Many constitutive models are nowadays available to simulate the mechanical behaviour of clays under different loading conditions. For geotechnical engineering applications in a soil dynamics context, the PM4Silt model, as proposed by Boulanger & Ziotopoulou (2018), can simulate the cyclic behaviour of low-plasticity silts and clays. Formulated in a bounding surface plasticity framework, this model adapts the capabilities of a previous model suited for sands and non-plastic silts, i.c. PM4Sand, and enables to simulate more clay-like soil behaviour. In this paper, published calibrations for silts with different plasticity properties are employed to simulate the experimental results of monotonic and cyclic undrained DSS test with the purpose to comment on the effect of some key parameters, including the initial stress ratio 𝐾 and the bounding surface parameter . Numerical simulations are performed with the finite element implementation of PM4Silt in PLAXIS. Besides the two original methods to define undrained shear strength (based on 𝑆􀯨 and 𝑆), a third method is proposed here based on the SHANSEP approach. The application of the model in view of the key parameters is demonstrated by means of a practical example.

Hoek & Brown (HB) failure criteria have been employed over the past decades in common engineering applications due to their extended capability to capture the non-linear yielding of different types of rocks. Often implemented within a perfect plastic framework, this constitutive approach is here enhanced by introducing a softening rule to simulate the post-peak behaviour of rocks in the brittle regime. For this purpose, the degradation of the material properties has been expressed as a function of an internal variable (i.e., the cumulated value of deviatoric plastic strains) which allows one to simulate the rock failure resulting from dilating shearing. Furthermore, to accurately describe the non-linear dilatancy after the peak, the same hyperbolic trend has been applied also to the material properties governing the expression of the plastic potential. The performance of these constitutive equations has been inspected through parametric analyses to emphasize the role of the softening parameters at material point level, as well as to study the strain localization potential of the Hoek & Brown model with Softening (HBS). As a further validation, the shear band angles predicted with the theory have been compared by performing the same tests with finite element code PLAXIS 2D, thus confirming the model capability to simulate failure mechanisms within a strain localization regime.

This paper presents the implementation, validation, and application of the PM4Sand model (version 3) formulated by Boulanger and Ziotopoulou (2015) in the PLAXIS finite element code. The model can be used for modelling geotechnical earthquake engineering applications, especially in the case liquefaction is likely to occur. The PM4Sand model represents an improvement of the elasto-plastic, stress ratio controlled, bounding surface plasticity model for sands formulated by Dafalias and Manzari (2004). The two-dimensional version has been implemented in PLAXIS and compared to the original implementation by Boulanger and Ziotopoulou (2015). The original implementation has been used in explicit finite difference simulations which can be sensitive to the size of the returned stress increment, based on the chosen time step size and loading rate. Therefore, the user needs to evaluate the sensitivity of the solution with respect to the chosen time step sizes. On the contrary, in the finite element method used here, the default time step together with the sub-stepping used at the constitutive model level provide a robust solution independent of the size of the returned stress increment.

In this paper, a constitutive model for masonry structures is presented. It is based on the Jointed Rock (JR) model with overall Mohr-Coulomb (MC) failure criterion, and it is implemented as a user-defined soil model in the finite element
code PLAXIS. The Masonry model is a linear elastic-perfectly plastic model capable of simulating the macroscopic, anisotropic response of masonry structures, by making use of different potential sliding planes (directions) with
different strength properties. A Coulomb criterion is used to simulate failure in each plane, whereas an overall Mohr-Coulomb criterion is used to represent failure of the masonry as a whole. The model is verified against analytical
formulations and validated against experimental data. Particular focus is given to its practical application, considering the response of a masonry structure located in Groningen (the Netherlands) under seismic excitation. A soil profile at a specific location between Loppersum and Huizinge is employed, and soil properties are determined based on available geotechnical data. Clayey soil layers are modelled using the Generalised Hardening Soil (GHS) model. Sandy soil
layers are modelled with the PM4Sand model. The liquefaction potential is also assessed under certain seismic conditions. The masonry, assumed to be shallow-founded, is subjected to an induced strong ground motion, and its response is studied via the proposed constitutive model.