The Discrete Element Method (DEM) numerical model, due to its inherent capability to reflect both macroscopic and microscopic mechanical characteristics of materials, has been widely adopted by many scholars in the field of rock mechanics research. However, the challenges of scale bridging and parameter calibration associated with DEM numerical simulations have posed significant challenges to researchers. Moreover, a unified and widely accepted quantitative analysis method has yet to be established. In this study, based on a DEM model of circular particles arranged in a regular pattern, we conducted a mechanical analysis of the correlation between microscopic contact failure modes and macroscopic tensile strength. Our findings indicate that the macroscopic tensile strength of rock specimens depends on the internal microscopic contact failure modes. These microscopic failure modes are influenced by several factors, including contact tensile strength, contact shear strength, contact normal stiffness, contact tangential stiffness, particle size, and arrangement. Through theoretical analysis and numerical simulation results, we proposed four microscopic failure modes and corresponding theoretical formulas for calculating macroscopic tensile strength. These formulas were then applied to DEM models of randomly arranged particles. From a microscopic perspective, we revealed the mechanisms of macroscopic tensile failure in DEM rock-like materials and established a correlation for macroscopic tensile strength parameters. The validity of the established correlation formulas was effectively verified by a large number of random numerical simulation results. This work provides an important reference for researchers in selecting and calibrating parameters for simulating brittle materials such as rocks and concrete using particle-based DEM numerical models.