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In this manuscript two BMO estimates are obtained, one for Linear Elasticity and one for Nonlinear Elasticity. It is first shown that the BMO-seminorm of the gradient of a vector-valued mapping is bounded above by a constant times the BMO-seminorm of the symmetric part of its gradient, that is, a Korn inequality in BMO. The uniqueness of equilibrium for a finite deformation whose principal stresses are everywhere nonnegative is then considered. It is shown that when the second variation of the energy, when considered as a function of the strain, is uniformly positive definite at such an equilibrium solution, then there is a BMO-neighborhood in strain space where there are no other equilibrium solutions.

A numerical and an empirical method for calculating nonlinear load-settlement curves for shallow foundations on sand are examined and used in a new methodology. Both methods have merits and drawbacks. The drawbacks are overcome by the methodology proposed and verified in the paper. This methodology combines the merits of each method. For this purpose, a modification of the empirical method is proposed that accounts for the finite initial soil stiffness at very small strains. Computer programs with sophisticated nonlinear stress-strain relationships, such as Hardening Soil Small in Plaxis 2D, which are versatile in solving complex foundation problems, can cover strains from very small to large. When the foundation soil is layered, it is proposed to fit such a numerical load-settlement curve against the modified empirical relationship for each sand layer separately. This requires cone penetration tests, measurements of the shear wave velocity, and basic laboratory tests. The methodology is described and applied at two locations where load tests on footings were carried out. At one location there was a top layer of clay, which was also taken into account. The results of the application of the proposed methodology are very good.

Experimental data for the strains and stresses is obtained for some classes of rock, for the compression and tension of a cylindrical sample without lateral loads, and for the triaxial load of a bar. A nonlinear constitutive equation is proposed to fit the data, wherein the infinitesimal strain tensor is assumed to be a nonlinear function of the stress tensor. The constitutive equation requires two sets of materials constants, namely the Young’s modulus and Poisson ratio in tension and compression. Some boundary value problems are studied to see the predictions of the above constitutive theory.

In the context of valorizing local materials at Saharan region for road constructions, a mixture composed of 65% tuff and 35% dune sand (named 65T35DS) was previously studied. The 65T35DS was shown to have the optimum geotechnical and mechanical properties. As an extension, this study consists in investigating the behavior of the 65T35DS mixture under coupled hydro-mechanical loadings. Suction-controlled drying-wetting tests were performed on the 65T35DS statically compacted at the modified Proctor optimum (MPO) state. A series of small-strain cyclic triaxial tests under constant water content condition was then followed. Key findings of this paper include i) the 65T35DS prepared at MPO state is able to resist severe drought condition without inducing significant shrinkage. However, it swells during wetting and the swelling indices are quantified by correlations; ii) the elastic modulus under small-strains is governed by suction and the applied confining stress. The effect of confining stress becomes dominantat lower suction level and negligible when suction increases; iii) at failure, the apparent cohesion drops quickly on the dry side of the MPO, on wet side, it decreases a little. The apparent friction angle decreases for the specimens with water content larger than 5.5%, i.e. wMPO - 5. The studied mixture satisfies the design standards of Saharan pavements and seems to be a good compromise for the valorization of local materials.

Numerička i empirijska metoda za proračun nelinearnih krivulja opterećenje-slijeganje za plitke temelje na pijesku ispitane su i primijenjene u novoj metodologiji. Obje metode imaju prednosti i nedostatke. Nedostaci su prevladani metodologijom predloženom i provjerenom u ovom radu. Ovom metodologijom kombiniraju se prednosti svake metode. U tu svrhu predlaže se promjena empirijske metode kojom se uzima u obzir konačna početna krutost tla pri vrlo malim deformacijama. Računalni programi sa složenim nelinearnim odnosima naprezanje-deformacija, kao što je Hardening Soil Small u Plaxisu 2D, koji su svestrani u rješavanju složenih problema s temeljima, mogu obuhvatiti deformacije od vrlo malih do velikih. Kad je temeljno tlo slojevito, predlaže se takvu numeričku krivulju opterećenje-slijeganje podesiti prema prilagođenom empirijskom odnosu za svaki sloj pijeska zasebno. To zahtijeva statičke penetracijske pokuse, mjerenja brzine posmičnih valova i osnovne laboratorijske pokuse. Metodologija je opisana i primijenjena na dvije lokacije na kojima su provedena probna opterećenja na temeljima. Na jednoj lokaciji nalazio se gornji sloj gline, što je također uzeto u obzir. Rezultati primjene predložene metodologije su vrlo dobri., A numerical and an empirical method for calculating nonlinear load-settlement curves for shallow foundations on sand are examined and used in a new methodology. Both methods have merits and drawbacks. The drawbacks are overcome by the methodology proposed and verified in the paper. This methodology combines the merits of each method. For this purpose, a modification of the empirical method is proposed that accounts for the finite initial soil stiffness at very small strains. Computer programs with sophisticated nonlinear stress-strain relationships, such as Hardening Soil Small in Plaxis 2D, which are versatile in solving complex foundation problems, can cover strains from very small to large. When the foundation soil is layered, it is proposed to fit such a numerical load-settlement curve against the modified empirical relationship for each sand layer separately. This requires cone penetration tests, measurements of the shear wave velocity, and basic laboratory tests. The methodology is described and applied at two locations where load tests on footings were carried out. At one location there was a top layer of clay, which was also taken into account. The results of the application of the proposed methodology are very good.

The problem is a continuation of the research conducted at the University of Warmia and Mazury in Olsztyn, Institute of Building Engineering. It concerns the development of methods for the interpretation of the shear modulus measurements based on the tests conducted on a torsional shear (TS) apparatus. The issue has significant importance in determining the deformation parameters, essential to perform numerical simulations of the interaction between a geotechnical structure and the subsoil. The purpose of this study was to conduct a comparative analysis of the various methods of interpretation of research results based on direct and reverse analysis, as well as automated classification of the first cycle of the relationship between the shear stress and the shear strain components obtained from the TS test. The methodology for verification of the presented interpretative methods consists in carrying out a series of laboratory tests on non-cohesive and cohesive samples of different granulation and state parameters. The course of the research includes the following steps: elaboration of the granulometric composition of several samples of soil, determination of soil index properties and execution of TS tests. Various methods of interpretation of obtained results were taken into account, in addition to conducting a comparative analysis. The study used a non-standard interpretation approach consisting of analysing one-fourth of the hysteresis loop of the first load–unload cycle of the tested samples. The obtained results confirmed the hypothesis that it is possible to estimate the degradation value of the shear modulus based on a part of the TS test results carried out under quasi-monotonic load conditions. The proposed methods of interpreting test results have confirmed their high usefulness, which is devoid of the uncertainty associated with standardised resonant column/TS testing.

A large proportion of the southern UK is underlain by stiff clays. Improving their geotechnical characterisation is important for many current and future infrastructure projects. This paper presents an integrated study of the complex stiffness behaviour of four key medium-plasticity, highly overconsolidated strata: the Gault, Kimmeridge, Oxford and London clays. The latter were deposited between the Jurassic and the Eocene under broadly similar marine conditions. Coordinated programmes of advanced static and dynamic laboratory measurements have been undertaken on high-quality samples, concentrating on samples taken from similar depths at inland sites and including triaxial and hollow cylinder stress path experiments employing high-resolution local strain, multi-axial bender element and resonant column techniques. A new approach was employed to interpret the hollow cylinder experiments and the laboratory measurements are examined in combination with independent field shear wave data. The clays' stiffness characteristics are shown to be markedly anisotropic, pressure dependent and highly non-linear. Synthesis allows key conclusions to be drawn regarding: the relative reliability of alternative measurement approaches; the potential spread of stiffness behaviours between the clays; and whether the clays' varying geological ages and burial depths have any systematic influence on their stiffness characteristics. The results have important geotechnical engineering implications.

Two different methods, power spinning and annealing (PSA), quenching and power spinning followed by annealing (QPSA), for manufacturing the cylindrical parts with ultrafine-grained (UFG) structure were reviewed, the dislocation density and microstructural evolution during the two different processes of PSA and QPSA were further studied. The results show that the required strains for obtaining the UFG structure by power spinning is only 0.92 when the initial microstructure of the material is in the phase of lath martensite. The dislocation density and storage energy are increased to 10 times that of the blank after quenching and power spinning and decreased to the level of the blank after recrystallization annealing. Microstructures with fine grain size after quenching, storage energy of 1.8 &times, 105 kJ/m3 obtained after power spinning and second phase particle with nano-scale precipitated during annealing are the necessary formation conditions for manufacturing the cylindrical parts with UFG structure based on small strains. Compared with the original tubular blank, the mechanical properties of the spun parts with UFG structure improves significantly. The tensile strength and hardness of the spun parts manufactured by QPSA method is 815 MPa and 305 HV, respectively, and the elongation is 17.5%.

cited By 41; International audience; Performance observation is a necessary part of the design and construction process in geotechnical engineering. For deep urban excavations, empirical and numerical methods are used to predict potential deformations and their impacts on surrounding structures. Two inverse analysis approaches are described and compared for an excavation project in downtown Chicago. The first approach is a parameter optimization approach based on genetic algorithm (GA). GA is a stochastic global search technique for optimizing an objective function with linear or non-linear constraints. The second approach, self-learning simulations (SelfSim), is an inverse analysis technique that combines finite element method, continuously evolving material models, and field measurements. The optimization based on genetic algorithm approach identifies material properties of an existing soil model, and SelfSim approach extracts the underlying soil behavior unconstrained by a specific assumption on soil constitutive behavior. The two inverse analysis approaches capture well lateral wall deflections and maximum surface settlements. The GA optimization approach tends to overpredict surface settlements at some distance from the excavation as it is constrained by a specific form of the material constitutive model (i.e. hardening soil model); while the surface settlements computed using SelfSim approach match the observed ones due to its ability to learn small strain non-linearity of soil implied in the measured settlements. © 2009 Elsevier Ltd. All rights reserved.

International audience; Standard nonlinear schemes for the the simulation of elastodynamic problems have several shortcomings when considering high-speed rotations. To tackle these problems, we use a corotational framework and a corresponding specific linearization to design new energy-conserving numerical schemes. In the two-dimensional case, an algorithm preserving also angular momentum is presented. The existence of a solution for the fully discrete setting of this algorithm is established. Numerical results illustrate the flexibility and efficiency of the proposed algorithms.

Tensile test curves of an austenitic stainless steel (AISI 316L) are described through the Voce equation in combination with the kinetic approach to strain hardening analysis proposed by Kocks and Mecking (KM) at temperatures ranging from 700 to 1000 °C with strain rates between 10 −2 and 10 −5 s −1 . The KM approach to strain hardening analysis is used to find the Voce parameters (saturation stress σ V , relaxation strain e C , back-extrapolated flow stress to zero strain σ o ) from the strain hardening rate d σ /d e vs. the flow stress σ . The obtained Voce equations can well describe the flow curves only at large strains in Stage III of strain hardening, while a significant discrepancy occurs at small strains. In order to reduce this discrepancy an improved KM approach is here proposed. The original KM approach assumes that in Stage III of strain hardening the mean free path of mobile dislocations Λ is defined as β / ρ with β constant and ρ the total dislocation density. Λ , and in turn β , are linked to the dislocation cell-pattern typical of Stage III. The proposed improvement of the KM approach consists of assuming that β is not constant at small strains, where dislocations are not organised in cell-pattern, but homogeneously distributed in the material. Based on TEM observations reporting dislocation distributions at small and at high strains, it is proposed that β varies from an initial value at small strains to achieve at high strains the equilibrium value predicted by the original KM approach in Stage III of strain hardening. This assumption provides very good modelling flow curves also at small strains.

This paper presents the analytical development of the cyclic behavior of clays at small strains using the model proposed by Martins (1992) as modifi ed by Alexandre (2006). Initially, discussions about the in fuence of the rate of strain, creep and stress relaxation are presented, which are followed by the development of di fferential equations of simple cases (and their respective solutions either in closed form or numerical) and predictions for some tests carried out by Mortezaie (2012) in a fabricated clay. It is shown that satisfactory predictions were achieved both qualitatively and quantitatively for the presented tests.

This Thesis deals with the determination of Young's modulus and Poisson's ratio from the measurement of small strains (10-3 - 10-5 ) in triaxial tests on the overconsolidated Miocene clay from Moravia (Brno Tegel). The tests were performed in a hydraulic triaxial chamber, fitted with submersible local LVDT sensors, which were fixed directly on the sample. The tests were carried out on undisturbed samples of standard height and diameter (76x38 mm). There were three types of tests - isotropic loading probe, axial loading probe and shear test to the failure. The measured data were analyzed and the results were discussed. The research part of the Thesis briefly describes previous works on stiffness of Brno Tegel and also some works on stiffness of similar material to Brno Tegel - London Clay.

Sociedade Portuguesa de Geotecnia, Universidade do Minho, Instituto Superior Técnico, LNEC, FCT-UNL, FCT, RAVE, REFER

The intensive use of urban subsoil and the evolution of the technical regulations require to develop new tools to calculate the displacements caused by the construction of new structures. The performance of usual calculation methods is often inadequate, because they have been developed mainly for the analysis of the pre-failure behaviour of structures; thus in these models, the soil behaviour for small strains is not well represented. The soil shear modulus exhibits significant variations between the field of very small strains and the field of usual deformations next to geotechnical structures during their construction. Experience shows that the displacements of a structure can not be correctly evaluated without taking into account these variations. Based on a bibliographical study on elastic-plastic constitutive models with non-linear elasticity, a model with few parameters has been chosen, which is nevertheless able to improve substantially the results of displacement calculations of the geotechnical structures. The proposed model is a slightly modified version of the constitutive model established by Fahey and Carter (1993) which has been combined to a Mohr-Coulomb plastic criterion. The main characteristic of the Fahey- Carter-model is that the shear modulus increases with the mean stress and decreases with the shear stress. The model has been implemented in the finite element code CESAR-LCPC. The identification of its parameters, based on classical soil mechanic tests, was an important part of this work. The model was tested by calculating various structures for which soil data as well as displacement and stress measurements were available. These examples confirm the interest of using a complex constitutive law to produce calculation results similar to the strain and displacement patterns of real structures. The present work was also a contribution to CESAR-LCPC's functionalities improvement., L'utilisation intensive du sous-sol urbain et l'évolution des règlements rendent nécessaire de développer de nouveaux outils pour calculer les déplacements induits par un ouvrage au cours de sa construction et lors de sa mise en service. Les performances des méthodes de calcul actuelles restent largement insuffisantes, parce qu'elles ont été développées principalement pour l'analyse des ouvrages vis-à-vis de la rupture, de sorte que le comportement des sols aux faibles niveaux de déformation n'est pas représenté de manière réaliste. Le module de cisaillement des sols varie très fortement entre le domaine des très petites déformations et celui des déformations qui se produisent au voisinage des ouvrages géotechniques lors de leur construction. L'expérience montre qu'on ne parvient pas à estimer correctement les déplacements des ouvrages sans prendre en compte ces variations. A partir d'une étude bibliographique sur les modèles de comportement élastoplastiques à élasticité non linéaire, on a choisi un modèle de comportement comportant peu de paramètres mais susceptible d'améliorer substantiellement les résultats des calculs en déplacement des ouvrages géotechniques. Il s'agit d'une version légèrement modifiée du modèle de comportement proposé par Fahey et Carter (1993) couplée à un critère de plasticité de Mohr-Coulomb. La principale caractéristique du modèle de Fahey et Carter réside dans le fait que le module de cisaillement augmente avec la contrainte moyenne et diminue avec la contrainte de cisaillement. Le modèle retenu a été implanté dans le code de calcul par éléments finis CESAR-LCPC et l'identification de ses paramètres à partir des essais classiques de mécaniques des sols constitue une préoccupation importante de ce travail. Le modèle a été testé en modélisant un certain nombre d'ouvrages réels pour lesquels on dispose à la fois de données de sol et de mesures de déplacements et d'efforts suffisantes. Les premiers exemples de mise en oeuvre du modèle confirment l'intérêt d'utiliser une loi de comportement plus complexe pour reproduire le comportement réel des ouvrages. Le travail réalisé constitue aussi une contribution à l'amélioration des fonctionnalités de CESAR-LCPC.

International audience; The effect of the mean effective stress on the elastic properties of unbound granular materials is a well-known experimental result. Power laws between the mean effective stress and the shear modulus G vhmax of three natural sands are established for isotropic stress paths using bender elements. Triaxial test results reveal that such power laws are also suitable for contracting deviatoric stress paths whereas it is no longer the case for dilating deviatoric stress paths. Fabric changes during shearing are therefore highlighted. These observations seem to be a typical feature of the behavior of granular materials.

This paper presents some new and significant aspects of pre-failure deformation characteristics, particularly stress-strain properties at small strains, of crushed unbound granular materials used in pavement construction. The data was obtained from a series of precision cyclic triaxial tests performed at the Institute of Industrial Science, University of Tokyo, using stress paths and strain levels representatives of pavement field conditions. Based in this data, effects of stress state and strain level in Young’s modulus are discussed to some depth., Cet article présente des aspects nouveaux et significatifs des caractéristiques des geomatériaux, en particulier les propriétés contraintedéformation en petites déformations des matériaux granulaires concassés non traités utilisés dans la construction routière. Les donnés ont été obtenus par des essais triaxiaux cycliques de précision réalisés à l’ "Institute of Industrial Science, University of Tokyo", en utilisant des chemins de contrainte et des niveaux de déformation représentatives dans les chaussées. Ces données ont permis de mettre en évidence les effets de l’état de contrainte et du niveau de déformation dans le Module d’Young.

Very small to large strains properties of a silty sand were measured at several water contents ranging from a few percents to saturation, using three triaxial devices with different types of transducers. In the analysis of the data, attention was focused on the influence of water content on the maximum (Young’s) modulus, the decay of modulus with strain, the effect of the confining stress, etc. Isotropic and triaxial tests, with measurement of negative pore water pressure, were performed on the same material. The effective stress concept, validated by a recent theoretical analysis by Coussy and Dangla (2002), was used to interpret the results. The predictions of a micromechanical model are compared with the experimental data in the elastic domain and on the failure criterion. The method highlights a simple way to relate the strength and stiffness of the soil to its negative pore water pressure.