MSCAGR / Department of Soil Science / Soil hydraulic and hydraulic-related physical properties are key to soil productivity and these properties are widely studied. Nevertheless, their spatial variability is least understood. Two sites were selected for this study (University of Venda Experimental farm and Roodeplaat, Agricultural Research Council farm). The objectives of this study were to determine the spatial variability of soil water content, water infiltration and hydraulic conductivity on selected soils. Field measurements were done on a 20 m × 20 m. Soil hydraulic and hydraulic-related physical properties were studied at two depths, 0 – 0.2 m top soil and 0.2 – 0.4 m sub soil. The field was irrigated to saturation and let to drain freely for two days. The soil was quickly secured in water cans to avoid further loss of water by evaporation and taken to the laboratory for analysis. Data was analysed using ordinary kriging method in ArcMap® software version 10.4 to generate spatial variability maps and semi variograms. The University of Venda Experimental farm had lesser spatial variability with coefficient of variation ranging from 9.6 to 33.4%. The spatial variability of soil was very low confirmed by contour maps depicting slightly homogeneity. Whereas, the soil hydro-physical properties displayed greater spatial variability at Roodeplaat, Agricultural Research Council Experimental farm. The empirical variograms of spherical model fits were also assuming weak spatial dependence with a curve variogram. The coefficient of variation ranged from 10.5 to 51.9%. Therefore, the greater variability at Roodeplaat, Agricultural Research Council Experimental farm indicated that coarse soil texture under conventional tillage has a greater influence on the spatial variability of the soil hydro-physical properties. / NRF

Cette thèse est une contribution à la construction de l’Approche Locale de la rupture à l’échelle microscopique à l’aide de la modélisation d’agrégats polycristallins. Elle consiste à prendre en compte la variabilité spatiale de la microstructure du matériau. Pour ce faire, la modélisation micromécanique du matériau est réalisée par la simulation d’agrégats polycristallins par éléments finis. Les champs aléatoires de contrainte (principale maximale et de clivage) dans le matériau qui représentent la variabilité spatiale de la microstructure sont ensuite modélisés par un champ aléatoire gaussien stationnaire ergodique. Les propriétés de variabilité spatiale de ces champs sont identifiés par une méthode d’identification, e.g. méthode du périodogramme, méthode du variogramme, méthode du maximum de vraisemblance. Des réalisations synthétiques des champs de contraintes sont ensuite simulées par une méthode de simulation, e.g. méthode Karhunen-Loève discrète, méthode “Circulant Embedding”, méthode spectrale, sans nouveau calcul aux éléments finis. Enfin, le modèle d’Approche Locale de la rupture par simulation de champ de contrainte de clivage permettant d’y intégrer les réalisations simulées du champ est construit pour estimer la probabilité de rupture du matériau. / This thesis is a contribution to the construction of the Local Approach to fracture at the microscopic scale using polycrystalline aggregate modeling. It consists in taking into account the spatial variability of the microstructure of the material. To do this, the micromechanical modeling is carried out by finite element analysis of polycrystalline aggregates. The random stress fields (maximum principal et cleavage stress) in the material representing the spatial variability of the microstructure are then modeled by a stationary ergodic Gaussian random field. The properties of the spatial variability of these fields are identified by an identification method, e.g. periodogram method, variogram method, maximum likelihood method. The synthetic realizations of the stress fields are then simulated by a simulation method, e.g. discrete Karhunen-Loève method, circulant embedding method, spectral method, without additional finite element calculations. Finally, a Local Approach to fracture by simulation of the cleavage stress field using the simulated realizations is constructed to estimate the rupture probability of the material.