# The Future of Abandoned Shallow Mines as a Function of Precipitation Under Changing Climate

Nathalie Conil, Marwan Al Heib

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Nathalie Conil, Marwan Al Heib. The Future of Abandoned Shallow Mines as a Function of Precipitation Under Changing Climate. Applied Sciences, 2025, 15 (2), pp.932. 10.3390/app15020932. ineris-04991229

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Article

# The Future of Abandoned Shallow Mines as a Function of Precipitation Under Changing Climate

Nathalie Conil and Marwan Al Heib

Institut National de l'Environnement Industriel et des Risques, 60550 Verneuil-en-Halatte, France;
nathalie.conil@ineris.fr

* Correspondence: marwan.alheib@ineris.fr

**Abstract:** The paper discusses the future of abandoned underground mines and the main hazards related to their instability, specifically local and large collapses. A database of over 500 large collapses is presented. The analysis of these events reveals that the primary causes are the extraction ratio, ageing and climatic factors (such as heavy rain, and increasing water levels). Furthermore, a back analysis of a large-scale collapse, the Château-Landon collapse of 1910, showed that the collapse resulted from a combination of the mining conditions and slope instability climate factor, particularly the impact of rainfall on mine stability. In the case of Château-Landon, the water had two effects: it reduced the resistance of the chalk and decreased the shear strength of the fault crossing the slope. The back analysis and database contribute to a better understanding of mine collapses caused by mining conditions and the modification of climate conditions.

**Keywords:** mines; hazards; ground movements; prediction; large collapse; precipitation; climate change; slope; database; modelling; back analysis

## 1. Introduction

There are hundreds of thousands of natural or anthropogenic underground cavities and abandoned mines worldwide. A significant portion of these man-made underground cavities are abandoned after the extraction of materials such as stones and minerals. These cavities are subject to natural degradation processes including the effect of climatic conditions, primarily water, and the decreasing of the bearing capacity of the rock and underground structures.

Recent climate studies looking at different scenarios indicate changes in the intensity and frequency of climatic events: such as heavy rainfall and longer dry seasons. Scientists worldwide have studied the effects of climate change on temperature, weather patterns, rainfalls and more [1,2]. Several studies have focused on the relationship between specific geohazards and climate change, primarily addressing hurricanes, volcanic activity, floods and heat waves. While the relationship between the ground movements (e.g., landslide, clay swelling) and climate change has also been explored, ground movements related to cavities such as underground mines have been less analysed in this context [3]. Precipitation is one of the parameters of climate change. The potential impact of climate change on the stability of underground cavities depends on the influence of water on the long-term hydromechanical behaviour of the rock [4]. The effect of water (the saturation impact) on chalk behaviour, short- and long-term, was fully studied at small scale and large scale.

The main objective of this study is to learn from past events to better manage future risks. To this end, a database containing over 500 cases of collapse was created, spanning

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updates

Academic Editor: Hang Lin

Received: 11 December 2024

Revised: 29 December 2024

Accepted: 6 January 2025

Published: 18 January 2025

**Citation:** Conil, N.; Al Heib, M. The Future of Abandoned Shallow Mines as a Function of Precipitation Under Changing Climate. *Appl. Sci.* **2025**, *15*, 932. https://doi.org/10.3390/app15020932

**Copyright:** © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
nearly three centuries, to identify the causes of these large-scale collapses. In this article, we present a study focusing on the historical and large-scale collapse of an underground chalk mine (the Beaulieu mine) in 1910, which resulted in seven fatalities. For this case, experts have suggested that an exceptional climatic event occurred before the collapse, but other factors should be investigated to better understand their interaction. The objective is to describe clearly the mechanism behind this massive collapse in the context of climate change. Based on their findings, operational recommendations are made for incorporating climate parameters into the assessment and prediction of collapse risks of abandoned underground mines.

## 2. History of Underground Mines in France

In France, between the 10th and early-20th centuries, many shallow mines (<50 m) were dug to extract materials such as talc, gypsum, alluvial sand, limestone, andalusite, kaolin, silica sand, diatomite and building stones for construction and industrial sectors. The geographical distribution of underground mines corresponds to the spatial distribution of the outcrops of the exploited rocks (Figure 1). The shallow underground mines of Paris form a network of old mines, dug from the 12th century to the 18th century, connected by inspection galleries. Over time, many of the city's old mines have been abandoned and degraded. After being exploited for stone, many of them were put to other uses such as growing salads and mushrooms because of the ideal growing conditions (darkness, constant temperature and humidity). Today, these mines are completely abandoned despite several attempts at valorisation. With ongoing urban development, new housing developments have been built above these underground mines today, posing a significant danger to public safety, especially when they are located beneath buildings and infrastructures.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Density of the underground cavities (chalk, gypsum, limestone), certain zones present more than 20 cavities per town.</figcaption></figure>

## 3. Extraction Methods and Potential Geohazards

The main extraction method used in underground shallow mines is the room and pillar method (Figure 2). This method is widely used in shallow mining operations (up to a few hundred meters below ground level). The principle of the method is to extract ore while leaving pillars in place to support the land above the deposit. Depending on the quality of the material, the thickness of the extraction, and the depth of the mining area, the dimension of the pillars left in place is more or less important. The height of the pillars can reach several tens of meters. The space cleared between the pillars is called the "room", hence, the name of the method.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Room and pillar method for shallow underground mines—example from Paris basin, limestone room and pillar mine.</figcaption></figure>

When mining ends, this is referred to as “mining by abandoned rooms and pillars”. If during or after mining, the rooms are backfilled, or when the pillars collapse, the land above the extraction zone presents a lower risk of collapse compared to when the rooms are abandoned, unless the extracted ore dissolves in water.

The objective of mining is primarily to increase production and optimise operation, by enhancing the operating rate while maintaining “acceptable” safety and stability conditions in the short term. However, these conditions are not sustainable in the long term given the degradation processes of underground mines; consequently, all underground mines are destined to collapse, to varying degrees, over the long term. These collapses can be localised (such as sinkholes) or generalised, with varying degrees of impact on the surface. Increasing the safety factor, defined as the ratio of the strength to the pillar load, more than two is not enough to avoid the mine’s collapse [5]. Ref. [6] presented 17 examples of massive collapses that occurred in various mining activities around the world, including salt, coal and limestone mining. The surface area of these collapses ranges from 0.1 hectares to approximately 300 hectares. These events have caused injuries and destroyed houses, such as the collapse in Clamart (Hauts-de-Seine) in 1961, which resulted in 21 deaths and 50 injuries. In Europe, several countries have experienced ground movements linked to underground cavities, for example, Belgium, Great Britain, Germany, the Netherlands, Italy, Spain, Poland, etc. In France, several dramatic collapses have occurred, for example, the Clamart collapse (1961) causing 21 deaths and 36 injuries, the Château-Landon collapse causing 7 deaths (1910), and the Hautil collapse (1991). While the loss of life is relatively low compared to other geohazards, such as massive landslides, the consequences for infrastructure can be significant.

The stability of an underground mine depends on the pillar stress and the strength of the extracted material. The average vertical stress of the pillar ($\sigma_p$) can be calculated using the tributary (Figure 3), considering the depth of the mine ($H$) and the extraction ratio ($t$). For complex configurations and abandoned mines, the average vertical stress pillar is a function of several parameters, as expressed by the following equation:

$$ \sigma_p = f(\gamma, \tau, F, H, G, T) \qquad (1) $$

where

$\gamma$: the density of the overburden.

$\tau$: the extraction ratio, which depends on the geometry of the rooms and the pillars.

$F$: the fault impact on the stress distribution.

$G$: the configuration impact (slope, valley, etc.) on the stress distribution.

$T$: the time and ageing impact.
Water influences the behaviour of faults and discontinuities, as well as the short- and long-term behaviour of rock mass. It can reduce the strength and the effective stresses. Estimating the real stress on the pillar is a challenging task, even using very sophisticated advanced constitutive laws and numerical models, which, however, can help to better understand and quantify these effects.

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Room-pillar mining method—pillar stress estimation using analytical calculation method: tributary air method using the geometry parameters and the density of the rock.</figcaption></figure>

Some scholars prefer to integrate various factors to determine the bearing capacity of the pillar by considering the width and height of the pillar, form factor, discontinuities, etc. Ref. [7] introduced a discontinuity factor in their empirical pillar strength formula, which reduces the uniaxial compressive strength of the intact rock. The general expression of the pillar strength is:

$$R_p = f(UCS, w, h, D, T) \qquad (2)$$

where

UCS: the uniaxial compression strength of the intact rock for the mining layer.

w: the width of the pillar.

h: the height of the pillar.

D: the discontinuity impact on the pillar strength.

T: the time, ageing and impact on the pillar strength.

## 4. Causes of the Instabilities of Underground Shallow Mines

The degradation of underground mines is evident and may well be amplified by changes in the climate. Different types of underground instabilities are generally observed and manifested on the surface, as well as in structures and infrastructures. Instability and associated movements result from both intrinsic and external factors. The intrinsic, internal factors of the underground mine are the lithological and structural environment, their typology, the natural fracturing of the rock mass, the extraction and mining techniques, and the geometry of the voids (particularly the exploitation plan). For the room-pillar method, the slenderness of the pillars and the superposition of the pillars in multi-level mining operations also play a role. External factors include water, vegetation, land use on the surface, and natural and/or induced vibration. Water is the most important external factor influencing the behaviour of soft and hard rocks surrounding the tunnels [8]. Its actions are manifold, including the reduction in the resistance of the soil and the increase
in hydraulic load. Water can also increase the dimensions of the galleries (rooms) through dissolution mechanisms, particularly in limestone and gypsum rocks. Water is the main factor related to climate change and can impact mostly the stability of the underground excavation. The collapse is generally the combination of internal and external factors. Figure 4 presents a risk assessment of underground cavities based on internal and external factors. Two configurations are considered. In the first configuration, the cavity is initially stable due to the extraction ratio and the quality of the rock mass; it generally remains stable over time except in exceptional, unfavourable conditions. In the second configuration, the cavity is initially unstable due to the extraction ratio and the quality of the rock mass; the collapse can be progressive or brutal. To reduce the risk, mitigation measures are often recommended to ensure long-term stability.

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Risk assessment analysis of abandoned underground cavities (shallow mines), highlighting the role of the external and internal factors in the ground movement occurrence.</figcaption></figure>

To mitigate the hazard of ground movement, the safest strategy involves restricting access to areas highly susceptible to significant collapses. Risk can be managed by either reducing the activity and severity of the processes (hazard), minimizing vulnerability or both. Various engineering techniques can be employed [9,10]. Special foundations, such as piles, micro-piles and rigid inclusions, are commonly used to transfer structural loads to stable soil layers or rigid bedrock, offering protection against localised and limited collapses [11]. Reinforcement of parks, linear infrastructures, roads and railways can be achieved by incorporating geosynthetics (GSY) over the substratum or within embankments [12]. The selection of mitigation techniques depends on the type of land use and the balance between safety, security and cost-effectiveness. Additionally, the chosen method should consider the thresholds of risk: intolerable risk, tolerable risk and broadly acceptable risk. Risks involving loss of life fall under the first category and must not be tolerated.

Before the collapse occurs, various disorders are often observed in underground mines, such as deflection of roof slabs, block falls, deformations and fractures in the pillars. When a pillar experiences significant overload compared to its resistance, it can fracture and collapse. The presence of discontinuities further aggravates the situation. Lithological alternation can cause disorders particularly due to the contrasting behaviour of different layers: ductile for some benches and brittle for others. Punching of the pillars is also
observed when the walls consist of low-strength rocks. Specific observations concern the mines that operate on multiple levels (two or more), as are characterised by breakages in the interlayers. This significantly increases the stress on the pillars and can lead to shearing due to poor pillar alignment.

The consequences of this underground damage can lead to surface ground movement. This manifestation depends on several factors including the depth of the mine, the failure mode, the nature of the overburden and the extent of the underground voids. Surface topography also plays a role, particularly the effects of slope. When a mine collapses beneath a slope, more complex phenomena such as landslides can occur; this is the case of under-caved cliffs. The rise of the collapse bell can suddenly cause a surface collapse, and based on its diameter, one can distinguish between a localised collapse and a massive collapse. The collapse takes the form of a pseudo-circular hole. Its diameter depends on the diameter of the sinkhole bell, the presence of water, and the geomechanical characteristics of the surface terrain. Massive collapses, which are accidents that typically affect room and pillar operations, result in large-scale subsidence or collapses (Figure 5). These spontaneous collapses are often accompanied by the rupture of the roof (upper layer) or wall (lower layer) of the operations and can be associated with tremors. Regardless of the operational context and geometric characteristics, the triggering factor in both cases is often a hydraulic overload resulting from exceptional rainfall events. Massive collapses concern a large area of the mine, affecting either the total or partial collapse, of several pillars. Figure 5 presents the configuration of a general collapse. The role of the hard rock bed in this case is still unclear. On the surface, the edges of the collapse are sharp, and they are generally marked by open fractures. The dimensions of the collapse can reach several hectares. Figure 5 presents the observation of the historic collapse of Clamart, 1961, where the magnitude of the subsidence exceeded 5 m [13].

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Large and massive collapse of an underground shallow room-pillar mine due to the ruin of a set of pillars, and large collapse induced large cervices; this example is of the collapse of the Clamart chalk underground mine, France (1961).</figcaption></figure>

When cavities are dug into the side of a vertical or subvertical cliff, the destabilisation of these voids is complex due to the natural degradation of an unstable hillside (Figure 6). Cliff collapses are particularly dangerous because they involve a considerable rock mass often on the scale of the site (several tens of thousands of cubic metres). The interaction between the cavity and the slope alters the distribution of induced stresses, which can lead to instabilities [14]. The consequences are often worsened by the fact that the areas at the foot of the cliff are generally urbanised. Such an accident occurred in Rochecorbon (Indre-et-Loire) in 1933, mobilising 30,000 m³ of rock, destroying four houses and causing several casualties. Another example is the landslide at the Vendôme subterranean cliff in 1910, which damaged several homes (Figure 6).
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Landslide of undermined cliff- example of Vendôme, France (1910). The collapse of the underground mine induced the fractures and the landslide of the slope.</figcaption></figure>

The presence of a cavity in a cliff increases the risk of instability, which depends on the geometry and topography of the cliff and the cavity. Several researchers have studied the stability of under-caved cliffs [15–17]. They observed that failure can be induced by tensile and shear stresses. The fracturing of the rock mass has also been studied by various authors [15,18–21]. The main impact results from the mechanical relaxation of the rocks at the edge of the slope, which induces decompression of the mass and creates cracks subparallel to the slope (Figure 5). However, according to [18], decompression does not create new fractures but merely makes pre-existing cracks more visible by opening them. Thus, it is more indicative of the previous state of discontinuity of the mass than the creation of new ruptures.

**5. Climate Change and Underground Mine Stability**

Climate parameters, such as precipitation, temperature changes and humidity varia-
tions can alter the initial conditions of the underground mines. Therefore, it is important
to investigate the role of climate change in the underground collapses. Few studies have
focused on natural cavities and sinkhole hazards [22]. The flooding of the underground
mines and the modification of the water levels increase the vulnerability of the under-
ground of these mines [23]. The future of abandoned underground mines in the context of
climate change raises crucial questions, particularly regarding risk management for people,
property and infrastructure. However, the relationship between the collapse of natural
and anthropogenic cavities linked to climate change is little explored [3]. The study of
climate change is hindered by the lack of recorded climatic data and their direct impact.
Therefore, the back analysis of historical data is the key tool for identifying the main causes
of collapses and understanding the role of climate change. Several researchers have studied
the consequences of changes in stability following changes in water conditions [8,24–26].
Their findings clearly show that the risk of instability increases, particularly in the long
term, due to a reduction in resistance, sometimes significantly, and on the development of
tensile stresses that favour the rupture.
**6. Database of Massive Collapses**

An analysis of the cases allowed for the identification of internal predisposing, such as the geometry and the geomorphology of the underground mines, and the nature of the materials exploited, as well as the influence of the water factor as an external triggering factor in its various forms (proximity to a watercourse, heavy precipitation, rising water tables, flooding, dewatering, etc.), all of which play a key role in triggering collapses.

Figure 7 shows collapse frequency as a function of the extraction ratio, as an internal factor, for the 184 mines for which this information exists (i.e., 34% of cases). For these cases, the extraction ratio is systematically higher than 50%, and a significant increase in the frequency of collapses is noted beyond 75%, corresponding to the almost total exploitation of the quarry surface. This can be explained by the fact that the higher the extraction ratio, the greater the load on the pillars.

<figure><img src="image_9.png" /><figcaption>**Figure 7.** Number of collapses of underground mines in France, and the function of the extraction ratio of the underground mine using the room-pillar mining method.</figcaption></figure>

The geomorphological-water correlation context is important, particularly to better understand water circulation within underground cavities (infiltration of meteoric water on plateaus, rising water table in valleys, etc.). Based on the feedback of the 184 events, typical geomorphological configurations are identified. Figure 8 presents the defined geomorphological configuration in the vertical or horizontal plan:

* Vertically, four main geomorphological configurations (in grey in the Figure 8):

* Configuration 1 “bottom of the slope” corresponds to underground mines located at an altitude close to that of the watercourse or the water table.

* Configuration 3 “top of the slope” corresponds to underground mines excavated just below the surface of a plateau but situated at a sufficient altitude above a watercourse and the water table to avoid the risk of flooding or submersion.

* Configuration 2 “mid-slope” corresponds to the middle of the slope.

* Configuration 4 “plateau” corresponds to the same case as the top one but is located outside the mechanically stressed zone associated with the proximity of a slope generally beyond 100 to 150 m [20,21].

* Horizontally, four main geomorphological configurations were identified (highlighted in yellow in Figure 8):
* Configuration 1 corresponds to the cornice, at the edge of a plateau where fracturing density is highest.

* Configuration 2 and configuration 3 correspond to mine excavated at the confluence of two valleys, such as spurs where two cracking directions parallel to each slope can coexist.

* Configuration 4 corresponds to the plateau, away from the fracturing zone.

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Diagram of typical underground mine configurations related to the position of the principal and secondary valleys, 7 configurations can be observed (3 vertically (grey) and 4 horizontally (orange)).</figcaption></figure>

Figure 9 presents the distribution of the collapse and stable mines according to the geomorphology configurations. Considering the horizontal and vertical geomorphological configurations (Figure 8), the first indicates the mine's distance from a watercourse, the second indicates the mine height in relation to the valley, and the study shows a predominance of the spur and mid-slope configurations in the collapses (Figure 8). There is no clear evidence of the role of the configuration. However, it can be observed that the cornice and the top of the slope configurations show the highest ratio of the collapsed mines. While the spur and mid-slope configurations present stable mines.

<figure><img src="image_11.png" /><figcaption>(a) Vertical geomorphology configurations</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>(b) Horizontal geomorphology configurations</figcaption></figure>

<caption>**Figure 9.** Histograms as a function of geomorphological configurations (cf. Figure 8).</caption>

Ageing, since the extraction time, is a complex parameter that combines internal and external factors. The statistical analysis of this database shows an increase in the number of collapses inducing subsidence from the second half of the 20th century (Figure 10).
<figure><img src="image_13.png" /><figcaption>**Figure 10.** Number of collapses of underground mines in France as a function of the occurrence year since 1741.</figcaption></figure>

The number of collapses per year, for the 473 collapse cases, shows that the number of collapses increased over time, mainly in the last fifty years (Figure 10). This phenomenon may reflect the ageing of these structures and the decreasing of the strength of the rock; it is very possible that the long-term resistance of a rock mass evolves, for example, by decreasing through ageing or by alteration [27]. Delayed failure then occurs when the resistance to failure becomes equal to the applied stresses. Certainly, the augmentation of the collapse number is due to several external and internal factors. The humidity and water are the main factors of the strength reduction [28,29].

Statistical studies are underway to take maximum advantage of the information collected from these collapse cases. Another benefit of this database is the ability to conduct back analysis of case studies, especially when there is a wealth of information available about a particular event. Below, we present one of these case studies.

# 7. Case Study—Chateau-Landon 1910

## 7.1. *Description of the Collapse*

Two major collapses in the databases affected chalk mines in France with fatalities, namely, the Beaulieu and Clamart shallow mines [13,30]. These cases are particularly well documented. The analysis presented below concerns the collapse of the Beaulieu shallow mine (Figure 11).

The sudden massive collapse of the under-excavated cliff in 1910, which spanned over 100 m and from a height of 20 m, resulted in seven victims and the destruction of several homes. It involved an abandoned chalk mine. The volume of materials was estimated at 1 Mm³ [30,31] (Figure 12). The mine used the room and pillar method, with galleries that are 3 to 5 m high. The main galleries were generally oriented perpendicular to the slope while the secondary galleries oriented parallel to the axis of the valley. The sections of the pillars increased towards the interior of the massif, but their arrangement and geometry remained quite irregular. The depth of the shallow mine ranged from a few metres near the excavations to around thirty metres in the deepest sectors.
<figure><img src="image_14.png" /><figcaption>**Figure 11.** Location of the chalk mines in France (yellow dots) with main collapse (green stars) on the left, and the Château-Landon area presenting the different mines (in red, collapsed mines).</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Figure 12.** Archive photos showing the mine before and after the collapse of the chalk mine and the landslide.</figcaption></figure>

The collapse of the under-excavated slope happened over 10 days; the last day being the most intense one. This meteorologic event caused a centennial flood of the Seine and its tributaries such as the Loing, which flooded the alluvial plain and reached the lower part of the underground chalk mine [32].

Several research efforts have been conducted since the collapse to explain the origin of the collapse. These studies are primarily concerned with the following: the effect of water, whether it was related to an exceptional climatic event, heavy rain over several days, and the behaviour of chalk altered by the water [31,33]. Refs. [28,29] studied the behaviour of the Chateau-Landon chalk under different water-content conditions. The laboratory test results showed that the strength of the chalk is highly dependent on its water content, particularly when the chalk is fully saturated, as it loses strength. The study also demonstrated that the creep behaviour of the Chateau-Landon chalk is influenced by hygrometry, which drastically increases the amplitude of visco-plastic deformations, leading to an increase in the delayed deformation rate.

Ref. [34] studied the influence of the rising water levels and the reduction in the fault friction angle. They concluded that the role of water is more important than the influence
of the fault friction angle. However, their analysis was limited to the behaviour of the pillar without analysing the impact of the fault on the slope. Recent research by [35] has shown that under wet conditions the fault induces shear stress, which can consequently induce the failure and plastic strain that can lead to failure. Ref. [36] investigated the lubrication of the discontinuities and mentioned that the shear strength approached zero when the discontinuities were completely filled in and saturated. Ref. [37] studied the behaviour of discontinuities under different water conditions, and the results show that the strength parameters (friction angle and cohesion) diminish for the saturated cases. The morphology of the site is questionable and corresponds to the first configuration presented in Figure 8. Ref. [38] emphasised the need to study the interaction between the collapse of the slope and the collapse of the underground mine. At that time, their observations highlighted the effect of water to explain the collapse.

The objective of this paper is to identify the mechanisms that lead to the large landslide conditions and to propose a plausible understandable mechanism.

## 7.2. Geological and Hydrological Context

The Château-Landon mine is located in the Senonian chalk of the Paris Basin (Figure 13). The mine extracted the Senonian chalk (Figure 14) with the thickness varying between 0 and 60 m, and occasionally reaching 100 m. In this region, Château-Landon, tectonic movements in the Château-Landon area have caused secondary terrain to rise and Tertiary formations to thin (erosion phase). While the plateau is crowned by the Tertiary limestone of Château-Landon, there are Campanian chalk (secondary) outcrops on the slopes (Figure 14). Near the slope, the chalk mass is intersected by tectonic fractures and decompression faults associated with the deepening of the valley.

The chalk is characterised by high porosity. Table 1 presents the physical parameters of the chalk from Château-Landon mines.

<figure><img src="image_16.png" /><figcaption>**Figure 13.** Geology map of the Paris Basin, Clamart (1961) and Château-Landon (1910) massive collapse location.</figcaption></figure>

<table><caption>**Table 1.** Physical properties of the Château-Landon chalk [28].</caption><thead><tr><th>Age</th><th>Designation</th><th>ρ<sub>d</sub></th><th>ρ<sub>sat</sub></th><th>ρ<sub>s</sub></th><th>n</th><th>w</th><th>SSA</th><th>k</th><th>CaCO<sub>3</sub></th></tr></thead><tbody><tr><td>Unit</td><td>Chalk</td><td>g·cm<sup>-3</sup></td><td>g·cm<sup>-3</sup></td><td>g·cm<sup>-3</sup></td><td>%</td><td>%</td><td>m<sup>2</sup>·g<sup>-1</sup></td><td>m<sup>2</sup></td><td>%</td></tr><tr><td>Campanian</td><td>Château-Landon</td><td>1.56</td><td>1.98</td><td></td><td>44</td><td>30</td><td>2.10–15</td><td>97</td><td></td></tr></tbody></table>

ρ<sub>d</sub>, ρ<sub>sat</sub> and ρ<sub>s</sub>: dry, wet and solid grain densities, n: total porosity, w: water content, k: permeability and CaCO<sub>3</sub> content of calcium carbonate, SSA: specific surface area, k.
Figure 14 presents a geology section of the Chateau-Landon site. The hydrogeology of the site is characterised by two aquifers: Loing alluvial aquifer and the regional chalk aquifer [30].

<figure><img src="image_17.png" /><figcaption>**Figure 14.** (a) Beaulieu room-pillar underground mine (%: extraction ratio); (b) schematic geology and geometry cross-section showing mine, slope and fault.</figcaption></figure>

The geometry of pillars and galleries is irregular, with the extraction ratio varying between 40% and 75% (Figure 14). The tributary method is used to estimate the pillar's vertical stress under dry and saturated conditions, which are then compared to the strength of the pillars. The saturated density is equal to 20 kN/m³, for the deepest zone, with the extraction ratio for the deepest mine zone being 40%, and the corresponding vertical stress is approximately equal to 1 MPa. For the shallow zone with an extraction ratio equal to 75%, the vertical stress is equal to 0.8 MPa. The pillar stress is very close to the strength of the saturated chalk (Figure 15), indicating a critical state but still stable mine configuration even under saturated conditions [39].

<figure><img src="image_18.png" /><figcaption>**Figure 15.** Influence of the water saturation degree on the initial yield stress of Chateau-Landon's chalk [29]; the red dot is the measurement values, the blue zone corresponds to the state of water saturation in the mine.</figcaption></figure>

However, given the geometry of the mine, the weakening of the pillars alone cannot explain the extent of the subsequent collapse. To better understand what might have happened, numerical calculations were performed, taking into account the presence of a fault.
### 7.3. *Numerical Model of the Landslide*

Due to the geometry of the underground mine and the cliff, a 2D model of the landslides zone at Beaulieu mine in 1910 was produced. Five configurations were carried out. Configuration 1 serves as the reference one, corresponding to the horizontal position (without slope). Configuration 2 incorporates a slope, while configurations 3 to 5 simulate the presence of a fault crossing the slope, the terrain and the cliff (Figure 16). A similar fault was observed recently near the site, with a dip of around 70°, and it is infilled with silty-clayey soil, with the information being used to construct the numerical model. The mechanical properties of the chalk and the overburden are shown in Table 1 [34].

<figure><img src="image_19.png" /><figcaption>**Figure 16.** Different configurations used for studying the effect of the geometry and the geometry and dimensions of the model including the fault.</figcaption></figure>

The presence of faults also plays a determining role mainly because the fault modifies the stress distribution [40]. UDEC (Itasca, IL, USA) is a software application that can simulate the response of discontinuous media (jointed rock mass, faults). The numerical method is known as the distinct element method. Figure 17 presents the main theoretical aspects of the distinct element method and discontinuity constitutive model. Additional information can be found in [41].

The model is 2D and corresponds to the plane strain hypothesis. The chalk properties were selected based on recent laboratory test results [28,29]. The fault properties were chosen based on in situ observations carried out in the mine located a few metres from the collapsed one and the state of the art. The perfect elasto-plastic Mohr–Coulomb plasticity
criterion was adopted. Table 2 presents the physical and mechanical properties used in the numerical modelling.

<figure><img src="image_20.png" /><figcaption>**Figure 17.** Distinct element method and discontinuity constitutive model (jkn: joint normal stiffness, jks: joint shear stiffness, jcoh: joint cohesion, jfric: joint friction angle and jtens: joint tensile strength).</figcaption></figure>

<table><caption>**Table 2.** Mechanical parameters (rock mass and fault) used in the numerical modelling, based on the literature [29,42], *: estimated values from cohesion and friction angle.</caption><thead><tr><th>Rock Unit</th><th>Density kN·m<sup>-3</sup></th><th>Young Modulus MPa</th><th>Poisson Ratio</th><th>Cohesion MPa</th><th>Friction Angle (°)</th><th>Compression Strength * MPa</th><th>Tensile Strength MPa</th></tr></thead><tbody><tr><td>Unsaturated Chalk</td><td>20</td><td>500</td><td>0.22</td><td>1</td><td>30</td><td>3.5</td><td>0.2</td></tr><tr><td>Saturated chalk</td><td>20</td><td>100</td><td>0.23</td><td>0.35</td><td>30</td><td>0.9</td><td>0.2</td></tr><tr><td>Puddingstone</td><td>22</td><td>2000</td><td>0.30</td><td></td><td></td><td></td><td></td></tr><tr><td>Limestone</td><td>25</td><td>4000</td><td>0.30</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td>Elastic</td><td></td></tr><tr><th>Joints/fault Symbol Unit</th><th>Normal Stiffness Jkn MPa·m<sup>-1</sup></th><th>Tangential Stiffness Jks MPa·m<sup>-1</sup></th><th>Cohesion Jcoh MPa</th><th>Friction Angle Jfric (°)</th><th>Tensile Strength Jten MPa</th><td></td><td></td></tr><tr><td>No degraded Fault</td><td>298</td><td>205</td><td></td><td>30</td><td></td><td></td><td></td></tr><tr><td>Degraded fault</td><td>298</td><td>205</td><td></td><td>10</td><td></td><td></td><td></td></tr><tr><td>Horizontal Joints</td><td>2500</td><td>1150</td><td>5</td><td>45</td><td>5</td><td></td><td></td></tr></tbody></table>

Figure 18 presents the decrease in the fault properties (reduction in the friction angle and cohesion and the decrease in effective stress) due to the saturation of the soil-rock mass.

<figure><img src="image_21.png" /><figcaption>**Figure 18.** Mohr-Coulomb Failure criterion—effect of the water condition (dry to saturated) on the fault shear behaviour.</figcaption></figure>
For each configuration presented in Figure 16, four phases were modelled: phase 1 simulates the initial state before mine excavation, phase 2 corresponds to the mine, phase 3 corresponds to the reduction in the friction angle of the fault, and phase 4 simulates the saturated chalk.

## 8. Discussion

The numerical calculation provides many useful and interesting results: such as strain, displacement, stresses, failure zones, etc. To assess the influence of the geometry and water effect, we focus on analysing the horizontal and vertical stresses. The stress amplitude scale is constant across all the configurations (Figure 19). Figure 19 highlights the difference in stress distribution between the four configurations. The destressing zones, characterised by low horizontal compression stress and tensile stress, cover larger areas compared to the reference configuration. The position of the fault (configuration 3 to 5) influences the interaction between the slope, the mine and the fault. This is particularly visible in configuration 4, where the vertical stresses are affected. At this stage of the analysis, the configurations integrating mine, slope and fault are the most critical ones because they develop higher destressing zones.

<figure><img src="image_22.png" /><figcaption>**Figure 19.** Horizontal and vertical stress distribution for the four configurations. Results show the effect of the geometry and the presence of fault on the stress distribution.</figcaption></figure>

Figure 20 presents the results of configuration 5. The analysis of the numerical results in terms of stress distribution highlights an increase in the tensile stresses, and a reduction
in the normal compressive stresses. The increase in the tensile stresses and the decrease in the compressive stresses favour the sliding of the unstable mass of rock. On the other hand, the reduction in the chalk's strength reduces the bearing capacity of the underground chalk mine's pillars. This excavation, coupled with the degradation of the fault's properties due to the water effect (lubrification) and the saturation of the pillars, leads to an increase in the tensile stresses in the stiffer limestone and puddingstone beds of the roof (with the beds acting as beams). The plastic deformation of the pillars due to the saturation favours the development of tensile stress on the roof.

<figure><img src="image_23.png" /><figcaption>**Figure 20.** Distribution of the horizontal and vertical stresses for the four calculation phases for configuration 4. Results show the effect of the lubrication of the fault (decreasing of the friction angle) and the saturation of the chalk (water effect).</figcaption></figure>

The verification of the numerical modelling is based mainly on the reported obser-
vations and the rare photos. The numerical modelling results allow us to compare the
different configurations and help us to identify a realistic mechanism. Based on both the in
situ observations of the collapse and the numerical modelling results, Figure 21 summarises
the main factors involved in the collapse. The collapse resulted from a combination of the
internal factors (mine geometry, extraction ratio, slope and fault) and the external factors
(heavy precipitation, raising and flooding of the underground mine, saturation of the strata
and reducing the shearing strength of the fault). The external factors are closely related to
climate parameters, particularly heavy rainfall, which triggered the collapse of the slope
and the mine. Two scenarios are possible: the first one involves the sliding of the slope,
where the sliding mass destabilised the weakened pillars and, finally, the mine collapsed.
The second scenario suggests the collapse of the weakened pillars due to flooding, and
then the mass of the slope, limited by the faults, followed by the sliding movement. The
first scenario is more realistic due to the observed form of the collapse pattern (Figure 12).
<figure><img src="image_24.png" /><figcaption>**Figure 21.** Internal (geometry, fault, slope) and external (triggering, water) factors leading to the collapse of the slope and the underground mine.</figcaption></figure>

The increase in rainfall due to climate change will certainly impact the stability analysis of underground mines. This influence will be particularly significant when the internal factors, such as the composition of the rock (e.g., chalk rock), are highly sensitive to the water. In such cases, the future of underground mines, especially those with these specific configurations, becomes uncertain, raising concerns about the safety and the security of the population, buildings and critical infrastructures.

## 9. Conclusions

The paper examines the future of abandoned underground mines in the context of the climate change parameter: precipitation, focusing on the risks associated with their instability, particularly ground movements: local and large-scale collapses. The national and international state of the art highlights these hazards as the primary concern for mine safety.

Two main areas of research are explored: the first involves constructing a database of large collapses, while the second focuses on a detailed back analysis of well-documented large-scale collapses. The large collapse database currently contains over 500 collapse events, and the number of collapses continues to increase. Analysis of the events reveals that the primary causes are the extraction ratio, the age of the mines and, certainly, external factors such as climatic factors (heavy rain, increase in water levels). While the analysis of the database shows no clear evidence linking mine configurations to collapses, it does show that the “cornice” and the “top of slope” configurations present the highest frequency of collapses. Conversely, spur and mid-slope configurations tend to have more stable configurations of mines.

The back analysis focuses on a large-scale collapse, Chateau-Landon in 1910. Early investigations focused on the geometry and geomechanical behaviour of the chalk. In this paper, 2D distinct element numerical modelling was carried out, incorporating both external and internal factors: such as the mine geometry, valley, fault, water conditions, the position of the fault and the characteristics of the chalk.

The results of the numerical modelling suggest that the collapse of the underground mine and the sliding of the slope were driven by a combination of external and internal factors. The external factor related to the climatic parameter: heavy rain, played the role of the triggering factor.
Two possible collapse scenarios were discussed, the first one involves the sliding of the slope followed by the collapse of the underground mine. The second one suggests the collapse of the mine first, triggering the sliding of the slope. Based on the in situ observations, the first one is deemed more likely.

The analysis of the Château-Landon case study enhances the understanding of risks related to under-excavated cliffs and slopes by considering the interaction between cavities and slopes. The climatic factor, particularly water, plays a significant role in critical configurations. The findings from the back analysis and the collapse database contribute to improving expertise and the management in the future of the many underground mines in light of the challenges posed by climate change.

Ineris is working on new technologies, primarily machine learning and artificial intelligence (AI) to better understand the impact of climate change and the causes of the massive collapses.

**Author Contributions:** Conceptualization, M.A.H. and N.C.; methodology, M.A.H. and N.C.; software, M.A.H.; validation, M.A.H. and N.C.; data curation, M.A.H.; writing—original draft preparation, M.A.H.; writing—review and editing, M.A.H. and N.C.; visualization, M.A.H. and N.C.; project administration, M.A.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** Ineris research program.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Statements are available in section.

**Conflicts of Interest:** The authors declare no conflict of interest.

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