Statistical size effects on compressive strength of concrete

Size effects on mechanical strength, i.e. the fact that larger structures fail under lower stresses than smaller ones, already highlighted by Leonardo da Vinci and Edmee Mariotte centuries ago, remain nowadays a crucial problem to establish structural design rules and safety regulations from an upscaling of laboratory data. These size effects are generally explained either from a deterministic energetic approach that predicts a non-vanishing asymptotic strength but, by construction, does not account for fluctuations around the mean strength and their size dependence, or from a statistical approach based on the weakest-link theory that implies a vanishing strength towards large scales.Recently, an alternative framework has been proposed based on an interpretation of compressive failure of heterogeneous materials as a critical transition from an intact to a failed state. This critical interpretation releases the underlying hypotheses of the weakest-link theory, pure brittleness and the independence of damage events, while predicting a non-vanishing asymptotic mean strength (σ_∞ ) but vanishing intrinsic fluctuations at large scales. The application this framework to the statistical size effects on compressive strength of concrete, a typical quasibrittle material of tremendous importance in civil engineering, is investigated in this thesis.From an extensive series of uniaxial compression experiments (527 tests) carried out on concrete samples with four different sizes and three different microstructures, we demonstrate (i) the failure of the weakest-link theory in this case, and instead (ii) the pertinence of the critical framework to account for size effects on compressive strength of concrete, in terms of average strength, associated fluctuations, and probability of failure. From a detailed analysis of the microstructural disorder of our materials, we show that the pore structure, rather than the concrete mix, plays a significant role on size effects on strength. In this framework, the asymptotic strength (σ_∞ ) represents the genuine characteristic compressive strength (f_ck ) of the material, a key property for the dimensioning large-scale structures from an upscaling of small-scale laboratory mechanical tests and for the quality control of concrete.As a consequence of the leading role of the pore structure in controlling the size effects on compressive strength of low-porosity concretes, when estimating the characteristic (asymptotic) strength from a series of tests with a single sample size, a condition on this size with respect to the characteristic scale of pore structure is proposed to be fulfilled.