# Numerical Modeling of an Asteroid Impact on Earth: Matching Field Observations at the Chicxulub Crater Using the Distinct Element Method (DEM)

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Characteristics of Chicxulub Crater

## 3. Methodology

#### Profile Reconstruction and Comparison Methodology

## 4. DEM Model

^{3}. The model was composed of nine different layers with increasing particle size from the surface to the container baseline, corresponding to the observed stratigraphy (i.e., ranging from 5 m to 40 m in diameter). Table 1 includes each layer depth and its corresponding particle size. Notice that the increase in particle size was considered to reduce computational costs, as well as to reflect the physical aspect of basement rocks and mantle layers. The first three layers had the properties of a weak sedimentary limestone layer, while the rest had properties of hard granite rocks. The stratigraphy configuration was obtained by reproducing a sedimentary process under gravity. The asteroid had identical properties to the sedimentary limestone layer. The model’s particle container size used in the numerical simulation was set to 4 km by 2 km after downscaling the actual stratigraphy, and the Earth’s gravitational force of 9.81 m/s

^{2}was considered throughout the simulations.

#### 4.1. Constitutive Model

#### 4.2. Boundary Conditions

#### 4.3. Control (Measurement) Circles

## 5. Simulation Results

#### 5.1. Crater Surface Topography

#### 5.2. Simulated vs. Target Profile Analysis

#### 5.3. Velocity Fields

^{−4}s/calculation cycle. Figure A5, Figure A6, Figure A7 and Figure A8 show simulations from the asteroid impact at 90°, 60°, 45°, 30° inclinations at 15 km/s impact velocity, and Figure A9, Figure A10, Figure A11 and Figure A12 show simulations at 90°, 60°, 45°, 30° inclinations and at 22.5 km/s. A comparative analysis across these two sets of simulations showed the relevance of the asteroid’s impact velocity and inclination, and its nonlinear association as depicted in Figure 8, which further provided a better understanding of the likely phenomenological behavior of the asteroid impact and the crater formation process.

#### 5.4. Horizontal and Vertical Stresses

#### 5.5. Contact Force Chains

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Final Crater Profile and Crater Evolution

#### Appendix A.1. Final Crater Profile after 2 Million Calculation Cycles

**Figure A1.**Final craters, corresponding to different asteroid velocities of 10 km/s (

**a**), 12.5 km/s (

**b**), 15 km/s (

**c**), 17.5 km/s (

**d**), 20 km/s (

**e**), and 22.5 km/s (

**f**), at an impact angle 90°.

**Figure A2.**Final craters, corresponding to different asteroid velocities of 10 km/s (

**a**), 12.5 km/s (

**b**), 15 km/s (

**c**), 17.5 km/s (

**d**), 20 km/s (

**e**), and 22.5 km/s (

**f**), at an impact angle 60°.

**Figure A3.**Final craters, corresponding to different asteroid velocities of 10 km/s (

**a**), 12.5 km/s (

**b**), 15 km/s (

**c**), 17.5 km/s (

**d**), 20 km/s (

**e**), and 22.5 km/s (

**f**), at an impact angle of 45°.

**Figure A4.**Final craters, corresponding to different asteroid velocities of 10 km/s (

**a**), 12.5 km/s (

**b**), 15 km/s (

**c**), 17.5 km/s (

**d**), 20 km/s (

**e**), and 22.5 km/s (

**f**), at an impact angle of 30°.

#### Appendix A.2. Evolution of the Crater Impact

**Figure A5.**Velocity field variation right after impact at 90° and asteroid velocity of 15 km/s, at calculation cycles of 5000 (

**a**), 10,000 (

**b**), 15,000 (

**c**), 20,000 (

**d**), 40,000 (

**e**), and 80,000 (

**f**).

**Figure A6.**Velocity field variation right after impact at 60° and asteroid velocity of 15 km/s, at calculation cycles of 5000 (

**a**), 10,000 (

**b**), 15,000 (

**c**), 20,000 (

**d**), 40,000 (

**e**), and 80,000 (

**f**).

**Figure A7.**Velocity field variation right after impact at 45° and asteroid velocity of 15 km/s, at calculation cycles of 5000 (

**a**), 10,000 (

**b**), 15,000 (

**c**), 20,000 (

**d**), 40,000 (

**e**), and 80,000 (

**f**).

**Figure A8.**Velocity field variation right after impact at 30° and asteroid velocity of 15 km/s, at calculation cycles of 5000 (

**a**), 10,000 (

**b**), 15,000 (

**c**), 20,000 (

**d**), 40,000 (

**e**), and 80,000 (

**f**).

**Figure A9.**Velocity field variation right after impact at 90° and asteroid velocity of 22.5 km/s, at calculation cycles of 5000 (

**a**), 10,000 (

**b**), 15,000 (

**c**), 20,000 (

**d**), 40,000 (

**e**), and 80,000 (

**f**).

**Figure A10.**Velocity field variation right after impact at 60° and asteroid velocity of 22.5 km/s, at calculation cycles of 5000 (

**a**), 10,000 (

**b**), 15,000 (

**c**), 20,000 (

**d**), 40,000 (

**e**), and 80,000 (

**f**).

**Figure A11.**Velocity field variation right after impact at 45° and asteroid velocity of 22.5 km/s, at calculation cycles of 5000 (

**a**), 10,000 (

**b**), 15,000 (

**c**), 20,000 (

**d**), 40,000 (

**e**), and 80,000 (

**f**).

**Figure A12.**Velocity field variation right after impact at 30° and asteroid velocity of 22.5 km/s, at calculation cycles of 5000 (

**a**), 10,000 (

**b**), 15,000 (

**c**), 20,000 (

**d**), 40,000 (

**e**), and 80,000 (

**f**).

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**Figure 1.**Chicxulub crater with the cross-section of interest ‘Chicx-A/A1′, and the corresponding drilling locations. Reconstructed from Salguero-Hernandez et al. [2].

**Figure 2.**Schematic graph of the model experimental design with varying impact angle and velocity (highlighted in red font).

**Figure 3.**Aerial map of the Yucatán Peninsula. Peak ring center, crater center, and mantle uplift center are marked, along with the cross-section of interest, Chicx-A/A1. Approximate surface topography, produced using 3D iSALE hydrocode for an impact direction from northeast to southwest [18,19], is also shown above for an asteroid impact of 60° at 12 km/s. Area bounded by the red line indicates the region with uplift, while the blue line indicates the region of depression. This image was reconstructed with data from Salguero-Hernandez et al. [2] and by Collins et al. [19].

**Figure 5.**Verification of the infinite boundary condition. Red particle is a rolling ball exerting a force in resting particles 1–5 who serve as control points to assess the influence of the boundary condition.

**Figure 6.**Locations of the 200 m control circles along the centerline and 20 m control circles along the wall boundaries. Colors or the circles only represent their independent locations.

**Figure 7.**Crater topographies for 90° (

**a**), 60° (

**b**), 45° (

**c**), and 30° (

**d**) impact angles at various speeds. Reconstructed topography from Collins et al. [18] was retrieved from the plane of the intersection of interest.

**Figure 8.**Mean squared error (MSE) surface of different combinations of velocity and impact angle. The red plot markers represent the profile simulated using PFC2D presented in this study, while the black plot markers represent the reconstructed profile from Collins et al. [19].

**Figure 9.**Vertical stress (

**a**) and horizontal stress (

**b**) histories for asteroid impacts at a velocity of 15 km/s with an impact angle of 90°.

**Figure 10.**Maximum vertical stress (

**a**) and maximum horizontal stress (

**b**) for asteroid impacts at 90° impact angle and with various velocities.

**Figure 11.**Maximum vertical stress (

**a**) and maximum horizontal stress (

**b**) for asteroid impacts at 60° impact angle and with various velocities.

**Figure 12.**Maximum vertical stress (

**a**) and maximum horizontal stress (

**b**) for asteroid impacts at 45° impact angle and with various velocities.

**Figure 13.**Maximum vertical stress (

**a**) and maximum horizontal stress (

**b**) for asteroid impacts at 30° impact angle and with various velocities.

**Figure 14.**Maximum vertical stress (

**a**) and maximum horizontal stress (

**b**) for asteroid impacts at 15 km/s and with different impact angles.

**Figure 15.**Maximum vertical stress (

**a**) and maximum horizontal stress (

**b**) for asteroid impacts at 17.5 km/s and with different impact angles.

**Figure 16.**Maximum vertical stress (

**a**) and maximum horizontal stress (

**b**) for asteroid impacts at 20 km/s and with different impact angles.

**Figure 17.**Maximum vertical stress (

**a**) and maximum horizontal stress (

**b**) for asteroid impacts at 22.5 km/s and with different impact angles.

**Figure 18.**Maps of linear contact force chains (

**a**) and linear parallel bond contact force chain (

**b**) before (

**top row**) and after (

**bottom row**) asteroid impact at a velocity of 15 km/s at an impact angle of 90°.

Layer | Material | Layer Depth (m) | Particle Diameter (m) |
---|---|---|---|

1 | Sedimentary Limestone | 10 | 5 |

2 | 30 | 5 | |

3 | Rock Basement | 90 | 5 |

4 | 180 | 10 | |

5 | 180 | 10 | |

6 | 180 | 10 | |

7 | 360 | 20 | |

8 | 360 | 20 | |

9 | 610 | 40 |

Name | Contact Type | Particle Normal Stiffness | Particle Shear Stiffness | Friction Coefficient | Bond Normal Stiffness | Bond Shear Stiffness | Bond Tension | Bond Cohesion |
---|---|---|---|---|---|---|---|---|

Pa | Pa | - | Pa | Pa | N | N | ||

Asteroid | Linear parallel bond | 4.0 × 10^{9} | 1.6 × 10^{9} | 0.3 | 4.0 × 10^{9} | 1.6 × 10^{9} | 4.0 × 10^{6} | 4.0 × 10^{6} |

Sedimentary limestone | Linear parallel bond | 4.0 × 10^{9} | 1.6 × 10^{9} | 0.3 | 4.0 × 10^{9} | 1.6 × 10^{9} | 4.0 × 10^{6} | 4.0 × 10^{6} |

Rock basement | Linear parallel bond | 40.0 × 10^{9} | 16.0 × 10^{9} | 0.3 | 40.0 × 10^{9} | 16.0 × 10^{9} | 40.0 × 10^{6} | 40.0 × 10^{6} |

Walls | Linear contact | 5 × 10^{10} | 5 × 10^{10} | 0 | - | - | - | - |

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**MDPI and ACS Style**

Duong, T.N.-M.; Hernawan, B.; Medina-Cetina, Z.; Urrutia Fucugauchi, J.
Numerical Modeling of an Asteroid Impact on Earth: Matching Field Observations at the Chicxulub Crater Using the Distinct Element Method (DEM). *Geosciences* **2023**, *13*, 139.
https://doi.org/10.3390/geosciences13050139

**AMA Style**

Duong TN-M, Hernawan B, Medina-Cetina Z, Urrutia Fucugauchi J.
Numerical Modeling of an Asteroid Impact on Earth: Matching Field Observations at the Chicxulub Crater Using the Distinct Element Method (DEM). *Geosciences*. 2023; 13(5):139.
https://doi.org/10.3390/geosciences13050139

**Chicago/Turabian Style**

Duong, Tam N.-M., Billy Hernawan, Zenon Medina-Cetina, and Jaime Urrutia Fucugauchi.
2023. "Numerical Modeling of an Asteroid Impact on Earth: Matching Field Observations at the Chicxulub Crater Using the Distinct Element Method (DEM)" *Geosciences* 13, no. 5: 139.
https://doi.org/10.3390/geosciences13050139