PSI - Issue 13

Evgeny V. Shilko et al. / Procedia Structural Integrity 13 (2018) 1508–1513 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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the dynamic macroscopic mechanical properties of contrast materials. Indeed, the high mobility of soft components and the low resistance to shear deformation lead to their intensive redistribution, accompanied by a dissipation of the elastic energy, even at small applied stresses. This is especially pronounced for soft matter components in liquid phase (fluids). The fluid flow-related energy dissipation mechanism determines the strong non-linear dependence of the effective mechanical parameters of contrast materials on the strain rate, even if the mechanical response of the “dry” solid phase skeleton is linear -elastic (brittle). Mechanical aspects of the influence of interstitial fluids on the mechanical properties of permeable brittle solids are widely studied both experimentally and theoretically (Fan et al. (2016), Nowak and Kaczmarek (2018), Ougier Simonin and Zhu (2015), Shilko et al. (2018)). Mechanical response of the samples of permeable fluid-saturated materials is conventionally studied with use of either of two problems statements: fully drained and undrained conditions. At the same time, a much smaller number of works is devoted to the study of physical and mechanical properties of brittle permeable materials in the range of variation of the loading rate, which provides an intermediate condition between fully drained and undrained regimes. The present work is devoted to the study of this problem on the basis of numerical modeling by the discrete element method with use of the fully coupled model of fluid saturated porous brittle materials. We modeled 3D macroscopic cylindrical samples of the model permeable fluid saturated brittle solid. The mechanical characteristics of the “dry” material corresponded to typical values of consolidated sandstones ( Young’s modulus E = 15 GPa, Poisson’s ratio  = 0.3, initial porosity  0 =0.1, uniaxial compressive strength  uct =40 MPa). The “basic” mechanical characteristics of the pore fluid (dynamic viscosity  and bulk modulus K fl ) corresponded to the water. The initial pore pressure P init of the interstitial fluid was atmospheric. The “basic” values of height and radius of the cylindrical sample are H =0.1 m and R =0.05 m. The model samples were numerically simulated by the discrete element method (Bicanic (2017)) using a fully coupled macroscopic model of fluid-saturated porous brittle materials (Psakhie et al. (2016)). Within this model the discrete elements simulating parts of the macroscopic samples are treated as porous and permeable (we assume the characteristic thickness of pores to be much smaller than the discrete element size). Discrete element is considered as a homogeneously deformable. Its stress-strain state is determined by the average stress (   ) and strain (   ) tensors. Mechanical response of a homogeneously deformable discrete element is described using the original many body formulation of the element-element interaction (Psakhie et al. (2014)). The influence of pore fluid in the volume of the element on its mechanical properties and response is described implicitly on the basis of the Biot linear model of poroelasticity (Detournay and Cheng (1993)). Interstitial (pore) fluid was considered as compressible. We used the following classical equations of state for fluid-saturated solid and interstitial fluid: where  ,  = x , y , z ; G and K are the shear and bulk elastic moduli of the “dry” material of discrete element;  mean is the value of mean stress in the volume of element;   is the Kronecker delta; a is the poroelastic constant proportional to the ratio of bulk moduli of porous and nonporous material; P pore is the average value of pore pressure in the volume of the element; K fl is the bulk modulus of interstitial fluid;  is fluid density in the pore space of discrete element and  0 is the equilibrium value of fluid density under atmospheric conditions. The fluid pressure gradient was assumed to be a driving force of filtration. We used the classical equation of fluid mass transfer in the pore space. This equation was numerically solved on a “grid” formed by an ensemble of interacting discrete elements. In DEM local fracture is modeled by changing the state of a pair of interacting elements from chemically bonded to unbonded. In the study we applied the failure criterion of Drucker and Prager in the following form:       c eq pore mean bP           0.5 1 1.5 1 , (2) 2. Problem statement           P K                   1 ,    1 2 2 0       fl pore mean pore K G K aP G , (1)