Analytical Study On Axisymmetric Consolidation Theory Of Ground With Vertical Drains

Drainage preloading has been found a economical and efficient method for ground improvement and widely used. Vertical drains are usually used to accelerate the consolidation process of soft clay. After several years of development, great deals of findings have been made to the consolidation theory of vertical drains foundation, but still there are many imperfections, and there is still a gap with the actually engineering. In order to further improve the consolidation theory of vertical drains foundation, based on the results of previous research, some useful studies are made on the consolidation of partially penetrated vertical drains foundation, multi-layered vertical drains foundation, vertical drains foundation under general time-dependent loading, vertical drains foundation with the non-linear soil and vacuum preloading vertical drains foundation. The main specific work and achievements are as follows:1. The consolidation of soft soil with partially penetrated vertical drains under single-drainage condition and double-drainage condition was studied. Vertical and radial seepage of soils under sand drains was considered through setting suppositional sand drains. Meanwhile, in order to consider the fact that the larger the distance from sand drain is, the lighter the disturbance of construction is, the horizontal permeability of soils was expressed in unified way through introducing a function. Three types of variation patterns of the horizontal permeability of soil in the disturbed soil zone were considered, including the constant distribution pattern, the linear distribution pattern and the parabolic distribution pattern, and an analytical solution was obtained. Corresponding computer program was developed and several problems that should pay attention to during the process of programming were expatiated, then the consolidation behavior of partially penetrated sand drains foundation was investigated. The results show that consolidation is the fastest if the parabolic distribution pattern was considered, the consolidation is slower if the linear distribution pattern was considered, the slowest if the constant distribution was considered; and that the larger the disturbance zone is, the slower the consolidation is, the greater the disturbance is, the slower the consolidation is; the deeper the sand drains penetrated, the faster the consolidation is; the larger the permeability coefficient of sand drains is, the faster the consolidation is. 2. The consolidation of multi-layered sand drains foundation under single-drainage condition and double-drainage condition was analyzed. Three types of variation patterns of the horizontal permeability of soil in the smear zone were considered, and an analytical solution was obtained. Corresponding computer program was developed and the consolidation behavior of double-layered sand drains foundation was investigated. The results show that the overall average degrees of consolidation of foundation in terms of pore pressure is equal to that in terms of strain only if compression modulus of every layer is equal to each other, otherwise the former is always larger than the later; the consolidation rate is at its maximum for the parabolic distribution pattern and is at its minimum for the constant distribution pattern whereas the one for the linear distribution pattern is in the middle. Increasing compression modulus of any layer could accelerate the dissipation of pore pressure.3. The consolidation behavior of soils with vertical drains subjected to a general time-dependent loading was studied in this paper. Firstly, an analytical solution was obtained accounting for the effects of soil smear, drain hydraulic resistance, coupled flows in the radial and vertical directions within the surrounding soil, time-dependent loading and the linear distribution of the horizontal permeability of soils in the disturbed soils zone. Then, the time-dependent loading was transferred to trigonometric series by the technique of Fourier Transform. By this method, the complex loading can be transformed into the sum of a series of sine and cosine function. Then the response of the complex loading was obtained by superimposing the responses of these relatively simple ones. A simple-to-use method was proposed according to this method. Consequently, a calculation computer program was developed and a comparison with a theoretical method is shown to assess the accuracy of the proposed method. Finally, the consolidation behavior of sand drains foundation under several conventional types of time-dependent loading was investigated, including multi-ramp loading, triangular cyclic loading and trapezium cyclic loading. Moreover, the consolidation behavior of sand drains foundation under parabolic cyclic loading was investigated by means of piecewise-linear approximation method.4. The characteristics of the nonlinear increase in the soil's compressive modulus and the non-linear decrease in the soil's permeability during consolidation are considered. Based on the non-linear characteristics of soil, an analytical solution for the consolidation of composite ground is developed. Then the non-linear consolidation behavior of vertical drains ground is analyzed and the results show that ADC in terms of stress is not equal to that in terms of deformation and furthermore the latter is always greater than the former. When the soil's compressive indices is less than the permeability indices, ignoring the soil's non-linearity will under-estimate the consolidation rate; however, when the soil's compressive indices is greater than the permeability indices, the reverse is true:ignoring the non-linearity will over-estimate the consolidation rate.5. A general analytical solution is obtained for the consolidation of vertical sand foundation under vacuum preloading considering simultaneously the variation of vacuum degree, the coupled variation of stress increment with depth and time together, both horizontal and vertical drainage, and the variation of horizontal permeability coefficient of soil. Furthermore, detailed solutions are obtained for excess pore water pressure and average degree of consolidation under the particular situation that the vacuum degree is linearly changed along the vertical drain depth, the stress increment is linearly changed along the column depth and the loading is applied in a single-stage way. Finally, the consolidation behavior of vertical drain foundation is analyzed. The results show that:If the loading is applied instantaneously, consolidation degrees of foundation have nothing to do with vacuum degree. If the loading is applied gradually, the larger the vacuum is, the faster the consolidation is, the slower the reducing of vacuum is, the faster the consolidation. Ignoring the vertical flow within the soil will under-estimate the consolidation rate. Furthermore, the less the radius ratio is, and the less the ratio of horizontal permeability to vertical permeability is, the greater the under-estimated value is.