Model‐Free Data‐Driven Computational Analysis for Soil Consolidation Problems

ABSTRACT Soils are inherently uncertain natural materials. In geotechnical engineering, soil properties are fundamentally characterised by testing small samples. The results will then be utilised to determine appropriate geomaterial constitutive models and associated parameters for implementation in conventional computational procedures such as finite element analysis (FEM). However, the accuracy and generalisation capability of such analyses largely depends on the selection of models, which may vary according to the specific applications. To overcome these limitations, computational approaches that do not rely on predefined soil constitutive models are emerging. In this paper, the formulation of data‐driven computing for fluid transport in porous media with particular reference to soil consolidation is derived. This does not rely on any constitutive flow law or models; instead, it directly uses the experimental data on fluid transport properties to compute fluid phase distribution during transient changes of the porous skeleton. For a discretised domain, the data‐driven solver assigns each element or quadrature point a state from an experimental dataset, satisfying mass conservation condition and fluid pressure gradient definition simultaneously. By introducing a penalty function defined by the quadratic distance between local state and material state, the problem is formulated as a constrained minimisation task solved explicitly by the Lagrange multipliers method. Subsequently, several cases were analysed using the proposed data‐driven method and compared with analytical and finite element (FE) solutions. In these tests, the data‐driven method shows good accuracy and convergence properties with further discussion on the influence of the scale and noise level of the dataset.