Extended finite element simulation of the influence ofnew-cracks on the propagation of fault spontaneous ruptures across stepover
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摘要:
采用扩展有限元方法计算了断层阶区内介质产生的新生破裂对地震破裂跨越断层阶区传播过程的影响。模型中新生的断层扩展遵循最大剪应力破坏准则，当最大剪应力超过岩石的承受极限时，完整介质产生破裂形成新的断层，并且新断层的扩展方向为最大剪应力方向。扩展有限元法模拟结果表明，断层阶区内新生的断层改变了断层阶区的几何形态，同时也改变了断层破裂后的应力状态。新生破裂可以改变库仑应力在空间的分布格局，特别是可以提高断层上的应力水平，从而提高地震破裂跨越断层阶区的能力。模拟结果还显示，断层阶区内新生破裂的产生，可以使得地震破裂跨越10 km宽的断层阶区，若阶区内部介质没有产生新生破裂，则地震破裂无法跨越该断层阶区。本研究有助于进一步认识地震破裂跨越断层阶区的传播过程，特别是对地震震源过程分析及地震灾害评估等具有重要的科学意义。
Abstract:The step over plays a significant controlling role in the propagation process of seismic rupture. Researchers, based on geological survey results of multiple strike-slip earthquakes globally, have indicated that it is challenging for seismic rupture to cross step over wider than 5 km. Results from numerous numerical simulations also demonstrate that seismic rupture, under conditions such as uniform elastic media and uniform stress fields, cannot extend beyond step over wider than 5 km. However, as research progresses, it has been observed that in few earthquakes, rupture does cross step over wider than 5 km. And research fellows offer various explanations for this phenomenon, including higher stress near step over, changes in material properties due to rock damage, or the presence of concealed faults, among others. Drawing inspiration from previous studies, this paper proposes a novel explanation. In numerical simulations of the seismic rupture process, it is commonly assumed that rupture occurs only on pre-existing faults. Nevertheless, it is highly likely that new ruptures may generate outside pre-existing faults during seismic events, giving rise to new faults. The rocks near step over are relatively brittle and are more likely to generate new ruptures during seismic events, thereby allowing rupture to cross wider step over. This study employs the extended finite element method to investigate the influence of newly generated ruptures near step over on the seismic rupture propagation process. A step over model with a width of 10 km is established. The newly generated ruptures in the model follow the maximum shear stress failure criterion; when the maximum shear stress exceeds the rock’ s ultimate limit, a new fault is formed in the intact medium, and the direction of the new rupture’ s expansion corresponds to the direction of maximum shear stress. According to the results of rock physical experiments, the model medium’ s maximum shear stress limit is set as 72 MPa. The simulation results using the extended finite element method in this study show that after an earthquake occurs, the rupture first propagates to the end of the pre-existing fault, and then new ruptures occur near the step over. The expansion direction of the new rupture is nearly perpendicular to the strike of the pre-existing fault, and the fault continues to expand for 1.8 s, with an expansion length of approximately 8.2 km and an expansion velocity of approximately 4 556 m/s. This study also establishes a model that does not consider newly generated ruptures for comparison. Without considering new ruptures, the rupture cannot cross a 10 km wide step over. The paper compares Coulomb stress distribution maps at a specific moment in these two scenarios. According to the Coulomb stress distribution, it is evident that without considering newly generated ruptures, the rupture in this model can only cross step over for the model approximately 5 km wide. The new ruptures alter the geometry of the step over and greatly change the spatial distribution pattern of Coulomb stress, especially by elevating stress levels on the fault, thereby enhancing the ability of seismic rupture to cross step over and allowing it to cross step over 10 km wide. This study contributes to a deeper understanding of the propagation process of seismic rupture across step over, particularly for seismic source process analysis and seismic hazard assessment.
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Keywords:
- stepover /
- new-crack /
- spontaneous rupture /
- extended finite element method
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图 4 模型2中不同时刻新生断层扩展长度的变化
Figure 4. Variation of the length of newly-generated fault at different time in Model 2
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图 2 模型1中断层破裂在不同时刻质点振动速度等值线云图的快照
Figure 2. Snap shots of spatial contour distributions of particle velocities at different times in fault rupture propagation in Model 1
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图 3 模型2中断层破裂传播过程中，不同时刻质点振动速度等值线云图快照
图中黑线表示新产生的断层 （下同），长度大约8.2 km，方向与断层1和断层2几乎垂直
Figure 3. Contour distributions of particle velocities at different time in fault rupture propagation in Model 2
The newly-created fault is shown as black line （the same below），and it is about 8.2 km long and is almost perpendicular to the strikes of faults 1 and 2
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图 5 模型1 （a）和模型2 （b）中库仑应力空间分布图
Figure 5. The spatial distributions of Coulomb stresses in Model 1 and 2
表 1 模型参数
Table 1 Model parameters
初始正应力
σ/MPa初始剪应力
τ/MPa横波速度
vS/（m·s−1）纵波速度
vP/（m·s−1）介质密度
ρ/（kg·m−3）成核区长度
/km岩石承受的最大剪应力
/MPa100 56 5 959 3 294 2 700 2 72 
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