A new model for the multi-scale simulation of solute transport in concrete is presented. The model employs plurigaussian simulations to generate stochastic representations of concrete micro- and meso-structures. These are idealised as two-phase medium comprising mortar matrix and pores for the micro-structure, and mortar and large aggregate particles for the meso-structure. The generated micro- and meso-structures are employed in a finite element analysis for the simulation of steady-state diffusion of solutes. The results of the simulations are used to calculate effective diffusion coefficients of the two-phase micro- and meso-structures, and in turn, the effective diffusion coefficient at the macro-scale at which the concrete material is considered homogenous. Multiple micro- and meso-structures are generated to account for uncertainty at the macro-scale. In addition, the level of uncertainty in the calculated effective diffusion coefficients is quantified through a statistical analysis. The numerical predictions are validated against experimental observations concerning the diffusion of chloride through a concrete specimen, suggesting that the generated structures are representative of the pore-space and coarse aggregate seen at the micro- and meso-scales, respectively. The method also has a clear advantage over many other structural generation methods, such as packing algorithms, due to its low computational expense. The stochastic generation method has the ability to represent many complex phenomena in particulate materials, the characteristics of which may be controlled through the careful choice of intrinsic field parameters and lithotype rules.

Random field generation through the solution of stochastic partial differential equations is a computationally inexpensive method of introducing spatial variability into numerical analyses. This is particularly important in systems where material heterogeneity has influence over the response to certain stimuli. Whilst it is a convenient method, spurious values arise in the near boundary of the domain due to the non-exact nature of the specific boundary condition applied. This change in the correlation structure can amplify or dampen the system response in the near-boundary region depending on the chosen boundary condition, and can lead to inconsistencies in the overall behaviour of the system. In this study, a weighted Dirichlet–Neumann boundary condition is proposed as a way of controlling the resulting structure in the near-boundary region. The condition relies on a weighting parameter which scales the application to have a more dominant Dirichlet or Neumann component, giving a closer approximation to the true correlation structure of the Matérn autocorrelation function on which the formulation is based on. Two weighting coefficients are proposed and optimal values of the weighting parameter are provided. Through parametric investigation, the weighted Dirichlet–Neumann approach is shown to yield more consistent correlation structures than the common boundary conditions applied in the current literature. We also propose a relationship between the weighting parameter and the desired length-scale parameter of the field such that the optimal value can be chosen for a given problem.

Self-healing cementitious materials with microcapsules are complex multiscale and multiphase materials. The random microstructure of these materials governs their mechanical and transport behaviour. The actual microstructure can be represented accurately with a discrete lattice model, but computational restrictions mean that the size of domain that can be considered with this approach is limited. By contrast, a smeared approach, based on a micromechanical formulation, provides an approximate representation of the material microstructure with low computational costs. The aim of this paper is to compare simulations of a microcapsule-based self-healing cementitious system with discrete-lattice and smeared-micromechanical models, and to assess the relative strengths and weaknesses of these models for simulating distributed fracture and healing in this type of self-healing material. A novel random field generation technique is used to represent the microstructure of a cementitious mortar specimen. The meshes and elements are created by the triangulation method and used to determine the input required for the lattice model. The paper also describes the enhancement of the TUDelft lattice model to include self-healing behaviour. The extended micromechanical model considers both microcracking and healing. The findings from the study provide insight into the relative merits of these two modelling approaches.