Extended fully coupled analysis of consolidation using the finite element method

Abstract

The thesis focuses on consolidation analysis using the poroelasticity theory, or Biot’s theory. It is written with a cumulative form including three research publications. The first two chapters of the thesis introduce briefly the topic, the poroelasticity theory, and finite element codes. Chapter 3 presents a fully coupled plug-in for FEFLOW software that aims to analyse land subsidence problem due to groundwater extraction. The plug-in was developed using the C++ programming language with FEFLOW APIs and Qt IDE. It is distributed freely on GitHub. Two techniques were used to increase the speed of the plug-in. First, the boundary conditions are applied for local stiffness matrices before they are assembled to the global stiffness matrix. Second, the global stiffness matrix is assembled using multicores of the central processing unit (CPU). Chapter 4 proposes a new approach to process data from the constant rate of strain test (CRST) for consolidation analysis. Instead of plotting test data on e-log(σ’) graph (where e is the void ratio and σ’ is the effective stress) to obtain the compression index Cc and the compression index Cr, the back-analysis method is used to obtain stress-dependent parameters for finite element models based on Biot’s theory. An open-source software called CONAXIS was developed for this purpose. Codes and algorithms for CONAXIS were partly taken from previous FEFLOW plug-in. The proposed approach was compared with a commercial software named PLAXIS and was verified with data of two soft soil improvement projects in Mekong Delta, Vietnam. Both projects used prefabricated vertical drains (PVD) combining with surcharge loading and vacuum pumping as the improvement method. Each PVD has an influence zone that is idealised as a cylinder called a unit cell. Consolidation analyses for both projects were performed with axisymmetric models of unit cells in CONAXIS. In the first project, nine CRSTs from the same borehole with various depth were used to set up the model in CONAXIS. The soft soil thickness was 17.5 m. For the second project, six CRSTs from three boreholes were used, and the thickness of soft soils was about 35.0 m. Model results from CONAXIS were compared to field monitoring data. Both models showed a good agreement with field data. Finally, chapter 5 deals with radial flows in 3D models of PVD systems. To capture radial flows around PVDs, finite element meshes around PVDs must be discrete with small element sizes that lead to a heavy computational effort, especially for 3D models. A new approach based on Vimoke-Taylor concept was proposed to overcome this difficulty. Instead of modelling both the PVD boundary and the smear-zone around PVD, a drained-zone was used to represent both PVD and the smear-zone. The horizontal hydraulic conductivity of the drained-zone was modified with a correction factor that was determined by fitting numerical results with analytical solutions of the unit cell. Factors related to characteristics of PVDs and soils affecting the correction factor Cd were investigated with six patch tests. The results of the patch tests indicate that the Cd value depends mainly on three factors: the size of the drained-zone, the size of the PVD and the smear-zone, and the mesh characteristic of the drained-zone. When one of these factors changes, Cd must be recalculated. Conversely, Cd is not affected by changes in the soil properties and the discharge capacity of the PVD.