Analytical Study On Consolidation Theory Of Soft Soils With Vertical Drains Under Complicated Condition

Vertical drains is an effective method to improve the soft soil,which has been widely used.The analytic theory of consolidation provides important references for the design of the ground by vertical drains.To predict consolidation process reasonably,a number of studies have been done on the theory of consolidation by vertical drain and lots of achievements have been made.However,there are still some limitations for its application in complicated projects and there is still a gap between the measurements and predictions.In order to further improve the consolidation by vertical drains,based on the results of previous reseachs,some endeavors are made in this paper on the analytic theories of consolidation by vertical drsins in consideration of the nonlinear compressibility and permeability of soil,and the well resistance varies with depth and time,and non-Darcy flow,as well as straight-line vacuum preloading method.The main specific work and achievements are follows:1.An excat analytical solution consildering smear effects is obtained for consolidation of soft soil with vertical drains by incorporating the nonlinear compression and flow relationship with e-lgp and e-lgk relationship based on equal-strain assumption.Then following the approach to solving well resitence proposed by Hansbo(1981),a closed-form analytical solution considering the effect of smearing and well resistance is also developed,and a comparion between this analytical solution and FEM is investigated.The result shows a good agreement between two methods.The difference between the approximate solution and the excat solution is analyzed.Consequently,the approximate solution agrees well with the when cc/ck<1,while there is a large difference when cc/ck>1,and the difference expand as the cc/ck increases.For this reason,a more practical approximate method is proposed,and the improved method can reduce the difference for cc/ck>1.The application range for the improved method is suggested.In addition,the consolidation characteristics by vertical drains under the nonlinear conditions are studied.Finally,the excat analytical solution is validated against a model test.2.The existing exponential model expressing well resistance changed over time is improved and a new hyperbolic model is proposed.A most rigorous analytical solution at present is deduced for the consolidation by vertical drains on the basis of the assumption that discharge capacity of vertical drains decreasing linearly with depth and exponentially with time.The results by contrast show that the exponential function model has a larger rate of decay than the hyperbolic function model.The selection of these two methods depends on the varied model of discharge capacity of vertical drans.The improved exponential function can be reduced to the model proposed by Deng et al.(2013).Comparing to the constant well resistance theory,the consideration of varying flow coefficient with time and depth may lead to a reducing consolidation rate as the time and depth increases.3.The equations for consolidation by vertical drains considering a threshold gradient and smear effect are developed based on the non-Darcy flow model proposed by Miller and Low(1963).The solution considering the initial gradient and smearing effect is obtained following the approach to solving well resitence proposed by Hansbo(1981).The influence of a threshold gradient,smear effect and well resistance on the moving speed of flow front,distribution of excess pore water pressure and degree of consolidation is studied.The following conclusions can be drawn:If the flow has an initial hydraulic gradient,the flow front will expand and move outward from the vertical drains triggered by the initial pore pressure,and the final location of the flow front only depends on the initial pore pressure and a threshold gradient,and the excess pore pressure in the soil would be residual.The moving speed of flow front in the soil and the consolidation rate are effected by the smear effect and well resistance,but the final location of flow front and residual degree of consolidation is independent of these two factors.4.A general solution for consolidation by vertical drains using straight-line vacuum preloading method is obtained with nonlinear flow and compression models.This solution considers a linear distribution of vacuum negative pressure along the depth of the vertical drains,and time history of additional stress due to surcharge.Detailed solutions were further investigated for three special loading schemes:instantaneous loading,ramp loading and multi-stage loading.This paper addressed the shortcomings that the available analytical solutions for the straight-line vacuum preloading method accounts for the nonlinear property of soil and the time-dependent loading simultaneously and extended its theory for more widely applications in practice.Through comparative analysis,the results show that the consolidation of degrees defined by the stress and deformation have different values,and the former leads to a smaller than the latter.For the same height of surcharge,the shorter the period of loading,the faster the consolidation and the larger the excess pore pressure in the soil.For the same height of surcharge,the larger the vacuum negative pressure,the higher the excess pore pressure.Therefore,increasing the vacuum negative pressure is beneficial for the stability of surcharge.For practical engineering,a optical economy and schedule of construction can be achieved by choosing a reasonable surcharge loading,period of loading and vacuum negative pressure.Therefore,the consideration of the nonlinearity of soil may lead to a better prediction,especially for complicated situations.