This paper presents an analysis of the yielding and plastic hardening of uniformly-graded samples of a silica sand subjected to one-dimensional normal compression. Single grains of silica sand have been compressed diametrically between flat platens to measure indirectly tensile strength. Approximately 30 grains were tested for each of the following nominal particle sizes: 0.5mm, 1mm and 2mm diameter. It was found that the data could be described by the Weibull statistics of brittle ceramics, and the Weibull modulus could be taken to be about 3. 1. Uniform aggregates of the same sand were then compacted to maximum density and subjected to one-dimensional compression. The initial particle size distributions were 0.3-0.6mm, 0.6-1.18mm and 1.18-2mm, and aggregates were subjected to stresses of up to 100MPa. All particles were initially of similar shape, and hence the initial voids ratios of the aggregates at maximum density were approximately equal. The yield stress was defined to be the point of maximum curvature on a plot of voids ratio against the logarithm of effective stress, and found to increase with decreasing particle size, and to be approximately proportional to the tensile strength of the constituent grains. However, the plastic compressibility index was found to be approximately constant and independent of the initial grading, and a fractal distribution of particle sizes appeared to evolve under increasing stress. There is evidence to suggest that the aggregates evolve towards a fractal dimension of 2.5 under high stresses.