Refined Consolidation Theory For Soft Soils Improved By Prefabricated Vertical Drain

In recent years,with the promotion of the strategy for building China’s strength in sea,vertical well assisted consolidation method has been increasingly used in the China’s coastal soft ground improvement projects.The prefabricated vertical drain（PVD）has become the most widely used vertical drain because of its advantages of low time consumption,high permeability and relatively low cost.As the theoretical basis for guiding related engineering design,the consolidation theory of vertical drain improved soils has always attracted academics in the geotechnical engineering field.However,numerous investigations have shown that existing consolidation theory of vertical drain leaves much to be desired.Moreover,new design requirement and emerging engineering problems have been posing new challenges to the consolidation theory of soft soils improved by vertical drains.Aiming at the consolidation problem of soft soils improved by PVD,this study firstly dissects the classical sand well consolidation theory,and summarizes the deficiencies in the existing consolidation theory.Then,using analytical method,semi-analytical method and finite element numerical method,the consolidation theory of soft soils improved by PVD is refined by progressively considering the shape effect of PVD,the nonlinearity of soils,the large-strain characteristics of soils,unsaturated soils,the working condition of partially penetrating PVD,the multi-PVDs improved soils;based on this,the consolidation behaviors of soils improved by PVD and the influences of related parameters on it are analyzed in depth.The main research contents are as follows:（1）Considering the shape effect of PVD in this study,an elliptical cylindrical equivalent model（ECEM）is established,and the corresponding analytical solutions are derived under the surcharge combined with vacuum preloading.Then,the case studies are conducted by combining the ECEM with common settlement calculation methods.The outcomes show that ECEM can accurately capture the settlement development of soils.Meanwhile,the common equivalent methods are assessed by comparing them with the ECEM,and the results show that the equivalent method from Long&Covo（1994）is the best one to describe the drainage performance of PVD,and with this equivalent method,an accurate predication for the consolidation development can be obtained;secondly,the equivalent method from Abuel-Naga&Bouazza（2009）underestimates the consolidation development,while the equivalent method from Hansbo（1979）overestimates the consolidation development;in contrast,the area equivalent method from Fellenius&Castonguay（1985）greatly underestimates the consolidation development.（2）Based on ECEM,a nonlinear consolation model is built up by further considering the dual non-linearity of compression and permeability of soils together with the over-consolidation history,using the nonlinear relationship of e-lgσ′and e-lgk;the analytical solutions are obtained by employing a linear simplification method.Through the comparison with finite differential solutions and the measured data,the correctness of present solution is verified.It is found through parametric analyses that neglecting the over-consolidation history of nonlinear soils would underestimate the development of the consolidation degree of the soils,and the greater the OCR,the more significant the underestimation.（3）A large-strain consolidation model for PVD improved soils is developed by further considering the large-strain characteristics of soils in ECEM;in this model,the sedimentation contributed by self-weight of the soils is considered,and then an analytical method for calculating the distributions of the initial effective stress and initial void ratio with depth is proposed.The numerical solution for this model is obtained by means of COMSOL Multiphysics,and its validity is verified by comparing it with existing solutions and measured data.Based on the parametric analyses,it is summarized that the difference between large-strain and small-strain consolidation can be ignored in following cases:（1）compression index C_c≤0.4,（2）ratio of load over initial effective stress qσ₀′≤4,（3）Cc≤0.6 andqσ₀′≤6.（4）A consolidation model for the unsaturated soils with PVD is developed by introducing the constitutive relationship of unsaturated soils into ECEM,and the corresponding analytical solutions are derived under the free-strain and equal-strain conditions.The correctness of present solutions is verified by comparing the present solutions with existing solutions.Based on the present solutions,the consolidation analyses for the unsaturated soils with PVD are carried out.It is found that there is a plateau during the consolidation development of the unsaturated soils.The consolidation behavior prior to the plateau depends mainly on the dissipation of the pore-air pressure,whereas consolidation behavior after the plateau is controlled by the dissipation of the pore-water pressure.（5）With the idea of the continuous drainage boundary,the continuity of pore water pressure between the upper layer with PVD and the lower layer without PVD is considered,and then a simplified calculation model for the consolidation of soft foundation with partially penetrating PVD is proposed.The rationality of present simplified calculation model is verified by comparing with existing calculation methods.It is found from the parametric analyses that the consolidation rate increases with increase of the penetration degree.Under PTPB condition,the vacuum pressure in the underlying soil gradually decreases along the depth.（6）Based on ECEM,an equivalent plane strain model is developed by using the permeability coefficient matching method;then,according to the working conditions of a case history,a multi-PVDs consolidation model is established using COMSOL Multiphysics.The correction of present numerical model is verified by comparing the predicted results with the measured data.The multi-PVDs consolidation analysis demonstrates that when the vacuum preloading keeps constant,as the total surcharge and/or loading rate increase,the outward lateral displacement of the soil around the PVDs-treating area would increase,and the overall outward movement trend of the soil would be more obvious.（7）To consider the thermal contraction behavior of soils,a linear thermal compression model is devised;with this model,further considering the thermo-osmosis effect,a consolidation model for the soils improved by thermo-PVD（PVTD）is proposed.The corresponding semi-analytical solutions are derived using Laplace transform and numerical inverse Laplace transform.The correctness of present solutions is verified by comparing them with FDM solutions.The consolidation analyses find that the PVTD technique could enhance the permeability of the soil,especially for that in the smear zone,thereby improving the consolidation rate.Aside from surcharge load,generation of excess pore water pressure in soils can also be induced by thermal compression,difference in thermal expansibility between pore water and soil grains,and thermo-osmosis,where the influence of thermal compression on the excess pore water pressure is the most prominent among the three factors.