  The frictional instability associated with earthquake initiation and
earthquake dynamics is believed to be mainly controlled by the dynamics of
fragmented rocks within the fault gauge. Principal features of the emerging
seismicity (e.g. intermittent dynamics and broad time and/or energy scales)
have been replicated by simple experimental setups, which involve a slowly
driven slider on top of granular matter, for example. Yet, these set-ups are
often physically limited and might not allow one to determine the underlying
nature of specific features and, hence, the universality and generality of the
experimental observations. Here, we address this challenge by a numerical study
of a spring-slider experiment based on two dimensional discrete element method
simulations, which allows us to control the properties of the granular matter
and of the surface of the slider, for example. Upon quasi-static loading,
stick-slip-type behavior emerges which is contrasted by a stable sliding regime
at finite driving rates, in agreement with experimental observations. Across
large parameter ranges for damping, inter-particle friction, particle
polydispersity etc. the earthquake-like dynamics associated with the former
regime results in several robust scale-free statistical features also observed
in experiments. At first sight these closely resemble the main empirical
relations of tectonic seismicity at geological scales. Yet, we show that the
correlations associated with tectonic aftershocks are absent such that the
origin of the Omori-Utsu relation, the aftershock productivity relation, and
B{\aa}th's relation in the simulations is fundamentally different from the case
of tectonic seismicity. We argue that the same is true for previous lab
experiments.
