Abstract Risk assessment of the propagation of stress waves induced by blast loading is an important aspect engineering design and practice. Pre-existing geological structures affect the propagation of stress waves in the rock masses/strata. For homogenous materials, the wave energy scatters in the forms of wave reflection, refraction, diffraction, and mode conversion. The coefficient of absorption and scattering losses can help to understand the structural (joints, cracks, and large-scale faults) and physical properties (strength, lithology) of the rock masses/strata. Therefore, to explore the influence of interacting faults on the propagation of blast loading-induced stress waves, six 3D high-resolution numerical models were developed and run on with COMSOL Multiphysics software to test the influence of the Young's Modulus (E) of two pre-existing and interacting faults on the attenuation, superposition, and reflection of nonlinear stress waves. The results show that propagation of the stress waves through the domain in between the two faults amplified the stress energy. Moreover, and the stress wave intensity increased noticeably as they entered and left the tips of the interacting faults. The optimal propagation path of the stress waves lie within the materials whose E differ the least from that of the surrounding rocks. The fluctuation of the displacement along fault A was relatively large when the E of fault A was small (R = 0.1). The maximum strain energy density ( S E D ) dropped by 84.2% from 3396 J/m3 to 536 J/m3 from the beginning tip to the middle domain of fault A; and further dropped by 28.9% as the waves traveled from the middle part to the tail of fault A. he reduction in the SED is in agreement to the power function (y = 3409x−0.406, R = 0.9994). The time interval (△FP) for having obtained the different △SED between the neighboring crest and trough of the frequency is significantly different. △FP yielded approximately 0.002, 0.0022 and 0.0325 s at an equal propagation distance from the beginning tip to the tail of the faults, respectively. This indicates that the energy loss during the first stage is large, and the stress wave decays quickly. This paper contributes significantly to our contemporary understanding of the attenuation, superposition, and reflection effects of the blast-loading induced stress wave propagation between the interacting tips of adjacent faults.

中文翻译：

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展开断层对控制爆炸载荷引起的非线性应力波传播的影响的 3D 建模

摘要 爆炸载荷引起的应力波传播风险评估是工程设计和实践的一个重要方面。预先存在的地质结构会影响应力波在岩体/地层中的传播。对于均质材料，波能以波反射、折射、衍射和模式转换的形式散射。吸收和散射损失系数有助于了解岩体/地层的结构（节理、裂缝和大型断层）和物理特性（强度、岩性）。因此，为了探索相互作用断层对爆炸载荷应力波传播的影响，开发了六个 3D 高分辨率数值模型，并在 COMSOL Multiphysics 软件上运行，以测试杨氏应力波的影响。s 两个预先存在且相互作用的断层对非线性应力波的衰减、叠加和反射的模量 (E)。结果表明，应力波通过两个断层之间的域的传播放大了应力能量。此外，应力波强度随着它们进入和离开相互作用断层的尖端而显着增加。应力波的最佳传播路径位于 E 与围岩 E 差异最小的材料内。当断层 A 的 E 较小时（R = 0.1），沿断层 A 的位移波动较大。最大应变能密度（ SED ）从断层A的始端到中间区域由3396 J/m3下降到536 J/m3，下降了84.2%；并进一步下降了 28。9% 的波从中间部分传播到断层 A 的尾部。SED 的减少与幂函数一致（y = 3409x−0.406，R = 0.9994）。频率的相邻波峰和波谷之间获得不同△SED的时间间隔(△FP)明显不同。△FP 在断层起始端到尾端等传播距离下分别产生了大约 0.002、0.0022 和 0.0325 s。这说明第一阶段能量损失大，应力波衰减快。本文对我们当代对相邻断层相互作用尖端之间爆炸载荷引起的应力波传播的衰减、叠加和反射效应的理解做出了重大贡献。SED 的减少与幂函数一致（y = 3409x−0.406，R = 0.9994）。频率的相邻波峰和波谷之间获得不同△SED的时间间隔(△FP)明显不同。△FP 在从断层的起始尖端到尾部的相等传播距离下分别产生了大约 0.002、0.0022 和 0.0325 s。这说明第一阶段能量损失大，应力波衰减快。本文对我们当代对相邻断层相互作用尖端之间爆炸载荷引起的应力波传播的衰减、叠加和反射效应的理解做出了重大贡献。SED 的减少与幂函数一致（y = 3409x−0.406，R = 0.9994）。频率的相邻波峰和波谷之间获得不同△SED的时间间隔(△FP)明显不同。△FP 在断层起始端到尾端等传播距离下分别产生了大约 0.002、0.0022 和 0.0325 s。这说明第一阶段能量损失大，应力波衰减快。本文对我们当代对相邻断层相互作用尖端之间爆炸载荷引起的应力波传播的衰减、叠加和反射效应的理解做出了重大贡献。频率的相邻波峰和波谷之间获得不同△SED的时间间隔(△FP)明显不同。△FP 在断层起始端到尾端等传播距离下分别产生了大约 0.002、0.0022 和 0.0325 s。这说明第一阶段能量损失大，应力波衰减快。本文对我们当代对相邻断层相互作用尖端之间爆炸载荷引起的应力波传播的衰减、叠加和反射效应的理解做出了重大贡献。频率的相邻波峰和波谷之间获得不同△SED的时间间隔(△FP)明显不同。△FP 在断层起始端到尾端等传播距离下分别产生了大约 0.002、0.0022 和 0.0325 s。这说明第一阶段能量损失大，应力波衰减快。本文对我们当代对相邻断层相互作用尖端之间爆炸载荷引起的应力波传播的衰减、叠加和反射效应的理解做出了重大贡献。这说明第一阶段能量损失大，应力波衰减快。本文对我们当代对相邻断层相互作用尖端之间爆炸载荷引起的应力波传播的衰减、叠加和反射效应的理解做出了重大贡献。这说明第一阶段能量损失大，应力波衰减快。本文对我们当代对相邻断层相互作用尖端之间爆炸载荷引起的应力波传播的衰减、叠加和反射效应的理解做出了重大贡献。