Delay bench blasting is commonly used in open-pit mining, where the effectiveness of rock fragmentation is closely linked to delay times. This study investigates the delay bench blasting process through theoretical analysis. Dimensional analysis is employed to derive similarity criteria for delayed blasting, and a dimensionless delay time parameter \(\tau_{\mathrm{m}}^{*}\) is introduced. A relationship between scaled experiments, numerical simulations, and practical applications is established. The Riedel-Hiermaier-Thoma (RHT) model parameters for sandstone are obtained from a double-hole delayed blasting funnel test. Additionally, a three-dimensional, six-hole delayed blasting numerical simulation is conducted to analyze stress wave superposition and rock fracture behavior under varying delay times. Field validation tests are also performed. The results indicate that the delay time parameter is effective in both small-scale experiments and numerical simulations, significantly enhancing testing efficiency. Moreover, delay time has a marked influence on the bench blasting effect. Analysis shows that the average damage value \(\bar{D}_{\text{ter}}\) and fragment size distribution effectively capture the impact of delay time on blasting outcomes. As the inter-hole delay time increases, \(\bar{D}_{\text{ter}}\) follows an “M”-shaped curve. In contrast, as the inter-row delay time increases, \(\bar{D}_{\text{ter}}\) exhibits a “∩”-shaped curve. The study also reveals that effective stress superposition occurs only near stress wave collision points, with the effective stress enhancement region limited to less than 5db. Based on these findings, it is recommended to combine small-scale tests, numerical simulations, and field experiments to optimize delay time parameters, achieving the best rock fragmentation and reducing overall mining costs.
