arXiv subjects

P. Evesque

Publications and source records attributed to P. Evesque.

44 records · Page 3Linked to original sources

arXiv2005

Topology of Roscoe's- and Hvorslev's- Surfaces in the Phase Space of Soil Mechanics

In general, the evolution of soil submitted to simple stress-strain paths is characterized using the 3d phase space (v,p',q) i.e. (specific volume, mean intergranular pressure, deviatoric stress); one finds that all trajectories end up at a line of attracting point called the critical-state line. The surface of Roscoe (Hvorslev) is defined as the surface made of the last part of the set of trajectories ending to a given critical point and coming from all states of normally consolidated soils (from all states of over consolidated soils). It is demonstrated that these two sets are part of the same surface, which is confirmed by experimental data.

cond-mat.soft↗

arXiv2005

On Jaky constant of oedometers, Rowe's relation and incremental modeling

It is recalled that stress-strain incremental modelling is a common feature of most theoretical description of the mechanical behaviour of granular material. An other commonly accepted characteristics of the mechanical behaviour of granular material is the Rowe's relation which links the dilatancy K to the ratio B of vertical to lateral stress during a test at constant lateral stress, i.e. B=(1+M)(1+K). We combine these two features and extract an incremental pseudo-Poisson coefficient which varies with the stress ratio . We solve the oedometric-test case, starting from isotropic sample and stress, for which the vertical stress is increased continuously. It is found that the stress ratio B evolves towards an asymptotic value ko which depends on the friction angle only. It is shown that this asymptotic value ko compares well with the experimental fit known as the Jaky constant.

cond-mat.soft↗

arXiv2005

Stress propagation in granular media: Breaking of any constitutive state equation relating local stresses together by a change of boundary conditions

The stress response of a granular assembly subject to different changes of boundary conditions is studied experimentally in order to define the stress propagation characteristics. These results demonstrate that no simple and single relationship between local stresses exists, which would be imposed by the local structure of the granular assembly only in general. On the contrary, it is demonstrated that these results are controlled by the boundary conditions themselves and that a tiny change of them may lead to strong variations in the incrememental stress relation; furthermore, in other cases, these changes may generate large variations of the stress field and can allow to understand partly the fluctuations already observed in these media. PACS: 46.10+z ; 46.30.-i ; 81.05.Rm

cond-mat.soft↗

arXiv2005

On undrained test using Rowe's relation and Incremental Modelling: Generalisation of the notion of Characteristic State

It is recalled that stress-strain incremental modelling is a common feature of most theoretical description of the mechanical behaviour of granular material. An other commonly accepted characteristics of the mechanical behaviour of granular material is the Rowe's relation which links the dilatancy K to the ratio B of vertical-to-lateral stress during a test at constant lateral stress, i.e. B =(1+M)(1+K). Using an incremental modelling, this law shall be interpreted as a pseudo-Poisson coefficient. We combine these two features to solve the problem of an axial compression under undrained condition. We demonstrate that the sample is submitted to a bifurcation of the transcritical type when it reaches the q=Mp line. This allows extending the notion of the characteristic state introduced by Luong to other situations and to anisotropic systems. We show also that these undrained tests are quite appropriate to study the characteristic-state behaviour.

cond-mat.soft↗

arXiv2005

A Simple Incremental Modelling of Granular-Media Mechanics

It is proposed a simple non linear incremental modelling of the axi-symmetric compression of granular materials and powders. It describes the main features of undrained compression and of oedometric compression using the results of compression tests at constant lateral stress . It generalises the concept of characteristic state. It shows that trajectories arriving at a given critical state shall pertain to a single surface in the (v,q,p) space, which confirms the recent result demonstrating that Hvorslev's and Roscoe's surfaces are part of the same surface. Effects of induced anisotropy are discussed; comparison with classical camclay model is performed.

cond-mat.soft↗

arXiv2005

Statistical mechanics of granular media: An approach A la Boltzmann

We use an analogy with the statistical mechanics of gas to build the statistical mechanics of granular media. The case of an isotropic disordered packing of equal spheres submitted to an isotropic stress is considered. We use the assumption of a maximal disorder and the method of the Lagrange multipliers to demonstrate that the distribution of the force moduli decreases exponentially and obeys an exponential-decay statistics. This distribution results from the above hypotheses and from the existence of a mean stress, which acts as a constraint. This distribution is confirmed by experiments and simulations. We apply the same method to find the distribution of void defects of a granular assembly. It follows also an exponential-decay statistics.

cond-mat.soft↗

arXiv2005

A Micro-mechanical Modelling of the Pressure Dependence of the Void Index of a Granular Assembly:

This paper models the increase of density of a virgin loose granular sample submitted to a progressive axisymmetric compression (either isotropic or anisotropic) as an irreversible process which destroys the larger voids; a statistical mechanics approach similar to the one proposed by Boutreux & de Gennes is performed which leads to the equation of the density of normally consolidated states as a function of pressure; this equation is in agreement with experimental data and the typical variation of e (void index) or v (specific volume) vs. ln(p) .

cond-mat.soft↗

arXiv2002

Stress fluctuations in granular matter: normal vs. seismic regimes in uniaxial compression tests

This paper is concerned with the trends of stress fluctuations in dry granular materials as functions of the sample size D and of the grain diameter d. Results are obtained in the plateau regime of large axial deformation, during axi-symmetric uni-axial compression. Two cases have to be distinguished depending on whether the material generates or does not generate stick-slip. When no stick-slip is generated (Fig.1), it is found that the relative stress fluctuations dq/q of the deviatoric stress q scales linearly with the ratio d/D >. The coefficient A relating dq/q and d/D ranges from 1 to 3 about, depending on the grain size d; this is probably due to the effect of the piston roughness. This result is compatible with a contact force network with a random force distribution and a short range correlation length L,i.e. L<3d; this leads to estimate the representative elementary volume REV to contain few grains (from 1 to 30) as it has been defended already in [1]. We turn now to cases exhibiting stick-slip (Fig. 2). It has been shown in [2] that the distribution of delays between events is rather "exponential" when the sample is small, and Gaussian-like when the sample is larger. The cross-over between the random to quasi periodic regime occurs for a typical sample which contains 10 000 000 grains [2]. In this paper we show an analogy between the statistics of stick-slip amplitude Dq/q and the seismicity of the Los Angeles area during 1979-1997 period [3]. Similarity of the two trends is quite surprising. The seismicity has been cut off at Magnitude M=3.5. These results have to be handled with care since similarity may be fortuitous.

cond-mat.dis-nn↗