In this letter, we address the relationship between the statistical fluctuations of grain displacements for a full quasistatic plane shear experiment, and the corresponding anomalous diffusion exponent, α. We experimentally validate a particular case of the so-called Tsallis-Bukman scaling law, α = 2/(3 − q), where q is obtained by fitting the probability density function (PDF) of the measured fluctuations with a q-Gaussian distribution, and the diffusion exponent is measured independently during the experiment. Applying an original technique, we are able to evince a transition from an anomalous diffusion regime to a Brownian behavior as a function of the length of the strain-window used to calculate the displacements of grains in experiments. The outstanding conformity of fitting curves to a massive amount of experimental data shows a clear broadening of the fluctuation PDFs as the length of the strain-window decreases, and an increment in the value of the diffusion exponent -anomalous diffusion. Regardless of the size of the strain-window considered in the measurements, we show that the Tsallis-Bukman scaling law remains valid, which is the first experimental verification of this relationship for a classical system at different diffusion regimes. We also note that the spatial correlations show marked similarities to the turbulence in fluids, a promising indication that this type of analysis can be used to explore the origins of the macroscopic friction in confined granular materials. Turbulence is one of the most complex, but ubiquitous, phenomena observed in Nature and it is related with the underlying mechanisms responsible for the micro-macro upscale causing wide-ranging effects on classical systems, like macroscopic friction in granular solids or turbulent flow regime in fluids [1][2][3][4]. The presence of multiple scales in time and space is an additional defy to a comprehensive theoretical description, and a particular effort is made in the literature to perform experiments and simulations in order to validate the proposed theoretical descriptions, particularly Tsallis nonextensive (NE) statistical mechanics [5][6][7][8].A paradigmatic work relating anomalous diffusion and turbulent-like behavior in confined granular media was presented by Radjai and Roux [4], using numerical simulations, and confirmed qualitatively by experiments by Combe and collaborators [7,8]. Radjai and Roux coined a new expression to characterize the analogies between fluctuations of particle velocities in quasistatic granular flows and the velocity fields observed in turbulent fluid flow in high Reynolds number regime, the "granulence". Most of the evidences of the granulence are based in simulations using discrete element method (DEM) but, unfortunately, one can verify a lack of quantitative experimental verification in the last years, limiting the knowledge of the micromechanics of this system based almost exclusively on numerical evidences.In the present work, we aim exactly to fill this gap by contributing with the experiment...

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Abstract. We relate the pressure 'dip' observed at the bottom of a sandpile prepared by successive avalanches to the stress profile obtained on sheared granular layers in response to a localized vertical overload. We show that, within a simple anisotropic elastic analysis, the skewness and the tilt of the response profile caused by shearing provide a qualitative agreement with the sandpile dip effect. We conclude that the texture anisotropy produced by the avalanches is in essence similar to that induced by a simple shearing -albeit tilted by the angle of repose of the pile. This work also shows that this response function technique could be very well adapted to probe the texture of static granular packing. The stress distribution below a pile of sand has been one of the problematic issues of the statics of granular materials in physics over the last few years [1]. In fact, experiments have shown that, when a granular pile is prepared from a point source, the bottom pressure profile has a clear local minimum -a 'dip' -below the apex [2,3,4]. The existence of this pressure dip has been strongly debated, and it is now well established that the presence or absence of this dip is closely related to the preparation history of the pile. This was demonstrated by Vanel et al. [4]. Using the same sand and experimental apparatus, these authors could generate the stress dip using a localized deposition technique or cause the dip to disappear by constructing a pile in successive horizontal layers. Similar conclusions were reached for two dimensional heaps with photo-elastic grains [5], and in numerical simulations [6,7,8].This interesting effect has inspired the development of new models to describe how forces are transmitted in dense granular materials. Among them are those proposed by Bouchaud et al., initially developed in the context of the sand pile dip [9,10,11,12], and further extended to other geometries like that of the silo [12,13]. This approach is also intended to describe a collection of systems including dense colloids, granular matter or foams [16]. At the macroscopic level, these features are modelled by hyperbolic, partial differential equations (PDE) for the stress tensor. Although no explicit link was established, the characteristics of these hyperbolic equations were intuitively thought to be related to the mesoscopic 'force chain' network whose structure and orientation were shaped by the previous history of the granular assembly -see also [14,15] concerning force chains. Plasticity theories for granular deformations are also of hyperbolic type, although conceptually different than the previous cited models. From the classical, soil mechanics point of view, below the plastic threshold, granular material is thought to behave as an effective elastic material with PDE's that belong to the elliptic class [17]. Finally, sound wave propagation techniques and numerical simulations of confined granular assemblies indicate that that assesment of effective elastic constitutive relations is still an open and diff...

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