PSI - Issue 18

Mikhail Eremin / Procedia Structural Integrity 18 (2019) 135–141 Mikhail Eremin / Structural Integrity Procedia 00 (2019) 000–000

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Sandstone is one of the most studied rocks. This is due to the fact that sandstone is often found in various en gineering fields. For example, in coal mining, sandstone is often a component of the roof and floor of a coal seam. When extracting liquid hydrocarbons, sandstone formations often contain a reservoir of oil or gas. Thus, study of mechanisms of sandstone failure, and generally, rocks failure is of a great importance for solving particular engineer ing problems. Indirect experimental techniques give a good insight into the failure mechanisms, allowing to estimate also fracture toughness. However, a uniaxial compression remains one of the most often applied techniques of rocks loading. Review of experimental data on dependence of uniaxial compressive strength (UCS) of sandstone specimens on porosity demonstrate a nonlinear decrease of UCS with increase of porosity Farrokhrouz and Asef (2017). In this work we developed a mathematical model that describes deformation and failure of porous sandstone spec imens subjected to the uniaxial compression. In the next sections we provide the material characterization, some model details and discuss the results. We paid attention to the porosity as one of the features influencing the strength characteristics and failure mechanisms of loaded sandstone specimens.

Nomenclature

density of pore-free sandstone

ρ µ

shear modulus bulk modulus

K E

Young’s modulus σ T uniaxial tensile strength σ C uniaxial compressive strength Y material constant of Drucker-Prager model related to cohesion α material constant of Drucker-Prager model related to angle of internal friction

σ i j components of stress tensor ε i j components of strain tensor V volume of media θ volumetric strain Λ dilatancy factor γ P intensity of accumulated inelastic strain t ∗ fracture incubation time x i Cartesian coordinates n j components of normal vector

2. Material characterization

2.1. Pore size distribution

Recently Zhang et al. (2016) reported a comprehensive investigation on the pore structure characteristics of tight sandstone reservoirs in Upper Triassic Ordos Basin China. For the needs of current work, the probability distribution function of pore sizes is of a particular interest. We don’t focus on the same sandstone as in aforementioned work, however, even if distributions of pore sizes vary from one formation to another, they basically obey the same statistical laws. Comparison of experimental distribution with di ff erent stochastic distribution laws shows that a log-normal distribution is a promising one and catches general trends of natural distributions, see Fig. 1a. Reproduction of Zhang et al. (2016) experimental data were made with some approximate accuracy which is a compulsory assumption since we used further the log-normal fitted law for simulation of pore size distribution. Utilizing the log-normal law, we simulated the distribution of pores in computational domain with pseudo-random number generator, see Fig. 1b. All pores are initially circle-shaped with radii of circles corresponding to log-normal pore size distribution. Fig. 1b illustrates that some pores coalescence into the bigger ones having more complex geometry. Total porosity is ≈ 12%.