The AHFO-based water content measurement method uses a fiber-optic sensor with the active heating function as a thermal probe. The fiber-optic sensor buried in the soil is both a heat source and a thermometer. The soil water content distribution along the sensor is calculated by measuring the temperature distribution along the sensor. The fiber-optic sensor buried in the soil can be regarded as an infinitely long cylindrical heat source. During the heating process, the temperature change of the infinite sensor is as follows (Ciocca et al., 2012): T t = T ( t ) − T 0 = Q 4 π λ [ ln ( t ) + 4 π R λ + ln ( 4 K a 2 c ) ]   t > > a 2 / K , (1) where T _t is the rise in temperature (C) or the temperature characteristic value, T(t) is the temperature of the heat source (C) corresponding to the heating time t, T ₀ is the initial soil temperature (C), Q is the heating power per unit length (W m⁻¹), λ is the soil thermal conductivity (W m⁻¹ K⁻¹), R is the thermal resistance per unit length (m K W⁻¹) between the fiber-optic sensor and the soil wall, K is the thermal diffusivity (m² s⁻¹) of the soil, a is the outer diameter (m) of the sensor, and c = 1.7811 = exp (γ) where γ is the Euler–Mascheroni constant (γ = 0.5772).

According to the research of Sun et al. (2020), when the fiber-optic sensor is in close contact with the soil, after heating for a certain time, Eq. 1 can be approximated as T t = m λ , (2) where m = Q ⁡ ln ( 4 K t / a 2 c ) 4 π is a constant.

The mineral composition and dry density of in situ soil can be considered as fixed values, so the λ is only related to the soil volumetric water content (θ), and there is the only corresponding functional relationship between λ and θ, namely, λ = f ( θ ) . (3) The following relationship can be obtained by combining Eqs 2, 3: T t = m f ( θ ) . (4) As can be seen from Eq. 4, θ can be calculated by measuring T _t on the basis of the T _t–θ relationship obtained by the calibration test. Therefore, based on the Côté and Konrad thermal conductivity calculation model and a large number of experimental analyses, the authors’ group proposes a calibration model describing the T _t–θ relationship, which is expressed as T t = 1 A θ / ( 1 + B θ ) + C , (5) where A = κ ( λ sat − λ dry ) m n , B = ( κ − 1 ) n , C = λ dry m are all constants; λ _sat is the saturated thermal conductivity (W m⁻¹ K⁻¹); λ _dry is the dry thermal conductivity (W m⁻¹ K⁻¹); n is the soil porosity; and κ is an empirical parameter related to the soil type and freezing state. Among them, A, B, and C are fitted by the results of the T _t–θ calibration test.

Humidity sensing can be realized by coating the moisture-sensitive material on the optical fiber with a specific process. When the ambient humidity increases, the moisture-sensitive material absorbs water molecules from the air under the action of humidity difference, and the volume of the material becomes larger, resulting in a tensile strain of the optical fiber. On the contrary, when the ambient humidity decreases, the moisture-sensitive material discharges the internal water molecules, and the volume of the material shrinks, which, in turn, produces compressive strains of the optical fiber. At present, the authors’ group selects moisture-sensitive materials with linear hygroscopicity, polyimide (PI) and inorganic–organic hybrid polymer (ORMOCER^®) to coat the FBG, and develop the corresponding soil pore gas humidity sensor. The PI/ORMOCER^®-coated FBG (PI/OR-FBG) humidity sensor includes two FBGs. One is coated with moisture-sensitive material (FBG1) for humidity sensing, and the other is an uncoated FBG (FBG2) for temperature compensation in the humidity measurement process. The developed humidity sensor can measure humidity and temperature simultaneously (Guo et al., 2021a): [ Δ T Δ R H ] = [ 0 1 K T 2 1 K R H − K T 1 K T 2 ] [ Δ λ 1 Δ λ 2 ] , (6) where K _T1 and K _T2 are the temperature sensitivity coefficients (°C/nm) of FBG1 and FBG2, respectively; K _RH is the humidity sensitivity coefficient of FBG1 (%RH/nm); and Δλ ₁ and Δλ ₂ are the Bragg wavelength variations (nm) of FBG1 and FBG2, respectively.

Whether the quasi-distributed AH-FBG soil water content test or the fully distributed AH-DTS soil water content test are used, the soil needs to be calibrated before the test. The aim of calibration tests is to establish the T _t–θ relationship of the soil. The calibration device can be a standardized device equipped with the test system, or it can be built temporarily according to the actual situation. Figure 5A is a calibration device made of PVC pipe. The top side of the PVC pipe is a movable plate, which can be removed during soil loading or excavation. Moreover, sealing plugs are installed at both ends of the PVC pipe to prevent water loss in the soil during the calibration process.

During the calibration test, the density of the soil sample in the calibration device should be the same as that of the tested in situ soil as much as possible to reduce the influence of density on the test results. The soil water content gravimetrically determined by oven-drying is used as the real value. Soil samples with different water contents were first prepared, and the calibrated sensor was embedded into the soil sample. Next, the temperature change curves with time were obtained under different soil water contents by the FBG or DTS temperature measurement system and the corresponding temperature characteristic value (T _t) was determined. Finally, the T _t–θ calibration curve can be obtained, and the calibration coefficients in Eq. 5 can be determined. It should be noted that the optimal heating power of AHFO sensors is 10–35 W/m. If the heating power is too small and the sensitivity of T _t to θ is low, it is difficult to reflect subtle θ change. On the contrary, if the heating power is too large, it causes water migration of the surrounding soil. Therefore, it is suggested that the specific heating power should be selected according to site conditions.

During calibration tests or field monitoring, the corresponding FBG/DTS demodulator needs to be used to obtain the data measured by the sensor. Figure 5B shows the NZS-FBG-A07 demodulator used for AH-FBG sensors and its technical parameters. Figure 5C shows the NZS-DMS-A03 demodulator used for AH-DTS sensors and its technical parameters. Note that the two demodulators are produced by NanZee Sensing Technology Co. Ltd., China.

The fiber-optic sensing technology for soil water content has been verified in engineering practice and well applied in the monitoring of loess ground, slopes, foundation pit, and landslides.

Figure 12A shows the encapsulated PI-FBG humidity sensor that can be used for soil pore gas humidity measurement. There is a PI-coated FBG and an uncoated FBG inside the sensor. Two FBGs are passed through the two small holes reserved on the stainless-steel thread. Then, the top ends of two FBGs are fixed on the stainless-steel bracket with UV-curable adhesive, which ensures the influence of strain on FBGs is eliminated. Note that the two gratings should be placed at the same height to improve the accuracy of temperature compensation. Next, the two FBGs fixed on the stainless-steel bracket are protected with a 12-mm-diameter powder-sinter. The connection between stainless-steel probe and thread is fixed and sealed with epoxy resin adhesive to prevent water. On the one hand, the stainless-steel probe can protect the FBGs from damage in harsh environments and prevent water and fine soil particles from entering the probe. On the other hand, this structure can play a role in air permeability and water resistance without affecting the exchange of air humidity. Afterward, the two optical fibers are respectively sheathed with a 0.9 mm-diameter fiber casing and passed through a black polyethylene fiber casing with a diameter of 2 mm. There is a stainless-steel spiral armoring tube in the black polyethylene fiber casing to protect the optical fibers from physical damage. Finally, the stainless steel is sealed with a green rubber cap to prevent external water from penetrating.

The structure of the OR-FBG humidity sensor is the same as that of the PI-FBG humidity sensor except that the FBG used for humidity sensing is coated with ORMOCER^®. The performance comparison of the two humidity sensors is shown in Table 2. It can be seen from Table 2 that the humidity sensitivity of the PI-FBG humidity sensor is higher than that of the OR-FBG humidity sensor; and its response time is only half of that of the OR-FBG humidity sensor. It is worth noting that the humidity sensing characteristics of the PI-FBG humidity sensor are basically unchanged before and after immersion, and it can be used in high humidity or even with condensed water. However, the hysteresis and repeatability errors of the PI-FBG humidity sensor are higher than those of the OR-FBG humidity sensor. Therefore, it is recommended to select the type of humidity sensor according to site conditions. Moreover, the performance comparison of the proposed sensors with other optical sensing techniques can be found in the literature of Guo et al. (2021b).

Figure 12B shows the calibration test device of the FBG humidity sensor. The saturated salt solution method is used to control the ambient relative humidity, and eight kinds of salts, such as LiCl, CH₃COOK, MgCl₂, K₂CO₃, NaBr, NaCl, KCl, and K₂SO₄, were selected to control different ambient humidity. The saturated salt solution should be fully stirred with a glass rod. Moreover, the supersaturated salt should be controlled to one third of the height of the salt solution to keep a supersaturated state no matter what the temperature is. Then, the prepared saturated salt solutions were sealed in the humidity control boxes, respectively. Next, the humidity control boxes were put into a test chamber with a temperature control accuracy of ±0.1°C. Subsequently, the FBG humidity sensors to be calibrated and an electronic hygrometer were introduced into the humidity control box and then were fixed and sealed at the top of the boxes with hot melt adhesive. The optical fibers were led out of the test chamber, and the outlet was sealed with cotton. In the end, the optical fibers were connected to the FBG demodulator (NanZee Sensing Technology Co. Ltd., China), and the Bragg wavelength data was recorded by the computer.

During the calibration test, the temperature was kept at 25°C first. After the wavelengths of the FBG humidity sensor were stable, the data of the FBG humidity sensor and electronic hygrometer in each humidity control box were recorded. Thus, the K _RH in Eq. 7 can be obtained by taking the humidity data measured by the electronic hygrometer as the real value and combining the wavelength data measured by the FBG humidity sensor. Then, the humidity was kept unchanged, and the temperature was varied from 10°C to 60°C with steps of 10°C. At each temperature, the stable wavelengths of the FBG humidity sensor were recorded. Thus, the K _T1 and K _T2 in Eq. 7 can be obtained by fitting the relationship between wavelength and temperature.

Figure 13A shows the test device of the PI-FBG humidity sensor used in the unsaturated soil. Ten types of soil samples with different sand–kaolin mixing ratios were configured, and each type of soil sample was configured with different water content. Each soil sample was put into the test box in turn, and its dry density remained constant. The FBG humidity sensor embedded in soil was used to measure the pore gas humidity of each soil sample, and the tests were carried out at a constant temperature. An electronic hygrometer is placed around the soil sample to record the ambient temperature and humidity. During the humidity tests, the FBG demodulator (NanZee Sensing Technology Co. Ltd., China) recorded the wavelengths of the FBG humidity sensor after the temperature and humidity in each soil sample. Then, the soil pore gas humidity can be obtained according to the calibration results. After the test of each soil sample, three soil samples were taken around the humidity sensor to measure its real water content by the oven-drying method, and the average value was taken as the final water content.

Figure 13B shows the relationships between pore gas humidity and water content of 10 sand–kaolin mixtures. The pore gas humidity in different sand–kaolin mixtures shows the same trend with the change of water content, which can be divided into two stages: when the water content is low, the pore gas humidity is very sensitive to the water content, and it increases linearly with the increase of water content; when the water content becomes higher with the further increase of water content, the pore gas humidity increases slowly and keeps stable after reaching 100 %RH. The minimum soil water content corresponding to the humidity of 100 %RH is defined as w _100%RH. The occurrence of w _100%RH indicates that the pore gas humidity in the soil has reached saturation. It is worth noting that, under the same water content, the higher the kaolin content, the smaller the humidity in the soil and the greater the w _100%RH. This is because clay has better water-holding capacity than sand. Therefore, the higher the kaolin content, the less free water in the soil pores and the lower the pore gas humidity. The laboratory test verifies the feasibility and applicability of the FBG humidity sensor for pore gas humidity measurement in unsaturated soil.