Application Study of Distributed Optical Fiber Seepage Monitoring Technology on Embankment Engineering

: It is very important for embankment engineering to consider the seepage factor. If the potential seepage is not discovered in time and seepage control measures are not appropriate, seepage is very likely to cause damage and deformation, resulting in embankment failure. Based on temperature and seepage fields theories, a temperature–seepage coupled model is established in this paper. It is combined with a distributed temperature sensing (DTS) system to measure the temperature field of the porous media. This approach allows for the inversion of the inner seepage field, realizing the real-time monitoring of embankment health to ensure its safety and long-term operation. According to the coupling analysis on the temperature–seepage fields, for practical engineering, the influence of temperature on the seepage field is small and neglectable. Only the effect of the seepage field on the temperature field is considered. The DTS optical fiber temperature measurement system is widely used in various projects nowadays because of its high stability and efficiency advantages. The optical fiber is sensitive to temperature and can give fast and accurate temperature feedback regarding seepage location. Combined with the Heat Transfer Module in COMSOL, the multi-line heat source method can be used to invert the seepage field according to the temperature field of the porous medium inside the embankment and derive the seepage flow rate of the stable seepage field. For unstable seepage, optical fiber is good at seepage measuring and location detecting. For different practical engineering, a different heating power can be used for different seepage conditions. By monitoring the temperature change, the seepage condition can be inverted which is one of the indicators for evaluating engineering safety.


Introduction
Embankment engineering safety is affected by many internal and external factors during the long-term service process.Possible unsafe conditions include leakage, piping, landslide, collapse, cracking, scouring cavitation, and slope.According to statistics, over one-third of embankment failure is caused by different degrees of seepage and relative problems.More than 90% of levee breaches are caused by leakage damage [1,2].A large number of engineering examples show that it is very important to strengthen the regular positioning and quantitative monitoring of leakage and infiltration deformation of earth dams to ensure the safe operation of the project.In the continuous improvement and development of traditional monitoring means, like pressure gauge and GPR survey in 3D geometry [3], more and more new technologies are introduced into the field of embankment safety monitoring, among which distributed optical fiber temperature sensing technology is the one most widely used [4,5].
Temperature as one of the natural tracers has unique advantages in seepage monitoring.In the early 1980s, the temperature tracing method was introduced in China for seepage detection in embankment engineering, and it was first applied in the Danjiangkou hydrojunction by inverting the seepage field through the analysis of the temperature field of the Appl.Sci.2024, 14, 5362 2 of 17 dam foundation [6,7].Xinjian Wang and Jiansheng Chen from Hohai University regarded the seepage tunnel as a liner heat source and established a relative temperature distribution equation [8,9].They successfully positioned the piping tunnel of the shijiao part of the Beijiang embankment.Distributed optical fiber temperature measurement technology uses optical fiber as the medium to transmit optical signals and has the advantages of anti-electromagnetic interference ability, high sensitivity, and high precision [10].It can accurately and in real time measure the temperature value of any point along with the optical fiber, and does not need to form a loop.It is widely used in practical engineering [11].Although the optical fiber can directly obtain the temperature, it cannot straightforwardly feedback the seepage inside the embankment.Therefore, how to invert the seepage field inside the embankment through the temperature field measured by the optical fiber is the key issue of the optical fiber permeability measurement technology application [12][13][14].
Seepage field and temperature field interact and influence each other in embankment engineering [12].On the one hand, due to the existence of a seepage field, the leakage flow participates in the heat transfer and the exchange of the porous media system inside the embankment, thereby affecting the distribution of the overall temperature field.On the other hand, the change in temperature field in porous media can not only cause a change in water viscosity and soil parameters but also result in the movement of water due to the existence of a temperature gradient [15][16][17].In addition, the temperature change in the system may also lead to the phase change of water, which to a large extent affects the distribution of the seepage field.The coupling process of temperature field and seepage field in porous media is actually the process of a continuous dynamic adjustment of heat energy and fluid in porous media.The instability of any factor in one of the two fields leads to a change in another [18][19][20].From the perspective of the physical process, heat energy is exchanged through the contact of media, while the seepage fluid is diffused and flows into the pores of porous media due to the potential energy difference.At the same time, as the medium of heat energy transmission, the fluid carries heat energy in porous media to exchange and diffuse along the trajectory line [21][22][23].From the physical and chemical process, it is mainly the coupling effect which manifests in the change in the volume effect of medium and fluid, and the change in fluid flow characteristic parameters.Therefore, the process of interaction between seepage and temperature actually includes the process of energy balance and dissipation caused by heat transfer and heat convection [24][25][26], and the process of physical and chemical reactions of media substances.Based on the above analysis, the seepage field of the embankment could be inverted by its soil temperature detected by the optical fiber.Then, the safety pre-warning and long-term service of the embankment could come to an end.
With the recent rapid development of optical fiber sensing technologies, the potential of distributed optical fiber temperature sensor systems for dams and dike seepage monitoring has been recognized.However, the technology is still in its infancy except for some qualitative identification.This paper mainly depends on the theoretical analysis and the model test.The principle and method of the seepage monitoring implementation based on DTS are studied to identify and monitor the saturation line and seepage velocity in embankment dams.

Coupling Calculation of Temperature and Seepage Field
Due to the permeability of the soil material itself, an internal seepage field exists in an embankment.In addition to the long-term service, the aging damage of the material is serious, and the local seepage is intensified, which seriously affects the performance of the embankment and increases the risk of embankment collapse.Therefore, it is of great significance to enhance the internal seepage monitoring of the embankment and establish a real-time pre-warning system for the seepage of the embankment to ensure its safe operation.

Influence of Temperature on Seepage
For embankment engineering, the temperature variation inside the system affects the physical and chemical parameters of water and porous media, thus affecting the distribution of the seepage field inside the dam body.The main parameters related to temperature distribution in seepage fields include porosity, specific heat capacity, thermal conductivity, and temperature conductivity.These parameters change little within the 10 • C range and can be regarded as constants [27][28][29].The basic physical and chemical parameters related to temperature and seepage field are density ρ, gravity γ, dynamic viscosity µ, thermal conductivity λ, thermal expansion coefficient θ, thermal diffusivity α, specific heat capacity c, and kinematic viscosity υ.Research shows that within the range of temperature variation of 15 • C, the specific heat, density, thermal conductivity, and thermal diffusivity of water change little, and their effects can be ignored when analyzing the influence of temperature change on the physical and chemical properties of water.The changes in the kinematic viscosity coefficient, dynamic viscosity coefficient, and thermal expansion coefficient of water directly affect the seepage characteristics of water.Therefore, the changes should be taken into account during coupling calculation and analysis.
The permeability coefficient of porous medium particles represents the degree of seepage, which is related to the type of porous medium, density, the dynamic viscosity coefficient, and the temperature of the permeable liquid.The Darcy permeability of the porous medium can be expressed as: where C is the factor determined by particle shape and size distribution; d is the particle diameter (m); Cd 2 reflects the permeability of the medium which is only related to medium structure (particle size, shape, and distribution); γ is the water gravity (N•m −3 ); µ is the dynamic viscosity of water (Pa•s); and J is the seepage slope.
It can be noticed from Equation (1) that the permeability coefficient of the porous medium is inversely proportional to its dynamic viscosity coefficient, and the dynamic viscosity coefficient of the porous medium is affected by temperature.Therefore, the permeability coefficient of the porous medium is a function of temperature.The temperature field affects the distribution of the seepage field by affecting the permeability coefficient on one hand.On the other hand, the temperature potential gradient formed by temperature difference also affects fluid flows.As the temperature potential calculation is a complicated problem, the influence of temperature potential on water flow can only be expressed by an empirical formula of the temperature potential gradient.For one dimension case, it is: where V T is the fluid flux caused by temperature (m•s −1 ); D T is the diffusivity under temperature potential which contains the influence of the fluid, the heat expansion coefficient, and the physical and chemical coefficient change of the porous medium (m•s −1 ); and ∂T/∂x is the temperature gradient along x-direction.Thus, the seepage velocity along the x-direction is: where H is the water head (m) and T is the temperature ( • C).
Similarly, the seepage velocities along the y-and z-directions are: By substituting Equation (3) to Equation (5) into the seepage continuity equation, it can be concluded that the control function of the seepage field under the influence of temperature is: where K = K(x, y, z) = K(T) is the isotropic permeability coefficient of the embankment (m•s −1 ) and is a function of temperature; S s is water storativity; and ∇ is the Hamiltonian.It can be seen from Equation ( 6) that temperature is closely related to the seepage field distribution of embankment engineering.On the one hand, temperature affects the seepage field by influencing the permeability coefficient; on the other hand, the existence of the temperature gradient itself also affects the movement of water flow, and the greater the temperature gradient is, the greater the impact on seepage is.

Influence of Seepage on Temperature Field
Due to the water level difference between the internal and external rivers in embankment engineering, the seepage flows from the inside of the river to the outside.When the water passes through the dam, if there is a temperature difference between the two media, heat exchange will inevitably occur.
In the case of one-dimensional heat conduction, when seepage exists, the heat flow includes two parts: one is caused by the conduction of the porous medium which is −λ(∂T/∂x); another is the heat reduction taken by the seepage water and is c w ρ w vT.In conclusion, the heat flux inside the embankment is: where c w is the specific heat capacity of water (J•K −1 ); ρ w is water density (kg•m −3 ); v is seepage water velocity (m•s −1 ); and λ is the heat conductivity of the soil (W•m −1 •K −1 ).In the x-direction of unit time, the net heat flowing into the unit volume is: The net heat should be equal to the heat absorbed by the temperature rise of the unit volume medium in unit time, that is: Expanding to a 3D condition and taking into account heat source Q T : With Darcy's law: The soil is considered to be isotropic and that is: which is simplified as: The temperature field is steady during the long service process and no source term is included, which means ∂T/∂τ = 0 and Q T = 0; substituting this into Equation (12): Setting a = λ and b = c w ρ w , Equation ( 12) can be transformed into:

Coupling Analysis of Temperature Field and Seepage Field
According to the analysis above, the control functions for the seepage field and temperature field coupling problem are: The temperature field and seepage field interact and influence each other in embankment engineering.Theoretically, there is an analytical solution that can simultaneously satisfy Equation ( 15), but it is difficult to obtain in most cases.To obtain a numerical solution, the one-dimensional problem is analyzed and discussed first.
Assuming that the permeability coefficient K and water diffusivity D T are constants, thermal conductivity λ is also a constant and does not change with temperature.The source and sink terms are not considered, and then Equation ( 15) can be rewritten as: The boundary conditions are: First of all, neglecting the influence of the seepage field on the temperature field sets k = 0 in Equation ( 16).The temperature distribution calculated by Equation ( 16) is: Substituting Equation ( 17) into Equation ( 16): Solving Equation ( 19), we can get: where 2)-( 16): Appl.Sci.2024, 14, 5362 6 of 17 With the boundary conditions, the solution of H 1 (x) is: where β = D T /K.Though the solutions of Equations ( 20) and ( 22) are not the analytical solutions of Equation ( 15), they satisfy the boundary conditions and could partially reflect the coupling effect.Thus, the approximate solution of Equation ( 15) is: (24)   where T 0 (x) is the temperature distribution caused by the gradient ( • C); T H (x) is the tem- perature distribution caused by the water gravity ( • C); H 0 (x) is the water head distribution caused by the gravity potential (m); and H T (x) is the water head distribution caused by the temperature potential difference (m).
For simplification, choosing embankment length and water head of upstream and downstream as l = 100 m, the physical and thermal parameters of the water and the porous medium are chosen as standard numbers: The permeability coefficients are chosen as follows: K = 10 −9 m/s, K = 10 −8 m/s, K = 10 −7 m/s and K = 10 −6 m/s for four different conditions to calculate α and β, and then calculate T 0 (x), T 1 (x), H 0 (x) and H 1 (x) relatively.
Figure 1 shows the influence of the seepage field on the temperature field under different permeability coefficients.Figures 2 and 3 mainly reflect the influence of the temperature field on the seepage field under different permeability coefficients.It can be seen from these figures that by comparing the solutions without considering the coupling effect T 0 (x), H 0 (x) and the solutions considering the coupling effect T 1 (x), H 1 (x), the latter is more satisfied with the actual engineering situation.With the increase in the permeability coefficient, the influence of the seepage field on the temperature field is greater than that of the temperature field on the seepage field.From the point of view of engineering applications, only the influence of the seepage field on the temperature field is considered, and the effect of the temperature field on the seepage field is neglected, which can meet the requirements of engineering accuracy and simplify engineering problems.x , the latter is more satisfied with the actual engineering situation.With the increase in the permeability coefficient, the influence of the seepage field on the temperature field is greater than that of the temperature field on the seepage field.From the point of view of engineering applications, only the influence of the seepage field on the temperature field is considered, and the effect of the temperature field on the seepage field is neglected, which can meet the requirements of engineering accuracy and simplify engineering problems.

Finite Element Method for Solving Seepage Field
For the semi-coupling problem of seepage field and temperature field in three-dimensional cases, it is assumed that the seepage field is in a stable state without considering the influence of temperature.At this point, when the temperature boundary conditions and seepage boundary conditions are known, the control function is: where a is the thermal conductivity of soil (KJ/(m•s•°C)), and the soil is considered to be isotropic which means: Discretizing the computing domain into 3D elements and the temperature at any point can be expressed by the node temperature through the interpolation of shape function: The temperature gradient can be represented as: where i N is the shape function and i T is the node temperature (°C).
Applying the weighted residual method with weight function i W , and choosing the shape function i N with the same form as i W , the control function can be trans- formed into:

Finite Element Method for Solving Seepage Field
For the semi-coupling problem of seepage field and temperature field in three-dimensional cases, it is assumed that the seepage field is in a stable state without considering the influence of temperature.At this point, when the temperature boundary conditions and seepage boundary conditions are known, the control function is: where a is the thermal conductivity of soil (KJ/(m•s• • C)), and the soil is considered to be isotropic which means: Discretizing the computing domain into 3D elements and the temperature at any point can be expressed by the node temperature through the interpolation of shape function: The temperature gradient can be represented as: where N i is the shape function and T i is the node temperature ( • C).
Applying the weighted residual method with weight function W i , and choosing the shape function N i with the same form as W i , the control function can be transformed into: For simplification, the control function can be transformed into: Using the backward difference method to solve Equation ( 28): where T is the unknow temperature matrix (

Numerical Example
In order to measure the overall seepage field of the embankment, combined with the above coupling theory of the seepage field and temperature field (ignoring the influence of the temperature field on the seepage field), the primary goal is to obtain the stable temperature field of the embankment.The traditional monitoring methods are mostly point-based.The temperature of the dam is measured using resistance temperature sensors.Although the point-based measurement can obtain the accurate value of the monitoring point, it cannot obtain the continuous temperature change inside the dam.Therefore, this paper selects the DTS distributed optical fiber temperature measurement system to monitor the temperature field inside the embankment.
In the DTS temperature measurement system, optical fiber can be used as both sensor and transmission medium to transfer deformation, temperature, damage, and other physical quantities; the dual use of optical fiber makes it possible to realize long-distance distributed distribution without forming a loop.In addition, the advantages of stability, small external interference, and strong corrosion resistance leads to the optical fiber's wide application in civil engineering structures, where good measurement results have been achieved.
The DTS temperature measurement system is mainly divided into two parts, namely, the optical fiber temperature measurement host and the distributed temperature sensing fiber.The temperature measurement host includes lasers, optical devices, and data storage modules for transmitting and receiving optical signals; in this paper, a ZTT-GYXTW-4A1a built-in steel wire-reinforced four-core-armored optical fiber cable, and a stainless-steel hose two-core-armored optical fiber cable are used for comparative tests.
Two model sinks with 5 m length, 0.6 m width, and 1.15 m height were established in the experiment.The wall was filled with sintered ordinary bricks and built with M5 cement mortar, with M10 mortar smeared on the surface.A slope was set at the bottom of the model sinks to form seepage, with a slope of 1:3 and an outlet hole drilled to calculate the seepage velocity.On the basis of the vertical height of 5 cm, the steel plate mesh was arranged, and two layers of filter cloth were laid on the steel plate mesh to prevent the medium from being taken away by the seepage water.In order to make force on the steel plate mesh uniform and prevent the stress damage of the filter cloth, gravel with a 10 cm thickness and slightly larger than the mesh hole size was laid between the two layers of the filter cloth.A 5 cm gap between the steel plate mesh and the foundation was reserved, and an outlet hole was set at the end of the sink to discharge the seepage water.Three PVC semi-tubes with a diameter of 4 cm were set on the edge wall of the model sink to simulate the concentrated seepage inside the embankment.The optical fiber was arranged as shown in the Figure 4, and yellow sand and clay were used to fill the two model sinks, respectively, denoted as medium I and medium II.The multi-line heat source method was adopted, and the double-row fiber was The fiber was set in the middle of the sink, and the sprinkler was set at the top of the to spray water evenly into the sink to simulate seepage.The change in temperature a the fiber during the whole process was recorded.The basic idea of the multi-line source method is as follows: (1) Assume the seepage velocity v , determining the heat flux q of the inner bound and temperature 0 T of the external boundary (the initial temperature of optical before heating); (2) Calculate temperature distribution using the coupling model of the temperature and seepage field under a uniform and stable seepage condition to obtain the num ical temperature value 2 T at the optical fiber position; (3) Compare the temperature calculated using the coupling model 2 T with the ac monitoring temperature 2 T ′ .If the two temperature values are the same or with certain range, the inversion step is completed, and the actual seepage velocity is e to the assumed seepage flow velocity.If the difference between the two tempera values is beyond this range, then re-assume the seepage velocity, going back to (1) until the end of the inversion.The assumption and adjustment of seepage velo should be adjusted according to the difference between 2 T and 2 T ′ .The multi-line heat source method was adopted, and the double-row fiber was set.The fiber was set in the middle of the sink, and the sprinkler was set at the top of the sink to spray water evenly into the sink to simulate seepage.The change in temperature along the fiber during the whole process was recorded.The basic idea of the multi-line heat source method is as follows: (1) Assume the seepage velocity v, determining the heat flux q of the inner boundary and temperature T 0 of the external boundary (the initial temperature of optical fiber before heating); (2) Calculate temperature distribution using the coupling model of the temperature field and seepage field under a uniform and stable seepage condition to obtain the numerical temperature value T 2 at the optical fiber position; (3) Compare the temperature calculated using the coupling model T 2 with the actual monitoring temperature T ′ 2 .If the two temperature values are the same or within a certain range, the inversion step is completed, and the actual seepage velocity is equal to the assumed seepage flow velocity.If the difference between the two temperature values is beyond this range, then re-assume the seepage velocity, going back to step (1) until the end of the inversion.The assumption and adjustment of seepage velocity should be adjusted according to the difference between T 2 and T ′ 2 .Figures 5-11 show the temperature distributions of the porous medium under different seepage conditions calculated using COMSOL combined with the temperature-seepage coupling theory.Figures 5 and 6 show the temperature distributions under no seepage conditions which are the initial state for later iteration.Setting the seepage velocity to 10 −7 m/s, the temperature fields of the porous medium calculated using the measured temperature of the second optical fiber are shown in Figures 7 and 8. Given the existence of the seepage field, the temperature fields are different from Figures 5 and 6   Figures 5-11 show the temperature distributions of the porous medium under different seepage conditions calculated using COMSOL combined with the temperature-seepage coupling theory.Figures 5 and 6 show the temperature distributions under no seepage conditions which are the initial state for later iteration.Setting the seepage velocity to 10 −7 m/s, the temperature fields of the porous medium calculated using the measured temperature of the second optical fiber are shown in Figures 7 and 8. Given the existence of the seepage field, the temperature fields are different from Figures 5 and 6     Figures [5][6][7][8][9][10][11] show the temperature distributions of the porous medium under different seepage conditions calculated using COMSOL combined with the temperature-seepage coupling theory.Figures 5 and 6 show the temperature distributions under no seepage conditions which are the initial state for later iteration.Setting the seepage velocity to 10 −7 m/s, the temperature fields of the porous medium calculated using the measured temperature of the second optical fiber are shown in Figures 7 and 8. Given the existence of the seepage field, the temperature fields are different from Figures 5 and 6

Analysis of Seepage Locating
It can be seen from the above analysis that the distribution of the seepage field can be inversed by the temperature field measured using the optical fiber, but the seepage

Analysis of Seepage Locating
It can be seen from the above analysis that the distribution of the seepage field can be inversed by the temperature field measured using the optical fiber, but the seepage

Analysis of Seepage Locating
It can be seen from the above analysis that the distribution of the seepage field can be inversed by the temperature field measured using the optical fiber, but the seepage

Analysis of Seepage Locating
It can be seen from the above analysis that the distribution of the seepage field can be inversed by the temperature field measured using the optical fiber, but the seepage field is steady at this time.In order to obtain the real-time change in seepage field using the optical fiber, the study of optical fiber seepage measurement and positioning is carried out.
The seepage locating technology using the optical fiber relies on the fact that the optical fiber can sensitively sense the temperature change in the surrounding medium.For the pre-heated optical fiber, the temperature distribution is constant and stable.When seepage flow exists, the temperature of the optical fiber decreases due to thermal convection.However, for the optical fiber part without the influence of seepage, the temperature will not change.Therefore, this paper discusses the optical fiber temperature measurements and seepage measurements in various states, mainly including the seepage in unsaturated state, the seepage in saturated state, and the seepage in saturated-unsaturated state.
For the seepage analysis of unsaturated soil shown in Figure 13, which represents the temperature rise in the optical fiber under the natural state condition, the temperature rise can be observed by changing the heating power of the optical fiber.The chosen heating power of the optical fiber is 6 W/m, 12 W/m, and 18 W/m, respectively.As the heating temperature of optical fiber increases, under the action of the seepage water, the temperature of the optical fiber decreases due to heat convection and heat exchange.The test mainly analyzes the accuracy and location of optical fiber seepage measurement through the pre-buried centralized leakage channel.The test shows that the optical fiber seepage measurement and positioning method can obtain good results for three different design conditions.tion.However, for the optical fiber part without the influence of seepage, the temperature will not change.Therefore, this paper discusses the optical fiber temperature measurements and seepage measurements in various states, mainly including the seepage in unsaturated state, the seepage in saturated state, and the seepage in saturated-unsaturated state.
For the seepage analysis of unsaturated soil shown in Figure 13, which represents the temperature rise in the optical fiber under the natural state condition, the temperature rise can be observed by changing the heating power of the optical fiber.The chosen heating power of the optical fiber is 6 W/m, 12 W/m, and 18 W/m, respectively.As the heating temperature of optical fiber increases, under the action of the seepage water, the temperature of the optical fiber decreases due to heat convection and heat exchange.The test mainly analyzes the accuracy and location of optical fiber seepage measurement through the pre-buried centralized leakage channel.The test shows that the optical fiber seepage measurement and positioning method can obtain good results for three different design conditions.
It can be noticed in Figure 14 that the temperature at the 14.2 m, 17.3 m, and 23.3 m positions in unsaturated soil is lower than that of the surrounding area, which means that those positions can be determined to be the concentrated seepage channels.Then, the averaged accuracy of seepage location is 1.3%.In Figure 15, for the seepage area, the temperature drop in the fiber is immediately affected by the seepage water, and the temperature drop period lasts for about 220s before temperature becomes stable.Combined with the coupling theory of the temperature field and seepage field in the third section, in the practical engineering application process, the internal temperature-seepage coupled field of the embankment can be generated in time, so as to realize real-time detecting and deal with risks such as seepage failure.It can be noticed in Figure 14 that the temperature at the 14.2 m, 17.3 m, and 23.3 m positions in unsaturated soil is lower than that of the surrounding area, which means that those positions can be determined to be the concentrated seepage channels.Then, the averaged accuracy of seepage location is 1.3%.In Figure 15, for the seepage area, the temperature drop in the fiber is immediately affected by the seepage water, and the temperature drop period lasts for about 220s before temperature becomes stable.Combined with the coupling theory of the temperature field and seepage field in the third section, in the practical engineering application process, the internal temperature-seepage coupled field of the embankment can be generated in time, so as to realize real-time detecting and deal with risks such as seepage failure.
The infiltration time overlaps with the heating time.The temperature is higher with increasing heating power.However, the degree of temperature reduction is larger through the infiltration time with a higher heating power, as shown in Figure 14.
Appl.Sci.2024, 14, x FOR PEER REVIEW 14 of 18 field is steady at this time.In order to obtain the real-time change in seepage field using the optical fiber, the study of optical fiber seepage measurement and positioning is carried out.
The seepage locating technology using the optical fiber relies on the fact that the optical fiber can sensitively sense the temperature change in the surrounding medium.For the pre-heated optical fiber, the temperature distribution is constant and stable.When seepage flow exists, the temperature of the optical fiber decreases due to thermal convection.However, for the optical fiber part without the influence of seepage, the temperature will not change.Therefore, this paper discusses the optical fiber temperature measurements and seepage measurements in various states, mainly including the seepage in unsaturated state, the seepage in saturated state, and the seepage in saturated-unsaturated state.
For the seepage analysis of unsaturated soil shown in Figure 13, which represents the temperature rise in the optical fiber under the natural state condition, the temperature rise can be observed by changing the heating power of the optical fiber.The chosen heating power of the optical fiber is 6 W/m, 12 W/m, and 18 W/m, respectively.As the heating temperature of optical fiber increases, under the action of the seepage water, the temperature of the optical fiber decreases due to heat convection and heat exchange.The test mainly analyzes the accuracy and location of optical fiber seepage measurement through the pre-buried centralized leakage channel.The test shows that the optical fiber seepage measurement and positioning method can obtain good results for three different design conditions.
It can be noticed in Figure 14 that the temperature at the 14.2 m, 17.3 m, and 23.3 m positions in unsaturated soil is lower than that of the surrounding area, which means that those positions can be determined to be the concentrated seepage channels.Then, the averaged accuracy of seepage location is 1.3%.In Figure 15, for the seepage area, the temperature drop in the fiber is immediately affected by the seepage water, and the temperature drop period lasts for about 220s before temperature becomes stable.Combined with the coupling theory of the temperature field and seepage field in the third section, in the practical engineering application process, the internal temperature-seepage coupled field of the embankment can be generated in time, so as to realize real-time detecting and deal with risks such as seepage failure.The infiltration time overlaps with the heating time.The temperature is higher with increasing heating power.However, the degree of temperature reduction is larger through the infiltration time with a higher heating power, as shown in Figure 14.
It can also be noticed from Figures 15 and Table 1 that the greater the heating power, the better the effect of the optical fiber permeability measurement.For different heating powers, the greater the heating power is, the greater the temperature drop of the optical fiber caused by seepage is.For the unsaturated soil, the temperature drop is about 6.88 °C, while the drop is 3.96 °C when a concentrated seepage channel is formed.This means that in a natural state, the sensitivity of the optical fiber is greater than in a saturated state as the heat taken by seepage is greater in the former state and the temperature drop is greater.For the selection of the heating power of the optical fiber, not only should the sensitivity of the optical fiber be considered, but also the excessive current caused by the excessive heating power on the optical fiber; the measuring instrument should also be considered as the optical fiber is the sensitive element.For application in actual projects, the heating power is chosen as 18 W/m, in which condition the permeability measurement is straightforward and will not have a great impact on the measuring instrument.In order to simulate the seepage of saturated-unsaturated soil, the optical fiber in medium II is used for positioning analysis.The soil in the medium II area is divided into natural water-bearing area and saturated water-bearing area through the control valve on the upper part of the sink.The optical fiber is heated to analyze the temperature change along the optical fiber, as shown in Figure 16.It can also be noticed from Figure 15 and Table 1 that the greater the heating power, the better the effect of the optical fiber permeability measurement.For different heating powers, the greater the heating power is, the greater the temperature drop of the optical fiber caused by seepage is.For the unsaturated soil, the temperature drop is about 6.88 • C, while the drop is 3.96 • C when a concentrated seepage channel is formed.This means that in a natural state, the sensitivity of the optical fiber is greater than in a saturated state as the heat taken by seepage is greater in the former state and the temperature drop is greater.For the selection of the heating power of the optical fiber, not only should the sensitivity of the optical fiber be considered, but also the excessive current caused by the excessive heating power on the optical fiber; the measuring instrument should also be considered as the optical fiber is the sensitive element.For application in actual projects, the heating power is chosen as 18 W/m, in which condition the permeability measurement is straightforward and will not have a great impact on the measuring instrument.In order to simulate the seepage of saturated-unsaturated soil, the optical fiber in medium II is used for positioning analysis.The soil in the medium II area is divided into natural water-bearing area and saturated water-bearing area through the control valve on the upper part of the sink.The optical fiber is heated to analyze the temperature change along the optical fiber, as shown in Figure 16.The influence of seepage on the fiber temperature curve is still great, as shown in Figure 16.When seepage occurs, the temperature of the stable fiber after heating is significantly lower than that of the fiber without seepage.When seepage continues, the temperature drop curve tends to be balanced; at the end of seepage, the fiber temperature returns The influence of seepage on the fiber temperature curve is still great, as shown in Figure 16.When seepage occurs, the temperature of the stable fiber after heating is significantly lower than that of the fiber without seepage.When seepage continues, the temperature drop curve tends to be balanced; at the end of seepage, the fiber temperature returns to the stable temperature without seepage; similarly, for different heating powers, the greater the heating power is, the better the permeability measurement and positioning effect is and the more accurate it is.However, compared with the optical fiber temperature drop under natural conditions, the accuracy is reduced.
In summary, in three different conditions of the embankment seepage measurement positioning problem, the effect of seepage measurement under saturated seepage condition is lower than that of unsaturated condition and saturated non-seepage condition.With the increase in seepage flow rate, the monitoring effect under the same heating power will decrease, but by increasing the loading heating power, we can still achieve the purpose of seepage monitoring and meet accuracy requirements.Therefore, in the process of practical engineering applications, the heating power of the optical fiber is no less than 6 W/m under unsaturated conditions, the heating power of the optical fiber is no less than 12 W/m under saturated conditions without seepage, and the heating power of the optical fiber is no less than 18 W/m under saturated conditions with seepage.

Conclusions
Based on the results of the quantitative coupling model of the seepage field and temperature field, combined with the distribution form of the optical fiber in embankment seepage monitoring, the distribution and interaction of the seepage field and the temperature field in the local area of the cable and its surrounding medium are analyzed.On this basis, considering the engineering practicability, the two-field coupling simplified model is studied and constructed, and the two-field quantitative coupling control differential equation suitable for the optical fiber monitoring of seepage flow inside the embankment is deduced.This lays a theoretical foundation for the monitoring of the seepage flow velocity of the embankment by means of a distributed optical fiber temperature measurement system and supports the monitoring model used in engineering.
Considering the coupling effect of the seepage field and temperature field in embankment engineering, based on the two-field coupling simplified model, combined with the DTS temperature measurement system and COMSOL software (with a computational time of less than 30 s), the seepage field inversion of the known temperature field inside the embankment is carried out.Based on the analysis of the experiment, the seepage field of the porous medium is successfully obtained through the inversion of the temperature field of sand or clay inside the sink, and the seepage flow velocity under stable seepage is obtained.At the same time, this paper discusses the accuracy and practicability of the optical fiber permeability measurement and positioning under different working conditions.The accuracy for seepage location detection is 1.3%.The greater the heating power, the better the monitoring effect.
However, due to the complexity of the coupling effect of the temperature field and seepage field, this paper only considers the influence of the seepage field on the temperature field and ignores the influence of the temperature field on the seepage field, which is often unfavorable for practical engineering applications.At the same time, how to reasonably lay the optical fiber during application and engineering practice still needs to be studied.Based on the dual-field coupling control equation in this paper, only the stable seepage field inside the porous medium is considered.For practical engineering problems, when seepage failure occurs inside the embankment, the seepage field is often not uniform.Therefore, how to timely and efficiently feedback the seepage inside the embankment and establish the embankment seepage early warning system still needs to be further studied.
In future, the field test will be finished.The field test will be based on the fact that there are currently various seepage problems hindering the clarity of the exploration process and principles, and the accurate verification of technology.Therefore, there will

18 Figure 1
Figure1shows the influence of the seepage field on the temperature field under different permeability coefficients.Figures2 and 3mainly reflect the influence of the temperature field on the seepage field under different permeability coefficients.It can be seen from these figures that by comparing the solutions without considering the coupling effect ( )0 T x ,

Figure 2 .
Figure 2. Water head H 0 (x) and water head H 1 (x) under different permeability K.
Appl.Sci.2024, 14, x FOR PEERREVIEW  10    simulate the concentrated seepage inside the embankment.The optical fiber was arran as shown in the Figure4, and yellow sand and clay were used to fill the two model si respectively, denoted as medium I and medium II.
. Taking the error as ε = 0.1, the difference between the calculated temperature T 2 = 15.08 • C and the measured temperature T ′ 2 = 12.11 • C is beyond the error value, and a new velocity should be assumed until the error value is met.The final temperature distributions are shown in Figures 10 and 11 . The relative seepage velocity is v = 0.06 × 10 −3 m/s which is the seepage velocity of the steady seepage condition.
Figure 12 is added to highlight the difference from Figures 5-11.

3 0
show the temperature distributions of the porous medium under different seepage conditions calculated using COMSOL combined with the temperature-seepage coupling theory.Figures5 and 6show the temperature distributions under no seepage conditions which are the initial state for later iteration.Setting the seepage velocity to 10 −7 m/s, the temperature fields of the porous medium calculated using the measured temperature of the second optical fiber are shown in Figures7 and 8. Given the existence of the seepage field, the temperature fields are different from Figures5 and 6.Taking the error as =0.1 ε Figure 12 is added to highlight the difference from Figures 5-11.

Figure 5 .
Figure 5.Initial temperature distribution in medium I without seepage.

Figure 6 .
Figure 6.Initial temperature distribution in medium II without seepage.

Figure 5 .
Figure 5.Initial temperature distribution in medium I without seepage.

3 0
show the temperature distributions of the porous medium under different seepage conditions calculated using COMSOL combined with the temperature-seepage coupling theory.Figures5 and 6show the temperature distributions under no seepage conditions which are the initial state for later iteration.Setting the seepage velocity to 10 −7 m/s, the temperature fields of the porous medium calculated using the measured temperature of the second optical fiber are shown in Figures7 and 8. Given the existence of the seepage field, the temperature fields are different from Figures5 and 6.Taking the error as =0.1 ε Figure 12 is added to highlight the difference from Figures 5-11.

Figure 5 .
Figure 5.Initial temperature distribution in medium I without seepage.

Figure 6 .
Figure 6.Initial temperature distribution in medium II without seepage.Figure 6.Initial temperature distribution in medium II without seepage.

Figure 6 .
Figure 6.Initial temperature distribution in medium II without seepage.Figure 6.Initial temperature distribution in medium II without seepage.

Figure 7 .
Figure 7. Temperature distribution in medium I with a seepage velocity of 10 −7 m/s.

Figure 8 .
Figure 8. Temperature distribution in medium II with a seepage velocity of 10 −7 m/s.

Figure 7 . 18 Figure 7 .
Figure 7. Temperature distribution in medium I with a seepage velocity of 10 −7 m/s.

Figure 8 .
Figure 8. Temperature distribution in medium II with a seepage velocity of 10 −7 m/s.

Figure 8 . 18 Figure 7 .
Figure 8. Temperature distribution in medium II with a seepage velocity of 10 −7 m/s.

Figure 8 .
Figure 8. Temperature distribution in medium II with a seepage velocity of 10 −7 m/s.

Figure 9 .
Figure 9. Temperature rising curve after heating.Figure 9. Temperature rising curve after heating.

Figure 9 .
Figure 9. Temperature rising curve after heating.Figure 9. Temperature rising curve after heating.

Figure 10 .
Figure 10.Temperature distribution in medium I with a seepage velocity of 0.6 × 10 −3 m/s.

Figure 12 .
Figure 12.Different distributions in different media.

Figure 14 .
Figure 14.Temperature distribution of optical fiber with concentrated seepage condition in unsaturated soil.

Figure 14 .
Figure 14.Temperature distribution of optical fiber with concentrated seepage condition in unsaturated soil.

Figure 14 .
Figure 14.Temperature distribution of optical fiber with concentrated seepage condition in unsaturated soil.

Figure 15 .
Figure 15.Temperature rise of optical fiber at concentrated seepage channel 1 in saturated soil.

Figure 15 .
Figure 15.Temperature rise of optical fiber at concentrated seepage channel 1 in saturated soil.

18 Figure 16 .
Figure 16.Temperature rise of optical fiber under different heating powers.

Figure 16 .
Figure 16.Temperature rise of optical fiber under different heating powers.

Table 1 .
Temperature decrease with different heating powers under two conditions.

Table 1 .
Temperature decrease with different heating powers under two conditions.