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

What is the relationship between the macroscopic parameters of the constitutive equation for a granular soil and the microscopic forces between grains? In order to investigate this connection, we have simulated by molecular dynamics the oedometric compression of a granular soil (a dry and bad-graded sand) and computed the hypoplastic parameters $h_s$ (the granular skeleton hardness) and $η$ (the exponent in the compression law) by following the same procedure than in experiments, that is by fitting the Bauer's law $e/e0 = exp(-(3p/hs)η)$, where $p$ is the pressure, and $e_0$ and $e$ are the initial and present void ratios. The micro-mechanical simulation includes elastic and dissipative normal forces plus slip, rolling and static friction between grains. By this way we have explored how the macroscopic parameters change by modifying the grains stiffness, V ; the dissipation coefficient, $γ_n$; the static friction coefficient, $μ_s$; and the dynamic friction coefficient, $μ_k$ . Cumulating all simulations, we obtained an unexpected result: the two macroscopic parameters seems to be related by a power law, $h_s = 0.068(4)η^{9.88(3)}$. Moreover, the experimental result for a Guamo sand with the same granulometry fits perfectly into this power law. Is this relation real? What is the final ground of the Bauer's Law? We conclude by exploring some hypothesis.

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