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Rock-like materials are heterogeneous and contain numerous defects. Under compression, the widely used two-dimensional wing crack models cannot accurately describe the three-dimensional behaviour of cracks because the three-dimensional secondary crack will wrap (curl) around the disc-shaped primary crack under uniaxial loading. Moreover, experimental results have shown that a single embedded crack expands easily when the lateral compression is higher than approximately 6% of the axial compression. To describe the three-dimensional behaviour of cracks under uniaxial compressive loading accurately, we propose a three-dimensional wing crack model that incorporates the crack propagation dynamics, the inertia effect, the dependence of the friction coefficient on the slip velocity of the crack faces, and the interaction between cracks. We numerically solve the crack propagation dynamics equation, crack interaction equations, friction coefficient equations, and constitutive equation to estimate the effects of the friction coefficient and crack density on the dynamic strength of samples containing mode I cracks. The numerical results indicate that as the crack density increases, the initiation of crack growth and failure of the sample both occur earlier, while the loading stress at the initiation and failure points decreases. The inertia-induced additional axial stress increases with increasing crack density. The failure of the sample occurs earlier at a lower loading stress when considering the modified friction law than when considering a constant friction coefficient.