<p>Experimental data.</p>

To address the issue that open-pit blasting delay designs struggle to concurrently mitigate vibration and optimize fragmentation, this article proposes an interval-based delay optimization framework integrating theory and experiments.Unlike traditional fixed-value delay designs, this framework responds to the variability of blasting parameters and rock mass properties, determining a reasonable delay time interval rather than a single fixed value to realize synergistic control of vibration mitigation and fragmentation optimization. It adopts Hanukayev's theory for delay time calculation, the Swebrec function for fragmentation evaluation, and the “vibration reduction rate” for vibration assessment. Experiments were conducted on C50 concrete specimens using a 3-hole model. The results indicate that inter-hole delays of 3-4 ms and inter-row delays of 1-3 ms enable effective coupling control. Among all schemes, the optimal 3 ms/3 ms (inter-hole/inter-row) scheme achieves remarkable effects: it reduces the peak particle velocity (PPV) in the free surface direction and reverse direction by 70% and 54% respectively, while decreasing the average fragment size and large fragment size by 10% and 9.3% respectively. This research provides crucial theoretical support for safe and efficient mine blasting operations.