# Numerical Simulation of Fluid Pore Pressure Diffusion and Its Mechanical Effects during Wenchuan Aftershocks

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}/s from the envelope line, with a corresponding permeability of k = 3.7 × 10

^{−15}m

^{2}[14]. The estimated value is reasonable compared to the seismogenic fault rock permeability [33]. Therefore, we select the area NA as the study area here and establish a three-dimensional hydraulic–mechanical coupling model based on the previous work.

## 3. Method

#### 3.1. The Mathematical Model

^{3}, $S$ is the saturation, $k$ is the permeability, m

^{2}, $P$ is the pore pressure, Pa, and $Q$ is the source term, m

^{3}/s.

#### 3.2. The Numerical Model

#### 3.3. Initial and Boundary Conditions

^{3}and $g$ is the gravitational acceleration of 10 m/s

^{2}.

^{3}/s for the Matsushiro earthquake swarm [40], but the magnitude of Wenchuan earthquake was much higher than those of the Matsushiro earthquakes. Hence, the source term is assumed as 1.5 m

^{3}/s in our model.

## 4. Results

#### 4.1. Pore Pressure Increases Caused by the Fluid Intrusion

#### 4.2. Changes in Maximum Horizontal Stress and Vertical Stress Caused by Fluid Intrusion

#### 4.3. Fault Reactivation Caused by Fluid Intrusion

## 5. Discussion

#### 5.1. Aftershock Triggering Mechanisms and Pore Pressure Diffusion

#### 5.2. Spatiotemporal Distribution of Aftershocks and Pore Pressure Diffusion

#### 5.3. Numerical Aspects of the Model

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Spatiotemporal distributions of aftershocks [1]. Reproduced with permission from Liu et al., Tectonophysics; published by Elsevier, 2014, with Number 5270230803519.

**Figure 2.**(

**a**) The area NA. The star denotes the location of the Wenchuan mainshock, the solid black lines denote faults, F1 denotes the back fault, F2 denotes the central fault, and F3 denotes the piedmont fault (Deng et al., 2003). (

**b**) Spatiotemporal distribution of aftershocks in the area NA. The grey color represents the topography of the area. (

**c**) The r–t plot for the area NA. The red lines are the envelope lines for different hydraulic diffusivities D and the blue circles denote aftershocks. (

**d**) The M–t plot for the area NA.

**Figure 3.**The model geometry and meshes used in the study. (

**a**) A 3D view of the grid. (

**b**) Plane view of the fault zone in the Y–Z plane. The triangle denotes the fluid intrusion point.

**Figure 4.**The distribution of increasing pore pressure at different times during the fluid intrusion.

**Figure 5.**The increases of pore pressure along the dip (solid line) and strike (dashed line) from the intrusion point in the fault plane.

**Figure 6.**The distribution of effective stress (

**a**) in the X-direction ${{\sigma}^{\prime}}_{H\mathrm{max}}$; (

**b**) in the Z-direction ${\sigma}_{v}^{\prime}$ during the fluid intrusion.

**Figure 7.**The distribution of the stress ratio ${{\sigma}^{\prime}}_{H\mathrm{max}}$/${\sigma}_{v}^{\prime}$ during the fluid intrusion.

**Figure 8.**A comparison of the spatiotemporal distribution of aftershocks and the numerical simulation of the fault reactivation area. (

**a**) The aftershock distribution at different times. (

**b**) The calculated fault reactivation area at different times.

**Figure 9.**Pore pressure along the dip from the intrusion point in the fault plane for varied model and grid dimensions.

Properties | Rock Matrix | Fault |
---|---|---|

Bulk modulus (Pa) | 4.667 × 10^{10} | 2.800 × 10^{10} |

Shear modulus (Pa) | 2.890 × 10^{10} | 1.646 × 10^{10} |

Rock density (kg/m^{3}) | 2600 | 2600 |

Fluid density (kg/m^{3}) | N/A | 1000 |

Static friction coefficient | N/A | 0.6 |

Fluid modulus (Pa) | N/A | 2.2 × 10^{10} |

Permeability (m^{2}) | N/A | 3.7 × 10^{−15} |

Biot coefficient | N/A | 1.00 |

Porosity | N/A | 0.05 |

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**MDPI and ACS Style**

Chen, T.; Liu, Y.; Zhang, G.
Numerical Simulation of Fluid Pore Pressure Diffusion and Its Mechanical Effects during Wenchuan Aftershocks. *Water* **2022**, *14*, 952.
https://doi.org/10.3390/w14060952

**AMA Style**

Chen T, Liu Y, Zhang G.
Numerical Simulation of Fluid Pore Pressure Diffusion and Its Mechanical Effects during Wenchuan Aftershocks. *Water*. 2022; 14(6):952.
https://doi.org/10.3390/w14060952

**Chicago/Turabian Style**

Chen, Tao, Yaowei Liu, and Guomeng Zhang.
2022. "Numerical Simulation of Fluid Pore Pressure Diffusion and Its Mechanical Effects during Wenchuan Aftershocks" *Water* 14, no. 6: 952.
https://doi.org/10.3390/w14060952