The expansion of a thick-walled hollow cylinder in soil is of non -self -similar nature that the stress/ deformation paths are not the same for different soil material points. As a result, this problem cannot be solved by the common self -similar -based similarity techniques. This paper proposes a novel, exact solution for rigorous drained expansion analysis of a hollow cylinder of critical state soils. Considering stress -dependent elastic moduli of soils, new analytical stress and displacement solutions for the nonself -similar problem are developed taking the small strain assumption in the elastic zone. In the plastic zone, the cavity expansion response is formulated into a set of first -order partial differential equations (PDEs) with the combination use of Eulerian and Lagrangian descriptions, and a novel solution algorithm is developed to ef ficiently solve this complex boundary value problem. The solution is presented in a general form and thus can be useful for a wide range of soils. With the new solution, the non -self -similar nature induced by the finite outer boundary is clearly demonstrated and highlighted, which is found to be greatly different to the behaviour of cavity expansion in in finite soil mass. The present solution may serve as a benchmark for verifying the performance of advanced numerical techniques with critical state soil models and be used to capture the finite boundary effect for pressuremeter tests in small -sized calibration chambers. (c) 2024 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY -NC -ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

This paper proposes a powerful hybrid Eulerian-Lagrangian (HEL) approach for the analysis of cavity expansion problems. The new approach is applied to analysing the non-self-similar expansion process of a hollow cylinder of critical state soils, considering arbitrary saturation states of soils and both drained and undrained conditions. A closed-form solution for the stresses and displacements in the elastic zone is presented, taking the state-dependent soil moduli and outer boundary effect of the soil cylinder into account. Adopting large strain theory in the plastic zone, the non-self-similar cavity expansion process is formulated into a set of partial differential equations in terms of both Eulerian and Lagrangian descriptions, which is solved by a newly proposed algorithm. The HEL approach is compared with the conventional Eulerian and Lagrangian approaches for the cavity expansion analyses. It is found that the new approach can reduce to the Eulerian approach when the self-similar assumption is satisfied and to the Lagrangian approach when stress-total strain relationships are obtained analytically. Finally, the expansion process is proven to be non-self-similar by showing the stress and deformation paths, and the finite thickness of soil cylinders may greatly influence the cavity expansion behaviour, especially with a small thickness ratio. The HEL approach can provide useful tools for validating advanced numerical techniques for both saturated and unsaturated soils and interpreting pressuremeter tests in small-size calibration chambers.