Understanding how soils behave under external loads is vital in geological and geotechnical engineering and helps to address problems such as land subsidence, secular settlement, and urban precipitation issues. Factoring in 3D layered soil consolidation, where natural soils are deposited into layered sediment, is challenging but can lead to a more reasonable prediction of the consolidation behavior of the soils.

To address the challenges involved in solving 3D consolidation problems of multilayered soil, researchers Lujun Wang, Bingfa Yan, and Xiaotian Liu developed an analytical layer element theory with the aid of an integral transform and displacement function. They compared their results with the existing numerical and analytical solutions and confirmed their theory in “Analytical Theory for 3D Consolidation of Layered Viscoelastic Soils Based on Displacement Function Method” in the Journal of Engineering Mechanics. The authors indicate that their theory can be extended to study the response of soils induced by other specific loads of external and internal force vectors, such as thermal loads and water pumping. Learn more about their research at https://doi.org/10.1061/(ASCE)EM.1943-7889.0002119. The abstract is below.


The analysis of long-term rheological consolidation behaviors of soft soils is the research focus in geotechnical and geological engineering. This paper develops an analytical theory to explore such behavior within layered viscoelastic sediments in a three-dimensional (3D) Cartesian coordinate system. Starting from the governing equations of 3D consolidation problems and introducing the displacement functions, the state vectors between the surface and an arbitrary depth of a finite soil layer are established in the transform domain. With the aid of this relationship and continuity conditions between adjacent layers and the boundary conditions of the layered system, an analytical solution for viscoelastic soils is then obtained. Detailed comparisons are given to confirm the applicability of the theory, followed by typical examples examining the effect of types of viscoelastic model, fractional order, and soil layered properties on the coupled rheological and consolidation responses. In the present theory, the state space equation containing eight coupling state vectors is uncoupled into two sets of equations of six and two state vectors based on three displacement functions and a decoupling transformation, which has the advantage of cutting the computation amount and proves to be remarkably efficient and practicable in solving the 3D rheological consolidation problems.

Read the complete paper in the ASCE Library: https://doi.org/10.1061/(ASCE)EM.1943-7889.0002119