1 Introduction

Il est important de comprendre la thermodynamique des cavités souterraines dans des applications comme le stockage de déchets [12] ou la préservation des grottes ornées [5]. L'état thermique d'un milieu souterrain est contrôlé par le flux géothermique [8], la diffusion de la température de surface à travers la roche, les circulations d'eau, les échanges d'air avec l'extérieur [3], ainsi que par la présence éventuelle de sources de chaleur, par exemple une personne, qui dégage une puissance entre 100 et 140 W [4,13]. L'air y est en général saturé en eau, et celle-ci a une influence majeure sur la réponse du milieu [7,10,11,14].

Dans cet article sont présentées les variations de température enregistrées depuis près d'un an et demi dans la carrière de Vincennes, ainsi qu'une estimation de l'effet de perturbations artificielles sur ces variations.

2 Dispositif expérimental

Pour suivre l'évolution thermique à long terme de la carrière, une salle, située à 120 m environ du puits d'accès, fut instrumentée en juin 2001. Sa surface est d'environ 23×9 m² pour une hauteur d'environ 2 m (Figs. 1 et 2). Trois dispositifs verticaux de dix thermistances (AI, AII et AIII) permettent de mesurer les variations de température dans l'air de la salle. En novembre 2001, un quatrième dispositif (S) fut installé pour avoir accès aux variations de température dans la roche. Les thermistances ont été intercalibrées en laboratoire, avec une erreur relative entre thermistances d'environ 4×10⁻³ °C [Perrier et al., soumis à Geophys. J. Int.].

3 Variations de la température sur le long terme

3.1 Profils verticaux de température

À la profondeur de la carrière (−18 m), le flux de chaleur, vraisemblablement dominé par le flux géothermique, en raison de l'absence d'infiltrations d'eau notables, est ascendant tout au long de l'année. Si ce flux est transporté dans l'air par convection thermique pure, le gradient vertical de température y est le gradient adiabatique :

$${\left(\frac{\partial \mathrm{T}}{\partial \mathrm{z}}\right)}_Q=-\frac{\alpha gT}{C_{\mathrm{p}}}$$

avec z positif vers le haut, α=3,7×10⁻³ K⁻¹ le coefficient d'expansion thermique de l'air, $\mathrm{g}=10\mathrm{m}{\mathrm{s}}^{-2}$ l'accélération de la pesanteur, T=285,7 K la température moyenne dans la salle et $C_{\mathrm{p}}=1000\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ la chaleur spécifique de l'air. On obtient (∂T/∂z)_Q=−10×10⁻³ °C${\mathrm{m}}^{-1}$ environ.

Quatre profils verticaux de température mesurés dans l'air de la salle à différentes périodes sont présentés sur la Fig. 3. Ils montrent que le gradient est faiblement positif, mais proche de la résolution du dispositif. Cependant, il semble que, tout au long de l'année, la salle soit divisée en deux couches : dans la moitié supérieure, le gradient est positif ((10±5)×10⁻³ °C${\mathrm{m}}^{-1}$) et dans la moitié inférieure, il est légèrement plus faible et négatif ((−6±5)×10⁻³ °C${\mathrm{m}}^{-1}$). Le flux de chaleur n'est sans doute pas uniquement transporté par convection thermique. Des transferts radiatifs ou des processus de convection compositionnelle doivent intervenir.

3.2 Variations annuelles de la température

Les températures enregistrées dans la carrière entre juin 2001 et novembre 2002 sont présentées sur la Fig. 4. L'amplitude des variations est d'environ 0,16 °C dans l'atmosphère (Fig. 4b) et 0,2 °C dans la roche (Fig. 4c). Les variations de courtes périodes dans l'atmosphère sont dues à des variations de la pression atmosphérique [10]. À long terme, l'évolution de la température montre que le cycle annuel est constitué d'une succession de phases approximativement linéaires. Ces variations sont dominées par la ventilation naturelle par le puits d'accès, comme le montre la chute de température aux mois de décembre 2001 et janvier 2002 (Fig. 4b).

En outre, un réchauffement de près de 0,1 °C par an est observé (Fig. 4b), largement supérieur aux dérives instrumentales possibles. S'il se confirme sur de plus longues périodes d'observation, il pourrait être attribué au réchauffement climatique global [2] ou à un réchauffement plus local lié à l'activité anthropique de surface ; mais il pourrait être aussi dû aux multiples passages dans la carrière. La puissance émise par une personne étant d'environ 100 W, trois expériences effectuées à l'aide de sources de 100 W peuvent être utilisées pour évaluer les effets des visites sur ce réchauffement.

4 Expériences de chauffage

Sur la Fig. 5 sont représentées les variations de température dans l'atmosphère et dans la roche au cours des trois expériences. Le chauffage se déroule en deux phases : la première, rapide, correspond au temps que met la source à atteindre sa température maximale ; lors de la seconde phase, la température augmente plus lentement. L'amplitude des variations de température dépend de façon non linéaire de la forme et de la position de la source. Les modèles exposés précédemment ne suffisent donc pas à décrire le système. De la même façon que pour le chauffage, la première phase de refroidissement correspond à l'inertie de la source. La température décroı̂t ensuite de façon quasi exponentielle, avec un temps de relaxation d'autant plus long que la durée du chauffage est grande et le capteur plus près du sol. Ce temps est deux à quatre fois plus élevé dans la roche que dans l'atmosphère.

La Fig. 6a montre les profils de température mesurés dans l'air au cours de la seconde expérience à quatre instants différents. Les profils de variation de température correspondants, obtenus en retranchant la température initiale (une minute avant le chauffage) sont présentés sur la Fig. 6b. Une stratification horizontale apparaı̂t dès la première heure de chauffage, et est encore plus marquée après 24 h : dans les 50 cm près du toit, le gradient est fort (environ 0,2 °C${\mathrm{m}}^{-1}$) ; il est plus faible (environ 0,04 °C${\mathrm{m}}^{-1}$), mais toujours positif, dans la partie inférieure de la salle. Cette stratification pourrait être la manifestation d'échanges horizontaux turbulents entre le panache et l'air environnant ou de transferts radiatifs.

5 Discussion et perspectives

Understanding the thermodynamics of underground cavities is important for many applications, such as underground waste disposal [12] or the preservation of painted caves [5]. The thermal state of underground cavities, characterized by a water saturated air phase in contact with a partially saturated porous rock, is controlled by several factors: the geothermal flux [8], thermal diffusion from the surface [Perrier et al., submitted to Geophys. J. Int.], water circulation and air exchange with the outside atmosphere [3]. In addition, human presence, equivalent to a heat source of about 140 W [13], is a significant factor that can affect the thermal equilibrium of a cavity [5]. The effect of these various factors is still poorly known. However, the role of water, because of its high vaporization latent heat, appears to be fundamental.

For example, the annual temperature cycle of a limestone quarry in Mériel (France) was found to be associated with an annual variation of rock resistivity, which reflects an annual variation of rock water content [7]. Pressure induced temperature variations in the atmosphere of another limestone quarry in Vincennes were found to be controlled by the thermal inertia of the wall and the phase changes of water as well [10]. Water exchange is also associated with natural ventilation [14] and this effect, for example, contributes in the access pit of the Vincennes quarry, where cold avalanches induce an evaporative feedback response from the wall [11].

In this paper, we present first data on the long-term thermal variations in the Vincennes quarry, and we estimate how these variations can be affected by artificial perturbations.

The underground Lutetian limestone quarry of Vincennes (near Paris), exploited between 1715 and 1860, is now abandoned. It is located at a mean depth of 18 m, and spreads over a surface of about 32,000 m² [6]. The quarry is made of rooms, with heights varying from 1.5 to 7 m, separated by pillars of about 4×6 m² section. The measured relative humidity is close to saturation, a fact confirmed by moist walls. The average temperature is 12.6 °C with yearly variations within 0.2 °C. The main access pit has a diameter of about 4.5 m and is the main opening for natural ventilation [11].

To study the long-term evolution of the quarry, thermistors have been installed in a room located in the west side of the quarry, about 120 m from the access pit. Its surface area is 23×9 m², for an average height of about 2 m (Figs. 1 and 2). The ceiling and the walls show that the encasing formation is made of an alternation of tabular limestone beds with thin clay levels [6]. The floor consists of 2-m-thick filling of quarry waste. Air exchange with the rest of the quarry takes place by two openings with section of about 3×2 m² each (2 m height from floor to ceiling) (Fig. 1).

In order to be able to observe possible stratification effects in the atmosphere of the room, three vertical set-ups (AI, AII and AIII) of ten thermistors have been installed in June 2001 (Fig. 2). A forth set-up has been added in the rock in November 2001, with thermistors at 1.5-cm depth, sampling the interface between the rock and the atmosphere (S). The thermistors have a sensitivity of about $135\Omega$°C⁻¹ at 12.8 °C. Their absolute calibration is not better than 0.1 °C, but they have been intercalibrated in the laboratory in a thermally controlled bath. This method permits to obtain a thermistor-to-thermistor relative error of about 4×10⁻³ °C (95% C.L.) [Perrier et al., submitted to Geophys. J. Int.]. The long-term stability is expected to be better than 10×10⁻³ °C yr⁻¹. Atmospheric pressure variations have also been measured between November 2001 and May 2002 with a sensor located in the experimental room.

3.1 Vertical temperature profiles

3.2 Annual variations of the temperature

If a localized heat source is introduced in the quarry, it is expected that a thermal turbulent plume will be initiated above the source, with a narrow opening angle of about 11° [9] (Fig. 2). In a filling-box model [1], the plume will develop into a steady state feeding a horizontal layer of hot air near the roof, with a front going down, slowly invading the whole room. This model can be extended in the presence of ventilation [4], but may not be valid with non-adiabatic walls and phase changes of water.

Three heating experiments have been performed, with two different heaters: one hot plate with dimensions 19×15 cm² and one smaller resistor with dimensions 5×7 cm². The positions of the sources were chosen so that the measuring set-ups in the atmosphere are located outside the plume (Fig. 2). Experiment 1 was performed with the hot plate located at position 1 (Fig. 1) during 4.5 h, experiment 2 with the hot plate at position 2 (Fig. 1) during 24 h; and experiment 3 with the resistor at position 2 (Fig. 1) during 24 h. The hot plate was installed on the floor, whereas the resistor was installed at a height of 58 cm, so that the plume virtual origin corresponds to the floor level [9]. Both heaters, which have an intrinsic thermal inertia, have been studied in the laboratory. The maximum temperature of the plate is reached about half an hour after the beginning of the heating, and the temperature decreases to its initial value in about 1 h. The resistor has a smaller inertia: its maximum temperature is reached after less than 15 min and the temperature decreases in about 50 min. During the experiments, temperature was recorded with a sampling interval of 1 min for the first experiment, and 15 s for the second and the third.

At the beginning of heating, no descending front was observed, but the temperature is increasing simultaneously on all sensors as soon as the heater is turned on. This does not necessarily mean that the front does not exist, but the filling time in this case would need to be smaller than the sampling time. Alternatively, the initial simultaneous temperature increase could be due to radiative contribution from the source. More work is needed to draw further conclusions.

Temperature variations measured by sensor 1 of set-up AIII (near the ceiling) and sensor 4 of set-up S (in the rock) during the three experiments are shown as a function of time in Fig. 5. For the three experiments, the heating takes place in two phases. The first phase is fast and corresponds to the time that the source takes to reach its maximum temperature. During the second phase, the increase is slower, with coherent fluctuations that remain poorly constrained at this stage. The maximum temperature is smaller in the second experiment (Fig. 5b) than in the first one (Fig. 5a), although the source is closer to the set-up (Fig. 1). In the third experiment (Fig. 5c), a larger amplitude is produced, although the second heater has the same power. Thus, the shape of the source and its position in the room are important parameters and models beyond a simple filling box are needed. Compared with the atmosphere, the temperature increase in the rock has a smaller amplitude (maximum 30×10⁻³ °C), with a possibly different time structure.

Fig. 6a shows the vertical temperature profiles in the atmosphere (set-up AIII) during the second experiment at four different times. Fig. 6b shows the corresponding vertical profiles of temperature excess associated with the heating, obtained by subtracting the initial temperature profile determined one minute before heating. After 1 h of heating, the source has reached its maximum temperature. The vertical pattern of temperature increase is similar on the three set-ups, indicating that, during heating, a horizontal stratification of the room atmosphere is established. Temperature has increased on the whole height of the room, but more near the ceiling (Fig. 6a). This stratification is even stronger after 24 h of heating: the gradient is about 0.2 °C${\mathrm{m}}^{-1}$ in the upper part of the room (50 cm from ceiling) and 0.04 °C${\mathrm{m}}^{-1}$ in the lower part. Radiative transfers or turbulent exchanges between the plume above the heater and the surrounding air must be at the origin of this stratification.

Three cooling phases can also be distinguished in Fig. 5. The first phase corresponds to the inertia of the heater (about 1 h). The second phase corresponds to an approximately exponential relaxation of the system, with a relaxation time that amounts to a few hours in the atmosphere for experiment 1 and varies from 7 to 10 h for experiments 2 and 3, with values tending to be larger for sensors near the floor. In the rock, the relaxation times tend to be longer by a factor 2 to 4, depending on the sensor considered and on the particular experiment. A third phase of longer duration will be described below.

Five days after the end of the heating, the gradient is close to its initial value (Fig. 6b), but a temperature excess of about 12×10⁻³ °C remains on all sensors. This temperature excess is larger than expected from the long-term trend discussed above. Indeed, during the week preceding the experiment, the corresponding increase amounts to 0.7×10⁻³ °C per day; thus, the observed temperature after 6 days is 7.8×10⁻³ °C above the expected value. This is confirmed in Fig. 5, which shows that the original temperature is not restored after 10 days in experiments 2 and 3, by contrast to experiment 1. This fact is not easy to interpret, but in the presence of water, small perturbations can induce non-linear and hysteresis effects, such as evaporation/condensation phenomena at the rock–atmosphere interface. The possibly irreversible response of the cavity to heating could thus contribute to the long-term temperature increase observed in the quarry. In any case, thermal relaxation of the atmosphere with long-time scales must be controlled by heat exchanges with the walls and their thermal response.

In this paper, we present indications that 24 h of low power heating produce long lasting, possibly irreversible, changes in an underground cavity. The observed long-term temperature increase might therefore be attributed to repeated visits in the quarry, and to the heating experiments themselves after April 2002. A similar long-term temperature increase has been observed in Japan [Perrier et al., submitted to Geophys. J. Int.], in a subsurface cavity unfortunately also affected by numerous visits. In either case, an interpretation of the temperature increase in terms of global warming thus cannot be safely proposed at the moment. In order to be able to monitor long-term temperature changes in underground observatories, perturbations due to visits or other artificial contributions have to be avoided or carefully monitored.

These experiments, in addition of providing accurate data on unknown aspects of the physic of turbulent plumes, also provide guidelines for the preservation of painted caves. Indeed, presence of visitors (tourist groups or research teams) induces heating in the cavity [13]. Accumulation of thermal effects could lead, in the long run, to significant damage to the flora, fauna [3] and to the archaeological remains, including, first of all, the wall paintings [5]. Our experiments support the idea that successive sets of short duration periods (4 h per day, for example) are safer than one single long duration of 24 h. In the presence of thermally active natural ventilation, as for example observed in December 2001–January 2002 in Vincennes (Section 3.2), the thermal effect of visits may be reduced.

A complex system such as an underground cavity may be able to tolerate perturbations (such as visits or artificial modifications of the natural ventilation), if they are restricted to a definite domain of parameters, which could be referred to as the resilience domain of the cavity. Theoretical and experimental work is needed to explore the various dynamical regimes of underground cavities and their sensitivity to external perturbations. This may be important also in industrial applications, such as underground waste disposals. In any case, the resilience domain of each individual cavity would need to be established carefully by dedicated experiments.