Multi-dimensional Consolidation Of Soft Soils Under Complicated Conditions

On the basis of the work so far available, this paper makes a further study from the non-linear one-dimensional small and finite-strain consolidation theory and then analysis the two-dimensional axisymmetric consolidation theory with or without the vertical drain considering complicated surcharging loadings conditions as well.First, based on the well-known empirical e～lgσ' and e～lgk_v relations, one-dimensional consolidation problems of soft soils under cyclic loadings are analyzed. On the basis of the solutions obtained and the computation through programming, the influence of some parameters and loading conditions on the non-linear one-dimensional consolidation behaviors under suddenly-imposed, sin, trapezoidal, triangular and rectangular cyclic loading, are investigated. And then the results are compared with Terzaghi's consolidation theory and linear consolidation theory under cyclic loadings.Second, on the basis of Gibson consolidation theory and by the method of Laplace transform, the analytic solutions in frequency domain are obtained. According to numerical examples, some characteristics of non-linear consolidation behaviors of finite consolidated soil under cyclic loadings are compared with those of normal consolidated soil.Third, based on Biot's governing consolidation equations for semi-infinite and also finite isotropic soil layer, general solutions are derived by applying the Laplace-Hankel transform technique. A numerical inverting procedure was used to study the consolidation behavior in the time domain for different external loading cases. Due to the real soil's original deposition in horizontal beds, the real soil is often anisotropic in that its horizontal properties are different from its vertic al properties. Thus, a more realistic solution to the consolidation problem which should account for the soil anisotropy was obtained.Fourth, the general solution in the Laplace transform field for the consolidation of soil with partially penetrated vertical drains under complicated time-dependent loadings is derived. And the method is used here has been proved to be an efficient and accurate method, which can be widely used in practice engineering.At last, a new computational model which can consider the non-linear material character of the soils is established. The analytical solutions for the non-linear consolidation of soft soil with vertical drains are obtained under both constant loading case and time-depending loading case.From this study, the following conclusions may be obtained: on the assumption of permeability index k_v changes linearly with volume compression index w_v, consolidation of soil is different from Terzaghi's consolidation theory. And under cyclic loading, the effective stress in soil is not synchronously changed with loading but is developed in a delayed way; the scope of effective stress is related with the parameters of loading and with c_c/c_k; when considering the self-weight of soil, this portion of settlement must be calculated in the finite-strain consolidation, if the result is obtained according to the infinite consolidation, it will be far less than the actual result. For the two-dimensional consolidation, a negative pore water pressure is observed when the soil under cyclic loadings, which is different form one-dimensional consolidation theory. With the numerical modelling, it is shown that the rate of consolidation of the soft soil with partially penetrated vertical drain is increased with the increase of the drain length. However, it is slow down as the length exceeds some extent. And the consolidation degree is overestimated by the one commonly used in China. When the external loading is big enough, it is necessary to take the non-linear character of the soil into consideration.