title: Hydro-mechanical network modelling of porous geomaterials
Creators: name: Athanasiadis, Ignatios
Publisher: name: University of Glasgow
Year: 2017
Subjects: subject: Network model, periodic boundary conditions, hydro-mechanical, coupling, microstructure, conductivity, degree of saturation, calibration, verification, representative volume element.

description: The microstructure of porous geomaterials strongly influences macroscopic hydro-mechanical properties, such as fluid retention, conductivity and stiffness. These properties are of importance for predicting the performance of many engineering applications, such as waste barriers and flood defence embankments. Predicting these properties with confidence requires a thorough understanding of processes at the microscale and their effect on macroscopic phenomenological properties. For unsaturated geomaterials, providing this understanding requires still further research. In this study, network models representing processes in the pore structure and solid skeleton were developed with the aim to improve the required understanding to link processes at the micro-scale to macroscopic properties. The objectives were to develop a new coupled hydro-mechanical network model, with main application the improvement of understanding of the influence of microstructure on the retention behaviour and conductivity of porous geomaterials, the mechanical response in the form of the elastic stiffness, and their interaction. The model is valid for investigation of transport and mechanical aspects geomaterials such as concrete, rocks, sand and clay soils with length scales of the pore radii spanning from sub-μm to mm. In the present network models, the microstructure of the material is idealised by means of a network of voids for the transport response and a network of grains/particles representing the solid skeleton response. For the transport network, the void structure is idealised by spheres representing large voids and pipes for the interconnecting narrow throats. The structural network of grains is modelled by rigid polyhedra connected by springs which contain information related to the constitutive response of the skeleton. The geometry of the networks is determined by dual irregular Delaunay and Voronoi tessellations based on random sets of points. For the transport network, the spheres and pipes were placed on the Voronoi polyhedral vertices and along the ridges, respectively. The mechanical elements were placed on the edges of the Delaunay tetrahedra. In addition to the irregular arrangement of elements, microstructural heterogeneity was introduced by assigning the radii of the spheres and pipes as well as the polyhedra contact areas from probability distributions. New techniques to provide Periodic Boundary Conditions for representative cells generated by the irregular networks were developed. Another new feature of the model is a pore scaling technique which improves The microstructure of porous geomaterials strongly influences macroscopic hydro-mechanical properties, such as fluid retention, conductivity and stiffness. These properties are of importance for predicting the performance of many engineering applications, such as waste barriers and flood defence embankments. Predicting these properties with confidence requires a thorough understanding of processes at the microscale and their effect on macroscopic phenomenological properties. For unsaturated geomaterials, providing this understanding requires still further research. In this study, network models representing processes in the pore structure and solid skeleton were developed with the aim to improve the required understanding to link processes at the micro-scale to macroscopic properties. The objectives were to develop a new coupled hydro-mechanical network model, with main application the improvement of understanding of the influence of microstructure on the retention behaviour and conductivity of porous geomaterials, the mechanical response in the form of the elastic stiffness, and their interaction. The model is valid for investigation of transport and mechanical aspects geomaterials such as concrete, rocks, sand and clay soils with length scales of the pore radii spanning from sub-μm to mm. In the present network models, the microstructure of the material is idealised by means of a network of voids for the transport response and a network of grains/particles representing the solid skeleton response. For the transport network, the void structure is idealised by spheres representing large voids and pipes for the interconnecting narrow throats. The structural network of grains is modelled by rigid polyhedra connected by springs which contain information related to the constitutive response of the skeleton. The geometry of the networks is determined by dual irregular Delaunay and Voronoi tessellations based on random sets of points. For the transport network, the spheres and pipes were placed on the Voronoi polyhedral vertices and along the ridges, respectively. The mechanical elements were placed on the edges of the Delaunay tetrahedra. In addition to the irregular arrangement of elements, microstructural heterogeneity was introduced by assigning the radii of the spheres and pipes as well as the polyhedra contact areas from probability distributions. New techniques to provide Periodic Boundary Conditions for representative cells generated by the irregular networks were developed. Another new feature of the model is a pore scaling technique which improves the modelling of the retention behaviour. For being able to perform simulations of representative cells of the coupled networks, the model was implemented in a finite element framework. The correct development and implementation of the network models was verified by comparison with a range of analytical solutions. Furthermore, a sensitivity study was performed to investigate the qualitative macroscopic response of the material in the form of retention behaviour, conductivity and stiffness for important model parameters. For the influence of the cell size on the macroscopic properties, it was found that for large cell sizes, the macroscopic response of the model is independent of a change of the cell size. For all macroscopic properties investigated, the mean converges to a representative value. Furthermore, the standard deviation approaches zero for large cells for almost all cases. Only for a small range of very low conductivities for highly unsaturated conditions, the standard deviation did not decrease with increasing cell size, which was attributed to the occurrence of percolation. In addition to the verification part, a calibration strategy was developed for the transport part of the model. Then, the model was used to predict the relative conductivity of unsaturated geomaterials reported in the literature. The agreement between the numerical prediction and the experimental results for degree of saturation and relative permeability was found to be very good. The model presented possibility to predict evolution of relative permeability when calibrated to match retention experimental data.