Broad-spectrum fracture toughness of an anisotropic sandstone under mixed-mode loading

Abstract

Fracture toughness of anisotropic rocks can vary with many factors such as geological anisotropy, geometrical properties of specimens used in the laboratory (e.g., pre-existing crack properties), and loading conditions. This fact has been widely acknowledged. Yet the variation in fracture toughness remains enigmatic, as there is still lack of a comprehensive study on how those influential factors affect fracture toughness behavior of anisotropic rocks.The present paper shows a broad-spectrum mixed-mode fracture toughness of an anisotropic sandstone from a numerical scheme, which is based on the Discrete Element Method (DEM). In this study, a total of 340 semi-circular bend (SCB) specimens with various geological and geometrical conditions were numerically prepared by systemically varying the orientations of planar anisotropy (i.e. incipient bedding plane), as well as the magnitudes of the ISRM-suggested geometrical parameters of the SCB specimens (i.e. crack length, crack angle, and span length). The numerical model used in the study was calibrated against a series of laboratory experiments to select proper micro-parameters to reproduce the mechanical characteristics of anisotropic Midgley Grit sandstone (MGS). Additionally, four different fracture criteria, which are based on stress and strain analysis, and the analysis of energy density, were used to predict the mixed-mode fracture behaviour of MGS.Numerical findings from this study were compared with experimental observations (qualitatively) and theoretical predictions (quantitatively). A broad agreement was observed in the comparison study. Highlights Broad-spectrum mixed-mode fracture toughness of an anisotropic sandstone based on a total of 340 DEM simulations. Influences of crack length and angle, span length, as well as geological anisotropy on fracture behaviour. Comparisons between results obtained from DEM simulations, laboratory experiments and theoretical analysis.

Three-dimensional DEM investigation of the fracture behaviour of thermally degraded rocks with consideration of material anisotropy

“…with different tensile strengths [27,33] were inserted into the SCB sample. Note that, short transverse-oriented layers were focused in the present study, as proposed by Roy et al [29] and Shang et al [16].…”

“…• Generation of pre-existing notches ─ Within each SCB sample, a notch with a length (a) of 25 mm and an inclination (β) between 0°-46° was generated (Fig. 1), allowing a full consideration of fracture modes for the specific combination (i.e., for the setup a/R = 0.5 and s/R = 0.55, β = 0° represents mode I, β = 46° mode II, and 0°<β<46° mixed mode [16,34]).…”

“…Previous investigations on fracture behaviour of rocks showed that fracture toughness can vary with factors like temperature, pressure [9][10][11], material anisotropy [12][13], geometrical properties of tested samples [14][15], experimental setup and the loading conditions [16]. Therefore, the rock fracture behaviour is complex and often difficult to be fully understood.…”

Calculation of Silo Wall Pressure considering the Intermediate Stress Effect

“…(1) e calculation of silo wall pressure can be regarded as a quasiplane strain problem [6]. e intermediate stress in bulk solids could be considered approximately as the intermediate principal stress σ 2 equal to the average value of the maximum principal stress σ 1 and the minor principal stress σ 3 without significant error [34][35][36][37][38]. is correlation is written as…”

“…As the influence of the intermediate principal stress on the material strength is in general significant, the M-C criterion is not appropriate to predict such strength. e silo wall pressure using the M-C criterion is then overestimated leading to a conservative silo design [34][35][36][37][38]. Consequently, choosing an appropriate true triaxial strength criterion, such as the Drucker-Prager (D-P) criterion, the Matsuoka-Nakai (M-N) criterion, the Lade-Duncan (L-D) criterion, or the unified strength theory (UST) can not only improve silo quality and durability but also generate economic benefits.…”