This study examines how coarse aggregate volume fraction (V_a) affects the double-K fracture toughness and fundamental mechanical properties of concrete. Wedge-splitting tests were conducted on specimens with six different V_a values: 19%, 25%, 31%, 37%, 43%, and 50%. The results indicate that compressive strength (f_c) and elastic modulus (E) consistently increase with V_a, reaching 59.8 MPa and 37.9 GPa at V_a = 50%, respectively. Conversely, tensile strength (f_t), double-K fracture toughness (including initiation toughness $K_{\mathrm{IC}}^{\mathrm{ini}}$ and unstable toughness $K_{\mathrm{IC}}^{\mathrm{un}}$), and fracture energy (G_IF) initially increase before decreasing, peaking at an optimal V_a of 37%. Specifically, $K_{\mathrm{IC}}^{\mathrm{ini}}$, $K_{\mathrm{IC}}^{\mathrm{un}}$, and G_IF reached their maximum values of 0.54 MPa·m^1/2, 1.20 MPa·m^1/2, and 225.0 N/m at V_a = 37%. The tortuosity of crack paths follows a similar trend, becoming more pronounced up to V_a = 37% before diminishing. Furthermore, quantitative exponential relationships were established between f_t and $K_{\mathrm{IC}}^{\mathrm{ini}}$, $K_{\mathrm{IC}}^{\mathrm{un}}$, and G_IF. A safety warning parameter (δ), derived from the double-K fracture toughness, was proposed to quantitatively assess the pre-peak ductility, with values ranging from 0.88 to 0.72 in this study. The findings offer valuable guidance for optimizing concrete mix design, suggesting that a V_a range of 25% to 31% provides an optimal balance between high crack initiation resistance and adequate safety warning capacity for critical engineering structures.