PHYSICAL AND PARAMETRIC MONITORING OF LEAKAGES IN EARTH DAMS USING ANALYSIS OF FIBRE OPTIC DISTRIBUTED TEMPERATURE MEASUREMENTS WITH IRFTA MODEL 1

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1 COMMISSION INTERNATIONALE DES GRANDS BARRAGES VINGT QUATRIÈME CONGRÈS DES GRANDS BARRAGES Kyoto, juin PHYSICAL AND PARAMETRIC MONITORING OF LEAKAGES IN EARTH DAMS USING ANALYSIS OF FIBRE OPTIC DISTRIBUTED TEMPERATURE MEASUREMENTS WITH IRFTA MODEL 1 Krzysztof RADZICKI Cracow University of Technology Poland Stéphane BONELLI Cemagref Aix en Provence France POLAND 1. INTRODUCTION Thermal monitoring of hydraulic structures is based on the relations defining related transport of heat and water. In this method, the values of the air temperature and water temperature in reservoir are the sources of thermal signals transmitted from the dam slopes to the measuring point in the dam body. Such a signal is subject to modifications when collecting data about the medium; it penetrates through, particularly that of water movement taking place within it [1], [2]. Both, the analysis of temperature measurements in the structure body and the opportunity to take these measurements with use of fibre optic cables are currently recommended for application for the purpose of surveillance of earthen hydraulic structures [3]. Application of fibre optic cable as the sensor, which provides for distributed temperature measurement throughout the structure's total 1 Surveillance physique et paramétrique de l érosion dans les barrages en terre en utilisant l analyse des mesures distribuées de température par fibre optique du modèle IRFTA. 93

2 length (the present standard calls for one each 1 m) resulted in the possibility of continuous leakage monitoring alongside the total structure length [4],[5]. The IRFTA (impulse response function thermal analysis) model presented in this article provides analysis, while applying the impulse response function methodology, of temperature measurements taken in any point within the dam body. The physical defining of its parameters enables the parametric and physical description of the filtration and leakage phenomena is a specific feature of this model. The downstream toe of existing hydraulic structures is the zone of the utmost importance for the thermal monitoring system [6], [7]. Installation of fibre optic cables in this part of the dam body is cost-effective, since it requires no essential intervention in the structure body, and usually causes neither downtime nor reduction in structure functionality, by e.g. a temporary lowering the water damming level. Moreover, the accumulation of filtration processes and leakages penetrating through a given structure cross-section, especially where drainage is situated therein, occurs mostly in that zone. The analysis of temperature measurements taken in the downstream toe was however very difficult or even unfeasible until the second half of the first decade of the New Millennium. The impediment was caused by the considerable complexity of the thermal and hydraulic description of this zone that required, firstly, the consideration of various soil saturation rates, and secondly, analysis taking into account the influence of both the soil temperature and that of the reservoir, water as well as the air temperature [7]. The IRFTA model enables not only identification of leakages in the zone in question, but also their parametric and physical description, including their intensity rate. This article describes the background of this model, and also examples of its application for the purpose of analysing the temperature measurements taken on two earth hydraulic structures. The final Chapter shows the equations, which define the IRFTA model parameters versus the measuring point location and water velocity functions. They enable calculation of water velocity in homogeneous soil medium. 2. BACKGROUND OF THE IRFTA MODEL In this article we describe the most important characteristics of the IRFTA model. Detailed description of the model is presented by Radzicki [7]. Heat transport in the body of the earth hydraulic structure is described by energy equation [1]. The second and the third term of this equation represent respectively the conductive and advective heat transport processes, where advective process is defined as the transport of heat with the mass of flowing water. 94

3 T C T T t x x vc 0 2 f 2 [1] Energy equation [1] describes a parabolic-linear problem. It means that heat transport (diffusional-advective) may be assumed to behave in a linear manner if the thermal porous medium properties and the water velocity are constant. In consequence we may use the Green's function methodology to build a suitable model of the relevant problem. Using this approach the loading (input signal) a(t) and the system s response (output signal) y(t) are connected by the impulse response function of the system h(t) as follows: t y( t) h a ( t) h( t ) a( ) d [2] 0 where * is the mathematical convolution operator. In other words, the impulse response function describes how input signal (in form of Dirac delta) is modified by the porous zone of the dam. In our model an approximation of the impulse response function was used in the form of the two-parameters (α,η) exponential decay: h( t) R(, ) [3] The role of the parameters is explained by harmonic analysis. Under slowly varying loading conditions, η representing time-lag, which quantifies the time elapsing between the onset of the loading and the response of the system at the point of measurements and α is the signal damping factor. Finally the IRFTA model has the following form: T ( x, t) C Rw x, t w t Rair x, t air t [4] where: θ C - constant R w, R air impulse response function approximation respectively for the water temperature and the air temperature loadings θ w, θ air water temperature and air temperature loadings on dam surface Measured temperature T(x,t) is formed by superposition of responses of 95

4 dam for the water temperature and the air temperature loadings, represented respectively in the second and the third term of Equation [4]. Finally the IRFTA model has four parameters. Two of them α w and η w quantify transformation of the thermal signal from the upstream face (water temperature loading). The downstream thermal signal (air temperature loading] modification is measured by next two parameters α air and η air. In particular conditions, IRFTA model can be applied in reduced form. If the temperature sensor is located directly in the saturated zone of seepage and the air temperature influence is neglected one may use the following model: T( x, t) h x, t t C w w [5] Conversely, if there is non-water temperature influence on the fibre optics temperature, it is possible to use model: T( x, t) h x, t t C air air [6] 3. EXAMPLES OF THE IRFTA MODEL APPLICATION TO PASSIVE TEMPERATURE MEASUREMENTS ANALYSIS This Chapter describes the application examples of the IRFTA model for analysing filtration processes on two French damming structures, which differ mutually in their size scale. One of them is the high canal dam of the Oraison Canal, while the other presents a small dike of the experimental basin in Aix-en- Provence. Modelling was performed of temperature measurement results obtained by fibre optic cabling situated in the downstream parts of these structure bodies. For such modelling, the zone requires description of the influence of both the air temperature and of water in the reservoir, as well as use of the soil saturation rate and the filtration velocity data (if any) for the time and space variables. Since a detailed and thus an extensive description of heat and water transport is the application result of the IRFTA model, then, in view of limited space of this article, only the examples of selected sections of both these structures are presented. 96

5 3.1. HIGH CANAL DAM TEMPERATURE ANALYSIS The Oraison Canal supplies water to a hydropower plant. Typical crosssection of the canal dam, about 27 m high, is shown in Fig. 1. The protection of its bottom and slopes is made from concrete slabs yet forming an impervious membrane. A 1 kilometre long approx. fibre optic cable for temperature measurement is installed at the downstream toe of the dike and then its position gradually rises to reach the point in which it enters the structure downstream crest of the berm, from where its position runs straight on. Fig. 2 shows an outline of the fibre optic installation. The fibre optic cable is laid at about 80 cm depth along its entire length. When using the IRFTA model, the analysis of temperature measurements was performed for measuring points each situated 1 m apart throughout the cable length. Duration of the measurement period analysed was 2 months. Representation of model data was indeed ideal at all the measuring points. The correlation coefficient between the model and data was not less than 0.99 for each of these points. The application of the IRFTA model throughout the length of the examined dike section enabled definition of the characteristic hydrothermally uniform zones of the structure and determination of the filtration process intensity rate in each of these zones. Existence of intense filtration or leakages was excluded. Three selected zones, which are distinguished from each other by their filtration process intensity rates, are discussed below in detail. Fig. 1 Cross-section of Oraison canal Profil type du canal d Oraison (A) Fiber optics position at the top of the (A) Position de la fibre optique au sommet berm de la berme (B) Fiber optics position at the land-side (B) Position de la fibre optique en pied toe aval C) Drainage (C) Drainage 97

6 Fig. 2 Outline of the fiber optic monitoring system Schéma de principe de la disposition de la fibre optique (A) Fiber optics (B) Pipe spillway (C) Canal (D) Hydraulic power station (A) Fibre optique (B) Évacuateur de crue (C) Canal (D) Usine hydraulique The first structure zone presented is situated at between 700 and 815 m of the cable length. Fig. 3 presents the values of the IRFTA model parameters calculated alongside the length of this section. In this zone, the values of the α air, parameter, which determines the amplitude damping rate of the signal coming from the downstream part (air temperature) change in the range between 0.8 and 0.7. In other words, the signal is attenuated just between 20 and 30%. The signal transition time between the downstream boundary and the measuring point is determined by the η air parameter, ranges between 20 and 30 days. As shall be demonstrated further on in this article, the influence of water temperature on temperature of the fiber optic cable is insignificant, thus the air temperature effects predominate in this zone. Additionally that provided for verification of the correctness of the model performance through comparison of the η air, lag time calculated against the real time lag. The real time lag was set out by determination of the time difference between the appearance of the maximum (or minimum) temperature values in the air temperature curve, and the temperature curve in one of the measuring points of the fiber optic cable in the zone analysed. This comparison is presented in Fig. 4. The real lag time value is about 30 days and it conforms to the η air lag time value obtained from the IRFTA model at the measuring point in question that also amounts to 30 days. As mentioned before, the influence of water temperature on temperature at measuring point is insignificant. Damping of the signal from the upstream boundary is high and it ranges between 80% and 90% (α w varies from 0.2 to 0.1), whereas the response lag time falls between 14 and 27 days interval. The values of the IRFTA model parameters obtained in the zone analysed have excluded any important seepage process in this zone of dam. 98

7 Fig. 3 The values of the IRFTA model parameters for 700 m to 815 m section of fiber optic cable Les valeurs des paramètres de modèle IRFTA pour la section de la fibre optique de 700 m à 815 m (A) α air - air temperature signal damping coefficient (B) α w - water temperature signal damping coefficient (C) η air - transition time of the air temperature signal (D) η w - transition time of the water temperature signal (E) Characteristic time (days) (F) Distance (m) (A) α air coefficient d amortissement de la température de l'air (B) α w coefficient d amortissement de la température de l'eau (C) η air - temps de transition du signal de la température de l'air (D) η w - temps de transition du signal de la température de l'eau (E) Temps caractéristique (jours) (F) Distance (m) Fig. 4 The time lag between the air temperature and temperature of fiber optic cable Retard entre la température de l air et la température de la fibre optique (A) Air temperature (B) Temperature of fiber optic cable (C) Temperature (ºC) (D) Time (days) (A) Température de l air (B) Température de la fibre optique (C) Température (ºC) (D) Temps (jours) 99

8 The second specific thermal and hydraulic zone presented in this article is situated between 880 m and 950 m of the fiber optic cable length. A comparison of the parametric values calculated for this zone with use of the IRFTA model, as shown in Fig. 5, against the values of parameters obtained for the aforementioned zone are presented below. When comparing modification of signal that originated from the upstream part for both zones in question, it is found that the signal damping is lower for the zone currently analysed, particularly at the distance from 880 m to 925 m, and it is between 75 and 80% (α w varies from 0.2 to 0.25), and also the η w, signal transition time is shorter, and it accounts for 9 to 20 days. In turn, when comparing the change in signal coming from the downstream boundary, the damping is also lower (α air is between 0.76 and 0.91), and the signal transition is accelerated (η air varies from 11 to 20 days). This means in the zone under analysis, when compared with that previously described, the water temperature and the air temperature effects are more intense. Physical interpretation of the data mentioned above follows. Fig. 5 The values of the IRFTA model parameters for 880 m to 950 m section of fiber optic cable Les valeurs des paramètres de modèle IRFTA pour la section de la fibre optique de 880 m à 950 m (A) α air - air temperature signal damping coefficient (B) α w - water temperature signal damping coefficient (C) η air - transition time of the air temperature signal (D) η w - transition time of the water temperature signal (E) Characteristic time (days) (F) Distance (m) (A) α air coefficient d amortissement de la température de l'air (B) α w coefficient d amortissement de la température de l'eau (C) η air - temps de transition du signal de la température de l air (D) η w - temps de transition du signal de la température de l'eau (E) Temps caractéristique (jours) (F) Distance (m) The enhanced filtration, as related to the preceding zone, caused an increase in the effects of signal, originated from the upstream part (from water temperature). Meanwhile, intensified filtration also caused a soil humidity 100

9 increase at the downstream toe of the structure, and also expansion of the soil area featuring increased humidity. Consequently, at the same time, the influence of the air temperature on the fiber optic cable temperature has also been intensified. However, the growth noted in both water and air temperature values is insignificant, and the air temperature impact still predominates there, while the effects of water temperature are only slight. This excludes any existence of intensified filtration, since had it occurred, these relations would usually be reversed. The third section presented is situated between 990 and 1100 m on the fiber optic cable length that only in this section runs close to the crest of the berm. Therefore, the cable here is beyond seepage influence. Thus, only the influence is the air temperature and absence of water temperature effects are expected to appear there. The values of the IRFTA model obtained for this section, as presented in Fig. 6, strictly reflect that assumption. Only significant air temperature influence (α air varies from 0.8 to 0.96) is observed. However, since the model was also to calculate the values of parameters setting out modification of the signal from the upstream part, the value of signal damping caused by water temperature is close to 100% (the α w values are close to 0), while the signal transition time reaches very high values, more than days. The physical interpretation means an absence of water temperature effects on temperature at measuring point. Fig. 6 The values of the IRFTA model parameters for 990 m to 1100 m section of fiber optic cable Valeurs des paramètres du modèle IRFTA pour la section de la fibre optique de 990 m à 1100 m (A) α air - air temperature signal damping coefficient (B) α w - water temperature signal damping coefficient (C) η air - transition time of the air temperature signal (D) η w - transition time of the water temperature signal (E) Characteristic time (days) (F) Distance (m) (A) α air coefficient d amortissement de la température de l'air (B) α w coefficient d amortissement de la température de l'eau (C) η air - temps de transition du signal de la température de l'air (D) η w - temps de transition du signal de la température de l'eau (E) Temps caractéristique (jours) (F) Distance (m) 101

10 3.2. DYKE OF THE EXPERIMENTAL BASIN IN AIX-EN-PROVENCE The basin in Aix-en-Provence was a test structure built for, amongst purposes, surveying the scope of application of the passive monitoring technology using distributed fiber optics temperature measurements taken in the downstream parts of the earth damming structures. Therefore, the results of temperature measurements that originated from this basin are of specific importance for verification of the effectiveness of the IRFTA model. The basin was rectangular and its 2.5 m high dykes were built from clay with permeability at saturation of ms -1. Several highly permeable sand zones enclosed in geotextile envelopes to create the artificial leakages were installed within the dykes. The leakage zones were situated in the dyke bodies at two levels - high and low. The yield of leakages was controlled through the weirs installed in the upstream zone. The downstream dyke bank was covered by geotextile with three fiber optic cables attached and running at different altitudes, perpendicularly to each other, alongside the bank and in its upper (T-OF), middle (M-OF) and the toe (B-OF) zones (see Fig. 8). The sandy leakage zones were in directly contact with the geotextile surface. Both the geotextile and the fiber optics were retained by a refill. This article presents the analytic results obtained by application of the IRFTA model analysis of temperature values taken in the west dyke of the basin that included three artificial leakage zones, the two of which were situated in the lower and one in the upper part of the dyke. The cross-section of this dyke and its overview are presented in Fig. 7 and 8, respectively. Duration of the measurements analysed by the IRFTA model was about 2 months. The leakage yields during most of that time oscillated between 2 and 4 litres per minute (as measured next to the weir in the upstream zone), but reached 12 litres per minute for about ten days. The water table level oscillated between 1.7 and 2.2 m. Only slight accumulations of moisture in the structure downstream bank were noted throughout the measurement period, while no trace of water flow was found there. 102

11 Fig. 7 View of the west dyke of experimental basin with location of the leakages Vue de dessus de la digue ouest avec les positions des fuites artificielles (A) Low position leakages (B) High position leakage (A) Fuites basses (B) Fuite haute Fig. 8 Sectional view of the dyke of basin with location of the leakages Coupe type d une digue constitutive du bassin avec les positions des fuites artificielles (A) Low position leakages (B) High position leakage (C) Fiber optics (A) Fuites basses (B) Fuite haute (C) Fibres optiques The preliminary analysis performed for characteristic temperature curves proved that the influence of water temperature on temperature of the fiber optic cable is negligibly low throughout the whole dyke length. That resulted from only slight yield of leakages, which caused rapid diffusion of water, subsequently, into the sand zone and the dyke body, and finally into the downstream side geotextile zone. That is the reason why zero water flow appeared in geotextile in the structure downstream zone, and it did not reach the fiber optic cables. Thus, the leakages caused only a change in the geotextile moisture in the zone where the fiber optic cables were situated. The absence of water temperature effects on temperature of fiber optic cables enabled application of dual-parameter IRFTA model designed for 103

12 analysing temperature values but only one thermal effect function, instead fourparameter IRFTA model modelling both the influence of water temperature and air temperature, thus essentially reducing calculation time. The first complete modelling was performed for all three fiber optic cables (B-FO, M-FO and T-FO) compared against the air temperature function. The analysis was carried out on the subsequent measuring points of each fiber optic cable, as situated every metre throughout their entire length. The values of the model parameters obtained fall within the range of their expected physical values. Nevertheless, their high variability throughout the dyke length prevented identification of the leakage zones. That related to the high local differences in the heat stream penetrating into the downstream bank. The reasons for such situation included the high variability of the grass cover, including the absence of grass in certain bank patches, and also grass tussocks and turves in places. Uneven daily solar exposure of the bank also varied considerably. Moreover, frequent strong winds in the reservoir area affected the bank, too. Reduction in variability of the thermal loadings could be attained in modelling by substituting the air temperature with the soil temperature measurements taken on sensor located several centimetres beneath the bank, beyond the impact zone of a possible leakage. In the second modelling series thus performed a considerable drop in variability of the model parametric values was noted along the whole dyke length. However, that drop was still continuously insufficient enough to identify any leakage clearly. Finally, the third modelling series was conducted through modelling the temperature values taken on the B- FO and the M-FO fiber optic cables compared with the T-FO fiber optic cable temperature function. When modelling the series for the subsequent points of the B-FO and the M-FO fiber optic cables, the temperature series was used which was taken on the subsequent measuring points of the T-FO fiber optic cable situated at the same cross-sections. That enabled precise consideration of the local variability of the thermal loadings throughout the structure length, and also produced very good results. At the same time, this approach enabled formulation of the recommendation to install additional fiber optic cable beneath the bank, or under the structure crown, beyond the reach of potential leakage for measuring the external thermal loadings. The modelling results produced are presented in Fig. 9, in which the cross marks and the triangle marks denote the results obtained on the B-FO and the M-FO cables, respectively. The Figure clearly shows location of the leakage zones for the B-FO fiber optic cable positioned in the lowest location, and those are indicated by significantly reduced values of the η air parameter. This parameter indicates the time lag of signal transition from the downstream bank to the measuring point. The reduction of the η air parameter value relates to the higher signal transition time in soil of increased humidity in the leakage zone, when compared with the less humid zone (i.e. absence of leakage). It is noteworthy that the B-FO fiber optic cable is situated below all the three leakage zones, including directly beneath the two lowest located leakage zones. Diffusion of moisture within 104

13 geotextile caused all the three leakages to merge together to some extent in the area between 14 and 28 metres in the vicinity of the B-FO fiber optic cable, and reduction in the η air parameter values was noted there throughout this length. However this reduction is the greatest throughout the leakage location points. Fig. 9 Results of the IRFTA analysis for the west dyke temperature measurements of the Aix-en-Provence basin (α air - damping factor; η air time lag). Résultats d analyse des séries de la température mesurée sur la digue ouest en Aix-en-Provence (α air coefficient d'amortissement; η air retard de signale). (A) Low position leakages (A) Fuites basses (B) High position leakage (B) Fuite haute (C) Fiber optic B-FO (C) Fibre optique B-FO (D) Fiber optic M-FO (D) Fibre optique M-FO (E) Distance (m) (E) Distance (m) The M-FO fiber optic cable is positioned above the two leakages situated lower, but directly under the upper leakage zone. Consequently, for the M-FO fiber optic cable, the effects of the lower leakages can be visible to a lesser extent when compared with the values of the η air parameter obtained on the B-FO fiber optic cable, but the influence from the upper leakage is stronger. The change in the α air parameter values, which describe the signal amplitude damping for the air temperature is not significant throughout the dyke length, thus featuring the medium being beyond direct influence of filtration (i.e. water velocity). Variation of this parameter depends specifically on direct contact between the thermal sensor and the water current. Consideration of this issue 105

14 falls beyond the scope of this paper. The values of the IRFTA model parameters are the mean values of the real values of the signal damping and transition time that will vary in time with any change in soil humidity or leakage parameters, in relation to the mean value. The time-variability increase of leakage intensity, results in the higher error embedded in representation of the real model data. Since the variability of the leakage yield in the dyke of the Aix-en-Provence basin was significant (between 2 and 12 litres per minute), then variation of the values of the 1-R2 function are shown in Figure 9 that describes correctness of the model data reproduction, with the R2 being a correlation coefficient. The zero values of the 1-R2 function would mean an ideal representation of the model data. A 1 value would mean entire absence of any correlation. The increase in the values of the 1-R2 function apparently shows the location of all three leakages for the B-FO fiber optic cable (positioned lowest), and the only influence of the upper leakage for the M-FO fiber optic cable positioned above lower leakages. That indicates the variability of the 1-R2 function may also be used for identification of the leakages, supplementing the analysis performed on the α and η parameters. Moreover, the analysis of the function 1-R2 values is informative regarding variability of the leakage intensity values in time, throughout the length of the fiber optic cable. Simultaneously the values of the 1-R2 function even for considerable changes in leakage intensity in the Aix-en-Provence basin dyke are lower than 0.08, thus very low and indicating very good data representation. Fig. 10 shows the data representation examples of the IRFTA model in the leakage zone and beyond, for two selected points of the B-FO fiber optic cable. Fig. 10 Examples of representation by the IRFTA model of the temperature measurements taken by the B-FO fiber optic cable in the Aix-en-Provence dyke. Exemples de la reconstitution des mesures de la température réalisés avec la fibre optique B-FO sur le basin en Aix-en-Provence. (A) Leakage zone (B) Null leakage zone (C) Real temperature (D) IRFTA model (E) Temperature (ºC) (F) Distance (m) (A) Zone avec fuite (B) Zone sans fuite (C) Température réelle (D) Modèle IRFTA (E) Température (ºC) (F) Distance (m) 106

15 4. CALCULATING THE SEEPAGE VELOCITY WITH APPLICATION OF THE IRFTA MODEL FOR A HOMOGENEOUS DAM. As shown in the Chapters above, the IRFTA model parameters are the physical parameters enabling analysis and determination of the filtration intensity processes and leakages in the dam body or the canal dyke. In this Chapter, an additional opportunity is described to directly calculate filtration velocity in homogeneous medium. The equations presented below link the Darcy velocity and the IRFTA model parameters. A set of dimensionless equations [7 to10] is formulated using equation [1]. They describe unstable heat transport in one-dimensional porous medium, generated by 1 C step of the water temperature increase (the upstream system boundary). Constant seepage velocity and constant thermal and hydraulic parameters of both the porous medium and water are assumed. T T T Pe t x x 2 0 [7] 0 x 1 T ( x,0) 0 [8] 0 si t 0 T(1, t ) 1 si t 0 [9] T(0, t ) 0 [10] D where: t t L 2 ; non-dimensional time [11] D ; thermal diffusivity [12] C x x / L ; non-dimensional distance [13] C f ql Pe [14] q Darcy velocity C f volumetric heat capacity of water λ thermal conductivity of saturated porous medium 107

16 Pe is the Peclet number expressing the ratio of the advective heat transport (heat transport with mass of water) and the conductive heat transport. Application of the Laplace transform to solve the above set of equations and the use of the method of moments yields the equations, which define the α w, η w parameters in the IRFTA model compared with the Peclet number function, and compared with the x/l measuring point situation function [7]. The amplitude damping factor of upstream thermal signal (water temperature) α w : ( x, Pe) e 1 Pex 2 Pe sinh 1 x 2 1 e Pe sinh 1 e 2 Pe( x 1) Pe [15] The transition time of upstream thermal signal (water temperature] η w : Pe Pe coth ( x 1) coth x ( x, Pe) Pe [16] When acting analogously, also the equations for the α air, and η air IRFTA model parameters were determined, which describe modification of the downstream thermal signal (air temperature). The amplitude damping factor of downstream thermal signal (air temperature) α air : 1 e 2( x, Pe) 1 e Pe(1 x) Pe [17] The transition time of downstream thermal signal (air temperature) η air : Pe Pe Pex e 1 e e Pe Pe Pex Pe Pe e e 2 x 1 e x e 1 2 2( x, Pe) [18] As a result of modelling with application of the IRFTA model, the temperature series, compared with water temperature or air temperature functions, or compared with both these thermal loadings, the values of model parameters are obtained. Inserting these values into equations [15 to 18] enables 108

17 calculation of the Peclet number. In turn, applying the equation, which defines the Peclet number [14], while knowing the C f and λ thermal parameters, and also the measuring point location, enables calculation of the q filtration velocity. Fig. 11 presents the application outline of the one-dimensional heat transport description presented in this Chapter in a two-dimensional earth dam body system, while assuming its application for saturated and homogenous part of the structure body. Fig. 11 Application outline of the description of one-dimensional heat transport in twodimensional earth dam body system (T w water temperature, T air air temperature, T FO fibre optic temperature). Schéma descriptif du transport du chaleur à une dimension dans le corps du barrage à deux dimensions (T w température de l'eau, T air température de l'air, T FO température de la fibre optique). Numerical tests performed by Radzicki [6] proved that application of equations [15 to 18] to calculate filtration velocity, for steady water flow, in homogenous saturated system, enables estimation of the order of magnitude of Darcy velocity. However, these equations may not be used for calculation of seepage velocity for non-homogenous media, including those with locally developing erosion process. In such a case, the influence of temperature transport in soil surrounding the erosion zone is of considerable importance for temperature distribution in the erosion zone, and that is not considered in the above formulae described above. The work will be continued to obtain the equations describing the IRFTA model parameters for erosion also. 5. CONCLUSIONS The article presents two IRFTA (impulse response function thermal analysis) model application examples to analyse distributed fiber optic temperature measurements taken on the high dam of the canal and at small dykes of experimental basin. Both these applications prove this model to be an effective tool enabling precise parametric and physical assessment of the 109

18 filtration processes intensity for both large and small earth hydraulic structures. Moreover, the tests performed on the experimental basin prove that application of this model also enables detection of very small leakages, where the filtration velocity around measuring sensor is still low, and which only cause a change in soil humidity. The opportunity to apply this model is specifically important for modelling temperature measurements taken in the structure downstream zone, regarding both the effects of air temperature and water temperature, and also variable soil saturation conditions. Currently, the impulse response function model is the only one, which in such instances enables analysis of physical parameters of leakage, but not only for identification. This model enables modelling the temperature measurement series taken on individual thermal sensors. Nevertheless, this model is especially applicable for analysis of distributed fiber optic temperature measurements. The above features of this model justify recommending application for the purpose of the thermal dam surveillance to assist experts in making clear physical interpretation of the thermal and hydraulic processes observed. REFERENCES [1] JOHANSSON S. (1997) : Seepage monitoring in Embankment Dams. PhD report, Royal Institute of Technology, Stockholm, Sweden. [2] DORNSTÄDTER J. (1997) : Detection of internal erosion in embankment dams. XIX ICOLD Congress, Q73 R.7, Florence. [3] JOHANSSON S., FARHADIROUSHAN T., PARKER T. (2000) : Application of fibre-optics systems in embankment dams for temperature, strain and pressure measurements-some comparison and experiences. 20eme Congres des Grandes Barrages, Beijing, Q.78-R.69, pp [4] ICOLD (2011) : Internal erosion of dams, dykes and their foundations. Draft of ICOLD Bulletin presented at Workshop of European Working Group in Internal Erosion of ICOLD, Brno, Czech Republic. [5] AUFLEGER M., STROBL T., DORNSTÄDTER J., (2000) : Fibre optic temperature measurements in dam monitoring- four years experience. 20eme Congrès des Grands Barrages, Beijing,, Q.78-R.1, pp.1-22 [6] AUFLEGER M., CONRAD M., PERZMAILER S., PORRAS P. (2005) : Improving a fiber optics tool for monitoring leakages, BWG, p [7] RADZICKI K. (2009) : Analyse retard des mesures de températures dans les digues avec application à la détection de fuites. PhD rapport, AgroParisTech, Paris. 110

19 SUMMARY The opportunity to detect, analyse intensity and forecast development of filtration and erosion processes is one of the key issues in monitoring earth dams. These processes pose the major danger to the safety of such structures. Thermal analysis of the distributed fibre optic temperature measurements carried out in the dam's body is currently the most effective monitoring method. This method requires application of models for analysing temperature measurements enabling the reading of information contained in thermal signal transmitted through the soil medium, including data on water filtration and erosion processes relating thereto. The IRFTA (impulse response function thermal analysis) model is one of such models developed by the Authors of this article. The model parameters have physical definition. They allows the expert concerned with dam surveillance to identify a leakage in its early development phase, to determine precisely by parametric physical description the intensity of the filtration process, and also to analyse of its time-variability. The opportunity to use this model for analysing filtration processes in the event of placing the temperature sensors in the dam downstream toe is a specific advantage of the IRFTA model. This article includes description of the model and effective application examples of two earth hydraulic structures equipped with distributed temperature fibre optic measurements networks. Besides, the Authors present the opportunity to determine water filtration velocity on the basis of scientific equations derived for the IRFTA model parameters. RÉSUMÉ Une des questions clés dans le cadre de la surveillance des barrages en terre est de pouvoir détecter, analyser et prévoir l évolution des phénomènes d infiltration et d érosion. Ces phénomènes sont la principale menace pour la sécurité de ces ouvrages. Actuellement, la méthode la plus efficace pour leur surveillance est l'analyse des mesures distribuées de température par fibre optique réalisées dans le corps du barrage. Cette méthode nécessite l utilisation de modèles spécifiques pour l analyse des mesures de température, afin d extraire du signal thermique des informations relatives aux écoulements et à l érosion. Le modèle IRFTA (impulse response function thermal analysis), développé par les auteurs, est l un de ces modèles. Les paramètres du modèle ont un sens physique. Ils permettent à l expert impliqué par la surveillance du barrage de détecter une fuite dans ses premiers stades de développement, de quantifier l intensité de l écoulement et également son évolution dans le temps. L un des avantages du modèle IRFTA est de pouvoir analyser les phénomènes d infiltration lorsque les capteurs de température sont situés en pied de talus aval. Dans cette communication, nous présentons le modèle, ainsi que des 111

20 exemples d application à deux ouvrages hydrauliques en terre équipés de systèmes à fibre optique de mesure distribuée de température. En outre, les auteurs expliquent comment il est possible de déterminer la vitesse d écoulement à partir des équations du modèle IRFTA. 112