M. Aldibirov, A model for viscous magma fragmentation during volcanic blasts, Bulletin of Volcanology, vol.56, issue.6-7, pp.459-465, 1994.
DOI : 10.1007/BF00302827

M. Aldibirov and D. B. Dingwell, Magma fragmentation by rapid decompression, Nature, vol.380, issue.6570, pp.146-148, 1996.
DOI : 10.1038/380146a0

S. Arbabi and M. Sahimi, Elastic properties of three-dimensional percolation networks with stretching and bond-bending forces, Physical Review B, vol.38, issue.10, pp.7173-7176, 1988.
DOI : 10.1103/PhysRevB.38.7173

S. Arbabi and M. Sahimi, Mechanics of disordered solids. I. Percolation on elastic networks with central forces, Physical Review B, vol.47, issue.2, pp.695-702, 1993.
DOI : 10.1103/PhysRevB.47.695

I. Balberg, Universal percolation-threshold limits in the continuum, Physical Review B, vol.31, issue.6, pp.4053-4055, 1985.
DOI : 10.1103/PhysRevB.31.4053

F. Craciun, C. Galassi, R. , and E. , Experimental evidence for similar critical behavior of elastic modulus and electric conductivity in porous ceramic materials, Europhysics Letters (EPL), vol.41, issue.1, pp.55-60, 1998.
DOI : 10.1209/epl/i1998-00115-8

J. De-dreuzy, P. Davy, and O. Bour, Percolation parameter and percolation-threshold estimates for three-dimensional random ellipses with widely scattered distributions of eccentricity and size, Physical Review E, vol.62, issue.5, pp.5948-5952, 2000.
DOI : 10.1103/PhysRevE.62.5948

D. Nijs and M. P. , A relation between the temperature exponents of the eight-vertex and q-state Potts model, Journal of Physics A: Mathematical and General, vol.12, issue.10, pp.1857-1871, 1979.
DOI : 10.1088/0305-4470/12/10/030

D. B. Dingwell and S. L. Webb, Structural relaxation in siloicate melts and non-Newtonian melt rheology in igneous processes, Phys. Chem. Miner, vol.16, pp.508-516, 1989.

J. W. Essam, D. S. Gaunt, and A. J. Guttmann, Percolation theory at the critical dimension, Journal of Physics A: Mathematical and General, vol.11, issue.10, pp.1983-1990, 1978.
DOI : 10.1088/0305-4470/11/10/016

H. Gaonac-'h, J. Stix, and S. Lovejoy, Scaling effects on vesicle shape, size and heterogeneity of lavas from Mount Etna, Journal of Volcanology and Geothermal Research, vol.74, issue.1-2, pp.131-153, 1996.
DOI : 10.1016/S0377-0273(96)00045-5

H. Gaonac-'h, S. Lovejoy, J. Stix, and D. Schertzer, A scaling growth model for bubbles in basaltic lava flows, Earth and Planetary Science Letters, vol.139, issue.3-4, pp.395-409, 1996.
DOI : 10.1016/0012-821X(96)00039-8

H. Gaonac-'h, S. Lovejoy, and D. Schertzer, Percolating magmas and explosive volcanism, Geophysical Research Letters, vol.402, issue.11, pp.1559-1563, 2003.
DOI : 10.1029/2002GL016022

J. E. Gardner, R. M. Thomas, C. Jaupart, T. , and S. , Fragmentation of magma during Plinian volcanic eruptions, Bulletin of Volcanology, vol.58, issue.2-3, pp.144-162, 1996.
DOI : 10.1007/s004450050132

H. M. Gonnermann and M. Manga, Explosive volcanism may not be an inevitable consequence of magma fragmentation, Nature, vol.426, issue.6965, pp.432-435, 2003.
DOI : 10.1038/nature02138

P. Grassberger, On the critical behavior of the general epidemic process and dynamical percolation, Mathematical Biosciences, vol.63, issue.2, pp.157-161, 1983.
DOI : 10.1016/0025-5564(82)90036-0

M. Ichihara, D. Rittel, and B. Sturtevant, Fragmentation of a porous viscoelastic material: Implications to magma fragmentation, Journal of Geophysical Research: Solid Earth, vol.102, issue.B10, pp.222910-1029, 2002.
DOI : 10.1029/2001JB000591

N. Jan and D. Stauffer, Random Site Percolation in Three Dimensions, International Journal of Modern Physics C, vol.09, issue.02, pp.341-347, 1998.
DOI : 10.1142/S0129183198000261

E. Kaminski and C. Jaupart, The size distribution of pyroclasts and the fragmentation sequence in explosive volcanic eruptions, Journal of Geophysical Research: Solid Earth, vol.9, issue.2, pp.759-788, 1998.
DOI : 10.1029/98JB02795

C. Klug, K. V. Cashman, and M. St, Vesiculation of, Helens magma Geology, vol.22, pp.468-472, 1980.

C. Klug, K. V. Cashman, and C. R. Bacon, Structure and physical characteristics of pumice from the climatic eruption of Mount Mazama (Crater Lake) Oregon, Bull, pp.486-501, 2002.

U. Kueppers, D. Perugini, and D. B. Dingwell, ???Explosive energy??? during volcanic eruptions from fractal analysis of pyroclasts, Earth and Planetary Science Letters, vol.248, issue.3-4, pp.800-807, 2006.
DOI : 10.1016/j.epsl.2006.06.033

C. M. Lorenz and R. M. Ziff, Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices, Physical Review E, vol.57, issue.1, pp.230-236, 1998.
DOI : 10.1103/PhysRevE.57.230

S. Lovejoy, H. Gaonac-'h, and D. Schertzer, Bubble distributions and dynamics: The expansion-coalescence equation, Journal of Geophysical Research: Solid Earth, vol.50, issue.11, pp.10-1029, 2004.
DOI : 10.1007/500445-004-0376-4

URL : https://hal.archives-ouvertes.fr/hal-00711730

S. Meille and E. J. Garboczi, Llinear elastic properties of 2D and 3D models of porous materials made froom elgongated objects, Modelling Simul, Mater. Sci. Eng, vol.9, pp.371-390, 2001.

M. Namiki and M. Manga, Response of a bubble bearing viscoelastic fluid to rapid decompression: Implications for explosive volcanic eruptions, Earth and Planetary Science Letters, vol.236, issue.1-2, pp.269-284, 2005.
DOI : 10.1016/j.epsl.2005.02.045

M. Namiki and M. Manga, Influence of decompression rate on the expansion velocity and expansion style of bubbly fluids, Journal of Geophysical Research: Solid Earth, vol.402, issue.B10, pp.11-208, 2006.
DOI : 10.1029/2004JB003113

P. Papale, Strain-induced magma fragmentation in explosive eruptions, Nature, vol.397, issue.6718, pp.425-428, 1999.
DOI : 10.1038/17109

M. Polacci, P. Papale, and M. Rosi, Textural heterogeneities in pumices from the climactic eruption of Mount Pinatubo, 15 June 1991, and implications for magma ascent dynamics, Bulletin of Volcanology, vol.95, issue.2-3, pp.83-97, 1991.
DOI : 10.1007/s004450000123

J. Quintanilla, Measurement of the percolation threshold for fully penetrable disks of different radii, Physical Review E, vol.63, issue.6, p.61108, 2001.
DOI : 10.1103/PhysRevE.63.061108

M. D. Rintoul, Precise determination of the void percolation threshold for two distributions of overlapping spheres, Physical Review E, vol.62, issue.1, pp.68-72, 2000.
DOI : 10.1103/PhysRevE.62.68

M. D. Rintoul and S. Torquato, Precise determination of the critical threshold and exponents in a three-dimensional continuum percolation model, Journal of Physics A: Mathematical and General, vol.30, issue.16, pp.585-592, 1997.
DOI : 10.1088/0305-4470/30/16/005

M. Sahimi and S. Arbabi, Mechanics of disordered solids. II. Percolation on elastic networks with bond-bending forces, Physical Review B, vol.47, issue.2, pp.703-712, 1993.
DOI : 10.1103/PhysRevB.47.703

H. Scher and R. Zallen, Critical Density in Percolation Processes, The Journal of Chemical Physics, vol.53, issue.9, pp.3759-3761, 1970.
DOI : 10.1063/1.1674565

D. Schertzer and S. Lovejoy, Generalised scale invariance in turbulent phenomena, Physico-Chemical Hydrodynamics Journal, vol.6, pp.623-635, 1985.

R. S. Sparks, The dynamics of bubble formation and growth in magmas: A review and analysis, Journal of Volcanology and Geothermal Research, vol.3, issue.1-2, pp.1-37, 1978.
DOI : 10.1016/0377-0273(78)90002-1

O. Spieler, B. Kennedy, U. Kueppers, D. B. Dingwell, B. Scheu et al., The fragmentation threshold of pyroclastic rocks, Earth and Planetary Science Letters, vol.226, issue.1-2, pp.139-148, 2004.
DOI : 10.1016/j.epsl.2004.07.016

D. Stauffer, Introduction to percolation Theory, 1985.

N. Thomas, C. Jaupart, and S. Vergniolle, On the vesicularity of pumice, Journal of Geophysical Research, vol.55, issue.B8, pp.633-615, 1994.
DOI : 10.1029/94JB00650

Y. B. Yi, Void percolation and conduction of overlapping ellipsoids, Physical Review E, vol.74, issue.3, pp.31112-031111, 2006.
DOI : 10.1103/PhysRevE.74.031112

Y. Zhang, A criterion for the fragmentation of bubbly magma based on brittle failure theory, Nature, vol.402, issue.6762, pp.648-650, 1999.
DOI : 10.1038/45210