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What is the relationship between the macroscopic parameters of theconstitutive equation for a granular soil and the microscopic forces betweengrains? In order to investigate this connection, we have simulated by moleculardynamics the oedometric compression of a granular soil (a dry and bad-gradedsand) and computed the hypoplastic parameters $h_s$ (the granular skeletonhardness) and $\eta$ (the exponent in the compression law) by following thesame procedure than in experiments, that is by fitting the Bauer's law $e/e0 =exp(-(3p/hs)\eta)$, where $p$ is the pressure, and $e_0$ and $e$ are theinitial and present void ratios. The micro-mechanical simulation includeselastic and dissipative normal forces plus slip, rolling and static frictionbetween grains. By this way we have explored how the macroscopic parameterschange by modifying the grains stiffness, V ; the dissipation coefficient,$\gamma_n$; the static friction coefficient, $\mu_s$; and the dynamic frictioncoefficient, $\mu_k$ . Cumulating all simulations, we obtained an unexpectedresult: the two macroscopic parameters seems to be related by a power law, $h_s= 0.068(4)\eta^{9.88(3)}$. Moreover, the experimental result for a Guamo sandwith the same granulometry fits perfectly into this power law. Is this relationreal? What is the final ground of the Bauer's Law? We conclude by exploringsome hypothesis.

Oedometric Test, Bauer's Law and the Micro-Macro Connection for a Dry Sand