For discriminating the strain and temperature effects, the use of reference grating [7], the use of dual wavelength gratings [8], and the use of two sensors associated with different strain and temperature responses were reported [9–14]. Another approach is to use the dual wavelength technique involving writing two superimposed Bragg gratings [8], in which the responses to temperature (κ_1T,κ_2T) and strain (κ_1ε,κ_2ε) at the same location on the structure are different. The change in the Bragg center wavelengths Δλ_i of the two gratings from the changes in temperature (ΔT_i) and strain (Δε_i) is given by the following matrix expression: (1) Δ λ i = κ i ɛ Δ ɛ i + κ iT Δ T i                   i = 1 , 2where κ_iε = ∂λ/∂ε_i is the strain coefficient of material related to the Poisson ratio, photoelastic constant and effective refractive index, and κ_iT = ∂λ/∂T_i is the temperature coefficient related to the thermal expansion and thermo-optic coefficients. The above matrix can be inverted to give temperature and strain provided that the ratio of temperature responses of the two gratings is different from that of their strain responses.

We have developed a simple and low-cost FBG sensor for monitoring civil infrastructure. Figure 1a shows the configuration of the sensor and the detection system, in which the proposed sensor was connected to the output port of a fiber coupler. The three fiber Bragg gratings at wavelengths of λ₁, λ₂, λ₃ were interrogated using a broadband amplified spontaneous emission (ASE) fiber source and an optical spectrum analyzer. The reference grating was used to measure only the temperature effect. The shift in Bragg wavelength λ₃ from temperature changes is given by: (2) Δ λ 3 = κ 3 T Δ T

The strain coefficient of the sensor was obtained by varying the applied strain from 200 to 2,200 με while keeping the temperature constant. An excellent linear response of wavelength shifts to applied strains was found. The slope of the linear fit to the measured wavelength shifts at various strain changes was determined as the strain coefficient (pm/με) of the investigated fiber sensor (for λ₁ and λ₂). For the second series of tests, those sensors were kept under strain-free conditions and temperature variations from 25 °C to 80 °C. Again, an excellent linear response of wavelength shifts to applied temperature variations was shown and the slope of the linear fit to the measured wavelength shifts at various temperature changes was determined as the temperature coefficient (pm/°C) of the investigated fiber sensor for those wavelengths of λ₁, λ₂, λ₃, and λ₄. Table 1 summarizes the experimental coefficients of the optical fiber grating sensors. The measured root mean squared errors for temperature T and strain ε were estimated to be 0.13 °C and 6 με, respectively. Using the estimation of expanded uncertainty at 95% confidence level with a coverage factor of k = 2.205, temperature and strain measurement uncertainties of the FBG sensor have been evaluated as 2.60 °C and 32.05 με, respectively. Figure 2 shows the 3-D surface plot of strain variation and temperature variation for simultaneous strain and temperature measurements within the temperature range 30–120 °C and strain range of 0–1,500 με [15]. If temperature and strain change, the FBG sensor system or the so-called reference dual-wavelength grating presented in this paper could measure temperature and strain separately.

In general, an LPFG usually has a photo-induced periodic modulation of refractive index along the core of a single-mode fiber, with a typical perturbation of Δn ∼ 10⁻⁴, periods between 100 μm–1 mm and length of 2–4 cm. The LPFG couples light from a guided fundamental core mode (LP₀₁) to different forward-propagating cladding modes (HE_1m) in an optical fiber, which is given by phase-matching condition [16]: (3) β core 01 − β cladding 1 m = 2 π Λ               m = 2 , 3 , 4 , ....where β core 01 and β cladding 1 m are propagating constants of the fundamental core mode and mth cladding mode, respectively, and Λ is the period of grating. The coupling of the light into the cladding region generates a series of resonant bands centered at wavelength λ_m in the transmission spectrum. The center wavelengths λ_m of an attenuation band are solutions of the following equation [16]: (4) λ m = [ n ¯ core 01 ( n 1 , n 2 , λ m ) − n ⇀ cladding 1 m ( n 2 , n s , λ m ) ] Λwhere n ¯ core 01 ( n 1 , n 2 , λ m ) is the effective index of the fundamental core mode at the wavelength of λ_m, which is also dependent on the core refractive index n₁ and cladding refractive index n₂. In Equation (4) n ⇀ cladding 1 m ( n 2 , n s , λ m ) is the effective refractive of the mth cladding mode at the wavelength λ_m, which is related to cladding refractive index n₂ and the refractive index of the surrounding medium n_s.

When the concentration or the refractive index of the surrounding medium changes, also n ⇀ cladding 1 m ( n 2 , n s , λ m ) changes and a shift in the central wavelength can be obtained. The cladding modes are very sensitive to change in the refractive index of the ambient (surrounding) environment.

The fabrication of LPFGs, for λ₄, has been reported elsewhere [17,18]. The LPFGs, for λ₅ to λ₉, were fabricated by the electric-arc discharge method [19] with hydrogen-free Corning SMF-28 fibers. LPFGs are especially suitable for measurements and applications when liquids or solutions undergo a change in temperature or refractive index (RI) which can be used for sensing temperatures, liquid-levels, and chloride ions [17–23].

The experimental setup for LPFGs fabrication consists of a computer-controlled electric-arc discharge associated with a translation stage, a broadband ASE fiber source and a high-resolution OSA (ANDO AQ6315A) used to in situ monitor the transmission loss as the grating was written. The electric-arc discharge-induced LPFGs were about 2.2–3.6 mm long and their grating periods were about 600 μm, written with a computer-controlled electric-arc discharge system. The transmission spectrum was interrogated during the writing and its characteristics such as insertion loss, resonance peak wavelength, and peak depth were analyzed after the grating was written. With suitable fabrication parameters such as electric-arc discharge power, discharge time, grating period, and scan speed, the resulting resonance wavelengths ranging from 1,200 nm to 1,600 nm with a greater than about 20 dB peak depth were obtained.

In this study, each transmission spectrum was referenced to the background spectrum of a bare fiber in air. The 3 dB bandwidth was determined by finding the peak of the ASE spectrum, and rising by 3 dB on each side. The spectral width of the ASE spectrum was determined by the separation of these two points because each has a power spectral density equal to one half the peak power spectral densities. The resonance wavelength was calculated as the average of two wavelengths determined in the 3 dB bandwidth measurements.

Portland cement concretes and asphalt mixtures are typical infrastructure materials. The plain-concrete specimen used was 150 mm in diameter and 300 mm in height. The maximum aggregate size was 19 mm and all aggregates were crushed siliceous materials from river deposits. Type I cement was used to fabricate the cylinder specimens. The 28-day compressive strength of this concrete specimen was 24.15 kPa. Figure 3(a) shows the surface-bonded FBG and LPFG sensors on a cylindrical concrete specimen.

The asphalt specimen was 150 mm in diameter and about 116 mm in height. The maximum aggregate size was 19 mm and a PG 64-22 asphalt binder was used to fabricate the asphalt specimen. The specimen was compacted by superior performing asphalt pavement (Superpave) gyratory compactor and the aggregate structure belonged to Superpave coarse gradation (below the restricted zone) [24,25]. Both FBG and LPFG sensors were bonded on the surface of asphalt and concrete specimens as presented in Figure 3(b).

The temperature tests include temperature fluctuation and temperature stability tests using both FBG and LPFG sensors, respectively. Random walk coefficient (RWC) is defined as the slope of Allan variance plot (Allan deviations of temperature differences between the FOS sensor and a thermocouple versus time clusters) before Allan deviation approaches the minimum value. Bias stability (BS) is then obtained as the minimum Allan deviation and occurs at the corresponding time cluster and BS is typically described within the minimum Allan deviation with the corresponding time cluster [26–28]. These two parameters were used to evaluate the sensing performance of FOSs for all temperature tests.

The indirect tensile strain test for infrastructure materials was conducted using a packaged FBG sensor bonded with an epoxy glue on the surface of an asphalt specimen under the indirect tensile loading condition. Figure 4 shows the experimental setup and an asphalt specimen with a packaged FBG sensor. The strain coefficients and measurement errors of the packaged grating sensor was measured to be 1.1 pm/με and 8.6 με. The packaged FBG sensor was bonded on the surface of asphalt specimens to measure the strains with the indirect tensile loading kit (steel frames and strips). A series of static loads of 98 N, 196 N, 294 N and 392 N, were applied on the loading strip vertically. One top vertical and two-side horizontal (along the diameter) dial gauges (accuracy of 0.01 mm) were used to monitor the corresponding deformations and ensure that the relationship between applied loads and measured deformations is indirect tensile and linear-elastic. Due to the relatively lower stiffness of asphalt, it is almost impossible to bond the general-purpose strain gauge on the surface of asphalt specimens. Therefore, in this study we compared the FBG measurements with numerical simulation results.

Our experimental setup for the LPFG liquid-level sensing system is shown in Figure 5. A 150 mm-inside diameter, 1,200 mm-high, and hollow cylindrical storage tank having at least a 1,000 mm liquid-level capacity was used for sensing tests. We focused on a liquid-level sensor constructed by cascading five different wavelength LPFGs (wavelengths of Nos 1–5: 1,505 nm, 1,524 nm, 1,549 nm, 1,570 nm, and 1,606 nm, respectively). The liquid-level sensing tests included five levels, or five LPFGs in series with Nos. 1–5 and their corresponding fixed liquid-levels were about 230 mm, 430 mm, 640 mm, 850 mm, and 1,050 mm (from bottom to top, see Figure 5). For each liquid-level, the sensing measurements were conducted for both measurements in air and immersed in water, respectively. The wavelength shift of the LPFG has been shown to be a reliable, repeatable, and accurate measurand for several different field applications [20]. Thus, the changes of wavelengths are suggested for clearly identifying the changes and eliminating experimental errors. We performed five times liquid-level tests, in which Nos. 1–5 were all immersed in water, to identify the changes of resonance wavelength shifts for the sensor constructed by cascading five different wavelength LPFGs.

In this work, 3-D indirect tensile loading simulation was used to model the strain measurement using a packaged FBG sensor bonded on the surface of an asphalt specimen under different indirect tensile loads. The physical model consists of an asphalt concrete cylinder specimen (150 mm in diameter and approximately 116 mm in height) and two strips (approximately 19 mm in width, 12 mm in thickness and 116 mm in height) with a FBG sensor horizontally centered along the diameter. The sensor was glued from positions at x = −40 mm to x = 40 mm. We created a 3D solid object using the Cartesian coordinate with the functions of geometry modeling and CAD tools. Figure 6a shows the geometry plot for FBG sensing with loading strips for modeling infrastructures or structures using asphalt mixtures subjected to a tensile load. The tetrahedral mesh element, Lagrange-quadratic element, was selected to create the model meshes. Three different mesh resolutions were used for the FEM simulation, corresponding to coarser, coarse, and normal model meshes that possessed a total of 4,826, 7,067, and 11,456 elements, respectively. The maximum element size default was 1/10 of the size of the geometry. The maximum element size scaling factor defaults value was 1.0. The element growth ratio was 1.4., the mesh curvature factor was 0.4, and the mesh curvature coefficient was 0.01. Figure 6(b) displays the schematic plot for a normal mesh for the asphalt specimen and loading strips. These models were used to simulate cylinders subjected to a tensile load.

Material properties of the steel loading strips are assumed to be homogeneous and isotropic. The steel loading strips possess an elastic modulus of 200 GPa, a Poisson’s ratio of 0.30, and a density of 7,850 kg/m³. The asphalt mixture specimen has a Poisson’s ratio of 0.35 and a density of 2,500 kg/m³. The elastic modulus of asphalt mixture specimen was about 0.21 GPa. The used solver was Direct (Spools), an effective direct solver for symmetric and unsymmetrical systems, based on Gaussian elimination method to solve this linear stationary problem. Table 2 summarizes the material properties of steel strips and a cylindrical asphalt mixture specimen.

Different loading conditions were performed to determine whether the strains measured from the packaged FBG sensor agree with those obtained from FEM results. The top vertical displacements, ν, and horizontal normal strains, ε_x, of the asphalt specimen along the x-direction were calculated using FEM method under a series of loads of 98-N, 196-N, 294-N and 392-N loading conditions. This aimed at simulating the strain measurements using the packaged FBG sensor under different indirect tensile loads.

The responses of temperature fluctuation with time for both asphalt and concrete specimens are shown in Figures 7 and 8, respectively. The results of temperature fluctuation tests using FBG and LPFG sensors are summarized in Table 3. The random walk coefficients of temperature variations between FBG sensor and thermocouple were found as −0.9134 °C/ h and −1.1293 °C/ h for asphalt and concrete specimens, respectively. This shows that the performance of this FBG sensor is comparable with that of conventional high-resolution sensors such as thermocouple. In addition, the bias stability for temperature variations during the fluctuation tests with FBG sensor were within 0.02 °C/h with 4–5 h time cluster and 0.09 °C/h with 3–4 h time cluster for asphalt and concrete specimens, respectively.

Using the measurements from the pair of gratings, λ₁ and λ₂, one can determine the residual strains on the surface of the specimens at the same location, which should be near zero for these tests. In fact, a small amount of RMS strain variations were found, less than 13 με (or ∼1 °C) in all cases, as indicated in Table 3, which were all within our experimental errors.

Furthermore, the random walk coefficients of temperature variations between LPFG sensor and thermocouple were found as −1.3548 °C/ h and −0.9994 °C/ h for asphalt and concrete specimens, respectively. The bias stability for temperature variations during the fluctuation tests with LPFG sensor were within 0.03 °C/h with a 5–8 h time cluster and 0.06 °C/h with a 4–6 h time cluster for asphalt and concrete specimens, respectively. Obviously, both the FBG and LPFG sensors exhibited as the same temperature variations compared with a thermocouple.

The results of temperature stability tests using FBG and LPFG sensors are summarized in Table 3 and the responses of temperature stability with time for both asphalt and concrete specimens are shown in Figures 9 and 10, respectively. With the FBG sensor, the random walk coefficients of temperature variations were −0.7499 °C/ h and −0.9944 °C/ h compared with the measurements of asphalt and concrete specimens, respectively. It can be seen that the bias stability values were 0.04 °C/h with 12–15 h time cluster and 0.01 °C/h with 15–18 h time cluster for asphalt and concrete specimens. By contrast, the random walk coefficients of temperature variations between the LPFG sensor and a thermocouple were −1.0144 °C/ h and −0.8360 °C/ h compared with the measurements of asphalt and concrete specimens, respectively. Moreover, the bias stability values were 0.05 °C/h with 7–8 h time cluster and 0.03 °C/h with 15–20 h time cluster measured for asphalt and concrete specimens, respectively. Results presented here illustrate that the monitoring of temperature fluctuation and stability using FBG and LPFG sensors, was capable of measuring temperature with accuracy in the range of −0.7499 °C/ h to −1.3548 °C/ h.

In addition, the bias stability for temperature variations, during the temperature fluctuation and stability tests with FBG (or LPFG) sensors were within the range of 0.01 °C/h with 15–18 h time cluster to 0.09 °C/h with 3–4 h time cluster. The excellent performance of FBG and LPFG sensors has made it possible to monitor infrastructure or structures under rugged conditions at a reasonable accuracy for a very long period of time (the fiber optic sensor is normally designed to work for at least 10 years).

Based on the results of FEM analysis, Figure 11 shows the plot of vertical displacements, horizontal displacements, and horizontal (diametrical) normal strains of an asphalt specimen subjected to a 294-N load, respectively. The FEM horizontal normal strains were compared with indirect tensile strains using a packaged FBG sensor. Figure 12 compares FBG experimental measurements and three different FEM mesh modeling results, which included coarser, coarse and normal mesh modeling. The measured horizontal normal strains, ε_x, from the packaged FBG sensor agreed well with three FEM simulation predictions. In Figure 12, we used measurement error of 8.6 με as the error bar of FBG strains. It is clear that the numerical values were all located within the FBG measurements error ranges. In addition, the strain differences between the packaged FBG sensor and FEM model predictions were in the range of 4.2–6.8%. There was no significant difference among the coarser, coarse, and normal mesh models for simulating infrastructures or structures subjected to an indirect tensile loading. The study presented here demonstrates that the FBG sensor could offer the potential of simultaneous measurement of strain and temperature for monitoring infrastructure materials.

The liquid-level sensing tests included five liquid levels, or five LPFGs in series indexed with Nos. 15 and their corresponding liquid-level were about 230 mm, 430 mm, 640 mm, 850 mm, and 1,050 mm. Figures 13a and 13b show transmission spectra of the liquid-level sensor with LPFGs Nos. 1–2 and Nos. 1–5 immersed in water, respectively.

After performing liquid-level tests five times, the average values (with standard deviations) of the resonance wavelength shifts for Nos. 1–5 were about 2.0 nm (within 0.16 nm), 1.3 nm (within 0.25 nm), 2.2 nm (within 0.07 nm), 3.7 nm (within 0.07 nm), and 9.2 nm (within 0.29 nm), respectively. These results are plotted in Figure 14. The wavelength shifts of resonance wavelengths showed the LPFG-based sensor could be used to measure five different liquid levels and had at least 1050-mm liquid-level measurement capacity.