Composite foundations improved by impermeable columns and vertical drains are widely applied in various actual projects. However, few existing studies have reported nonlinear consolidation solutions for such composite foundations. In this study, a nonlinear consolidation model is developed with a time-dependent permeability coefficient for vertical drains. Then, the equation governing the consolidation of the composite foundation is derived, and the corresponding analytical solution is obtained. An iterative approach is adopted to minimize the errors generated in the simplified solution process. Through extensive calculations, the effect of time-dependent well resistance of vertical drains on the consolidation of such composite foundations is analyzed. The results show that ignoring changes in well resistance over time leads to an overestimation of the stress concentration effect of impermeable columns, consolidation of the composite foundation, and settlement rates. Finally, the proposed analytical solution is applied to the settlement calculations for a section of the Huai-Yan Highway and a section of the Lin-Lian Highway. Compared with the consolidation model with constant well resistance, the one with variable well resistance provides results that are more consistent with the measured data.

The large strain and nonlinear consolidation characteristics of soft soils with high compressibility have obvious effects on their consolidation, but few analytical solutions for large-strain nonlinear consolidation of soils with vertical drains have been reported in the literature. By considering the large deformation characteristics of soft soils with high compressibility during consolidation, a large-strain nonlinear consolidation model of soils with vertical drains is developed and an analytical solution for this consolidation model is obtained based on Gibson's large deformation consolidation theory, in which a double logarithmic nonlinear compressibility and permeability model is adopted to describe the variation of the compressibility and permeability of soft soils. The proposed analytical solutions are compared with the numerical solutions of large-strain nonlinear consolidation of soils with vertical drains and the analytical solutions of small-strain linear consolidation under specific conditions to verify its reliability. On this basis, the nonlinear consolidation properties of soils with vertical drains under different conditions are analyzed by extensive calculations. The results show that the consolidation rate increases with decreasing the permeability parameter alpha, when the compression index I-c, keeps constant. The consolidation rate increases with decreasing the compression index I-c, when the permeability parameter alpha remains constant. The consolidation rate of soils with vertical drains increases with an increase in external load, and decrease with an increase in the ratio of influential zone radius to vertical drain radius when the compressibility and permeability parameters remain constant. Finally, the proposed analytical solution is applied to the reclaimed foundation treatment project of Shenzhen Western Corridor boundary control point(BCP). The settlement curve calculated by proposed solutions is in good agreement with the measured curve, which further illustrates the engineering applicability of the proposed analytical solution.

With the developments of the geotextiles industry, some electro-kinetic geosynthetics are used for the indoor tests of treating soils with electro-osmosis. Electro-osmotic treatment of soft soils has promising applications as synthetic electrodes are environmentally benign and have good hydraulic conductivity. However, the consolidation theory for soils treated by electro-osmosis combined with vacuum and surcharge preloading in which electrodes are installed in a hexagonal array has been rarely reported in the existing literature. Therefore, a consolidation model for such technologies is established in this study and the corresponding analytical solution is obtained. Then, the correctness of the proposed model is verified by comparing the results calculated by it with those calculated by the existing solutions and measured data. Finally, extensive calculations are performed to investigate the consolidation behaviors of soils under such condition, and the results show that the DC power supply is suggested to be cut off in the late stage of consolidation to reduce the cost; the energy consumption per unit volume of water discharged increases as the effective voltage increases; high benefits can be obtained by using the electro-osmosis for the treatment of soils when the thickness of soils is thin or the influential zone of each cathode is large.

When stone columns or vertical drains are applied to improve soils, it is common to face situations where the soft soil layer is too thick to be penetrated completely. Although consolidation theories for soils with partially penetrated vertical drains or stone columns are comprehensive, consolidation theories for impenetrable composite foundations containing both two types of drainage bodies have been few reported in the existing literature. Equations governing the consolidation of the reinforced zone and unreinforced zone are established, respectively. Analytical solutions for consolidation of such composite foundations are obtained under permeable top with impermeable bottom (PTIB) and permeable top with permeable bottom (PTPB), respectively. The correctness of proposed solutions is verified by comparing them with existing solutions and finite element analyses. Then, extensive calculations are performed to analyze the consolidation behaviors at different penetration rates, including the total average consolidation degree defined by strain or stress and the distribution of the average excess pore water pressure (EPWP) along the depth. The results show that the total average consolidation rate increases as the penetration rate increases; for some composite foundations with a low penetration rate, the consolidation of the unreinforced zone cannot be ignored. Finally, according to the geological parameters provided by an actual project, the obtained solution is used to calculate the settlement, and the results obtained by the proposed solution are in reasonable agreement with the measured data.

The composite foundation reinforced by stone columns and vertical drains is widely used in various projects. However, available calculation methods for such consolidation are rarely reported in the literature. Firstly, a set of basic equations are proposed to describe the seepage relations among stone columns, vertical drains, and soft soils in this study. Then, the governing consolidation equation, in which the average total excess pore water pressure (EPWP) serves as a variable, is derived by considering the deformation of stone columns during consolidation under the assumption of equal strain conditions. Moreover, the analytical solution for the consolidation equation is obtained by the method of separation of variables, and its reliability is verified by degenerating into the solution for the consolidation of composite foundations reinforced by stone columns and comparing it with the field measurements. Finally, a parametric study is performed to investigate the consolidation behavior. The results show that the consolidation rate can be significantly increased by installing vertical drains between the stone columns compared to reducing the column spacing; for some composite foundations reinforced by stone columns with a high ratio of replacement, the deformation of columns during consolidation cannot be ignored; the smear effect caused by vertical drains can be ignored in such composite foundations.

The nonlinear compressibility and permeability of soft soils is a key factor in the consolidation of both composite and natural foundations. However, there are few corresponding consolidation theories for vertical drain-stone column composite foundations in which the nonlinear consolidation characteristics of soils can be taken into account. In this study, a nonlinear consolidation model is established to describe the seepage relations between soft soils, vertical drains and stone columns. Then, a consolidation governing equation is derived, where the total excess pore water pressure (EPWP), u¯, is a variable, and the average consolidation degree defined by strain and stress of the composite foundation is obtained, respectively. Numerous calculations are performed to analyze the consolidation behaviors of such composite foundations. The results show that the installation of vertical drains can enhance the consolidation rate effectively; the external load and the initial modulus ratio of column to soil have an influence on the stress concentration effect of stone columns. Finally, the proposed analytical solution is applied to the settlement calculation for an actual project, and the calculated results are in good agreement with the measured data in the early and late stages of consolidation.

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), respectively. In addition, the reliability of the proposed solutions is verified by comparing them with existing analytical solutions. Extensive 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 rate. Finally, 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.

To make up for the shortcomings of single-pile composite foundations, combined composite foundations are increasingly used in engineering. However, studies for the consolidation theory of composite foundations reinforced by high replacement ratio gravel piles and vertical drains, in which the radial flow within gravel piles is considered, have been rarely reported in the literature. The establishment of a comprehensive composite foundation consolidation model is of significance for more reasonable design for stone columns and vertical drains, such as penetration depth, replacement ratio, distribution pattern and so on. Therefore, to solve such consolidation issues, a gravel pile-soil unit with several vertical drains around the perimeter is regarded as a calculation model. Then, the related analytical solution to the total average express pore water pressure (EPWP) is derived by considering the radial flow within gravel piles, and the reliability is verified by comparison with existing solutions. Moreover, extensive calculations are made to investigate the consolidation behaviors, and the results show that vertical flow in soils has little effect on the consolidation of this composite foundation; the effect of radial flow within high replacement ratio gravel piles is nonnegligible; installing vertical drains between piles can enhance the consolidation rate. Finally, the model is applied to the settlement calculation of an embankment in Malaysia, and the results by proposed solutions are in good agreement with the measured data, further indicating the applicability of the calculated model.