in modified torsional ring shear machine: Methods and implications.” Int. J. Geomate., Vol. 1, No. 1, pp. 39–43, DOI: https://doi.org/10.21660/2011.1j.
Bhat, D. R., Bhandary, N. P., and Yatabe, R. (2013). “Residual-state creep behavior of typical clayey soils.” Nat. Hazards, Vol. 69, No. 3, pp. 2161–2178, DOI: https://doi.org/10.1007/s11069-013-0799-3.
Cai, W., Chen, W., and Xu, W. X. (2016). “Characterizing the creep of viscoelastic materials by fractal derivative models.” Int. J. Nonlin. Mech., Vol. 87, pp. 58–63, DOI: https://doi.org/10.1016/j.ijnonlinmec.2016.10.001.
Cai, W., Chen, W., and Xu, W. X. (2018). “The fractal derivative wave equation: Application to clinical amplitude/velocity reconstruction imagin.” J. Acoust. Sco. Am., Vol. 143, No. 3, pp. 1559–1566, DOI: https://doi.org/10.1121/1.5027237.
Cao, P., Wen, Y. D., Wang, Y. X., Yuan, H. P., and Yuan, B. X. (2016). “Study on nonlinear damage creep constitutive model for high-stress soft rock.” Environ. Ear. Sci., Vol. 75, No. 10, pp. 900, DOI: https://doi.org/10.1007/s12665-016-5699-x.
Chen, W. (2006). “Time-space fabric underlying anomalous diffusion.” Chaos. Solitons. Fract., Vol. 28, No. 4, pp. 923–929, DOI: https://doi.org/10.1016/j.chaos.2005.08.199.
Chen, W., Sun, H. G., and Li, X. C. (2010a). Fractional derivative modeling in mechanics and engineering. Science Press, Beijing, China (in Chinese).
Chen, W., Sun, H. G., Zhang, X. D., and Korošak, D. (2010b). “Anomalous diffusion modeling by fractal and fractional derivatives.” Comput. Math. Appl., Vol. 59, No. 5, pp. 1754–1758, DOI: https://doi.org/10.1016/j.camwa.2009.08.020.
Chen, W., Zhang, X. D., and Korošak, D. (2010c). “Investigation on fractional and fractal derivative relaxation-oscillation models.” Int. J. Nonlin. Sci. Num., Vol. 11, No. 1, pp. 3–10, DOI: https://doi.org/10.1515/IJNSNS.2010.11.1.3.
Chen, X. P. and Liu, D. (2014). “Residual strength of slip zone soils.” Landslides, Vol. 11, No. 2, pp. 305–314, DOI: https://doi.org/10.1007/s10346-013-0451-z.
Di Maio, C., Scaringi, G., and Vassallo, R. (2015). “Residual strength and creep behaviour on the slip surface of specimens of a landslide in marine origin clay shales: Influence of pore fluid composition.” Landslides, Vol. 12, No. 4, pp. 657–667, DOI: https://doi.org/10.1007/s10346-014-0511-z.
Fabre, G. and Pellet, F. (2006). “Creep and time-dependent damage in argillaceous rocks.” Int. J. Rock Mech. Min., Vol. 43, No. 6, pp. 950–960, DOI: https://doi.org/10.1016/j.ijrmms.2006.02.004.
Feng, Z., Bin, L., Cai, Q. P., and Cao, J. W. (2016). “Initiation mechanism of the Jiweishan landslide in Chongqing, Southwestern China.” Environ. Eng. Geosci., Vol. 22, No. 4, pp. 341–351, DOI: https://doi.org/10.2113/gseegeosci.22.4.341.
Grimstad, G., Karstunen, M., Jostad, H. P., Sivasithamparam, N., Mehli, M., Zwanenburg, C., Haan, E. D., Amiri, S. A. G., Boumezerane, D., Kadivar, M., Ashrafi, M. A. H., and Rønningen J. A. (2017). “Creep of geomaterials–some finding from the EU project creep.” Eur. J. Environ. Civ. En., pp. 1–16, DOI: https://doi.org/10.1080/19648189.2016.1271360.
He, Z. L., Zhu, Z. D., Ni, X. H., and Li, Z. (2017). “Shear creep tests and creep constitutive model of marble with structural plane.” Eur. J. Environ. Civ. En., pp. 1–19, DOI: https://doi.org/10.1080/19648189.2017.1347066.
Hong, Y., Sun, T., Luan, M. T., Zheng, X. Y., and Wang, F. W. (2009). “Development and application of geotechnical ring shear apparatus: An overview.” Chin. J. Rock Soil Mech. Vol. 30, No. 3, pp. 628–634, (in Chinese), DOI: https://doi.org/10.3969/j.issn.1000-7598.2009.03.009.
Jostad, H. P. and Yannie, J. (2017). “A procedure for determining long-term creep rates of soft clays by triaxial testing.” Eur. J. Environ. Civ. En., pp. 1–16, DOI: https://doi.org/10.1080/19648189.2017.1347065.
Kang, J. H., Zhou, F. B., Liu, C., and Liu, Y. K. (2015). “A fractional nonlinear creep model for coal considering damage effect and experimental validation.” Int. J. Nonlin. Mech., Vol. 76, pp. 20–28, DOI: https://doi.org/10.1016/j.ijnonlinmec.2015.05.004.
Ladanyi, B. and Melouki, M. (1991). “Determination of creep properties of frozen soils by means of the borehole stress relaxation test.” Can. Geotech. J., Vol. 30, No. 1, pp. 170–186, DOI: https://doi.org/10.4095/132479.
Lai, X. L., Wang, S. M., Ye, W. M., and Cui, Y. J. (2014). “Experimental investigation on the creep behavior of an unsaturated clay.” Can. Geotech. J., Vol. 51, No. 6, pp. 621–628, DOI: https://doi.org/10.1139/cgj-2013-0064.
Leoni, M., Karstunen, M., and Vermeer, P. (2008). “Anisotropic creep model for soft soils.” Géotechnique, Vol. 58, No. 3, pp. 215–226, DOI: https://doi.org/10.1680/geot.2008.58.3.215.
Li, J. Z., Peng, F. L., and Xu, L. S. (2009). “One-dimensional viscous behavior of clay and its constitutive modeling.” Int. J. Geomech., Vol. 9, No. 2, pp. 43–51, DOI: https://doi.org/10.1061/(asce)1532-3641(2009)9:2(43).
Liang, Y. J., Ye, A. Q., Chen, W., Rodolfo, G. G., Luis, C., Thomas, H. M., and Richard, L. M. (2016). “A fractal derivative model for the characterization of anomalous diffusion in magnetic resonance imaging.” Commun. Nonlinear. Sci., Vol. 39, pp. 529–537, DOI: https://doi.org/10.1016/j.cnsns.2016.04.006.
Lu, Y. L. and Wang, L. G. (2017). “Effect of water and temperature on short-term and creep mechanical behaviors of coal measures mudstone.” Environ. Earth Sci., Vol. 76, No. 17, pp. 597, DOI: https://doi.org/10.1007/s12665-017-6941-x.
Ma, L. J., Liu, X. Y., Fang, Q., Xu, H. F., Xia, H. M., Li, E. B., Yang, S. G., and Li, W. P. (2013). “A new elasto-viscoplastic damage model combined with the generalized Hoek-Brown failure criterion for bedded rock salt and its application.” Chin. J. Rock Mech. Eng., V o l. 46, No. 1, pp. 53–66 (in Chinese), DOI: https://doi.org/10.1007/s00603-012-0256-8.
Ministry of Water Resources of the People’s Republic of China (1999). GB/T 50123-1999: Standard for soil test method. China Planning Press, Beijing, China, (in Chinese).
Mishra, B. and Verma, P. (2015). “Uniaxial and triaxial single and multistage creep tests on coal-measure shale rocks.” Int. J. Coal Geol., Vol. 137, pp. 55–65, DOI: https://doi.org/10.1016/j.coal.2014.11.005.
Nixon, J. F., and Lem, G. (2011). “Creep and strength testing of frozen saline fine-grained soils.” Can. Geotech. J., Vol. 21, No. 3, pp. 518–529, DOI: https://doi.org/10.1139/t84-054.
Ovanesova, A. V. and Suarez, L. E. (2004). “Application of wavelet trans-forms to damage detection in frame structure.” Eng. Struct., Vol. 26, No. 1, pp. 39–49, DOI: https://doi.org/10.1016/j.engstruct.2003.08.009.
Pusch, R., Zhang, L., Adey, R., and Kasbohm, J. (2010). “Rheology of an artificial smectitic clay.” Appl. Clay Sci., Vol. 47, No.. 1–2, pp. 120–126, DOI: https://doi.org/10.1016/j.clay.2009.08.031.
Schmidtke, R. H. and Lajtai, E. Z. (1985). “The long-term strength of Lac du Bonnet granite.” Int. J. Rock Mech. Min., Vol. 22, No. 6, pp. 461–465, DOI: https://doi.org/10.1016/0148-9062(85)90010-5.
Shen, M. R., Chen, H. J., and Zhang, Q. Z. (2012). “Method for determining long-term strength of discontinuity using shear creep test.” Chin. J. Rock Mech. Eng., Vol. 31, No. 1, pp. 1–7 (in Chinese), DOI: https://doi.org/10.3969/j.issn.1000-6915.2012.01.001.
Skempton, A. W. (1985). “Residual strength of clays in landslides, folded strata and the laboratory.” Geotechnique, Vol. 35, No. 1, pp. 3–18, DOI: https://doi.org/10.1680/geot.1985.35.1.3.
Sun, H. G., Meerschaert, M. M., Zhang, Y., Zhu, J., and Chen, W. (2013). “A fractal Richards’ equation to capture the non-Boltzmann scaling of water transport in unsaturated media.” Adv. Water. Resour., Vol. 52, No. 4, pp. 292–295, DOI: https://doi.org/10.1016/j.advwatres.2012.11.005.
Sun, J. (2007). “Rock rheological mechanics and its advance in engineering applications.” Chin. J. Rock Mech. Eng., Vol. 26, No. 6, pp. 1081–1106 (in Chinese), DOI: https://doi.org/10.3321/j.issn:1000-6915.2007.06.001.
Tan, T. K. and Kang, W. F. (1980). “Locked in stresses, creep and dilatancy of rocks constitutive equation.” Rock Mech., Vol. 13, No. 1, pp. 5–22, DOI: https://doi.org/10.1007/bf01257895.
Tang, H. M., Li, C. D., Hu, X. L., Su, A. J., Wang, L. Q., Wu, Y. P., Criss, R. E., Xiong, C. R., and Li, Y. A. (2015). “Evolution characteristics of the Huangtupo landslide based on in situ tunneling and monitoring.” Landslides, Vol. 12, No. 3, pp. 511–521, DOI: https://doi.org/10.1007/s10346-014-0500-2.
Tika, T. E. and Hutchinson, J. N. (1999). “Ring shear tests on soil from the vaiont landslide slip surface.” Géotechnique, Vol. 49, No. 1, pp. 59–74, DOI: https://doi.org/10.1680/geot.1999.49.1.59.
Wang, G. J. (2004). “A new constitutive creep-damage model for salt rock and its characteristics.” Int. J. Rock Mech. Min., Vol. 41, pp. 61–67, DOI: https://doi.org/10.1016/j.ijrmms.2004.03.020.
Wang, S., Xiang, W., Cui, D. S., Yang, J., and Huang, X. (2012). “Study of residual strength of slide zone soil under different ring-shear tests.” Chin. J. Rock Mech. Eng., Vol. 33, No. 10, pp. 2967–2972 (in Chinese), DOI: https://doi.org/10.16285/j.rsm.2012.10.006.
Wang, X. G., Hu, B., Tang, H. M., Hu, X. L., Wang, J. D., and Huang, L. (2016). “A constitutive model of granite shear creep under moisture.” J. Earth Sci-China, Vol. 27, No. 4, pp. 677–685, DOI: https://doi.org/10.1007/s12583-016-0709-1.
Wang, S., Wu, W., Wang, J. E., Cui, D. S., and Xiang, W. (2018a). “Residual-state creep of clastic soil in a reactivated slow-moving landslide in the Three Gorges Reservoir Region, China.” Landslides, Vol. 15, No. 12, pp. 1–10, DOI: https://doi.org/10.1007/s10346-018-1043-8.
Wang, X. G., Yin, Y. P., Wang, J. D., Lian, B. Q., Qiu, H. J., and Gu, T. F. (2018b). “A nonstationary parameter model for the sandstone creep tests.” Landslides, Vol. 15, No. 7, pp. 1377–1389, DOI: https://doi.org/10.1007/s10346-018-0961-9.
Wen, B. P., Aydin, A., Duzgoren- Aydin, N. S., Li, Y. R., Chen, H. Y., and Xiao, S. D. (2007). “Residual strength of slip zones of large landslide in the Three Gorges area, China.” Eng. Geol., Vol. 93, No.. 3–4, pp. 82–98, DOI: https://doi.org/10.1016/j.enggeo.2007.05.006.
Wu, F., Liu, J. F., and Wang, J. (2015). “An improved Maxwell creep model for rock based on variable-order fractional derivatives.” Environ. Ear. Sci., Vol. 73, No. 11, pp. 6965–6971, DOI: https://doi.org/10.1007/s12665-015-4137-9.
Xiong, L. X., Li, T. B., and Yang, L. D. (2014). “Biaxial compression creep test on green-schist considering the effects of water content and anisotropy.” KSCE J. Civ. Eng., Vol. 18, No. 1, pp. 103–112, DOI: https://doi.org/10.1007/s12205-014-0276-x.
Xu, H. Y. and Jiang, X. Y. (2017). “Creep constitutive models for viscoelastic materials based on fractional derivatives.” Comput. Math. Appl., Vol. 73, No. 6, pp. 1377–1384, DOI: https://doi.org/10.1016/j.camwa.2016.05.002.
Xu, T., Tang, C. A., and Zhao, J. (2012). “Modeling of rheological deformation of inhomogeneous rock and associated time-dependent response of tunnels.” Int. J. Geomech., Vol. 12, No. 2, pp. 147–159, DOI: https://doi.org/10.1061/(asce)gm.1943-5622.0000130.
Xu, G., Wu, W., and Qi, J. (2017). “A triaxial creep model for frozen soil based on hypoplasticity.” Eur. J. Environ. Civ. En., pp. 1–12, DOI: https://doi.org/10.1080/19648189.2017.1344145.
Yin, J. H. (2015). “Fundamental issues of elastic viscoplastic modeling of the time-dependent stress–strain behavior of geomaterials.” Int. J. Geomech., Vol. 36, No. 3, p. A4015002, DOI: https://doi.org/10.1061/(asce)gm.1943-5622.0000485.
Yin, Z. Y., Xu, Q., and Yu, C. (2012). “Elastic-viscoplastic modeling for natural soft clays considering nonlinear creep.” Int. J. Geomech., Vol. 15, No. 5, p. A6014001, DOI: https://doi.org/10.1061/(asce)gm.1943-5622.0000284.
Yu, H. C., Liu, H. D., Huang, Z. Q., and Shi, G. C. (2017). “Experimental study on time-dependent behavior of silty mudstone from the Three Gorges Reservoir Area, China.” KSCE J. Civ. Eng., Vol. 21, No. 3, pp. 715–724, DOI: https://doi.org/10.1007/s12205-016-3645-9.
Zhang, Q. Z., Shen, M. R., and Ding, W. Q. (2012). “Study of mechanical properties and long-term strength of Jinping green schist.” Chin. J. Rock Mech. Eng., Vol. 31, No. 8, pp. 1642–1649 (in Chinese), DOI: https://doi.org/10.3969/j.issn.1000-6915.2012.08.018.
Zhang, B. Y., Chen, T., Peng, C., Qian, X. X., and Jie, Y. X. (2017) “Experimental study on loading-creep coupling effect in rockfil material.” Int. J. Geomech., Vol. 17, No. 9, p. 04017059, DOI https://doi.org/10.1061/(asce)gm.1943-5622.0000938.
Zhou, H. W., Wang, C. P., and Han, B. B. (2011). “A creep constitutive model for salt rock based on fractional derivatives.” Int. J. Rock Mech. Min., Vol. 48, No. 1, pp. 116–121, DOI: https://doi.org/10.1016/j.ijrmms.2010.11.004.
Acknowledgments
The present work is supported by the National Key R&D Program of China (2018YFC1507200, 2017YFC1501304), the National Natural Science Foundation of China (No. 41672317, 41472261, 41772252, 41772259), the Natural Science Foundationof Hubei Province (CN) (2018CFB385), and the Research program for geological processes, resources and environment in the Yangtze River Basin (No. CUGCJ1701). The comments from the Editor and the two anonymous reviewers are constructive and very helpful for us to improve the quality of the manuscript. We sincerely thank them for their unselfish service.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yao, W., Hu, B., Zhan, H. et al. A Novel Unsteady Fractal Derivative Creep Model for Soft Interlayers with Varying Water Contents. KSCE J Civ Eng 23, 5064–5075 (2019). https://doi.org/10.1007/s12205-019-1820-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-019-1820-5