By R Dungar; G N Pande; J A Studer
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Additional resources for Numerical models in geomechanics
5 Zone 2 In order to model the volume fraction variation of pores in Zone 2, some information about the amount of affected macropore volume fraction that is going to be added to the micropores is required. (a) Soil sample with aggregated particles (b) volume decrease of macropores (consolidation) (c) transformation of macropores to micropores (d) illustration of PSD evolution as a result of micro and macro pore volume variation. As a result, the modelled volume fraction of pores located in Zone 2 can be estimated by: (14) 3 NUMERICAL VALIDATION OF THE MODEL The model presented is conceived for the simulation of the modification of the pore space geometry of double porosity structured soils subjected to a suction increase.
In mathematical terms, this is a nonlinear constrained optimization problem with respect to σ which, for a given set of parameters c1, c2,n, requires a numerical solution. In what follows, the identification procedure is briefly outlined and the key numerical results are presented. Geometry of the problem. (a) distribution of axial strength; (b) orientation ofcriticalplane. (a) distribution of axial strength; (b) orientation of critical plane. 490). The solution also gave the corresponding orientations of the critical plane for both these cases.
Decomposition of the homogenization problem (P). This interesting property (5) with: (6) reads: (7) for which (2) has been used. ) representing the 2D cracks density parameter introduced by Budiansky et O’Connel (4), and Bnn=k 2+k1 cos2φ;Btt=k 2−k 1cos2φ, (14) Bnt=2k1sinφcosφ. the condition β=0. Combining (19) and (18), one obtains: (20) Page 28 Note that (20) cover also both the cases of opened and closed cracks (a closed crack is characterized by β=0). For such processes, the dissipation D cancels: (21) Using expression (18) for W, and observing that the nullity of D must hold for any , (21) leads to: (22) which can be inverted to express α and β as function of the macroscopic stress tensor and the cracks normal n: such expression between the macroscopic stress and the component of displacement jump vector are the so called localization relations for the cracked medium.
Numerical models in geomechanics by R Dungar; G N Pande; J A Studer