Drained solution for cylindrical cavity expansion in modified Cam clay soil under constant vertical stress

Cavity expansion is a fundamental theoretical problem in geomechanics. For the cylindrical cavity expansion problem, derivations of solutions are usually based on the assumption that the soil is subject to the plane strain condition. However, this is untrue for cavity expansion in pressuremeter tests. This study first derived the equilibrium equation for cylindrical cavity expansion under the constant vertical stress condition. Then, the equilibrium equation was solved for modified Cam clay soils with different overconsolidation ratios (OCRs). The solutions were compared with the responses in the same soils under the plane strain condition. It was found that the ratio of the limiting cavity pressure in the latter to that in the former ranged from 1.31 to 2.76 and increased with an increase in the OCR. Under the constant vertical stress condition, significant heaving occurred in the vicinity of the cavity, and volumetric strain evolved from contraction to dilation as the OCR increased. Significant differences were noted in the stress paths of the two different loading conditions. These results indicate that the assumption of the plane strain condition will lead to overestimation of the limiting cavity pressure and inaccurate prediction of the stress path in the pressuremeter test, especially for heavily overconsolidated soils.

Thermo-Mechanical Response of Multilayered Cylinders Under Pressure and Thermal Loading With Generalized Plane Strain Condition

Multilayered cylindrical structures subject to pressure and thermal loading are commonly seen in many industries. In this study, the formulas for multilayered cylinders under pressure and thermal loading are derived with an assumption that the cylinders meet generalized plane strain condition, i.e., there is no external constraint in the axial direction and the axial growths of the cylindrical layers are the same. A numerical solution procedure for double-layered cylinders subject to both pressure and thermal load is developed and implemented in a mathcad program. To validate the solution, a finite element model for a double-layered cylinder is prepared with abaqus, and its responses under pressure and thermal loading are compared to those from the mathcad program. The algorithm of the method can be extended to three or more layered cylinders. The method developed in this study allows quick optimization and efficient design refinement for multilayered cylinders without running finite element analysis (FEA).

Analytical Solution of Mixed Boundary Value Problems Using the Displacement Potential Approach for the Case of Plane Stress and Plane Strain Conditions

Two elastic plate problems made of duralumin are solved analytically using the displacement potential approach for the case of plane strain and plane stress conditions. Firstly, a one end fixed plate is considered in which the rest of the edges are stiffened and a uniform load is applied to the opposite end of the fixed end. Secondly, a plate is considered in which all of the edges are stiffened and a uniform tension is applied at its both ends. Solutions to both of the problems are presented for the case of plane stress and plane strain conditions. The effects of plane stress and plane strain conditions on the solutions are explained. In the case of stiffening of the edges of the plate, the shape of the plate does not change abruptly, which is clearly observed in both of the cases. For the plane strain condition, the plates become stiffer in the loading direction as compared to the plane stress condition. For the plane strain condition, there is a significant variation of the normal stress component, σzzat different sections of the plate. The graphical results, clearly identify the critical regions of the plate for the case of the plane stress and plane strain condition.