# Numerical Simulation and Characterization of the Hydromechanical Alterations at the Zafarraya Fault Due to the 1884 Andalusia Earthquake (Spain)

^{*}

## Abstract

**:**

## 1. Introduction

^{2}, affecting about one hundred urban centers in the provinces of Granada and Málaga. The most affected areas, with significant building collapses, deaths, and injuries, were Southwest of the province of Granada and to the East of the province of Malaga. Arenas del Rey was the most affected town: 90% of the houses collapsed, and the rest suffered damages; there were 135 dead and 253 wounded people. Alhama de Granada had the highest number of victims, with 463 dead and 473 injured. More than 70% of the houses collapsed. Following that, a new quarter was built near the Hoya del Ejido. After the 1755 Lisbon earthquake, the only quake in the Iberian Peninsula with greater magnitude than the 1884 event occurred in 1954, with its epicenter in Granada. However, the destruction in this case was not as great. The tremor caused rock falls and landslides on slopes, aggravating the earthquake effects. The former also caused the formation of numerous cracks. In addition, the earthquake induced hydrogeological effects of diverse ranges [6,7,8].

**Figure 1.**(

**Above**) location of the study area and trace of the Zafarraya Fault, source of the 1884 Andalusia earthquake (Adapted from [16]). (

**Below**) tectonic schematic of the simultaneous development of folds with possible blind thrust faults and two normal fault systems in a detachment roof block. Type I faults, such as the Zafarraya Fault, would be produced by external arc extension and collapse of the antiforms that constitute the main E–SW reliefs. Type II faults would respond to the regional stress field with a NE–SW extension direction (Adapted from [17]).

**Figure 2.**Alterations after the 1884 event. Left: map of the hydrogeological alterations produced. Right: diagram of the variation of the phreatic level (Right inset accronyms: Z, Zafarraya; VZ, Ventas de Zafarraya; A.G., Alhama de Granada).

- To describe and analyze the hydrogeological phenomena induced by the Andalusian earthquake of 1884.
- To establish a hydromechanical conceptual model of the Zafarraya Fault that explains and allows understanding of these hydrological alterations.
- To implement a hydromechanical numerical model to simulate the conditions of the massif surrounding the main fault during the pre-seismic and co-seismic phases. The results obtained from this simulation allow us to understand and explain the features and effects of the 1884 major event.
- To perform both matching and calibration of both models.

## 2. Methodology

- Description of the hydrological alterations due to the 1884 Andalusia earthquake according to historical surveys.

- Based on bibliographic background, the next stage seeks the setup of the geological and hydrogeological framework and the seismotectonic characterization of the Zafarraya Fault surrounding area.
- Setup of a preliminary hydromechanical conceptual model.

## 3. The Zafarraya Fault Geology and Hydrological Phenomena Induced by Andalusia Earthquake

#### 3.1. The Zafarraya Fault: Tectonic Context, Displacement, and Recurrence Periods

- A.
- Sierra Gorda Karstic Aquifer: it holds a free aquifer with Jurassic limestone and dolomite and a Keuper impermeable bottom. The carbonate formations are more than 1000 m thick. The average rainfall in the area is 840 mm. Its hydrogeological parameters are: transmissivity T = 40 − 16.4 m
^{2}; storage coefficient S = 1.5%. - B.
- Polje of Zafarraya detrital aquifer: made up of Miocene and Quaternary infill sediments from the basin, having a maximum thickness of 280 m. The upper Miocene and Quaternary sediments are about 60 m thick and include sandy and gravel alluvial deposits with clay intercalations. In general, this upper detrital aquifer feeds the limestone aquifer underneath, but sometimes the reverse happens due to heavy rains that flood the polje. The flow is directed mainly towards the NE, with a gradient of 0.085–1.7%. This aquifer is heavily exploited, with 400 wells, and the water table is shallow, less than 15 m deep.

#### 3.2. Hydrogeological Alterations: Types and Geographical Distribution

## 4. Geological Model of the Zafarraya Fault and Numerical Model Setup

#### 4.1. 2D Geological Model of the Fault

#### 4.2. Coupled Physics Included in the Simulation Model

- ${\rho}_{f}$ is the fluid (water) density.
- ${S}_{\epsilon}$ is the constrained specific storage coefficient, which represents the volume of water either extracted from or added to storage in a confined aquifer per unit area of aquifer per unit decline or increase in the piezometric head. This unknown coefficient needs to be estimated through a model calibration. When the solid phase consists of a single constituent, the constrained specific storage becomes [40,41]:$${S}_{\epsilon}=\varphi {\chi}_{f}+\left({\alpha}_{B}-\varphi \right){\chi}_{s}=\varphi {\chi}_{f}+\frac{\left({\alpha}_{B}-\varphi \right)\left(1-{\alpha}_{B}\right)}{K}.$$

- $k$ is the intrinsic permeability of the porous medium $\left[{\mathrm{m}}^{2}\right]$.
- ${\eta}_{f}$ is the dynamic viscosity of the fluid.
- $\mathsf{\sigma}$ is the Cauchy stress tensor.
- ${\rho}_{b}$ is the bulk rock density, ${\rho}_{b}=\varphi {\rho}_{f}+\left(1-\varphi \right){\rho}_{d}$ and ${\rho}_{d}$ the dry rock density.
- $\mathbf{g}$ is the gravity acceleration vector.

**u**of the solid matrix, i.e., the acceleration field of the solid points.

#### 4.3. Numerical Model Setup

#### 4.4. The Fault Frictional Model

- ${\tau}^{*}$ is the shear resistance at any fault point.
- $c$ is the cohesion term of the resistance, neglected in this study.
- We include a radiation damping term that acts as a velocity-dependent cohesion, $\xi V$, in the definition of fault strength to resolve the rupture dynamics. Then we consider a damping factor $\xi =G/3.6{C}_{s}$, with ${C}_{s}=\sqrt{G/{\rho}_{b}}$ being the shear wave speed. The phenomenon of radiation damping accounts for the volumetric dissipation mechanism of seismic waves in the definition of the friction resistance of the fault [39,43,44].
- $\mu $ is the friction coefficient of the contact.
- ${\sigma}_{n}^{\prime}$ is the effective contact (normal) pressure at any fault contact point. It is given by ${\sigma}_{n}^{\prime}=p-{T}_{n}$, with ${T}_{n}$ being the contact pressure between the fault edges (compressive pressures are positive). Its value is chosen as the maximum on both sides of the fault, $p=max\left({p}^{-},{p}^{+}\right)$ [45]. The fault remains locked when the shear stress acting on the fault, $\tau $, is lower than the frictional strength, $\tau <{\tau}_{f}$; otherwise, it slips.

- ${q}_{in}^{-}={T}_{f}\left({p}^{+}-{p}^{-}\right),{q}_{in}^{+}={T}_{f}\left({p}^{-}-{p}^{+}\right).$

#### 4.5. The Ground Model and Properties

#### 4.6. The Finite Element Domain

## 5. Results and Discussion

_{2}sequestration [38,59], salt water or wastewater disposal [60], enhanced geothermal systems [61,62,63], hydrogen storage, and enhanced oil recovery and hydraulic fracturing during wells construction in the oil and gas industries [64,65], among other applications.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Left: geological section of the Zafarraya fault. Right: Detail section of the near-surface region with the filling of the Zafarraya Polje (adapted from [29]).

**Figure 4.**Schematic flowchart of the hydromechanical coupling of the diverse physics involved in the numerical simulation.

**Figure 5.**State of initial stresses (von Mises) (

**left**) and shear stress state at the fault plane (

**right**) at the beginning of the interseismic period. The acting shear stresses (blue) at the highlighted segment are close to the shear strength (green), thus this region is likely to nucleate the earthquake. (

**a**) Initial static stress state. It includes an alteration due to the tectonic history. (

**b**) Shear stress state at the fault plane.

**Figure 7.**Discretization of the 2D finite element mesh in accordance with the scheme of Figure 3.

**Figure 8.**Results from the dynamic analysis: (

**a**) Total acceleration field ($\mathrm{m}/{\mathrm{s}}^{2}$); (

**b**) Maximum pore overpressure ($\mathrm{Pa}$) induced by the earthquake. White lines represent the flow trajectories. Abscissae represent the fault line ($\mathrm{m}$), starting from its bottom.

**Figure 9.**Time progress of the earthquake rupture: the patch grows in size during rupture. Abscissae represent the fault line ($\mathrm{m}$), starting from its bottom. Green arrow pairs indicate the time evolution of the depicted quantities. (

**a**) Velocities tangent to the fault plane ($\mathrm{m}/\mathrm{s}$). As seismic rupture goes on, the patch enlarges and the rupture velocity decreases. (

**b**) The maximum relative slip between fault edges ($\mathrm{m}$) induced during the earthquake rupture is $0.62\mathrm{m}$.

Density ${\mathit{\rho}}_{\mathit{d}}$ (Ton/m ^{3})
| Effective Porosity $\mathit{\varphi}$ (%) | Permeability $\mathit{\kappa}$ (m/s) | Depth of Water Table (m) | |
---|---|---|---|---|

1 | 2.00 | 13 | 1 m/day | <15 |

2 | 2.00 | 10 | 10^{−4}–10^{−7} | - |

3 | 2.00 | 0.5 | 10^{−6} | - |

4 | - | 0.5 | - | - |

5 | 2.67 | 1.5 | 10^{−3}–10^{−9} | - |

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**MDPI and ACS Style**

Mudarra-Hernández, M.; Mosquera-Feijoo, J.C.; Sanz-Pérez, E.
Numerical Simulation and Characterization of the Hydromechanical Alterations at the Zafarraya Fault Due to the 1884 Andalusia Earthquake (Spain). *Water* **2023**, *15*, 850.
https://doi.org/10.3390/w15050850

**AMA Style**

Mudarra-Hernández M, Mosquera-Feijoo JC, Sanz-Pérez E.
Numerical Simulation and Characterization of the Hydromechanical Alterations at the Zafarraya Fault Due to the 1884 Andalusia Earthquake (Spain). *Water*. 2023; 15(5):850.
https://doi.org/10.3390/w15050850

**Chicago/Turabian Style**

Mudarra-Hernández, Manuel, Juan Carlos Mosquera-Feijoo, and Eugenio Sanz-Pérez.
2023. "Numerical Simulation and Characterization of the Hydromechanical Alterations at the Zafarraya Fault Due to the 1884 Andalusia Earthquake (Spain)" *Water* 15, no. 5: 850.
https://doi.org/10.3390/w15050850