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.

类岩石材料是异质的并且包含许多缺陷。在压缩下，广泛使用的二维翼形裂纹模型无法准确描述裂纹的三维行为，因为三维二次裂纹会在单轴加载下包裹（卷曲）在盘状一次裂纹周围。此外，实验结果表明，当横向压缩高于轴向压缩的约 6% 时，单个嵌入裂纹容易扩展。为了准确描述单轴压缩载荷下裂纹的三维行为，我们提出了一种三维翼形裂纹模型，该模型结合了裂纹扩展动力学、惯性效应、摩擦系数对裂纹面滑动速度的依赖性，以及裂缝之间的相互作用。我们对裂纹扩展动力学方程、裂纹相互作用方程、摩擦系数方程和本构方程进行数值求解，以估计摩擦系数和裂纹密度对含I型裂纹样品动态强度的影响。数值结果表明，随着裂纹密度的增加，试样的裂纹扩展开始和破坏都发生得更早，而开始和破坏点的加载应力减小。惯性引起的附加轴向应力随着裂纹密度的增加而增加。与考虑恒定摩擦系数时相比，考虑修改后的摩擦定律时，在较低负载应力下，样品的失效发生得更早。和本构方程来估计摩擦系数和裂纹密度对包含 I 型裂纹样品的动态强度的影响。数值结果表明，随着裂纹密度的增加，试样的裂纹扩展开始和破坏都发生得更早，而开始和破坏点的加载应力减小。惯性引起的附加轴向应力随着裂纹密度的增加而增加。与考虑恒定摩擦系数时相比，考虑修改后的摩擦定律时，在较低负载应力下，样品的失效发生得更早。和本构方程来估计摩擦系数和裂纹密度对包含 I 型裂纹样品的动态强度的影响。数值结果表明，随着裂纹密度的增加，试样的裂纹扩展开始和破坏都发生得更早，而开始和破坏点的加载应力减小。惯性引起的附加轴向应力随着裂纹密度的增加而增加。与考虑恒定摩擦系数时相比，考虑修改后的摩擦定律时，在较低负载应力下，样品的失效发生得更早。试样的裂纹扩展开始和破坏都发生得更早，而开始和破坏点的加载应力降低。惯性引起的附加轴向应力随着裂纹密度的增加而增加。与考虑恒定摩擦系数时相比，考虑修改后的摩擦定律时，在较低负载应力下，样品的失效发生得更早。试样的裂纹扩展开始和破坏都发生得更早，而开始和破坏点的加载应力降低。惯性引起的附加轴向应力随着裂纹密度的增加而增加。与考虑恒定摩擦系数时相比，考虑修改后的摩擦定律时，在较低负载应力下，样品的失效发生得更早。