Simple prediction of the undrained displacement of a circular surface foundation on non-linear soil

Abstract

Textbooks and university courses teach elasticity and plasticity as separate methods for analysing the stiffness and strength of a shallow foundation. The behaviour of real soil is neither linear elastic nor perfectly plastic. In this paper, two simple techniques for incorporating nonlinearity in routine design have been validated using finite element (FE) analysis. These two techniques-Atkinson's method and the mobilisable strength design (MSD) approach-assume that the responses of an individual soil element and the boundary value problem being considered are self-similar. Using this assumption, the soil element response can be scaled to predict the response of the boundary value problem. Atkinson's method is based on elasticity whereas MSD uses plasticity. Non-linearity has been captured in the FE analysis using a power law soil model. This approach uses minimal parameters, but is shown to capture accurately the undrained stressstrain response of typical clays under monotonic loading. Comparison with elastic and plastic solutions showed that the FE analysis was accurate to within < 5% at the elastic and plastic extremes of the loading range. The responses of the soil and the boundary value problem are shown to be sufficiently self-similar up to two-thirds of the failure load for the foundation response to be predicted simply by a linear scaling of the soil response. Previously reported scaling factors for vertical loading are confirmed, and new factors for horizontal and moment loading are derived. These results show that, for this particular boundary value problem, soil non-linearity can be captured with sufficient accuracy for routine design, without recourse to sophisticated numerical analysis. These self-similarity methods are simple enough to be taught to undergraduates, and could be incorporated in textbooks alongside the core sections on elasticity and plasticity, providing guidance on the application of these techniques to real non-linear soil.

Laboratory measurement of strength mobilisation in kaolin: link to stress history

“…For example, deformations are important in the design of offshore wind turbines, both in terms of dynamic structural response under severe loads and due to the vulnerability of the drive and gearbox to tilting of the mast. Research has been undertaken at Cambridge University to define and validate simplified mechanistic models in conjunction with soil stress-strain data to enable routine calculations of footing settlements (Osman & Bolton, 2005;Osman et al, 2007) and the displacement of braced retaining structures (Osman & Bolton, 2006;Lam & Bolton, 2011), for example. The calculation procedure is based on conservation of energy and is known as mobilisable strength design (MSD).…”

Energy-Based Approach: Analysis of a Vertically Loaded Pile in Multi-Layered Non-Linear Soil Strata

“…The pile deflection equation can be solved when the soil and geometry related parameters k, C and m are known; however, these parameters depend on the unknown dimensionless soil function ϕ, which can be estimated by calculating 𝛾 and 𝛾 . Soil displacement is obtained when the initial numbers of these values 𝛾 and 𝛾 , are inserted [39] after Dasari [51]).…”

“…The stiffness of soil was high at a very small strain level and decreases with the increase in the strain [33]. Many researchers [34][35][36][37][38][39] conducted triaxial tests and reported high values of soil stiffness when the shear strains are less than 10 −5 . Several factors including the mean effective stress, void ratio, stress history, rate of loading, soil plasticity for silts and clays, stress anisotropy for sands and the effective confining stress affect the small strain stiffness G max [40][41][42][43].…”

“…where a = G 0 ε n q0 is a constant determined empirically; n describes soil nonlinearity which is equal to (−0.5) according to the experimental data analyzed by Osman et al [39] (Figure 6);…”

Flachgründungen

“…Inzwischen ist dieses Verfahren auf den allgemeinen Fall einer Fundamentbelastung durch Vertikal-, Horizontal-und Momenteneinwirkungen erweitert worden [64], scheint jedoch noch keinen Eingang in die englische Praxis gefunden zu haben, in der wohl das konventionelle Vorgehen als ausreichend angesehen wird. Außer der Winkelverdrehung kann der vom Abstand Dl zwischen Gründungselementen mit den Setzungen s 1 bis s 3 abhängige Krümmungsradius R einer Setzungsmulde oder eines Sattels …”