The Micro-macro Connection for a Dry Sand: Oedometric Test, Bauer's Law and the Microscopic Dependence of Two Hypoplastic Parameters

What is the relationship between the macroscopic parameters of the constitutive equation for a granular soil and the microscopic forces between its grains? How this relationship changes with geometrical properties like the granulometry? In order to investigate these connections we have simulated by molecular dynamics the oedometric compression of a granular soil (a dry and bad-graded sand) and computed the hypoplastic parameters [1] h(s) (the granular skeleton hardness) and eta (the exponent in the compression law) by following exactly the same procedure than in experiments, i.e. by fitting the Bauer's empirical law [2] e/e(0) = exp (- (3p/h(s))eta], where p is the vertical stress and e(0) and e are the initial and present void ratios. Grains are simulated as spheres with normal elastic and dissipative forces plus sliding, pure rolling and static friction between them [3]. Translations and rotations are integrated by using optimized velocity Verlet and Omelyan leap-frog algorithms, respectively. Once a granulometry is fixed, we explore how the two hypoplastic parameters change by modifying the grain stiffness V, the normal damping coefficient gamma(n), and the static mu(s), and dynamic mu(k), friction coefficients. Accumulating all simulations for a fixed granulometry we found, unexpectedly, that the two macroscopic parameters seem to be related by a power law, h(s) = 0.068(1)eta(-9.88)(3) and, moreover, that the experimental values for a Guamo sand with the same granulometry fits into this power law [4]. Next, we have investigated how this power law changes with granulometry, with increasing number of particles in the simulations and with further experiments on many different sands. The results open interesting questions on the microscopic origin of these constitutive parameters and, moreover, on the origins of Bauer's Law.