Clay-rich geological formations are considered as host rocks for deep geological disposal of radioactive waste. Over the long term, gas will be produced and will migrate through the surrounding geological formation. Gas transport mechanisms have been investigated in laboratory tests. However, the effects of material heterogeneity remain insufficiently explored. This paper presents a stochastic analysis of two-phase flow in clays under gas injection, incorporating spatially correlated porosity. The study evaluates the effects of sample size, gas injection pressure, and the choice between two-dimensional (2D) and two-dimensional (3D) conditions on the statistical outputs, including mean behaviour and variability. The results indicate that larger samples exhibit reduced variability in the degree of saturation and gas permeability due to enhanced averaging effects. Moreover, the variation in results is higher under high gas injection pressure compared to low gas injection pressure. In addition, the variability of results is significantly reduced in 3D simulations compared to 2D, with high-permeability regions more likely to form continuous pathways under 3D conditions, emphasising the necessity of accounting for 3D effects. The findings indicate that sample size is a critical factor in experiments, as it influences the number of tests required to achieve results within a desired level of accuracy.

Despite the advantages of using Bayesian networks for probabilistic risk assessment, adoption in practice has been limited due to the lack of realistic, facility-scale studies. Scaling up from systems to facility-level safety assessments poses challenges in (i) integrating external hazards and their cascading effects, and (ii) resolving non-homogeneity of various technical and human reliability models. The novelty of the study is in formalising risk integration using Bayesian networks, at facility scale, and demonstrating its effectiveness in addressing associated challenges. A Bayesian network-based multi-hazard risk framework is introduced and demonstrated for a nuclear power plant subject to flooding and earthquake hazards, capturing dependencies among hazards and consequences. Individual reliability models – conventionally extraneous to facility-wide risk models – are included as subnetworks by using Bayesian network-based surrogate models for technical systems and a Bayesian networks approach for human reliability modelling. Two approaches are used for subnetwork integration – object-oriented and unified Bayesian networks. The unified approach allows for prediction, diagnostics and inter-causal reasoning since Bayesian inference is bi-directional. Conversely, in the object-oriented approach, diagnostics are limited to within individual subnetworks and as a consequence the model can potentially neglect dependencies between objects. However, the object-oriented model requires only 50 % of the computational memory and consumes less than 25% of the runtime as the unified network, while improving visual clarity of the risk model. The model reveals key insights – for example, variations in operator stress or available response time during a hazard event can result in up to a 77 % change in top event probability – demonstrating its effectiveness in capturing critical relationships in complex, facility-scale risk scenarios. These findings can be used to suitably allocate resources towards risk mitigation and plant safety management.

The anisotropic behaviour of sands, which is associated with their grain-scale microstructural characteristics such as the distribution of voids and the spatial orientation of particles, can lead to significant variations in macro-scale predictions. In this paper, a bounding surface plasticity based anisotropic semi-micromechanical constitutive model is developed, within the multilaminate framework, to describe the effects of fabric on the cyclic behaviour of sands. A novel plastic strain driven semi-micromechanical fabric evolution framework fulfilling the premises of anisotropic critical state theory is proposed. Rather than using a single scalar-valued fabric anisotropic variable, which is the general practise in anisotropic critical state theory based models, independently evolving fabric anisotropic variables are employed at so-called sampling planes. In addition, the semifluidised state concept is utilised at low mean effective stresses to realistically capture post-liquefaction responses, including large shear deformations and accumulative plastic strains during flow liquefaction and cyclic mobility types of behaviour. The procedure for calibrating model parameters is briefly described and the prediction capabilities of the proposed model under drained and undrained monotonic and cyclic loading conditions at different stress states, relative densities and loading orientations are demonstrated by simulating experimental data for Toyoura sand using a single set of parameters.

Three-dimensional and spatial variability effects on slope failure processes are investigated for an idealised slope stability problem with the random material point method (RMPM). A 45 degree slope is brought to failure by either its own weight or by a combination of its own weight and an additional surface load applied at the crest. The ultimate failure load and potential failure processes are studied for various (heterogeneous) material strength profiles. In 3D, failures tend to spread sideways and backwards. For the slope geometry considered, the resistance to initial and secondary failures in 3D simulations tends to be higher than in 2D simulations, probably due to the additional resistance from the ends of the failure surfaces. The failure behaviour changes when a depth trend in the material strength is introduced. A depth trend in the material strength triggers a flow-like failure process, instead of distinct (approximately) circular failure surfaces which are encountered in a material without a depth trend. The flow-like behaviour causes an expansion in the failure zone in all directions while avoiding (where possible) local strong zones.

Geological materials exhibit spatial variability in their properties as a result of their formation. Many studies have focussed on how to characterise this spatial variation by means of the correlation length θ. Such a characterisation has been applied in the geotechnical design of geostructures at numerous sites where cone penetration tests (CPTs) were available, because θ can be relatively easily estimated from this in-situ information. However, the CPTs available at a given site are often part of the initial site investigation, and hence carried out before the application of any ground improvement technique. This raises the question of how (and by how much) the estimated θ is affected by subsequent stages of the construction project and, more specifically, by the application of ground improvement processes intended to alter the initially poor mechanical condition of the in-situ soil. This paper investigates in-situ data from three trial test sites, where CPT data before and after application of vibro-compaction are available. In addition to the expected overall mechanical improvement of the soil, the application of vibro-compaction has a significant impact on soil heterogeneity, with a substantial reduction in the coefficient of variation and θ of the cone tip resistance and sleeve friction.

This paper investigates the implementation of a nonlocal regularisation of the material point method to mitigate mesh-dependency issues for the simulation of large deformation problems in brittle soils. The adopted constitutive description corresponds to a simple elastoplastic model with nonlinear strain softening. A number of benchmark simulations, assuming static and dynamic conditions, were performed to show the importance of regularisation, as well as to assess the performance and robustness of the implemented nonlocal approach. The relevance of addressing stress oscillation issues, due to material points crossing element boundaries, is also demonstrated. The obtained results provide relevant insights into brittle materials undergoing large deformations within the MPM framework.

As the Material Point Method (MPM) uses both a mesh and a point discretisation scheme, the application of boundary conditions is difficult, currently limiting the flexibility of the method. While many boundary condition options have been used in the literature, the accuracy of Neumann boundary condition options has not yet been studied. Four options have here been evaluated for 1D and 2D benchmarks, although none of the options were found to be both accurate and generally applicable in MPM. However, for the generalised interpolation material point method (GIMP), the application of surface tractions on support domain boundaries or on a detected surface are valid options. Large differences between these two accurate options and the application of tractions at surface material points, a method regularly used in the literature, have been observed.

The stability of six regional dyke cross-sections in the Netherlands was re-assessed using the random finite element method (RFEM), which explicitly accounts for the spatial variability of strength parameters. The RFEM assessments of the cross-sections were shown to result in significantly narrower response distributions than those obtained by ignoring the spatial variability, and therefore would result in more economical designs. Given the complexity of RFEM for applications in daily engineering practice, the results obtained from the re-assessments of the six dyke cross-sections were used to propose partial factors that can be used in practice to achieve the desired reliability levels for regional dykes. When applied in a conventional semi-probabilistic assessment of a dyke cross-section, these partial factors would result in the same level of reliability as would have been obtained by carrying out an RFEM analysis of the same cross-section.