Micromechanics-based evaluation of strain rate effect on direct tensile failure in brittle rocks during dynamic geohazards

Brittle rocks exhibit significantly lower dynamic direct tensile strength compared to their compressive strength, and the tensile strength is relatively difficult to be quantitatively measured through experiments. While extensive research has characterized dynamic tensile behavior through indirect testing methods, the direct tensile strength remains critical for evaluating rock fracture mechanisms and ensuring the safety of deep underground engineering systems. Notably, the microcrack propagation dynamics governing dynamic direct tensile fracture in brittle rocks remain understudied. To address this gap, we develop a micro-macro dynamic tensile fracture model that elucidates the stress-strain constitutive behavior of brittle rocks under dynamic loading. The model integrates four key components containing the quasi-static microcrack growth kinetics, the microcrack length-macroscopic strain relationships, the crack growth rate-strain rate coupling, and the transition from quasi-static to dynamic fracture toughness. A critical strain rate causing the crack initiation stress to be the peak strength is investigated. Parametric investigations quantify the influence of crack extension rate on stress-crack length relation, strain rate on stress-strain relation, and the governing parameters (initial damage D 0 , microcrack size a , inclination angle φ , and density N v ) on dynamic crack initiation thresholds, peak strength and critical strain rate. Its validity is rigorously verified through comparative analysis with experimental data. The results will have significance for disaster evaluation in rock engineering. • A micro-macro dynamic direct tensile fracture model in brittle rocks is proposed. • Effect of strain rate and crack extension rate on the direct tensile strength is analyzed. • A critical strain rate causing the crack initiation stress to be the peak strength is found.