Consolidation Of Multi-layered Soils Research Articles

Consolidation of multilayered soil with fractional derivative viscoelasticity due to surface loading and internal pumping

Classical Terzaghi’s solution provides a useful tool to predict the one-dimensional consolidation of homogeneous elastic soil layer with fully drained/undrained boundary condition under instantaneous loading. Due to the sedimentation process and complex internal structure, natural soils usually exhibit multilayered inhomogeneity and viscoelastic behavior. In practical cases, the drainage capacity of the boundaries can change with time. Thus, these practical factors should be well in considered for accurate prediction of the consolidation. This paper extends the classical Terzaghi’s solution to multilayered viscoelastic soil with continuous drainage boundaries and subjected to time dependent loading. The fractional derivative Kelvin-Voigt model is used to describe the viscoelasticity of soil. Two loading cases namely surface loading and internal pumping are considered. The consolidation problem is solved by Laplace transform technique and a transfer matrix formulation. Analytical solutions for excess pore water pressure, effective stress and settlement are given. The present solution is general and can reduce to existing solutions available in the literatures. Numerical studies are conducted to investigate the effects of viscoelastic parameters, boundary drainage capacity and loading rate on the consolidation behavior. It is shown that the multilayered soil system with large viscosity coefficient and small fractional order can consolidate fast. For the consolidation due to internal pumping, the drainage parameters have no influence on the consolidation process.

A vertical and radial consolidation analysis incorporating drain degradation based on the spectral method

The use of prefabricated vertical drains (PVDs) to improve soft soil has received much attention in the recent past, however, there is still a lack of rigorous analytical solutions that can incorporate the time- and depth-dependent behaviour of drains into the consolidation of multi-layered soil. This study thus presents a novel approach where the spectral method is used to capture the degradation in discharge capacity of drains over time and depth, while the average consolidation of different soil layers with regard to vertical and radial drainage is computed. In this approach, the excess pore water pressure profile across different soil layers is described as a single expression using matrix operations. This proposed method is then verified with laboratory and field investigations where the degradation of PVDs is captured and compared with other solutions. The results show that this method can predict the soil behaviour with greater accuracy and flexibility whereas there is a significant deviation in the predicted consolidation when the degradation of drains is not considered properly. A parametric investigation is also carried out using the proposed solution to further highlight its ability to evaluate the effect that drain degradation can have on the consolidation of multi-layered soil.

Transfer matrix solutions to axisymmetric and non-axisymmetric consolidation of multilayered soils

Transfer matrix solutions are presented in this paper to study the axisymmetric and non-axisymmetric consolidation of a multilayered soil system under an arbitrary loading. Starting with the governing equations for consolidation problems of saturated soils, the relationship of displacements, stresses, excess pore water pressure, and flux between the points at the depth z, and on the ground surface (z = 0) is established in a transformed domain by introducing the displacement functions and using the integral transform technique. Then the transfer matrix method is used with the boundary conditions to obtain the analytical solutions in the transformed domain for the multilayered soil system. Numerical inversion of the integral transform of these analytical solutions results in the solutions for the actual problems. The numerical results for axisymmetric and non-axisymmetric Biot’s consolidation problems of a single layer and a multi-layered soil system are obtained and compared with existing results by others.

Transfer matrix solutions to plane-strain and three-dimensional Biot’s consolidation of multi-layered soils

Starting from the governing equations of a saturated poro-elastic soil in the Cartesian system, and introducing the displacement functions, the transfer matrix relationship of displacements, stresses, excess pore water pressure, and flux between the ground surface ( z = 0) and an arbitrary depth z of a finite soil layer is established in the Laplace-Fourier transforms domain. Based on this relationship and transfer matrix concept and by considering the continuity conditions between adjacent layers and the boundary conditions of the layered soil system, the solutions for plane-strain and three-dimensional Biot’s consolidation problems of a multi-layered soil system in the transformed domain are derived, respectively. The actual solutions in the physical domain can be acquired by the inversion of the Laplace-Fourier transforms. The numerical results for plane-strain and three-dimensional Biot’s consolidation problems of a single layer and multi-layered soil system are performed, and the feasibility and accuracy of the proposed solutions in this study are proved by comparing with some existing results.

Analytical and computational studies on the consolidation of multilayered soils

Analytical and computational studies on the consolidation of multilayered soils

One-Dimensional Consolidation of Multi-Layered Soils

Synopsis The distribution of consolidating load in a soil is directly related to the distribution of pore-water pressure. The current differential equation used to describe this distribution is based on certain linearizing assumptions which may not be justified in practice. Thelinearized equation has certain mathematical advantages but these are of little value when dealing with non-homogeneous soils. A numerical method is therefore developed. The current equation is retained for a study of non-homogeneity in soils, but the method used may be modified for a later non-linear formulation of the problem. With a view to its practical application the method is designed for evaluation on a digital computer. The method is applied to a well documented case of consolidation and the calculated and prototype settlements compared. The results indicate that a non-linear formulation, involving variations of permeability and compressibility, is necessary to account for the observed behaviour. The nature of these variations must be critically investigated, this investigation involving a re-evaluation of current methods of soil sampling and interpretation. La répartition de charge de consolidation sur un sol est directement en relation avec la répartition de pression de l'eau interstitielle. L'équation différentielle normale employée pour décrire cette répartition est bas6e sur certaines assumptions linbaires qui ne se justifient peut-être pas en pratique, L'équation linéaire a certains avantages mathé matiques mais ceux-ci ont peu de valeur en traitant des sols non-homogènes. Aussi développe-t-on une méthode numérique. On garde l'équation normale pour une étude de non-homogénéité dans les sols, mais il se peut que la méthode employée soit modifiée pour taire par la suite une élaboration non linéaire du problème. En vue de son application pratique la méthode est conçue pour évaluation sur “computateur digital”. On applique la méthode à un cas bien documenté de consolidation et on compare les tassements prototypes calculés. Les résultats indiquent qu'une élaboration non-linéaire tenant compte des variations de perméabilité et de compressibilité est nécessaire pour justifier ce qu'on observe. on doit faire un examen critique sur la nature de ces variations, cet examen entraînant une ré-évaluation des méthodes courantes d'échantillonnage et d'interprétation du sol.