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The Plastic Response of Circular Footings on Sand Under General Planar Loading
Geotechnique
Abstract
Data from a set of tests of model circular footings on dense sand are presented. The footings were subjected to a variety of combinations of vertical, horizontal and moment loading. The tests were designed to provide the information necessary to construct a complete model of the footing behaviour, based on the concepts of plasticity theory. In particular, the tests provide detailed information about the shape of the yield surface, and so allow generalization of bearing capacity calculations to cases other than purely vertical loading. Information is also obtained about the hardening law and flow rule appropriate for a plasticity model, and the elastic response within the yield surface.
Nous présentons ici les données provenant d'un ensemble d'essais sur des modèles d'assises circulaires sur un sable dense. Ces assises ont été soumises à une variété de combinations de charge verticale, horizontale et de moment. Les essais avaient été con&ecil;us pour donner l'information nécessaire à la construction d'un modéle complet du comportement de l'assise, en se basant sur les concepts de la théorie de plasticité. Notamment, les essais donnent une information détaillée sur la forme de la surface d'écoulement, ce qui permet de généraliser les calculs de résistance de portée et de les Réndre à des cas autres que les cas de charge purement verticale. Iis renseignent aussi sur la loi de durcissement et la règle d'écoulement convenant à un modée de plasticitéla réastique àieur de la surface d'écoulement.
... In several studies of the tensile resistance of suction caisson anchors, the finite element method has been employed to confirm the influence factors such as the loading rate, the drained condition, the soil permeability, and the caisson dimensions, e.g., Sukumaran et al. [35], Achmus and Thieken [2], Thieken et al. [36], and Ahmed and Hawlader [3]. Hardening plasticity models based on the nonassociated flow rules have been adopted to investigate yield surfaces and plastic potentials for caissons in sand, e.g., Gottardi et al. [11], Houlsby and Cassidy [21], and Fiumana et al. [8]. ...
There has been little analytical research work to clarify the influence of the pullout rate on the ultimate capacity of suction caisson anchors subjected to vertical tensile (V), horizontal (H), and moment (M) loads in soils. In this study, an analytical approach is proposed by employing a three-dimensional displacement method to elucidate the effect of the pullout rate on the ultimate vertical tensile, horizontal, and moment capacities of suction caisson anchors in sands. The vertical displacement of the inside and outside soils adjacent to the skirt of the caisson is obtained from considering the vertical equilibrium of an annular element of the skirt via vertical tractions inside and outside the skirt of a caisson subjected to a vertical tensile load. An appropriate bearing capacity equation for predicting experimental results of suction caisson anchors in sand is proposed. Reasonable agreement is found between the results obtained from laboratory and field tests and those predicted by the present method, comparing the relationships among the capacity, suction, and displacement of suction caisson anchors in sand subjected to inclined tensile loads with various pullout rates. Failure envelopes in the H–V plane are shown taking into account the effect of the pullout rate on the ultimate inclined tensile capacity for a suction caisson anchor in sand.
... Later on, other studies were done to model shallow foundation behaviour using macro-element method by Gottardi, Houlsby, and Butterfield (1999), Cremer, Pecker, and Davenne (2001), Grange, Kotronis, and Mazars (2008), and Grange, Kotronis, and Mazars (2009). In addition, Martin and Martin (1994) applied the same concept but in case of offshore foundations. ...
Geotechnical engineering is a crucial field in the design and construction of foun- dations, embankments, tunnels, and other structures interacting with soil and rock. However, the description of the elastoplastic response of soil, with preponderant non- linear and non-reversible deformations together with a non-associative flow rule, is complex. The difficulty is even higher in the case of non-monotonous loading paths where phenomenological constitutive relations require ad-hoc history parameters and advanced experimental tests for their calibration.
Discrete element method has been proved to be an effective method in predicting quantitatively the constitutive response of soils, even in the case of complex loadings (with rotation of principal stress directions, or loading/unloading cycles) where con- ventional elastoplastic constitutive relations may fail to simulate realistic responses. For granular soils with a narrow grading, a direct representation of soil grains by polyhedral particles or with the level set method is possible, whereas for finer soils, or soils with a wider grading, alternative solutions should be considered. Spherical particles with enriched contact laws (e.g. by introducing rolling resistance at the contact) or rather simplified clumps of spheres can be used to keep the model rel- atively light to tackle further boundary value problems with limited computational cost. However, even if the models provide satisfying results for direct shear tests or drained triaxial compression loading paths compared to experimental measurements, their validation with respect to more complex loading paths as the isochoric com- pression or the path at constant stress deviator still present difficulties, in particular for initially loose granular assemblies.
First, this study aims to compare such different approaches in terms of the prediction abilities at the macroscopic scale of the constitutive responses of soils, particularly for complex loading paths. Two kinds of discrete models are considered: (i) spherical particles with rolling resistance, (ii) simple clumps made of 2 to 6 spheres. The mod- els are calibrated from two drained triaxial compressions on dense and loose Hostun sand. They are then assessed, according to the macroscopic response, on loading paths significantly different from the calibration loading paths (isochoric compres- sions, circular stress paths in the deviatoric plane, constant deviatoric stress path, etc.).
Then, we investigate the importance of the description of the anisotropy of the initial fabric and of the inter-particle friction law in the simulated responses of loose gran- ular assembly to different kinds of loading paths. It shows how the combination of both can modify importantly the simulated responses to some kinds of loading paths. This investigation is carried out for a numerical discrete model made of spheres by comparison with experimental results on sand.
Finally, the model is used to simulate the nonlinear interaction between a shallow foundation of building structure and the supporting soil during strong seismic load- ings, as tested experimentally for the TRISEE project with a full scale physical model. An adaptative discretization technique is implemented to limit the number of particles in such a boundary value problem and make the computation possible with a conventional desktop computer. Numerical results are benchmarked against experimental measurements from the TRISEE project, and FEM numerical simula- tions or macro-element models.
... Offshore wind turbines are subjected to combined loading conditions, including vertical, lateral, and moment loads, induced by wind, waves, currents, and man-made loadings (Houlsby et al., 2005;Wang et al., 2019). The combined loadings envelope was often scaled by the vertical load capacity, therefore the assessment of the vertical load capacity of the bucket foundation is necessary to design and analysis more complex loading conditions for offshore wind turbines (Gottardi et al., 1999). More significantly, applied vertical compressive loads increase the effective confining stress in soil elements beneath the skirt, substantially increasing the horizontal-moment load capacity of the bucket (Achmus et al., 2013). ...
Bucket foundations are circular surface foundations with thin skirts around the circumference. They have been successfully installed using economical suction or vibratory methods. Large-diameter buckets, up to 22 m, have been successfully deployed. In offshore wind power applications, bucket foundations are commonly configured in a tripod arrangement for fixed foundation wind turbines. While bucket foundations may be subjected to complex conditions of combined loading, this study presents an in-depth focus on a single loading mode: vertical compression. This study presents a finite element investigation of the performance and vertical load capacity of skirt foundations installed in the sand and subjected to vertical load passing through the bucket center. To take advantage of symmetry for problem geometry and applied load, an extensive parametric study was performed in this research utilizing an axisymmetric (two-dimensional) finite-element analysis employing the non-associated flow rule of the Mohr-Coulomb soil model. Comparisons to previously published 3D FE and experimental studies showed good agreement. The results showed that the pure vertical capacity of the bucket foundation significantly depends on skirt diameter D, aspect depth ratio (L/D), and relative density Dr. This research introduced simple design charts relating the vertical bearing capacity of skirted foundations to aspect ratio, diameter, and relative density.
This paper introduces a numerical investigation aimed at evaluating the Vertical, Horizontal, and Moment (VHM) yield surface of suction anchors. It employs a generalized elliptical function guided by a predefined fitting strategy. The resulting yield surfaces are then juxtaposed with findings from previous studies, establishing the groundwork for the macro model of suction anchors in clay. This model plays a pivotal role in the integrated analysis of mooring systems for floating wind turbines.
This paper considers the possibility of constructing a three- dimensional failure envelope for a shallow sand-supported footing. Earlier two- dimensional work is outlined and data taken from a number of sources to produce best-fit eliptical cross-sections. Equations are then presented for a complete three-dimensional failure envelope, comprising a system of inclined elipses and intersecting parabolas. The equations are normalised and compared with test data. It is suggested that the three-dimensional surface will provide a simpler method for predicting failure loads and the effect of specific combinations.
Extensive data of the strength and dilatancy of 17 sands in axisymmetric or plane strain at different densities and confining pressures are collated. The critical state angle of shearing resistance of soil which is shearing at constant volume is principally a function of mineralogy and can readily be determined experimentally within a margin of about 1 degree , being roughly 33 degree for quartz and 40 degree for feldspar. The extra angle of shearing of 'dense' soil is correlated to its rate of dilation and thence to its relative density and mean effective stress, combined in a new relative dilatancy index.
p>The thesis is concerned with the behaviour of rigid surface strip footings on sand when subjected to eccentric and/or inclined loads. Experiments have been performed in two apparatuses, the one having a three times greater sand-bed width than the other, together with a preliminary investigation in a smaller apparatus. The bearing capacity predictions from various published theoretical and semi-empirical solutions are compared with the experimental results. Contact stress distributions which were measured in each case are also presented. The effect of the tank to footing width ratio on the bearing capacity and the contact stress distribution is examined by means of comparative results from nominally identical tests. The deformation of the sand mass has been measured by both X-ray and Stereo photogrammetric techniques and representative results obtained by each method are presented and discussed. The effect of the sand-glass friction on the photogrammetrically measured displacement fields has been investigated by comparing results obtained from identical load increments in identical tests~using each of the techniques. A new rational approach to the bearing capacity problem, based upon concepts from plasticity theory, and supported by the author's experimental evidence, has been advanced. This analysis, which utilises the concept of the plastic potential, describes the planar translation of a footing in a very satisfactory way under inclined central loads both qualitatively and even quantitatively in tests carried out so far. Finally, a generalization of the analysis has been devised to cover the case of footings under general loading, its potentialities have been discussed with particular reference to offshore oil platforms and areas recommended for future research in this field.</p
Prediction of the ultimate load capacity of shallow, sand supported foundations carrying vertical (Y), horizontal (H) and moment (M) loads is a fundamental offshore engineering problem. The paper demonstrates how the complete failure envelope of such a foundation, represented by a system of parabolas and rotated ellipses, can be transformed into either a 45° inclined straight line or a unit circle by referring the applied loads to an origin located below the foundation centreline. The conjugate transformation applied to the corresponding displacements generates a symmetry amongst them, for symmetrical load paths, not otherwise apparent. Extensive, model-scale, experimental data are presented that provide strong support for the simple, transformed failure-envelopes.
The method of characteristics is used to establish consistent factors for the vertical bearing capacity of circular and strip footings on soil which satisfies a linear (c, phi) Mohr-Coulomb strength criterion. This method of solution avoids the assumption of arbitrary slip surfaces, and produces zones within which equilibrium and plastic yield are simultaneously satisfied for given boundary stresses. Although similar solutions have previously been published for circular footings, their application has been hindered by errors and confusions over terminology. These are resolved, and the method of solution is explained. It is confirmed that Terzaghi's approach to the superposition of bearing terms containing N-q, N-y, and N-c is both safe and sufficiently accurate for circular footings, as for strip footings. The values to be adopted are tabulated as functions of phi. Differences between the factors applicable to circular and strip footings far exceed the allowances of the empirical shape factors in common use. Some new shape factors are suggested that better represent the relationship between the limiting equilibrium of circular and strip foundations. Some current shape factors attempt to allow simultaneously for the differences in equilibrium solutions and the differences in axisymmetric (triaxial) and plane strain soil parameters. This cannot succeed, since the relationship between strength parameters depends strongly on relative density. The new bearing factors facilitate a more rational approach in which soil parameters appropriate to the geometry can first be determined and then used to find appropriate bearing capacity factors.