PSI - Issue 25

Mikhail Eremin / Procedia Structural Integrity 25 (2020) 465–469

466

2

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

In this work, a failure of the Kuznetsk coal basin sandstone samples subjected to uniaxial compression is simulated with explicit consideration of pore space. At all other factors being equal, an amount of pores is varied in the range of ≈ 5–25%. The problem of evaluating the uniaxial compressive strength as a function of porosity is addressed. In the next sections, we provide the mathematical formulation, discuss the results, and draw some conclusions.

Nomenclature

density of pore-free sandstone

ρ µ

shear modulus K 0 final bulk modulus σ T uniaxial tensile strength σ C uniaxial compressive strength Y material constant of Drucker-Prager model related to cohesion of the Coulomb-Mohr criterion α material constant of Drucker-Prager model related to angle of internal friction of the Coulomb-Mohr crite rion Λ dilatancy factor a model parameter φ volumetric strain of microcracks closure P 0 isotropic pressure of microcracks closure The sandstone samples of the Kuznetsk coal basin, Siberia, Russia, are considered. All textural features of samples but porosity are disregarded for the sake of simplicity. The collected data of the UCS dependence on porosity suggest that the strength obeys an exponential descending law with a high level of confidence R 2 ≈ 0 . 7. For further details, the reader is referred to Olkhovatenko (2014). The Finite-di ff erence method (FDM) is used to simulate the deformation and failure of sandstone samples. An assumption of 2D plain strain is made. For a comprehensive formulation of the method applied, as well as basic equations, the reader is referred to Wilkins (1999). The continuum damage mechanics (CDM) is also employed to describe the softening of a material. Since the pore space is considered explicitly, the pore-free sandstone has to be characterized. We assume that the pore-free sandstone represents an isotropic continuum. It is made so to reduce the overcomplications in a constitutive response. Hence, only two non-zero constants in the equation of state are easily obtained from the corresponding experiments, namely the bulk modulus K , and the shear modulus µ . To describe the nonlinear constitutive response of loaded sandstone samples, the non-associated circumscribed Drucker-Prager criterion is employed Drucker and Prager (1952); Stefanov (2018) and coupled with continuous damage mechanics approach. A variant of the model applied can be found in Eremin (2019a). For further details of the mathematical formulation and some other parameters of the model not listed here, the reader is referred to Eremin (2019b). Table 1 summarizes physical-mechanical properties of pore-free sandstone which are used in the simulation. 3. Mathematical formulation of the problem 2. Materials and methods

Table 1. Physical-mechanical properties of pore-free sandstone. K 0 , GPa a φ P 0 , MPa ρ , g / cm 3

µ , GPa

T , MPa

σ C , MPa

Y , MPa

σ

α

15.276

0.95

0.0001

3.5

2.54

13.04

37.6

113.6

46

0.5