# Influence of Relative Sea-Level Rise, Meteoric Water Infiltration and Rock Weathering on Giant Volcanic Landslides

## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Slope Stability Model

_{c}= σ

_{n}tanϕ + C until the landslide occurs, where σ

_{n}is the normal stress, ϕ is the friction angle of the slope-forming material, and C is the cohesion, and could be used to describe bedded rocks [27]. Considering the angle for which the effective cohesion is maximized for a value equal to β/2 + ϕ/2, it is assumed that θ = β/2 + ϕ/2 [25,28]. This model allows us to calculate the maximum stable height for a simple geometry (Figure 2A):

_{r}g[1 − cos (β − ϕ)])

_{r}is the bulk rock density, and g is the gravitational acceleration. This model has been widely used in geomorphological studies to predict the maximum unfailed height of slopes [25]. In the theoretical calculation, vertical loading, pore pressure increase and volcanic rock properties with depth are included. Including the pore pressure U and considering the load of the sea water column of thickness H

_{m}with a bulk density of the water ρ

_{m}, the following can be obtained:

^{2}− 4 H (C sin β cos ϕ − U sin ϕ cos β)/(ρ

_{r}g [1 − cos (β − ϕ)]) + ρ

_{m}H

_{m}

^{2}/ρ

_{r}= 0

_{1}+ H

_{1}cos β sin (β/2 + ϕ/2)/sin (β/2 − ϕ/2)

_{1}can be calculated by resolving the following equation:

_{1}

^{2}− 4H

_{1}(C cos ϕ − U sin ϕ)/(ρ

_{r}g[sin β – sin ϕ])

+ ρ

_{m}H

_{m}

^{2}sin (β/2 − ϕ/2)/(ρ

_{r}sin β cos β/2 + ϕ/2) = 0

_{S}= resisting forces/driving forces ≈ [τ × S]/[ρ

_{r}V g sin θ] when the slope is destabilized only by its own weight [6,24,29].

#### 2.2. Mechanical Properties of Volcanic Rocks

^{l}, where H is the slope height, and k and l are coefficients determined experimentally for different volcanic rocks [5]. For weathered, massive lavas, k = 0.04 and l varies from 0.41 to 0.60. For weakly cemented pyroclasts, k = 0.05 and l = 0.5. The angle of friction ϕ could also be estimated using the equation ϕ = a ln(H) + b, where a and b are obtained experimentally. Rodriguez-Losada et al. [5] showed that very low friction angles of <13° are obtained at depths >1000 m for low cemented pyroclasts (a = 6; b = 54). A volcanic edifice composed of low cemented pyroclasts has cohesion values between 0.5 and 1 MPa at depths of 1500–3000 m (Figure 3A). At this depth, a theoretical volcanic edifice with weakly cemented pyroclasts has friction angles between 6° and 10° (Figure 3B).

#### 2.3. Modeling Hydroclimatic Variations

^{18}O variation [35,36]. A δ

^{18}O curve [37] was used to simulate climate forcing. This curve was recalibrated to simulate Quaternary sea level variations reaching an amplitude of 120 m.

^{18}O curves [38]. In this study, it is assumed that more humid conditions are capable of causing an increase in the effective pore pressure. The purpose of this assumption is to discuss the timing of potential giant landslides in relation to Quaternary climatic conditions (i.e., precipitation rates). The time required for the water to flow from the surface to a depth of 4.5 km was estimated to be ~150 days in Oregon [39]. In the model, the propagation is considered instantaneous, which is justified on a long time scale (>1 kyr). The amplitude of the variation of the pore pressure ΔP due to water infiltration into the crust is 0.01 MPa at Mt. Hood [39] and 2 MPa on the south flank of Kilauea volcano [17]. In this study, different values for the pore pressure variation were tested in the case where sea level effects are dominant (0 < ΔP < 0.125 MPa) and in the case where pore pressure processes are dominant (0 < ΔP < 0.5 MPa).

#### 2.4. Pressure Variation in the Magma Reservoir

_{SL}(t) = gρ

_{m}H

_{m}(t).

_{M})

_{S}(dP

_{M}/dt − U·▽P

_{M})

_{M}is the magma reservoir pressure, F is the melt fraction, t is the time, and U is the mean mantle upwelling rate.

_{M}/dt can be considered as a function of the seawater unloading variation δΔL

_{SL}/dt under adiabatic conditions and for very high viscosity (i.e., η

_{c}=10

^{23}Pa.s) of the crustal rocks. In this case, δΔP

_{M}/dt = −δΔL

_{SL}/dt.

_{c}< 10

^{22}Pa.s; [40]), the equation is δΔP

_{M}/dt +ΔP

_{M}(E

_{c}/η

_{c}) = −δΔL

_{SL}/dt, where E

_{c}is the elastic modulus, and a delay of ~10 kyr after the forcing by sea water unloading is expected.

## 3. Results

#### 3.1. Influence of Water Column Loading on Slope Stability

#### 3.2. Influence of the Pore Pressure on Slope Stability

#### 3.3. Competing Influence of Sea Level Loading vs. Pore Pressure Variations over Time on Slope Stability

## 4. Discussion

#### 4.1. Rock Weathering and Slope Instability

#### 4.2. Weakness Zones and Geological Inheritance

#### 4.3. Sea Level Variation Effect on Landslides and Volcanic Activity

_{S}as the loading decreases. When a significant loading is above the center of mass of the potential landslide, it causes the destabilization of the slope by triggering rock failure (Figure 7B).

#### 4.4. Pore Pressure Variation

#### 4.5. Climate Variation and Correlation with Giant Landslides

^{22}Pa.s), it could also be correlated with the magma chamber unloading due to sea level lowering. This result could be influenced by the data set considered, and further studies on giant landslides on volcanic islands would improve this interpretation.

Volcano | Age (ka) | References |
---|---|---|

Canary Islands (El Hierro, El Golfo) | 10–17 | [60] |

La Réunion | 20–68 | [61] |

Hawaii (Alika phase 1) | 112 | [43] |

Hawaii (Alika phase 2) | 127 ± 10 | [43] |

Canary Islands (El Hierro, El Golfo) | 134 ± 6 | [3] |

Hawaii (Southern Lanai) | 135 | [62] |

Canary Islands (Tenerife) | 150–170 | [63] [64] |

Hawaii (Southern Lanai) | 240 | [62] |

La Réunion | 290–320 | [61] |

Martinique | 337 ± 5 | [65] |

Canary Islands (La Palma) | 537 ± 8 | [66] [67] |

Guadeloupe | 629 ± 13 | [68] |

Hawaii (Haleakala, Hana) | 860 | [69] |

Tahiti-Nui (north) | 872 ± 10 | [30] |

#### 4.6. Discussion of Giant Landslides Real Cases

#### 4.7. Small Landslides vs. Giant Landslides

## 5. Conclusions

_{c}< 10

^{22}Pa.s), a delay of 10 kyrs could occur. During the last million years, several giant landslides in tropical areas have been correlated with sea level unloading during glacial periods of uplift, suggesting that this effect is a driving mechanism in many cases.

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Complex evolution of volcanic edifices and locations of deep weakness zone, (

**T1**) Young volcanic edifice composed of massive lavas, (

**T2**) Volcanic edifice after a giant landslide caused by a volcanic process, where pyroclastic flows, as well as soil and lava weathering, occur, (

**T3**) Filling of the landslide scar by thick volcanic lavas above the pyroclastic debris and the weathered soils, (

**T4**) Deep rooting of the landslide into the weakness zone favored by meteoric water infiltration and/or sea level loading in the case of an old and complex volcano and/or the presence of deeply incised canyons.

**Figure 2.**Effect of the initial slope β on the maximum stable relief H for two different landslide geometries. (

**A**) Cullman wedge model, (

**B**) concave geometry model. ρ

_{c}= 3000 kgm

^{−3}, C = 1 MPa, ϕ = 10

^{0}.

**Figure 3.**Effect of depth on mechanical properties. (

**A**) Cohesion for low cemented pyroclasts (k = 0.05; l = 0.5) and fresh (k = 0.37; l = 0.60) and weathered (k = 0.04; l = 0.41 and 0.60) massive lavas, (

**B**) Angle of friction for low cemented pyroclasts (a = 6; b = 54) and fresh (a = 5.6; b = 82) and weathered (a = 7; b = 75) massive lavas.

**Figure 4.**(

**A**) Effect of increasing pore pressure and sea water loading on the relief stability. The light gray area represents the field where a theoretically stable relief changes to an unstable relief when submitted to an increase in the sea water column loading between 0 and 400 m and an increase in pore-water pressure between 0 MPa and 2 MPa. (

**B**) Schematic representation of the effect of subsidence. (

**C**) The details are as follows: a relief of ~200 m with a slope of 25° < β < 30° could be affected by water loading (dark gray square). ρ

_{c}= 3000 kgm

^{−3}, C = 1 MPa, ϕ = 10° and the geometry of the landslide is identical to those presented in Figure 2A.

**Figure 5.**(

**A**) Maximum height H before the landslide occurred. The geometry of the island is shown in Figure 4. The effects of sea level loading and pore pressure are simulated. The sea water loading depends on the variation in sea level, while the effect of the pore pressure depends on the fluctuation in precipitation. In the first case (sea level-dominated), the pore pressure is considered to range between 0 and 125 kPa depending on the climatic variation. In the second case (pore pressure-dominated), the pore pressure is assumed to range between 0 and 500 kPa depending on the climatic variation. The absolute values of H are indicative, and only the trends are interpreted in this study. g = 9.81 ms

^{−2}, C = 1 MPa, ϕ = 10°, ρ = 2800 kg/m

^{−3}, β = 7°, and a subsidence rate of 0.25 mm/yr are considered. (

**B**) Simulated sea level variations during the last million years using the δ

^{18}O curve of Lisiecki and Raymo [37]. The light blue lines represent the giant landslides on volcanoes during the last 1 Ma of Table 1.

**Figure 7.**Influence of the sea level variation with respect to the position of the center of mass of the potential sliding area: (

**A**) Slope instability caused by sea level lowering when the load is located at the base of the slope, (

**B**) slope instability caused by a sea level rise above the center of mass with seawater infiltration.

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**MDPI and ACS Style**

Gargani, J.
Influence of Relative Sea-Level Rise, Meteoric Water Infiltration and Rock Weathering on Giant Volcanic Landslides. *Geosciences* **2023**, *13*, 113.
https://doi.org/10.3390/geosciences13040113

**AMA Style**

Gargani J.
Influence of Relative Sea-Level Rise, Meteoric Water Infiltration and Rock Weathering on Giant Volcanic Landslides. *Geosciences*. 2023; 13(4):113.
https://doi.org/10.3390/geosciences13040113

**Chicago/Turabian Style**

Gargani, Julien.
2023. "Influence of Relative Sea-Level Rise, Meteoric Water Infiltration and Rock Weathering on Giant Volcanic Landslides" *Geosciences* 13, no. 4: 113.
https://doi.org/10.3390/geosciences13040113