Analysis of Seepage in a Laboratory Scaled Model using Passive Optical Fiber Distributed Temperature Sensor

water Article Analysis of Seepage in a Laboratory Scaled Model Using Passive Optical Fiber Distributed Temperature Sensor Yaser Ghafoori 1,* , Matej Maˇcek 1, Andrej Vidmar 1, Jaromírˇ Ríha 2and Andrej Kryžanowski 1 1 Faculty of Civil and Geodetic Engineering, University of Ljubljana, Jamova Cesta 2, 1000 Ljubljana, Slovenia; [email protected] (M.M.); [email protected] (A.V.); andr[email protected] (A.K.) 2Faculty of Civil Engineering, Brno University of Technology, Veveˇrí331/95, 602 00 Brno, Czech Republic; [email protected].cz *Correspondence: yaser[email protected]; Tel.: +386-51-788-105 Received: 22 December 2019; Accepted: 25 January 2020; Published: 29 January 2020   Abstract: Seepage is the key factor in the safety of dikes and earth-fill dams. It is crucial to identify and localize the seepage excesses at the early stages before it initiates the internal erosion process in the structure. A proper seepage monitoring system should ensure a continuous and wide area seepage measurement. Here, continuous monitoring of seepage at the laboratory-scale is achieved by a passive optical fiber Distributed Temperature Sensing (DTS) system. An experimental model was designed which consists of initially unsaturated sand model, water supply, seepage outflow, optical fiber DTS system, and water and air temperature measurement. Initially, the sand temperature was higher than the temperature of the seepage water. An optical fiber DTS system was employed with a high-temperature resolution, short sampling intervals and short time intervals for temperature monitoring in the sand model. In the system, the small variation in the temperature due to groundwater flow was detected. The numerical analysis was conducted for both the seepage process and the heat transfer progression in the sand model. The results of the heat flow simulation were evaluated and compared with the measured temperature by the optical fiber DTS. Obvious temperature reduction was obtained due to seepage propagation in the sand. The rate of temperature reduction was observed to be dependent on the seepage flow velocity. Keywords: seepage; optical fiber DTS; temperature; saturation; flow velocity 1. Introduction Control of seepage is crucial for the safety of earth-fill dams and levees. One of the failure mechanisms in hydraulic structures is internal erosion, which is initiated by detaching and transferring the soil particles due to seepage forces [ 1 , 2 ]. Internal erosion is the cause of half of all dam failures [ 3 ] and more than one-third of all levee accidents [ 4 ]. Overall about 1 in 80 embankment dams have failed or experienced an accident by seepage and internal erosion [ 5 ]. The other seepage induced failure due to the increase in pore pressures is drop in effective stress and shear strength and consequent loss of stability [ 6 ]. In order to decrease the negative effect of seepage on the overall stability, impervious central core and drainage systems are constructed inside earth-fill dams. A seepage monitoring system should be installed to check whether seepage is in the limit defined by the designed project and that dams and levees are safe enough. It would be beneficial to use measurements that give results continuously in time and space. One of the seepage monitoring techniques, which can provide continuous measurement both in time and space, is the thermometric method using optical fiber Distributed Temperature Sensor (DTS). The thermometric method is defined as continuous or time periodically repeating measurements of the temperature in the ground to trace the groundwater flow. Water 2020,12, 367; doi:10.3390/w12020367 www.mdpi.com/journal/water Water 2020,12, 367 2 of 16 Kappelmeyer [ 7 ] firstly employed the thermometric method by embedding the thermometers into the shallow soil layer and studied the temperature regime during the seepage process. The method has been developed and used in the field by installing the thermometers in existing boreholes and vertical standpipes [ 8 , 9 ]. Using the thermometers for seepage monitoring guarantees the temperature measurement in short time intervals; however, the monitoring system was still subjected to some shortages because it measures the temperature only in vertical profiles and not over a wide area. With the development in optical fiber technology and the invention of the optical fiber distributed temperature sensor (DTS) in the 1980s [ 10 ], a new window was opened for the seepage monitoring by the temperature measurements [ 11 ]. Optical fiber DTS made it possible to expand the area of investigation and the temperature measurement [ 3 ] with high sensitivity, low cost, and small influences on the mechanical properties of the soil [ 12 ]. The optical fiber cable can be embedded in the soil at the downstream face of the existing embankments and earthen dams, where the signs for increased seepage and erosion is mostly observed. Additionally, the cable can be installed into the vertical standpipes to monitor the presence of the seepage in deeper parts of the dam body. For the new embankments, the cables can be embedded into the structure’s body during the construction phase. The thermometric method by DTS can be applied by measuring the natural temperature of the embankment body, which is called the passive method. However, sometimes it is advisable to identify seepage characteristics by imposing the heat into the embankment and monitoring its dissipation, called active method [3]. In this study, the passive approach was used. Johansson and Sjodahl [ 13 ] used passive temperature monitoring by the optical fiber DTS for seepage observation. Considering the seasonal variation of the temperature in air and reservoir water, the seasonal thermal response was observed in the dam body. The results of a long-term monitoring present that the constant temperature in a dam indicates small seepage, while large seasonal temperature variation indicates significant seepage. During the winter, the water in the seepage zone warms up the relatively cooler body of the embankment, while in the summer the seepage water cools down the dam body [14]. The other method for leakage detection using the optical fiber DTS was developed by Perzlmaier et al. [15] . The method is based on the active temperature measurement, inserting heat into the dam along the optical fiber cable and monitoring the heat dissipation. This can be implemented by introducing heat into a metal wire within the optical fiber coating [ 16 ] or a separate wire along the optical fiber cable. The active method was used to estimate the seepage velocity [ 15 , 17 ] and the degree of saturation [ 15 ] in the vicinity of the optical fiber cable. The accuracy of the method depends on the heating power [ 17 ] that is introduced into the embankment, thus, for long cables, a high power source is required. Yosef et al. [ 18 ] performed a coupled hydro-thermal modeling and analyzed one year temperature measurements in an embankment. They presented the ability of hydro-thermal coupled analysis to trace the anomalies of the heat sources, variation in the permeability, and the existence of anomalies such as a sinkhole in dam. Using DTS temperature monitoring, techniques were developed to distinguish the temperature variation due to seepage from other reasons such as seasonal temperature variation of soil, existing structure in the dam, precipitations, and soil heterogeneity [15,19,20]. This work focuses on the monitoring of the seepage process in a laboratory scaled model by a passive DTS system. Most of the studies on this topic were performed by laboratory or field experiments. In this work, we combined a laboratory experiment with the numerical study for both thermal and groundwater flow. The study consists of the determination of material properties, a set-up of an experimental model of seepage while the optical fiber cable is embedded in the sand model and the numerical modeling of the seepage and heat flow in a geotechnical engineering software for two-dimensional finite element analysis (PLAXIS 2D). The experimental results from the physical model were compared with the numerical results obtained from the thermal and groundwater flow analysis. No optimization of material parameters was made, all the calculations were performed by using material parameters obtained from the laboratory tests and the related reference literature. Water 2020,12, 367 3 of 16 For the low temperature difference between the entered water and the soil, the active method was developed [ 15 ]. However, in this study, we showed the ability of the passive optical fiber DTS to monitor the seepage at the low temperature difference between the unsaturated sand and water in a laboratory scaled sand model. 2. Materials and Method This study consists of the determination of material properties by the respective laboratory tests, an experimental model of seepage while the optical fiber cable is embedded in the sand model and the numerical modeling of the seepage and thermal flow in the PLAXIS 2D software. 2.1. Seepage and Heat Flow The heat is transferred in soils by three mechanisms: conduction, convection, and radiation. In the thermometric analysis of seepage, the influence of the radiation process can be neglected because it affects only the surface layers of the soil due to its short day-night cycles duration [ 8 ]. A simplified equation based on energy conservation presents the heat transfer mechanism in the porous media which is shown in Equation (1) [ 21 ]. The second and third terms represent the heat transfer due to convection and conduction, respectively: ρc∂T ∂t+ρwcwq× ∇T− ∇ × (λ∇T)=0 (1) where ρ is the bulk density of soil, T is temperature, c is the specific heat of the soil, t is time, ρw presents the water density (1000 kg/m 3 ), cw is the specific heat of water (4181 J/kg/ ◦ C), q is the specific discharge or Darcy velocity, and λis the soil thermal conductivity. Both λ and c are dependent on the saturation ( S) and porosity ( n) for a given mineral composition [21,22]. Specific discharge is calculated using the continuity equation for mass conservation of water in porous media: ∂(ρwθ) ∂t+∇ × (ρwq) = 0 (2) Considering constant ρw , the equation for the volumetric water content θ=n×S , and Darcy’s law q=−k∇H, Equation (2) leads to: ∂(nS) ∂t=∇ × (k∇H)(3) where k is the hydraulic conductivity and depends on the saturation and porosity, and H is the piezometric head. Oftentimes, the Soil Water Characteristic Curve (SWCC) is used to describe the saturation - negative pore pressure (i.e., suction) relationship. We described the SWCC by the van Genuchten model [23] that relates the saturation Sto the pressure head ψ: Sef f =h1+gaψgni−gm(4) where: Sef f =S−Sres Ssat −Sres (5) where Ssat is the saturation of the sand at the saturated condition usually equals to 1, Sres is the residual saturation and ga , gn , and gm are empirical fitting parameters for the van Genuchten model. ga is related inversely to the air entry value (suction at which the soil begins to de-saturate). gn is the slope of SWCC once the air entry value has been exceeded [ 24 ] and gm is related to the curvature of the SWCC model in the high suction range. gm is usually fixed to 1 − 1 /gn in order to have an analytical solution Water 2020,12, 367 4 of 16 for hydraulic conductivity. The hydraulic conductivity of material at the unsaturated condition ( k(S) ) can be calculated using SWCC as seen from Equation (6) [23]: k(S)=ksat "Sef f gl1−1−Se f f −gmgm2#(6) where ksat is hydraulic conductivity of saturated soil, glis the fitting parameter (mostly 0.5). The thermal conductivity of the soil ( λ) and the heat capacity ( c ) as a function of soil saturation and porosity were estimated as [25]: λ=(1−n)λs+nSλw+n(1−S)λair (7) ρc=nρwcw+(1−n)ρscs(8) where λs , λw , and λair are the thermal conductivities of the particles, water (0.6 W/m/ ◦ C), and air (0.026 W/m/ ◦ C at normal laboratory conditions; 101.3 kPa, 20 ◦ C) [ 26 ], respectively, ρs is the particle density, and csis the heat capacity of particles. The heat flow boundaries are described by the Dirichlet and Neumann boundary condition types. In the Dirichlet type, a known temperature TD is prescribed on the boundary domain ΓBT ⊂Γ and time t[25,27]: T(x,t)=TD(t)on ΓBT ×t[t0,∞)(9) The Neumann type boundary condition for the heat transfer can be described by Equation (10): qT(x,t)=qDT (t)on ΓBq ×t[t0,∞)(10) where qTis the heat flux across the boundary ΓBq and qDT is the prescribed Neumann heat flux. 2.2. Soil Silica dominated sand was used in this study. The material was purchased in 2019 from TERMIT d.d., a mining company that produces silica sand from the mines located in Moravˇce, Slovenia. We determined the saturated hydraulic conductivity, SWCC, dry and saturated densities, porosity, and the grain size distribution of the sand in the laboratory tests. The vendor provided the chemical composition of the sand [ 28 ]. The heat capacity and thermal conductivity of the sand particles were estimated from the literature based on the chemical composition of the material ( λs= 1.36 W/m/ ◦ C [ 29 ], cs=730 J/kg/◦C [30]). The chemical composition of the material, dry density ρd , particle density ρs , porosity n , and coefficient of uniformity Cu are presented in Table 1. Table 1. The material characteristics. Chemical Composition Sand Properties % SiO2% Fe2O3% Al2O3% TiO2% K2Oρs(g/cm3)ρd(g/cm3)n Cu 99.17 0.120 0.348 0.071 0.097 2.7 1.54 0.435 1.52 We determined the grain size distribution of the sand by the sieve analysis test, which is given in Figure 1. Water 2020,12, 367 5 of 16 Water 2020, 12, 367 5 of 16 Figure 1. The grain size distribution curve. SWCC was developed using the HYPROP evaporation method device (Meter group) [31,32] on a compacted sample. The sample was compacted to the same dry density as in the experimental model. With the HYPROP device, a continuous SWCC is obtained by simultaneously and continuously measuring suction with two high capacity tensiometers installed at different heights of the soil sample and weight change during drying. The typical range of the HYPROP device is from 0 to slightly above 100 kPa. When the suction difference between upper and lower tensiometer is greater than hydrostatic, the hydraulic conductivity as a function of saturation, 𝑘(𝑆), could be measured for the unsaturated state. In the case of sand without fine particles (<0.063 mm), the volume change during the test is negligible and from the change in the mass of water the saturation could be calculated. The saturated hydraulic conductivity, 𝑘 , was measured in constant head rigid wall permeameter using local total head measurements without saturation control (class 2 measurements). A permeameter with a diameter of 113 mm and a height of 405 mm was used. The sand was compacted to the same dry density as in the experimental sand model. 2.3. Experimental Model The physical model consisted of a rectangular box filled with sandy soil supported by wire mesh on the upstream and downstream faces and plexiglass at the sidewalls, with upstream and downstream tanks attached to it (Figure 2). Soil fill was 33.5 cm × 27 cm × 12 cm (length, width, height). The optical fiber cable was installed during soil placement. Homogeneous sand fill was assumed. It was anticipated that installed optical cables did not significantly influence the water and heat flow. Additionally, two thermometers were used to measure air and water temperature. The water level in the upper tank was controlled only by manual adjusting the position of a ball valve. (a) (b) Figure 2. Geometry of the experimental model. (a) Side view of the model; (b) top view of the model at the elevation of 2.9 cm. 0 10 20 30 40 50 60 70 80 90 100 0.01 0.1 1 passing (%) particle size (mm) sil sand Figure 1. The grain size distribution curve. SWCC was developed using the HYPROP evaporation method device (Meter group) [ 31 , 32 ] on a compacted sample. The sample was compacted to the same dry density as in the experimental model. With the HYPROP device, a continuous SWCC is obtained by simultaneously and continuously measuring suction with two high capacity tensiometers installed at different heights of the soil sample and weight change during drying. The typical range of the HYPROP device is from 0 to slightly above 100 kPa. When the suction difference between upper and lower tensiometer is greater than hydrostatic, the hydraulic conductivity as a function of saturation, k(S) , could be measured for the unsaturated state. In the case of sand without fine particles (<0.063 mm), the volume change during the test is negligible and from the change in the mass of water the saturation could be calculated. The saturated hydraulic conductivity, ksat , was measured in constant head rigid wall permeameter using local total head measurements without saturation control (class 2 measurements). A permeameter with a diameter of 113 mm and a height of 405 mm was used. The sand was compacted to the same dry density as in the experimental sand model. 2.3. Experimental Model The physical model consisted of a rectangular box filled with sandy soil supported by wire mesh on the upstream and downstream faces and plexiglass at the sidewalls, with upstream and downstream tanks attached to it (Figure 2). Soil fill was 33.5 cm × 27 cm × 12 cm (length, width, height). The optical fiber cable was installed during soil placement. Homogeneous sand fill was assumed. It was anticipated that installed optical cables did not significantly influence the water and heat flow. Additionally, two thermometers were used to measure air and water temperature. The water level in the upper tank was controlled only by manual adjusting the position of a ball valve. Water 2020, 12, 367 5 of 16 Figure 1. The grain size distribution curve. SWCC was developed using the HYPROP evaporation method device (Meter group) [31,32] on a compacted sample. The sample was compacted to the same dry density as in the experimental model. With the HYPROP device, a continuous SWCC is obtained by simultaneously and continuously measuring suction with two high capacity tensiometers installed at different heights of the soil sample and weight change during drying. The typical range of the HYPROP device is from 0 to slightly above 100 kPa. When the suction difference between upper and lower tensiometer is greater than hydrostatic, the hydraulic conductivity as a function of saturation, 𝑘(𝑆), could be measured for the unsaturated state. In the case of sand without fine particles (<0.063 mm), the volume change during the test is negligible and from the change in the mass of water the saturation could be calculated. The saturated hydraulic conductivity, 𝑘 , was measured in constant head rigid wall permeameter using local total head measurements without saturation control (class 2 measurements). A permeameter with a diameter of 113 mm and a height of 405 mm was used. The sand was compacted to the same dry density as in the experimental sand model. 2.3. Experimental Model The physical model consisted of a rectangular box filled with sandy soil supported by wire mesh on the upstream and downstream faces and plexiglass at the sidewalls, with upstream and downstream tanks attached to it (Figure 2). Soil fill was 33.5 cm × 27 cm × 12 cm (length, width, height). The optical fiber cable was installed during soil placement. Homogeneous sand fill was assumed. It was anticipated that installed optical cables did not significantly influence the water and heat flow. Additionally, two thermometers were used to measure air and water temperature. The water level in the upper tank was controlled only by manual adjusting the position of a ball valve. (a) (b) Figure 2. Geometry of the experimental model. (a) Side view of the model; (b) top view of the model at the elevation of 2.9 cm. 0 10 20 30 40 50 60 70 80 90 100 0.01 0.1 1 passing (%) particle size (mm) sil sand Figure 2. Geometry of the experimental model. ( a ) Side view of the model; ( b ) top view of the model at the elevation of 2.9 cm. Water 2020,12, 367 6 of 16 A passive optical fiber DTS system (SILIXA-XT-DTS) with 50/125 µ m multi-mode optical fiber was used for the experiment. Optical fiber DTS employs the Optical Time Domain Reflectometry (OTDR) technique and uses characteristics of the Raman Spectroscopy of the light for temperature measurement. In this technique, DTS launches short pulses of light into the fiber optic cable and detects the Raman backscatter photons (Stokes and anti-Stokes) at regular time intervals by the fast photonic detector system [ 33 , 34 ]. The distance from the measurement point is determined by the runtime of the light, knowing its propagation velocity. The Raman scattering will be generated due to the transfer of energy between the launched laser photons and molecules of the material in optical fiber cable. The temperature in the vicinity of cable changes the energy state of molecules in the cable and influences the characteristics of Raman scattered photons. The Stokes intensity is irrelevant to the temperature, while the anti-Stokes intensity is highly dependent on the temperature. DTS measures the intensity of detected Raman scattered photons and use their ratio to obtain the temperature [35]. We performed the DTS measurement based on the duplexed single-ended configuration [ 36 ]. The distance between each temperature successive measurement (sampling interval) was selected as 10 inches (25.4 cm; the minimum allowable sampling interval for our system) to provide as many measuring points as possible in the model. The sampling time interval was 30 s. These intervals were appropriate to provide accurate and reliable measurements in our experiment. DTS temperature measurement is not fully independent for the adjacent sampling interval [ 37 ] and the abrupt change in temperature may be missed by the system. The distance between points reporting 10 to 90%, respectively, the true temperature changes at a step shift in temperature along the cable is called spatial resolution [ 38 ], which in our case was around 64 cm. In order to measure point temperature accurately, the length of the cable surrounds each measuring point (sensory ring) was increased to more than 50 cm by using two loops with the diameter of circa 8 cm. The loops were placed horizontally in the soil so the water flow was along the optical fiber cable. We made 12 measuring points by the cable loops as shown in Figure 2. After the placement of the dry sand, the model was left in the laboratory for more than 48 h in order to equilibrate its temperature with the ambient temperature in the room (approximately 23 ◦ C). Then, the measurement started to obtain the initial temperature of dry unsaturated sand. Filling of the upstream tank and seepage experiment started by opening the valve of the tap water. A PT100 thermometer was replaced in the upstream tank to measure the water temperature. The water temperature during the test was 19.6 ± 0.1 ◦ C. The water level in the upstream tank was measured manually by measuring tape at given time intervals. After the maximum desired level at the upstream tank was reached the valve was closed. It was found that the volume of the upper tank was too small to maintain a nearly constant water level. As the water level dropped more than expected, due to the flow of water into the sand, the valve was temporarily opened again and after reaching the maximum desired level, the valve was closed (see Figure 6). At the downstream tank, the outflow gauge was opened for the free outflow from the tank. The water depth at the downstream tank corresponding to the steady-state flow was about 4 mm. The DTS system is equipped with two PT100 thermometers. One of the thermometers was installed in the upstream tank to continuously measure the water temperature and the other one was used to measure the air temperature adjacent to the experimental model. The temperature measurement in our model was based on the internal calibration of the DTS system. A constant differential loss of light power equals to 0.255 dB/km was assigned for the system, as this was advised by the system guideline [ 39 ]. In the adjacent of the experimental model, a PT100 thermometer was placed to measure the ambient temperature. In this location, we placed 10 m of the cable as a reference section for the system to calibrate its measurements. SILIXA XT-DTS is calibrating its measurements using one or two reference sections where the PT100 thermometers are placed. In addition to that, the system calibrates the measurement using 200 m of the cable reference coil and a highly precise internal thermometer that existed inside the system. We calibrated the system and validated the DTS measurements by the Water 2020,12, 367 7 of 16 internal calibration before the experiment, using two reference water baths containing hot and cold water with the constant temperatures. To describe the effect of the DTS system response time on the measurement of the step change in temperature, we conducted a separate experiment by embedding 50 cm of the cable together with a PT100 thermometer into an isolated hot water bath with a constant temperature of 43.8 ◦ C. The result for the time response of the DTS system to reach 90% of the temperature change is shown in Figure 3. Water 2020, 12, 367 7 of 16 To describe the effect of the DTS system response time on the measurement of the step change in temperature, we conducted a separate experiment by embedding 50 cm of the cable together with a PT100 thermometer into an isolated hot water bath with a constant temperature of 43.8 °C. The result for the time response of the DTS system to reach 90% of the temperature change is shown in Figure 3. Figure 3. Response time of the system. The temperature measurement by the DTS reached to 90% of the temperature shift at the second reported temperature (60 s after cable entered in the hot water). 2.4. Numerical Modeling The numerical modeling of the seepage was performed in the geotechnical program PLAXIS 2D. PLAXIS 2D provides a continuous time-dependent analysis of groundwater and thermal flow in unsaturated media considering both conduction and convection in transient state. The soil is considered as homogeneous media and is not divided into different phases (local thermal equilibrium). The heat transfer due to vapor flow was neglected and heat transfer into the core of sand particles is not considered. Equations given in Section 2.1 are used by the PLAXIS for thermal and seepage analysis. The van Genucthen model (with parameters in Table 2) was used to describe the behavior of the sand at the unsaturated condition. The numerical model was designed based on the material properties, the geometry of the experimental model, and the thermal and hydraulic boundary conditions of the experimental model. A coupled thermo-hydro analysis was performed using a two-dimensional (2D) numerical model consists of 913 15-nodes finite elements (Figure 4). Initially, the soil temperature was the same as measured before the seepage started and the sand was at residual saturation. The boundary conditions of the model with respect to the flow are presented in Figure 4. On the left, a time-dependent water head boundary has been assigned based on the experimental measurements (Figure 6). The top and right boundaries are seepage boundaries, which are closed boundaries until fully saturated when they start to allow outflow of water at pore pressure of 0 kPa (atmospheric pressure). Figure 3. Response time of the system. The temperature measurement by the DTS reached to 90% of the temperature shift at the second reported temperature (60 s after cable entered in the hot water). 2.4. Numerical Modeling The numerical modeling of the seepage was performed in the geotechnical program PLAXIS 2D. PLAXIS 2D provides a continuous time-dependent analysis of groundwater and thermal flow in unsaturated media considering both conduction and convection in transient state. The soil is considered as homogeneous media and is not divided into different phases (local thermal equilibrium). The heat transfer due to vapor flow was neglected and heat transfer into the core of sand particles is not considered. Equations given in Section 2.1 are used by the PLAXIS for thermal and seepage analysis. The van Genucthen model (with parameters in Table 2) was used to describe the behavior of the sand at the unsaturated condition. Table 2. Obtained parameters for the van Genuchten approximation for best fit to the results of the test by the evaporation method (HYPROP device) and the measured saturated hydraulic conductivity of the sand. Ssat Sres ga(1/m) gngcglksat (m/s) 1 0.11 9.70 8.06 0.876 0.00 1.23 ×10−3 The numerical model was designed based on the material properties, the geometry of the experimental model, and the thermal and hydraulic boundary conditions of the experimental model. A coupled thermo-hydro analysis was performed using a two-dimensional (2D) numerical model consists of 913 15-nodes finite elements (Figure 4). Initially, the soil temperature was the same as measured before the seepage started and the sand was at residual saturation. The boundary conditions of the model with respect to the flow are presented in Figure 4. On the left, a time-dependent water head boundary has been assigned based on the experimental measurements (Figure 6). The top and right boundaries are seepage boundaries, which are closed boundaries until fully saturated when they start to allow outflow of water at pore pressure of 0 kPa (atmospheric pressure). Water 2020,12, 367 8 of 16 Water 2020, 12, 367 8 of 16 Figure 4. Discretization of the model into finite elements in the PLAXIS 2D software and definition of boundary condition with respect to the flow condition. The boundary conditions in terms of temperature were defined as follows: at the upstream face, the Dirichlet boundary condition (see Equation (9)) was governed by the water temperature in the upstream tank, right and upper boundary had constant temperature equal to initial soil temperature, and at the bottom zero thermal flow was considered (see Neumann boundary condition, Equation (10)). The first 30 min of the experimental model was simulated by the numerical model. The results of the calculations were saved every 30 s. The thermal conductivity, heat capacity, and hydraulic conductivity in each node were calculated continuously due to the change in saturation using Equations (4)–(8) based on the calculated pressure head by the PLAXIS 2D program. 3. Results 3.1. SWCC and Hydraulic Conductivity The saturated hydraulic conductivity measured in constant head permeameter with local head measurements is given in Table 2. This table also presents the obtained parameters of the van Genuchten model for the best fit to the measured SWCC. Table 2. Obtained parameters for the van Genuchten approximation for best fit to the results of the test by the evaporation method (HYPROP device) and the measured saturated hydraulic conductivity of the sand. 𝐒 𝐬𝐚 𝐭 . 𝐒 𝐫𝐞𝐬 𝐠 𝐚 (1/m) 𝐠 𝐧 𝐠 𝐜 𝐠 𝐥 𝐤 𝐬𝐚 𝐭 (m/s) 1 0.11 9.70 8.06 0.876 0.00 1.23 × 10 −3 SWCC measured in the HYPROP device and the hydraulic conductivity as a function of suction are shown in Figure 5. The van Genuchten model for SWCC (blue lines in Figure 5) was fitted to the measured HYPROP data (Table 2) using the least-squares method in Excel spreadsheet. It was possible to measure unsaturated hydraulic conductivity by the evaporation method at the high suction end of SWCC. The van Genuchten model predicts hydraulic conductivity well to the suction (negative pore pressure) of 2.5 kPa. At greater suctions, the discrepancy between the measured and predicted hydraulic conductivity might be due to limitations of the evaporation method and probably does not represent true material behavior beyond the suction of 2.5 kPa. Figure 4. Discretization of the model into finite elements in the PLAXIS 2D software and definition of boundary condition with respect to the flow condition. The boundary conditions in terms of temperature were defined as follows: at the upstream face, the Dirichlet boundary condition (see Equation (9)) was governed by the water temperature in the upstream tank, right and upper boundary had constant temperature equal to initial soil temperature, and at the bottom zero thermal flow was considered (see Neumann boundary condition, Equation (10)). The first 30 min of the experimental model was simulated by the numerical model. The results of the calculations were saved every 30 s. The thermal conductivity, heat capacity, and hydraulic conductivity in each node were calculated continuously due to the change in saturation using Equations (4)–(8) based on the calculated pressure head by the PLAXIS 2D program. 3. Results 3.1. SWCC and Hydraulic Conductivity The saturated hydraulic conductivity measured in constant head permeameter with local head measurements is given in Table 2. This table also presents the obtained parameters of the van Genuchten model for the best fit to the measured SWCC. SWCC measured in the HYPROP device and the hydraulic conductivity as a function of suction are shown in Figure 5. The van Genuchten model for SWCC (blue lines in Figure 5) was fitted to the measured HYPROP data (Table 2) using the least-squares method in Excel spreadsheet. It was possible to measure unsaturated hydraulic conductivity by the evaporation method at the high suction end of SWCC. The van Genuchten model predicts hydraulic conductivity well to the suction (negative pore pressure) of 2.5 kPa. At greater suctions, the discrepancy between the measured and predicted hydraulic conductivity might be due to limitations of the evaporation method and probably does not represent true material behavior beyond the suction of 2.5 kPa. Water 2020,12, 367 9 of 16 Water 2020, 12, 367 9 of 16 (a) (b) Figure 5. (a) Soil Water Characteristics Curve (SWCC). Results for both the HYPROP device test and the van Genuchten approximation are presented; (b) relative hydraulic conductivity curve. 3.2. Result of the Experimental Model The recorded water levels at the upstream and downstream tanks are shown in Figure 6. Figure 6. Time dependency of water level at upstream and downstream tanks (left and right boundaries). Figure 7 presents the measured temperature by the optical fiber cable embedded in the soil before and during the experiment. The length of the cable corresponded to each measuring point is marked in Figure 7 by the dashed line. The measured temperature during the first two minutes presents the soil temperature when the water flow was not yet started. Almost a homogenous temperature distribution is observed before the seepage flow into the model was taken place. The water inflow into the upstream tank was started at 14:34:00. Points 2 and 3 are located near the upstream tank and the temperature decrease in these points is evident at the first reported time after the start of filling the upstream tank. It is clear from the measured temperature that points 7, 8, 9, and 12 are experiencing the temperature decline respectively after points 2 and 3. All these points are located at the upstream zone of the model and with increasing the water level the seepage flow is propagating towards these locations. The temperature results show that each pair of symmetrically located points with respect to the model vertical central plane (e.g., P1 and P4 in Figure 2) provide similar temperature variation during the experiment. Figure 5. ( a ) Soil Water Characteristics Curve (SWCC). Results for both the HYPROP device test and the van Genuchten approximation are presented; (b) relative hydraulic conductivity curve. 3.2. Result of the Experimental Model The recorded water levels at the upstream and downstream tanks are shown in Figure 6. Water 2020, 12, 367 9 of 16 (a) (b) Figure 5. (a) Soil Water Characteristics Curve (SWCC). Results for both the HYPROP device test and the van Genuchten approximation are presented; (b) relative hydraulic conductivity curve. 3.2. Result of the Experimental Model The recorded water levels at the upstream and downstream tanks are shown in Figure 6. Figure 6. Time dependency of water level at upstream and downstream tanks (left and right boundaries). Figure 7 presents the measured temperature by the optical fiber cable embedded in the soil before and during the experiment. The length of the cable corresponded to each measuring point is marked in Figure 7 by the dashed line. The measured temperature during the first two minutes presents the soil temperature when the water flow was not yet started. Almost a homogenous temperature distribution is observed before the seepage flow into the model was taken place. The water inflow into the upstream tank was started at 14:34:00. Points 2 and 3 are located near the upstream tank and the temperature decrease in these points is evident at the first reported time after the start of filling the upstream tank. It is clear from the measured temperature that points 7, 8, 9, and 12 are experiencing the temperature decline respectively after points 2 and 3. All these points are located at the upstream zone of the model and with increasing the water level the seepage flow is propagating towards these locations. The temperature results show that each pair of symmetrically located points with respect to the model vertical central plane (e.g., P1 and P4 in Figure 2) provide similar temperature variation during the experiment. Figure 6. Time dependency of water level at upstream and downstream tanks (left and right boundaries). Figure 7presents the measured temperature by the optical fiber cable embedded in the soil before and during the experiment. The length of the cable corresponded to each measuring point is marked in Figure 7by the dashed line. The measured temperature during the first two minutes presents the soil temperature when the water flow was not yet started. Almost a homogenous temperature distribution is observed before the seepage flow into the model was taken place. The water inflow into the upstream tank was started at 14:34:00. Points 2 and 3 are located near the upstream tank and the temperature decrease in these points is evident at the first reported time after the start of filling the upstream tank. It is clear from the measured temperature that points 7, 8, 9, and 12 are experiencing the temperature decline respectively after points 2 and 3. All these points are located at the upstream zone of the model and with increasing the water level the seepage flow is propagating towards these locations. The temperature results show that each pair of symmetrically located points with respect to the model vertical central plane (e.g., P1 and P4 in Figure 2) provide similar temperature variation during the experiment. With the propagation of the seepage through the model, the temperature decreases in the soil towards the downstream side. A time difference related to the temperature drop in consecutive measuring points can be used for the estimation of seepage propagation in the model. This estimation assumes thermal retardation to be negligible. With continuing the seepage flow the temperature in all seepage zone tends to be stable. Water 2020,12, 367 16 of 16 30. Hemingway, B.S. Quartz; heat capacities from 340 to 1000 K and revised values for the thermodynamic properties. Am. Mineral. 1987,72, 273–279. 31. Schindler, U.; Müller, L. Soil hydraulic functions of international soils measured with the Extended Evaporation Method (EEM) and the HYPROP device. Open Data J. Agric. Res. 2017,3, 10–16. [CrossRef] 32. UMSP. Manual HYPROP, Version 2015-01; UMS GmbH: Munich, Germany, 2015. 33. Hartog, A.H.; Gold, M.P.; Leach, A.P. Optical Time-Domain Reflectometry. United States Patent No. 4823166, 18 April 1989. 34. Odic, R.M.; Jones, R.I.; Tatam, R.P. Distributed Temperature Sensor for Aeronautic Applications. In Proceedings of the 15th Optical Fiber Sensors Conference, Portland, OR, USA, 6–10 May 2002; IEEE: Piscataway, NJ, USA; pp. 459–562. [CrossRef] 35. Long, D.A. Raman spectroscopy; McGraw-Hill International: New York, NY, USA, 1977; ISBN 0070386757. 36. Hausner, M.B.; Su á rez, F.; Glander, K.E.; van de Giesen, N. Calibrating Single-Ended Fiber-Optic Raman Spectra Distributed Temperature Sensing Data. Sensors 2011,11, 10859–10879. [CrossRef] 37. Selker, J.S.; Tyler, S.; van de Giesen, N. 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New sophisticated analysis method of crystallizer temperature profile utilizing optical fiber DTS based on the stimulated Raman scattering. Adv. Electr. Electron. Eng. 2012,10, 106–114. [CrossRef] 42. Hausner, M.B.; Kobs, S. Identifying and Correcting Step Losses in Single-Ended Fiber-Optic Distributed Temperature Sensing Data. J. Sensors 2016. [CrossRef] 43. Mcdaniel, A.; Tinjum, J.M.; Hart, D.J.; Fratta, D. Temperature Sensing Networks. IEEE Sens. J. 2018 ,18, 2342–2352. [CrossRef] © 2020 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 (http://creativecommons.org/licenses/by/4.0/).