Analytical Theory And Finite Element Analysis For Consolidation Of Soft Soils By Vertical Drains

Vertical drain combined with preloading offer significant benefits in improving sites with thick soft soil deposits by accelerating the consolidation process and it has been used extensively in the large-scale infrastructure construction for highways, railways, ports, airports and so on. A lot of achievements have been made both in theoretical approaches and numerical methods for the reliable simulation of the consolidation process by vertical drains. It was also found that a certain gap exists between the measured values and calculation results by different methods. The predictions of the post construction settlement and the differential settlement are usually in poor accuracy. Additionally, the situations of the long depth of a vertical drain for deep soil deposits and limited construction period are challenging the design and calculation procedure of vertical drain consolidation. To this end, this paper carried out the study for the simulation of the consolidation process by vertical drains from both the analytic theory and the finite element method.1. The previous researches for both theoretical methods and parameters are summarized at first. It was found that the widely accepted formulas for the calculation of the radial average degree of consolidation can be expressed as a uniform expression. Different approaches have a slight difference in the consideration of the smear effect and the well resistance. The latest developments of the consolidation theory for vertical drained ground consist of non-linear theory, non-Darcy flow theory, the variety of soil permeability within the smear zone and the consolidation theory for the vacuum preloading method. A large number of studies have also been carried out for parameters in the analysis of the vertical drained foundation, but the value ranges of these parameters are large and it will reduce the reliability of the calculation results.2. The discharge capacity qn has been investigated by several studies in recent years. General conclusions have been obtained by laboratory tests that the discharge capacity qw can be reduced by several factors throughout the consolidation process in field, such as the deformation of the drain, lateral stress, siltation, hydraulic gradient and so on. Based on this consideration, this paper assumed qw varies linearly with depth z and decreases exponentially with tim t and formed a mathematical model for varied well resistance effect. Then, a series of closed-form solutions following with the approaches of Hansbo’s approximate solution and Xie’s rigorous solution were developed with the instant loading condition, respectively. The impact of variable discharge capacity on the development of consolidation was investigated. And the following conclusions have been obtained that the existing unit cell method with a constant short time discharge capacity will over predict the consolidation rate. The development of the radial degree of consolidation may be totally interrupted when the permeability of the drain is reduced to that of the surrounding soil. The varied well resistance apparently affects the patterns of the distribution of average excess pore water pressure along the depth. Besides, the proposed method is applied in the simulation of a large indoor model test and an engineering practice. By comparing the results of the new method with classical solutions, it was found that the present method with varied well resistance could predict the consolidation process better since the behavior of PVDs is more accurately described.3. A non-linear flow relationship, which assumes that the fluid flow in the soil skeleton obeyed Hansbo’s non-Darcian flow and the coefficient of permeability decreased with the consolidation time, was incorporated into Biot’s general consolidation theory for the consolidation simulation of soft ground with vertical drains. Governing equations with the coupled non-linear flow model were presented and the finite element (FE) formulations were derived based on the weighted residual method. The effect of the coupled non-linear flow on the development of consolidation was investigated. It was found that the consolidation rate became slow when the non-Darcian flow with varied permeability was considered. The retardation on the consolidation process was taken on an accelerating tendency when increasing the values of the non-linear flow parameters. The loading size also had significant effect on the consolidation behavior in the non-linear analysis of the coupled consolidation problem.4. With the introduction of a piecewise linear e-lgp assumption, this paper further presents an FE analysis which takes into account one-dimensional non-linear property of compression and permeability. Combined with the consolidation-seepage joint test for Ningbo soil samples, the acquisition process for parameters of the one-dimensional nonlinear model is presented. Governing equations with the coupled non-linear flow model were presented firstly for force equilibrium condition and continuity condition, respectively. Based on the weighted residual method, the FE formulations were then derived and an existing FE program was modified considering the non-linear flow model. Comparative analyses with established theoretical solutions and numerical solutions were carried out and the results were satisfactory. On this basis, the effect of the coupled non-linear flow on the development of consolidation was investigated, and some useful conclusions were obtained correspondingly.5. The two-dimensional equivalent methods are widely used in the finite element analysis of vertical drained ground. Summaries and comments about the equivalent methods are firstly carried out based on the existing researches. Then, six equivalent methods are examined for two numerical examples for layered soil foundation and partially penetrated vertical foundation. The results show that the parameter values for layered soil have significant impact on the reliability of equivalent methods, while the length of the drain has no significant effect. For the parameter values applied in the example, errors for the degree of consolidation for different methods vary considerably. Relatively, the calculation results of Chai’s (2001) method and Tran’s (2008) method are reliable and the largest errors for the two methods are within10%. Chai’s method is worth promoting since the operation of the method is rigorous and with high computational efficient. Additionally, aims to simplify the pre-process of three dimensional analysis of vertical drain foundation and to improve the computation efficiency, the one dimensional equivalent method with1D deformation and1D seepage element was proposed based on Chai’s equivalent vertical seepage idea. Numerical results were compared with traditional FEM results for a series of calculation conditions to verify the accuracy of the simplified method. And the results showed that the computation efficiency is greatly improved. However, compared with Chai’s equivalent method, the accuracy of the newly proposed method is not improved and the calculation process is relatively complex.6. Since drains are small both in spacing and size, resulting in enormous computing costs for a traditional3D FE analysis, a new spatial element that contains the drain well and its neighboring smear zone was presented. This new combined element was depicted by10nodes element, which contains8global independent nodes and2local dependent nodes. A classical analytical theory was introduced to set up the relationship between the two kinds of nodes. Since permeability diversity between the drain and the smear zone was considered, both the effects of smearing and well resistance were taken into account in the composite element method (CEM). A detailed derivation of the CEM was performed using the weighted residual method. To verify the accuracy of the CEM. numerical results were compared with analytical solutions and with traditional FEM results for two cases. These comparative analyses demonstrated that acceptable results were obtained by the CEM. Additionally, the proposed method saves1/4-1/2mesh elements and avoids slender elements for the full-scale FE analysis of vertical drain foundation.7. Finally, numerical simulation for a vertical drain foundation under a power plant seawall was carried out based on a large-scale commercial software and by a self-coding program. The theoretical bases for the two approaches are Chai’s two-dimensional equivalent method and Xie’s PDSS model. It was found by the comparison of the two numerical methods that the deformation simulations of the ground by the two methods are roughly the same as each other; the settlement of the foundation predicted by the later method is relatively bigger than Chai’s method since the PDSS model took into account the spatial seepage. Conclusions also obtained by the numerical simulation that the development of consolidation for the ground is obvious:the excess pore water pressure are dissipated significantly in the intermittent period of loading; the development rates of ground consolidation are within the security value.