This article presents the findings of a comprehensive assessment of the predictive capabilities and limitations of advanced geotechnical numerical tools utilizing two sophisticated constitutive models for sands: the hardening soil model with small strains and hypoplasticity with intergranular strain. The evaluation is based on simulations of laboratory and centrifuge tests under monotonic and cyclic loading conditions. Initially, these models were calibrated and assessed using an experimental database on Fontainebleau sand. This database encompasses a range of laboratory results, including isotropic compression, drained monotonic triaxial, and undrained cyclic triaxial tests with varying initial conditions. The models, in general, provided good representation for monotonic experiments while some discrepancies were observed in undrained cyclic experiments. Subsequently, the calibrated models were employed to replicate a series of centrifuge tests involving a pile embedded in the same sand. The pile was subjected to various episodes of monotonic and cyclic lateral loading. In general, the models accurately replicated the experimental observations from tests conducted under monotonic loading conditions. Some small discrepancies were found in pile tests subjected to cyclic loading, these were however minor when compared to issues in predicting cyclic element tests at undrained conditions.

In this paper, a new approach for rotational hardening in elastic-plasticity is formulated. After discussing the standard yield criteria employed for geomaterials and the rotational hardening models proposed in the past, the authors introduce the concept of pure rotational hardening, that is a rigid rotation of the yield surface not implying any distortion of it. In the second part of the paper, a new approach for rotational hardening, based on Householder transformations, is proposed. The method, that allows to reflect vectors with respect to a given hyper-plane, is briefly described since not usually employed in geomechanics. Moreover, the authors clarify that any yield surface or plastic potential rotation, not being a rolling, is a transformation keeping unaltered first and second invariants, but not the third. As a consequence, when rotational hardening is introduced, the use of the third mixed invariant, for defining in the deviatoric plane the yield surface shape, is not appropriate. Finally, the application of the proposed approach in the formulation of anisotropic elastic-plastic strain hardening constitutive models is briefly discussed for the classes of uncoupled and hybrid yield criteria that include a dependence of the yield surface on Lode angle.

This paper proposes a coupled hydro-mechanical constitutive model for unsaturated clay and sand (CASM-U) in a critical state framework. The mechanical behaviour of unsaturated soils is modelled by modifying the unified clay and sand model (CASM) with Bishop's effective stress, bounding surface concept and loading collapse (LC) yield surface. The hydraulic behaviour is described by a soil-water characteristic curve (SWCC) with nonlinear scanning law, considering the coupled effects of soil deformation and hysteresis. CASM-U is implemented into a commercial finite element software through the user-defined material subroutine (UMAT), and the implementation is benchmarked by a new semi-analytical cavity expansion solution adopting CASM-U. Finally, the performance of CASM-U in predicting hydro-mechanical behaviour of unsaturated clays and sands is examined by comparing with experimental data from tests along various loading paths, including isotropic compression, cyclic drying-wetting, triaxial shearing, and their combinations. It is shown that CASM-U can provide reasonable predictions for hydro-mechanical behaviour of unsaturated soils with a total of 15 material parameters.

The elasticity law is a great challenge in soils, due to the well-known non-linear, anisotropic, pressure-dependent soil response even at negligibly small strains. A new hyper-elastic formulation is proposed, based on a polynomial expression (including a fabric tensor defining the elastic anisotropy) with two branches, one for the negligibly small stresses, ensuring good convergence properties at low confining pressure, and one for the soil response at intermediate strains, corresponding to stress states inside a single large-sized, yield surface defining the occurrence of large irreversible strain. Typical numerical simulations are discussed for isotropic and oedometric compression and swelling tests, and for undrained triaxial compression tests. The results are compared with those obtained with similar hyper-elastic models proposed in the literature. A comparison with experimental oedometric and drained and undrained triaxial tests on undisturbed samples of London clay is provided, revealing that the proposed model has great flexibility in selecting both the shear stiffness and the evolution of elastic anisotropy, which can be chosen independently, thus providing a general applicability. For instance, the great flexibility of the proposed hyper-elastic formulation can be exploited to model the non-linear swelling curves typically observed in oedometric swelling tests of structured clays or active clays.

This paper reports the second part of the keynote lecture, whose part I has been already published in this journal, presenting extensive experimental research on the investigation of clay microstructure and its evolution upon loading. Whether the first part focused on the micro to macro behaviour of different reconstituted clays, this part instead concerns the microscale features of the corresponding natural clays, their changes under different loading paths and the ensuing constitutive modelling implications. The experimental investigation is carried out according to the methodology outlined in the part I-paper, hence micro-scale analyses are presented on natural clays subjected to macro-scale mechanical testing, with the purpose to provide experimental evidence of the processes at the micro-scale which underlie the clay response at the macroscale. As for the reconstituted clays in the part I-paper, original results on stiff Pappadai and Lucera clay, this time in their natural state, are compared to literature results on clays of different classes, either soft or stiff. The results presented in this paper, together with those discussed in the part I, allow for a conceptual modelling of the microstructure evolution under compression of natural versus reconstituted multi-mineral clays, providing microstructural insights into the macro-behaviour described by constitutive laws and advising their mathematical formalization in the framework of either continuum mechanics or micro-mechanics.

This paper presents a novel critical state model for both clay and sand considering the inherent and induced anisotropy, named as CASM-h. The CASM-h model is developed based on the wellcalibrated CASM model and incorporates the concepts of subloading surface and fabric anisotropy. To describe the induced anisotropy, a hybrid-driven fabric evolution law is proposed, defining fabric evolution as driven jointly by stress and strain rates. Subsequently, the fabric tensor together with its evolution law is appropriately incorporated into constitutive relation by employing the anisotropic transformed stress approach, without introducing additional mechanical mechanisms. The CASM-h model is validated under a series of stress paths, including triaxial tests, simple shear tests, shear tests with fixed principal stress direction as well as principal stress rotation (PSR) tests. The simulation results show that CASM-h model can satisfactorily capture the anisotropic behaviours of both clay and sand, such as the loading direction dependency of strength, non-coaxial behaviour, PSR effects and so on.

The dynamic behaviour of saturated coarse-grained soils has recently received wide attention because of its impact on the seismic performance of geotechnical and structural systems. This is due to the peculiarities of their cyclic response (e.g., liquefaction, ratcheting and volumetric-deviatoric coupling). Consequently, the seismic risk mitigation of the built environment requires efficient predictive models applicable in design and assessment. To this end, several constitutive models have been developed for a realistic description of the cyclic soil behaviour. From this perspective, this paper describes the implementation and testing of the bounding surface plasticity model developed by Papadimitriou and Bouckovalas (2002) in OpenSees as a means for advanced assessment of soil-structure systems. The implemented model includes essential features of the cyclic soil response. Moreover, a modified fabric tensor evolution equation is introduced for improving the response and numerical stability in boundary value problems, at the cost of an extra model constant. The workflow concerning the integration of the model into OpenSees is presented, followed by instructions about its use in boundary value problems. A comprehensive verification of the model response is discussed. The numerical simulations demonstrated the robustness of the implemented code in capturing soil behaviour from small to large strain levels.

This study presents a novel formulation for incorporating anisotropy into the generalized plasticity constitutive model. Generalized plasticity is a hierarchical framework allowing for extensibility, in order to encompass new phenomena and improve its predictive capabilities. Anisotropy formulation is based experimentally on the phase transformation state and considers explicitly the direction of the maximum principal stress and the magnitude of the intermediate principal stress, through an anisotropy state variable that contributes to the state parameter. Additionally, the model incorporates the fabric using an evolving fabric variable that reflects initial fabric due to sample preparation method for granular soils. The formulation is simple and introduces three constitutive parameters, allowing for straightforward implementation into the constitutive model and direct application in finite element analysis. The model is validated with undrained triaxial tests conducted on Toyoura sand, covering a wide range of initial conditions with a unique set of constitutive parameters, and yielding overall satisfactory results despite some limitations.

Geotechnical processes related to offshore monopiles for supporting OWTs in soft clay involve intermittent episodic remoulding during storm events and reconsolidation during calm conditions. To assess the resulting response of monopiles, this study employs a three-dimensional finite element analysis. The methodology incorporates a kinematic hardening soil constitutive model within the critical state framework, calibrated against cyclic triaxial experiments and validated against the centrifuge test results on a 6m diameter monopile in soft clay subjected to multiple episodes of cyclic loading and reconsolidation. Thereafter, we investigate the performance of a reference 15MW OWT supported on a 10m diameter monopile in clay, subjected to three ten-minute storms of combined wind and wave loading representative of a 10-year return period, with reconsolidation periods between each storm. The results show a reduction in effective stress around the monopile during storms followed by recovery during reconsolidation, leading to a reduction in the level of monopile displacement accumulated in each subsequent storm event. This beneficial effect is overlooked in design practice, but can be anticipated through the approach presented here, which can form the basis for the validation of a digital twin that monitors the lifetime integrity of a monopile foundation.