Abstract
The Fractional calculus theory is introduced into the Merchant model to study the mechanical characteristics of saturated soils. Laplace transform is applied to the 1D consolidation and the fractional derivative Merchant model constitutive equations of saturated soils. In the transform domain, the analytical solutions of effective stress and settlement are obtained by solving the simultaneous equation. The Crump’s method is used to the numerical inversion of Laplace transform, and the semi-analytical solution of the one-dimensional consolidation is obtained. A series of parameters, such as the fractional order, compression modulus, coefficient of viscosity, permeability coefficient and the variation models of groundwater level, are studied. Considering the continuity conditions, the 1D consolidation equation of single-layer saturated soil is generalized to multi-layer soils, and then the influence of different boundaries on several kinds of consolidation behavior was analyzed.
Similar content being viewed by others
References
Alex HN, Ge LL, Li XJ, Abidin HZ, Andreas H, Zhang K (2012) Mapping land subsidence in Jakarta, Indonesia using persistent scatterer interferometry (PSI) technique with ALOS PALSAR. International Journal of Applied Earth Observation and Geoinformation 18:232–42, DOI: https://doi.org/10.1016/j.jag.2012.01.018
Biot MA (1941) General theory of three-dimensional consolidation. Journal of Applied Physics 12(2):155–64, DOI: https://doi.org/10.1063/1.1712886
Crump KS (1976) Numerical inversion of laplace transforms using a fourier series approximation. Association for Computing Machinery 23(1):89–96
Cui ZD, Tang YQ (2010) Land subsidence and pore structure of soils caused by the high-rise building group through centrifuge model test. Engineering Geology 113(1–4):44–52, DOI: https://doi.org/10.1016/j.enggeo.2010.02.003
Galloway DL, Burbey TJ (2011) Review: Regional land subsidence accompanying groundwater extraction. Hydrogeology Journal 19(8): 1459–86, DOI: https://doi.org/10.1007/s10040-011-0775-5
Gemant A (1938) XLV. On fractional differentials. Philosophical Magazine 25(168):540–9, DOI: https://doi.org/10.1080/14786443808562036
Hawlader B, Muhunthan B, Imai G (2003) Viscosity effects on one-dimensional consolidation of clay. International Journal of Geomechanic 3(1):99–110, DOI: https://doi.org/10.1061/(ASCE)1532-3641(2003)3:1(99)
Kempfle S, Schäfer I, Beyer H (2002) Fractional calculus via functional calculus: Theory and applications. Nonlinear Dynamics 29(1):99–127, DOI: https://doi.org/10.1023/A:1016595107471
Ma FS, Yang YS, Yuan RM, Yao BK, Guo J (2011) Effect of regional land subsidence on engineering structures: A case study of the 6 km long Su-tong Yantze River Bridge. Bulletin of Engineering Geology 70(3):449–59, DOI: https://doi.org/10.1007/s10064-010-0336-5
Poland JF, Green JH (1962) Subsidence in the Santa Clara Valley, California—A progress report
Qin AF, Sun DA, Zhang JL (2014) Semi-analytical solution to one-dimensional consolidation for viscoelastic unsaturated soils. Computers and Geotechnics 62:110–17, DOI: https://doi.org/10.1016/j.compgeo.2014.06.014
Scott Blair GW (1947) The role of psychophysics in rheology. Journal of Colloid Science 2(1):21–32, DOI: https://doi.org/10.1016/0095-8522(47)90007-X
Shi XQ, Xue YQ, Wu JC, Ye SJ, Zhang Y, Wei ZX, Yu J (2008) Characterization of regional land subsidence in Yangtze Delta, China: The example of Su-Xi-Chang area and the city of Shanghai. Hydrogeology Journal 16(3):593–607, DOI: https://doi.org/10.1007/s10040-007-0237-2
Tang YQ, Cui ZD, Wang JX, Lu C, Yan XX (2008) Model test study of land subsidence caused by high-rise building group in Shanghai. Bulletin of Engineering Geology and the Environment 67(2):173–9, DOI: https://doi.org/10.1007/s10064-008-0121-x
Taylor DW, Merchant W (1940) A theory of clay consolidation accounting for secondary compression. Journal of Mathematics and Physics 19(1–4):167–85
Terzaghi K (1943) Theoretical soil mechanics. New York: John Wiley
Wang L, Sun DA, Li P, Xie Y (2017) Semi-analytical solution for one-dimensional consolidation of fractional derivative viscoelastic saturated soils. Computers and Geotechnics 83:30–9, DOI: https://doi.org/10.1016/j.compgeo.2016.10.020
Wang YH, Tham LG, Tsui Y, Yue ZQ (2003) Plate on layered foundation analyzed by a semi-analytical and semi-numerical method. Computers and Geotechnics 30(5):409–18, DOI: https://doi.org/10.1016/S0266-352X(03)00014-4
Xu XB, Cui ZD (2020) Investigation of a fractional derivative creep model of clay and its numerical implementation. Computers and Geotechnics 119:103387, DOI: https://doi.org/10.1016/j.compgeo.2019.103387
Yao WM, Hu B, Zhan HB, Ma C, Zhao NH (2019) A novel unsteady fractal derivative creep model for soft interlayerswith varying water contents. KSCE Journal of Civil Engineering 23(12):5064–5075, DOI: https://doi.org/10.1007/s12205-019-1820-5
Yin DS, Wu H, Cheng C, Chen YQ (2013) Fractional order constitutive model of geomaterials under the condition of triaxial test. International Journal for Numerical and Analytical Methods in Geomechanics 37(8):961–72, DOI: https://doi.org/10.1002/nag.2139
Yin JH, Zhu JG, Graham J (2002) A new elastic viscoplastic model for time-dependent behaviour of normally and overconsolidated clays: Theory and verification. Canadian Geotechnical Journal 39(1): 157–73, DOI: https://doi.org/10.1139/t01-074
Yuan WH, Wang HC, Zhang W, Dai BB, Liu K, Wang Y (2021) Particle finite element method implementation for large deformation analysis using Abaqus. Acta Geotechnica 12:1–14, DOI: https://doi.org/10.1007/s11440-020-01124-2
Zhang CC, Zhu HH, Shi B, Fatahi B (2018) A long term evaluation of circular mat foundations on clay deposits using fractional derivatives. Computers and Geotechnics 94:72–82, DOI: https://doi.org/10.1016/j.compgeo.2017.08.018
Acknowledgments
This work presented in this paper was supported by the National Natural Science Foundation of China (Grant No. 51208503).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xu, XB., Cui, ZD. Investigation of One-dimensional Consolidation of Fractional Derivative Model for Viscoelastic Saturated Soils Caused by the Groundwater Level Change. KSCE J Civ Eng 26, 4997–5009 (2022). https://doi.org/10.1007/s12205-022-1949-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-022-1949-5