Homogenisation method for braced excavations stabilised with deep-mixed columns

Abstract

The stabilisation of deep excavations using columnar inclusions introduces three-dimensional (3D) complexities into design calculations. Often the intricate nature of the wall-soil-column interaction is simulated using simplified averaging techniques based on elasticity theory. This paper introduces a numerical technique to accurately describe the nonlinear elastoplastic response of both stabilised and natural soft clay for the case of excavations stabilised with deep-mixed columns. The technique allows mapping the 3D problem into a plane-strain (2D) counterpart by replacing the composite material made of natural clay and a region of overlapping deep-mixed columns with an equivalent homogenised material. The stress–strain response of the homogenised continuum is computed with a volume averaging technique (VAT) based on the volume fraction of each component (i.e. clay and column). The technique is implemented into a 2D finite element code enabling an effective representation of the behaviour of each constituent represented by advanced elastoplastic material models. After presenting the theoretical background and implementation procedure, the proposed method was verified against the results from the 3D calculations. The technique emerges as an efficient tool for the numerical analysis of stabilised deep excavations since it allows for plane strain analysis to yield results akin to computationally expensive 3D analysis. Thus, the method can significantly reduce the computational costs and can facilitate the easier incorporation of sensitivity studies.