One-dimensional nonlinear consolidation analysis of soil with continuous drainage boundary

Abstract

Following the assumptions proposed by MESRI and ROKHSAR, the one-dimensional nonlinear consolidation problem of soil under constant loading is studied by introducing continuous drainage boundary. The numerical solution is derived by using finite difference method and its correctness is assessed by comparing with existing analytical and numerical solutions. Based on the present solution, the effects of interface parameters, stress ratios (i.e., final effective stress over initial effective stress, N_σ) and the ratio c_c/c_k of compression index to permeability index on the consolidation behavior of soil are studied in detail. The results show that, the characteristics of one-dimensional nonlinear consolidation of soil are not only related to c_c/c_k and N_σ, but also related to boundary conditions. In the engineering practice, the soil drainage rate of consolidation process can be designed by adjusting the values of interface parameters.

Keywords

one-dimensional nonlinear consolidation / continuous drainage boundary / finite difference method / interface parameter

References

[1] DavisE H, RaymondG P. A non-linear theory of consolidation [J]. Géotechnique, 1965, 15(2): 161-173

[2] XieK-H, XieX-Y, JiangW. A study on one-dimensional nonlinear consolidation of double-layered soil [J]. Computers and Geotechnics, 2002, 29(2): 151-168

[3] KimP, KimH S, PakC U, et al.. Analytical solution for one-dimensional nonlinear consolidation of saturated multi-layered soil under time-dependent loading [J]. Journal of Ocean Engineering and Science, 2021, 6(1): 21-29

[4] XieK-H, ZhouJ, DongY-Q. Analytical solution for one-dimensional nonlinear consolidation of soil under cyclic loadings [J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(1): 21-26(in Chinese)

[5] ZongM-F, WuW-B, MeiG-X, et al.. An analytical solution for one-dimensional nonlinear consolidation of soils with continuous drainage boundary [J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(12): 2829-2838(in Chinese)

[6] ZONG Meng-fan, WU Wen-bing, EL NAGGAR M H, et al. Analytical solution for one-dimensional nonlinear consolidation of double-layered soil with improved continuous drainage boundary [J]. European Journal of Environmental and Civil Engineering, 2020. DOI: https://doi.org/10.1080/19648189.2020.1813207.

[7] BardenL, BerryP L. Consolidation of normally consolidated clay [J]. Journal of the Soil Mechanics and Foundations Division, 1965, 91(5): 15-35

[8] MesriG, RokhsarA. Theory of consolidation for clays [J]. Journal of the Geotechnical Engineering Division, 1974, 100(8): 889-904

[9] PoskittT J. The consolidation of saturated clay with variable permeability and compressibility [J]. Géotechnique, 1969, 19(2): 234-252

[10] LiB-H, WangK-H, XieK-H, et al.. One dimensional non-linear consolidation analysis of soft clay by FDM [J]. Journal of Zhejiang University (Engineering Science), 2000, 34(4): 376-381(in Chinese)

[11] LiB-H, XieY-L, XieK-H, et al.. Semi-analytical solution of one dimensional non-linear consolidation of soft clay [J]. Journal of Xi’an Highway University, 1999, 19(1): 24-29(in Chinese)

[12] XieK-H, ZhengH, LiB-H, et al.. Analysis of one dimensional nonlinear consolidation of layered soils under time-dependent loading [J]. Journal of Zhejiang University (Engineering Science), 2003, 37(4): 426-431(in Chinese)

[13] HuA-F, XiaC-Q, CuiJ, et al.. Nonlinear consolidation analysis of natural structured clays under time-dependent loading [J]. International Journal of Geomechanics, 2018, 18(2): 04017140

[14] LekhaK R, KrishnaswamyN R, BasakP. Consolidation of clays for variable permeability and compressibility [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2003, 129111001-1009

[15] LiC-X, HuangJ-S, WuL-Z, et al.. Approximate analytical solutions for one-dimensional consolidation of a clay layer with variable compressibility and permeability under a ramp loading [J]. International Journal of Geomechanics, 2018, 18(11): 06018032

[16] LiC-X, WangC-J, LuM-M, et al.. One-dimensional large-strain consolidation of soft clay with non-Darcian flow and nonlinear compression and permeability of soil [J]. Journal of Central South University, 2017, 244967-976

[17] LiC-X, XieK-H, HuA-F, et al.. Analysis of one-dimensional non-linear consolidation with exponential flow [J]. Journal of Central South University (Science and Technology), 2012, 43(7): 2789-2795(in Chinese)

[18] GengX-Y, XuC-J, CaiY-Q. Non-linear consolidation analysis of soil with variable compressibility and permeability under cyclic loadings [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2006, 30(8): 803-821

[19] KimP, RiK S, KimY G, et al.. Nonlinear consolidation analysis of a saturated clay layer with variable compressibility and permeability under various cyclic loadings [J]. International Journal of Geomechanics, 2020, 20(8): 04020111

[20] KimP, KimH S, KimY G, et al.. Nonlinear radial consolidation analysis of soft soil with vertical drains under cyclic loadings [J]. Shock and Vibration, 2020, 2020: 1-12

[21] GrayH. Simultaneous consolidation of contiguous layers of unlike compressible soils [J]. Transactions of the American Society of Civil Engineering, 1945, 1101327-1356

[22] SchiffmanR L, SteinJ R. One-dimensional consolidation of layered systems [J]. Journal of the Soil Mechanics and Foundations Division, 1970, 96(4): 1499-1504

[23] XieK-H. One dimensional consolidation analysis of layered soil under semi permeable boundary conditions [J]. Journal of Zhejiang University (Natural Science), 1996, 30(5): 567-575(in Chinese)

[24] WangK-H, XieK-H, ZengG-X. A study on consolidation of soils exhibiting rheological characteristics with impeded boundaries [J]. Chinese Journal of Geotechnical Engineering, 1998, 20(2): 34-36(in Chinese)

[25] MeiG-X, ChenQ-M. Solution of Terzaghi one-dimensional consolidation equation with general boundary conditions [J]. Journal of Central South University, 2013, 20(8): 2239-2244

[26] MeiG-X, LokT M H, XiaJ, et al.. One-dimensional consolidation with asymmetrical exponential drainage boundary [J]. Geomechanics and Engineering, 2014, 6(1): 47-63

[27] LiuJ-C, LeiG H. One-dimensional consolidation of layered soils with exponentially time-growing drainage boundaries [J]. Computers and Geotechnics, 2013, 54: 202-209

[28] WangL, SunD-A, QinA-F. Semi-analytical solution to one-dimensional consolidation for unsaturated soils with exponentially time-growing drainage boundary conditions [J]. International Journal of Geomechanics, 2018, 18(2): 04017144

[29] WuW-B, ZongM-F, ElN M H, et al.. Analytical solution for one-dimensional consolidation of double-layered soil with exponentially time-growing drainage boundary [J]. International Journal of Distributed Sensor Networks, 2018, 1410155014771880671

[30] FengJ-X, NiP-P, MeiG-X. One-dimensional self-weight consolidation with continuous drainage boundary conditions: Solution and application to clay-drain reclamation [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2019, 4381634-1652

[31] ZhangY, WuW-B, MeiG-X, et al.. Three-dimensional consolidation theory of vertical drain based on continuous drainage boundary [J]. Journal of Civil Engineering and Management, 2019, 25(2): 145-155

[32] TianY, WuW-B, JiangG-S, et al.. One-dimensional consolidation of soil under multistage load based on continuous drainage boundary [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2020, 44(8): 1170-1183

[33] JiangW-H, ZhanL-T, YangC. Analytical solution for one-dimensional large strain consolidation of saturated soft soils with continuous drainage boundary [J]. Journal of Central South University (Science and Technology), 2020, 51(5): 1289-1298(in Chinese)