Piled embankments are traditionally designed by using either guidelines based on simplified limit-equilibrium theories or advanced finite-element (FE) numerical analyses. Both methods have limitations: the former do not allow the assessment of settlements at the top of the embankment, whereas the latter easily become overly complex, hence limiting practical applications. This paper introduces a new mathematical model capable of reproducing, with minimal computational effort, the mechanical response of piled embankments modelled by means of FEs. The model is based on a set of fundamental principles, assumptions and phenomenological equations obtained from a deep understanding of the mechanics behind the FE problem. The model, evaluating average and differential settlements at the top of the embankment during the consolidation of the soft soil, is validated against full-scale test data and benchmarked against independent numerical results. The results are compared with existing formulas to evaluate the critical height of the embankment, demonstrating the great potential of the new model for engineering practice (giving nearly instantaneous displacement-based solutions for the design of piled embankments in a preliminary stage).

Piled foundations are commonly employed to reduce settlements of artificial earth embankments on soft soil strata and geosynthetic reinforcements are installed at the embankment base to increase pile spacing and reduce construction costs. Despite the well-documented effectiveness of this technique, the mechanical processes, developing during the construction in the different elements constituting the ‘geo-structure’, are not fully understood and the design approaches are based on very simplified assumptions. They disregard the deformability of the various elements constituting the system and cannot be employed to estimate settlements. With the aim of introducing a displacement-based design approach to optimise the use of reinforcements and piles, in this article, the mechanical response of the system during the embankment construction is studied by means of large displacement non-linear finite difference numerical analyses, in which the geosynthetic reinforcement is modelled as an elastic membrane. The arching effect developing within the embankment body is described and the evolution of the process zone, where shear strains localise, is discussed. The global system response is described in terms of (i) average, (ii) differential settlements at the top of the embankment and (iii) maximum tensile force within the geosynthetic reinforcement.

Piled foundations are commonly employed to reduce settlements in artificial earth embankments founded on soft soil strata. To limit the number of piles and, consequently, construction costs, popular is the use of geosynthetic reinforcements laid at the embankment base. Nowadays, the complex interaction between geosynthetics, piles and soil is not yet fully understood and, in the scientific literature, simplified displacement-based approaches to choose reinforcements, pile diameter and spacing are missing. In this paper, the authors, starting from the critical analysis and theoretical interpretation of finite difference numerical results, introduce a new mathematical model to rapidly assess both (i) differential/average settlements at the top of the embankment and (ii) maximum tensile forces in the basal reinforcement. The model, conceived to reproduce the response of a pile belonging to the central part of the embankment, is the result of an upscaling procedure based on a suitable sub-structuring of the spatial domain (an axisymmetric unit cell) and on the concept of plane of equal settlements. For the foundation soil, drained conditions are considered, the pile skin roughness is disregarded, and piles are assumed to get the rigid bedrock. As generalised kinematic variables average and differential settlements are employed, whereas as generalized static ones the embankment height and the geosynthetic axial force. The model is validated against field measurements (where layered foundation soil and pile caps are included) and an application example of the model, used as a preliminary design tool in a displacement-based perspective, is finally provided.