What does make the b-value change? The role of the mechanical conditions.

Since the works of Mogi (1962) and Scholz (1968) on acoustic emission (AE), we know that the Gutenberg Richter empirical law can be observed at the laboratory sample scale. They showed that a significant overlap exists between the definition of AE (usual term at lab scale) and earthquake respectively. This is further reinforced by the evidence for brittle fracture as observed by AE to obey similar statistics (i.e. Gutenberg-Richter law) over source dimensions spanning more than eight orders of magnitude, possibly ranging from the hundred of kilometers of tectonic earthquakes to the dislocation movement smaller than the micron size (Miguel et al, 2001). As the b-value characterizing the earthquakes dynamics displayed regional and temporal departures from its mean value, the need raised for understanding what does make the b-value change. Hence, since Mogi and Scholz, the laboratory results have been often used to better understand the earthquakes dynamics. Mogi showed the role of material heterogeneity on b-value, and Scholz showed that the b-value decreased before the failure and suggest this exponent to be related to the stress. These very first studies open the route for several authors to investigate at the lab the origins of the b-value variations. More recently, numerical simulations allowed reproducing the power-law distribution of damage events and then to investigate more easily what are the parameters controlling the b-value. In this presentation, basing on natural observations at different scale (rock slopes, mines, rock masses, tectonic faults), on laboratory experiments and numerical simulations, we investigate what are the relationships between the b-value and the mechanical condition of the material (stress, confining pressure, state of failure). In particular we show a set of converging observations (lab, crust, simulation) indicating a strong dependence between the brittle-ductile transition and the b-value that allows us to give a mechanical interpretation for certain b-value variations observed in the earth crust.