Tensile Elastic Response of Holed Rock Specimens under Coupled Effects of Hole Shape and Nominal Size

Abstract

To distinguish local field concentration governed by hole-boundary geometry from global compliance governed by void fraction and residual ligament, two-dimensional plane-stress models of 100 mm × 100 mm holed rock specimens were established in Abaqus. Circular, equilateral-triangular, square, and straight-walled semicircular-arched holes were considered at nominal sizes R = 20, 30, and 40 mm. The area void ratio φ and minimum lateral-ligament ratio η were introduced to quantify the geometric non-equivalence associated with different definitions of R, and the von Mises equivalent stress, displacement magnitude, and maximum in-plane principal strain were jointly analysed. The locations of high-response zones are controlled by boundary-curvature continuity and corner orientation: they occur at the lateral sidewalls of the circular hole, the two lower corners of the triangular hole, the upper corners of the square hole, and the springing regions of the arched hole. At small sizes, the response is dominated by local concentration at corners or curvature transitions; with increasing R, void fraction and ligament reduction become increasingly important. At R = 40 mm, the circular-hole model has φ = 0.503 and η = 0.10, and its peak equivalent stress, maximum displacement, and maximum principal strain reach 18.47 MPa, 6.670 × 10⁻¹ mm, and 7.505 × 10⁻³, respectively, indicating pronounced finite-boundary amplification. The triangular and square holes mainly exhibit progressively enhanced corner localization, whereas the arched hole shows weakly non-monotonic peaks but an expanding affected zone. No scale-independent ranking of hole shapes exists under the same nominal R; area void ratio and minimum ligament ratio should therefore be reported together with the nominal size. The proposed multi-field framework separating local concentration from global compliance provides a more interpretable basis for geometric design and comparison of finite holed specimens and engineering openings.