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Analytical solutions for consolidation of stone column composite foundations considering time-dependent boundary and loading

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Rock Mechanics Bulletin

Rock Mechanics Bulletin 2023年第3期2卷 106-118页

作者： Xiangzong Lu Chuanxun Li Department of Civil Engineering Jiangsu UniversityZhenjiangJiangsu212013PR China

In response to the existing consolidation theory for stone column composite foundations which cannot consider the time-dependent loading and the well resistance effect of stone columns under time-dependent boundaries,a consolidation model that can reflect these characteristics is developed in this study,and the corresponding analytical solutions are obtained under permeable top surface with permeable bottom surface(PTPB)and permeable top surface with impermeable bottom surface(PTIB),*** addition,the reliability of the proposed solutions is verified by comparing them with existing analytical *** calculations are then performed by the proposed solutions to analyze the consolidation behaviors of stone column composite foundations under time-dependent boundaries,the results show that the interface parameters have a large effect on the distribution of excess pore water pressure(EPWP)along the depth;for projects with longer construction time,the permeability of the top and bottom surfaces of the composite foundation has a smaller effect on the average consolidation ***,the proposed solution is applied to the settlement calculation in an actual engineering project,and the theoretical results show a general agreement with the measured data by considering the influence of the interface parameters.

关键词： Stone column Composite foundations time-dependent loading time-dependent boundaries Analytical solutions

One-dimensional nonlinear consolidation of soft clay with the non-Darcian flow

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2013年第6期14卷 435-446页

作者： Chuan-xun LI Kang-he XIE Faculty of Civil Engineering and Mechanics Jiangsu University Research Center of Coastal and Urban Geotechnical Engineering Zhejiang University

Based on the non-Darcian flow law described by exponent m and threshold gradient i 1 under a low hydraulic gradient and the classical nonlinear relationships e-lgσ′ and e-lgk v (Mesri and Rokhsar, 1974), the governing equation of 1D nonlinear consolidation was modified by considering both uniform distribution of self-weight stress and linear increment of self-weight stress. The numerical solutions for the governing equation were derived by the finite difference method (FDM). Moreover, the solutions were verified by comparing the numerical results with those by analytical method under a specific case. Finally, consolidation behavior under different parameters was investigated, and the results show that the rate of 1D nonlinear consolidation will slow down when the non-Darcian flow law is considered. The consolidation rate with linear increment of self-weight stress is faster than that with uniform distribution one. Compared to Darcy's flow law, the influence of parameters describing non-linearity of soft soil on consolidation behavior with non-Darcian flow has no significant change.

关键词： Non-Darcian flow Nonlinear consolidation time-dependent loading Uniform distribution of self-weight stress Linear increment of self-weight stress

General semi-analytical solutions to one-dimensional consolidation for unsaturated soils

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Applied Mathematics and Mechanics(English Edition) 2017年第6期38卷 831-850页

作者： Lei WANG De'an SUN Aifang QIN Department of Civil Engineering Shanghai University

This paper presents general semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation equations for unsaturated soils subject to different initial conditions, homogeneous boundaries and time-dependent loadings. Two variables are introduced to transform the two-coupled governing equations of pore-water and poreair pressures into an equivalent set of partial differential equations （PDEs）, which are solved with the Laplace transform method. The pore-water and pore-air pressures and settlement are obtained in the Laplace transform domMn. The Crump＇s method is used to perform inverse Laplace transform to obtain the solutions in the time domain. The present solutions are more general in practical applications and show good agreement with the previous solutions in the literature.

关键词： semi-analytical solution unsaturated soil one-dimensional consolidation,homogeneous boundary condition time-dependent loading

Lattice Boltzmann method for consolidation analysis of saturated clay

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Journal of Ocean Engineering and Science 2019年第3期4卷 193-202页

作者： Pyol Kim Yong-Gun Kim Chung-Hyok Paek Jun Ma Faculty of Geology Kim Il Sung UniversityPyongyang 999093Democratic People’s Republic of Korea Faculty of Global Environmental Science Kim Il Sung UniversityPyongyang 999093Democratic People’s Republic of Korea

The lattice Boltzmann method(LBM)has been widely employed in various areas of practical engineering to solve non-linear problems,due to such advantages as the simplicity of programming and the numerical *** this paper,a new numerical method for onedimensional(1D)consolidation analysis of saturated clay is proposed on the basis of the lattice Boltzmann *** first,the lattice Bhatnagar-Gross-Krook(LBGK)model is used for 1D consolidation problem of saturated clay subjected to time-dependent loading under different types of initial and boundary *** addition,the multiscale Chapman-Enskog expansion is applied to recover mesoscopic lattice Boltzmann equation to macroscopic consolidation *** a result of the numerical simulation for verification,the numerical results are proved to be in good agreement with the analytical solutions available in previous *** the evaluation of convergence and accuracy,it is demonstrated that the proposed method is more accurate and reliable than the finite difference method(FDM)for 1D consolidation analysis of saturated clay.

关键词： Saturated clay Lattice Boltzmann method Consolidation time-dependent loading

Solution to 1-D consolidation of non-homogeneous soft clay

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2005年第B8期6卷 29-34页

作者：谢康和温介邦夏建中 Institute of Geotechnical Engineering Zhejiang University Department of Civil Engineering Zhejiang University of Science and Technology

In this work, semi-analytical methods were used to solve the problem of 1-D consolidation of non-homogeneous soft clay with spatially varying coefficients of permeability and compressibility. The semi-analytical solution was programmed and then verified by comparison with the obtained analytical solution of a special case. Based on the results of some computations and comparisons with the 1-D homogeneous consolidation (by Terzaghi) and the 1-D non-linear consolidation theory (by Davis et al.) of soft clay, some diagrams were prepared and the relevant consolidation behavior of non-homogeneous soils is discussed. It was shown that the result obtained differs greatly from Terzaghi’s theory and that of the non-linear consolidation theory when the coefficients of permeability and compressibility vary greatly.

关键词： Non-homogeneous soil time-dependent loading One-dimensional consolidation Layered system Semi-analytical solution

Analysis of one-dimensional consolidation of soft soils with non-Darcian flow caused by non-Newtonian liquid

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Journal of Rock Mechanics and Geotechnical Engineering 2012年第3期4卷 250-257页

作者： Kanghe Xie Chuanxun Li Xingwang Liu Yulin Wang Institute of Geotechnical Engineering Zhejiang University Hangzhou 310058 China School of Civil Engineering and Mechanics Jiangsu University Zhenjiang 212013 China Zhejiang Province Institute of Architectural Design and Research Hangzhou 310006 China

Based on non-Darcian flow caused by non-Newtonian liquid, the theory of one-dimensional (1D) consolidation was modified to consider variation in the total vertical stress with depth and time. The finite difference method (FDM) was adopted to obtain numerical solutions for excess pore water pressure and average degree of consolidation. When non-Darcian flow is degenerated into Darcian flow, a comparison between numerical solutions and analytical solutions was made to verify reliability of finite difference solutions. Finally, taking into account the ramp time-dependent loading, consolidation behaviors with non-Darcian flow under various parameters were analyzed. Thus, a comprehensive analysis of 1D consolidation combined with non-Darcian flow caused by non-Newtonian liquid was conducted in this paper.

关键词： one-dimensional (1D) consolidation non-Darcian flow caused by non-Newtonian liquid non-uniform distribution of total vertical stress time-dependent loading