Research and Application of an Inner Thrust Measurement System for Rock and Soil Masses based On OFDR

For measuring internal stresses in rock and soil masses, specifically on unstable slopes, the fiber Bragg grating (FBG) and optical time-domain reflectometer (OTDR) methods based on fiber sensing technology have disadvantages such as low spatial resolution, low measurement accuracy, and non-distributed measurements. This paper presents a quasi-distributed 10 thrust measurement system based on an optical frequency domain reflectometer (OFDR). First, the optical fiber stress sensing head was designed based on the micro-bending effect of the optical fiber, the cubic spline interpolation method was then used to compensate for the nonlinear effects of the OFDR stress sensing system, the compensation effects of different software methods were compared and analyzed simultaneously, which significantly improved the resolution and spatialpositioning capabilities of the OFDR sensing system, and error calibration was then performed through laboratory 15 experiments of lateral stress. The test results showed that the OFDR sensing system achieved a spatial resolution of 20 cm using a 500 m test fiber (the resolution of an OTDR sensing system is generally approximately 1 m), the maximum measurement pressure can reach 1.059 MPa and the maximum relative error is 8.9%. Finally, the field engineering application was carried out in the Chenjiagou landslide in Fengjie County, Chongqing City, Three Gorges Dam, China. The application results showed that the system can accurately locate six fiber optic micro-bending stress sensors installed within 20 the landslide body over a range of 0~420 m and can obtain the pressure values of their lateral thrusts. This system is a quasidistributed stress monitoring instrument that provides long measurement distances, high spatial resolutions, high sensitivities, and fast responses that can be used for unstable slopes, slope engineering, water conservation and hydropower dams, and tunnel chambers, and thus, has good engineering application prospects in the safety monitoring field.


Introduction 25
For monitoring of unstable slopes, slope projects, water conservation hydropower dams, and tunnel chambers, surface displacement monitoring and underground deep displacement and stress monitoring methods are predominantly used domestically and abroad (Tang et al., 2012;Bellotti et al., 2014;Scaioni, 2015). GNNS and InSAR, close-range photogrammetry, and 3D laser scanning methods are surface monitoring methods used for unstable slopes (Gili et al., 2000;Wright, 2004;Werner et al., 2007;Liu, 2014). These methods provide only basic data for the study of regional surface 30 deformations of unstable slopes and the instability criteria for these methods are mostly based on displacement and deformation monitoring systems that cannot reflect the deformation and stress characteristics of deep rock and soil bodies.
The deformation and development of a monitored body is a multi-dimensional and complex process. It is difficult to accurately detect the potential sliding position of an unstable slope and establish the corresponding relationships between the time parameters, displacements and force changes. Therefore, early warning and prediction of the disaster body movement 35 cannot be accurately achieved.
When increased deformation or a large local deformation of rock and soil occurs, inclinometer tubes deform sharply and drilling inclinometers cannot work using conventional monitoring methods. However, the sensing fiber in an optical fiber sensing system is able to work normally as long as it is not cut off; the sensing fiber contains many pressure-sensing points https://doi.org/10.5194/gi-2020-6 Preprint. Discussion started: 26 March 2020 c Author(s) 2020. CC BY 4.0 License. in series. Moreover, the sensing fiber has strong resistance to scraping (Naruse et al., 2007). Among various methods, the 40 optical time-domain reflectometer (OTDR), Brillouin time-domain reflection (BOTDR), and fiber Bragg grating (FBG) technologies have been applied for bridges, hydraulic engineering, construction, and geological hazard monitoring (Kee et al., 2000;Bao et al., 2002;Bernini et al., 2006). Kihara et al. placed optical fibers on the embankments of the Niyodo and Sendai Rivers in Japan and used polarized time-domain reflection to monitor the landslide displacements of the embankments and achieved good results (Kihara et al., 2002). Dehua Liu et al. established a mechanical model of the FBG 45 structure substrate-protective, layer-sensing fiber, analyzed the factors affecting the measurement accuracy of the FBG sensor, theoretically deduced the strain transfer relationship between the structural matrix and the fiber optic sensor under the action of tension and three-point pressure, obtained an analytical solution, and then proposed measures to improve the measurement accuracy . The University of Electronic Science and Technology in China has used the OTDR technology to accomplish quasi-distributed monitoring of the inner thrusts of landslides and has conducted large-scale 50 landslide monitoring in the Three Gorges Dam area . Klar et al. used a distributed optical fiber component monitoring network to automatically detect disturbances, settlements, and other phenomena caused by tunnel excavation processes, and this optical fiber monitoring network provides a large amount of spatial distribution data and the tunnel mechanical model is analyzed and verified indoors using the measured optical fiber data (Klar et al., 2010). Surre et al. placed distributed optical fibers on the surface of a steel bridge in the form of steel fiber ribbons; the sensing unit included a 55 bare fiber sensor and a new bonded fiberglass tape with embedded fiber strain measurement capability and thermal compensation; the AQ8603 BOTDR strain analyzer was used to test the strain and stress distribution of the bridge during the loading process (Surre et al., 2013). Bin Shi et al. conducted monitoring analyses and health diagnoses of a tunnel using a BOTDR fiber strain gauge, proposed the installation of sensor fibers and temperature compensation methods, and discussed the influence of environmental factors such as temperature and vibration on the measurement results (Shi et al., 2005). 60 Minardo et al. used a BOTDR fiber strain gauge to perform static load tests on highway bridges and compared the data collected by fiber measurements with finite-element simulations and vibration-wire strain gauges to verify the effectiveness of the BOTDR method for monitoring large structural deformations (Minardo et al., 2011).
At present, the main problems of the OTDR technology are lower spatial resolution, lower sensitivity, and lower measurement accuracies. Compared with the OTDR, BOTDR technology can achieve simultaneous measurements of strain 65 and temperature and has the advantages of high sensitivity, high measurement accuracy, and distributed measurements.
However, its optical path structure is complex, signal adjustment is difficult, and the cost of the demodulator is expensive; therefore, the engineering practicality is poor and it is difficult to popularize. Compared with the OTDR and BOTDR, the optical frequency domain reflection (OFDR) presents the advantages of quasi-distributed monitoring, high spatial resolution, high measurement accuracy, reliable performance, and strong anti-interference ability; therefore, the OFDR is suitable for 70 internal stress monitoring of rock and soil masses during the entire process from creep to accelerated deformation.
In this paper, the OFDR technology is used to measure the inner stresses of rock and soil masses. First, a fiber optic microbending stress sensor was designed as the stress detection device and a detuning filter algorithm was used to compensate for the spatial measurement errors created using the nonlinear sweep frequency band of the light source. In laboratory tests, quasi-distributed stress measurements were realized within a sensing distance of 500 m. The spatial resolution was less than 75 20 cm, the maximum measurement pressure reached 1.059 MPa, and the maximum relative error did not exceed 8.9%. Field engineering application results show that the system can accurately sense stress locations and magnitudes.
https://doi.org/10.5194/gi-2020-6 Preprint.       (Wang, 2015). To improve the signal-to-noise ratio of the coherent OFDR signals, the balanced detector used is a Thorlabs PDB430C with a bandwidth of 350 MHz; the acquisition card uses a Spectrum M4i.4421 with four channels and the highest sampling rate for each channel is 250 MHz. Additionally, to suppress the polarization fading effect of the single-mode fiber, a polarization diversity receiving device has been added, 125 the splitting ratio of the optical couplers OC1 is 95/5, OC2 is 99/1, and OC3, OC4, and OC5 are all 3 dB optical couplers, meaning that the splitting ratios are 50/50 for these couplers (Malatesta et al., 2000). To ensure that the wavelength scanning of the light source is synchronized with the data acquisition, the TTL trigger signal of the TSL-710 can be used as an external trigger signal for the data acquisition card. Since the transmission of light in the optical path takes time, the data initially collected by the acquisition card are actually the data from the previous scan period, so the trigger delay needs to be 130 set for the acquisition card. The trigger delay time is determined by the optical path delay time.

Design of a Nonlinear Effect Compensation Algorithm
To address the problem of low spatial resolution of the OFDR for long-distance measurements, this section uses the cubic spline interpolation method to perform accurate phase estimations for the light source outputs and a short-time Fourier algorithm to obtain the time-frequency curve to determine the length of the delay fiber in the auxiliary interferometer. The 135 nonlinear phase is then estimated by a high-order Taylor expansion to obtain the nonlinear phase of the intrinsic light.

Cubic Spline Interpolation Method
The cubic spline interpolation method is a type of one-dimensional interpolation method that is an algorithm which constructs a simple function on known discrete data and facilitates calculations of some unknown points in the interval. The interpolation function curve constructed by this method is smoother but slower in terms of calculation speed (Song et al., 140 2012). As shown in Figure 6, the specific process for the cubic nonlinear spline interpolation for OFDR light source compensation is as follows: (1) Obtain the discrete normalized instantaneous optical frequency information ν 1 , ν 2 , …, ν n from the beat signal of the auxiliary interferometer. At this time, the intervals between ν 1 , ν 2 , …, ν n are uneven.
(2) One-dimensional interpolation is performed on the original beat frequency data point x(ν n ) obtained by the main 145 interferometer to get an interpolation curve; new uniform optical frequency interval points ν ' 1, ν ' 2, …, ν ' n are then selected and the obtained interpolation curve is resampled to obtain a new data point x(ν ' k ) for a uniform optical frequency interval. This process is shown in Figure 6.
150 https://doi.org/10.5194/gi-2020-6 Preprint. Discussion started: 26 March 2020 c Author(s) 2020. CC BY 4.0 License. Figure 6: Sampling diagram of the cubic spline interpolation (the red hollow circles are the primary data points of the main interferometer with a non-uniform optical frequency interval, the blue curve is a one-dimensional interpolation curve, and the green solid circles are the resampled points with a uniform optical frequency interval).

Simulation Analysis
To verify the effectiveness of the cubic spline interpolation method in compensating for the nonlinear frequency sweep 155 effect of the light source, this section uses LabVIEW software for simulation and then compares this simulation with the laboratory experimental data.
Assume that the nonlinear phase of the reference light is e(t) = A n •cos(2πf n t), and A n and f n are the amplitude and frequency, respectively. The frequency sweep rate γ(t) can be written as where γ 0 is the linear frequency sweep rate and a constant term, (2πf n )2•A n •cos(2πf n t) changes with time as a sinusoid that is the interference term. To 160 represent the degree of fluctuation of the frequency sweep rate γ(t), the ratio of the amplitude (2πf n )2 A n of the interference term of γ(t) to the constant term γ 0 is defined as K. The larger the K value, the greater the degree of fluctuation of γ(t), indicating that the linearity of the frequency sweep of the light source is worse. In the simulation, the linear frequency sweep rate is taken as a fixed value γ 0 = 625 GHz/s and the corresponding wavelength sweep rate is 5 nm/s (the central wavelength is 1,550 nm). Simultaneously, it is assumed that a strong reflection peak exists at a certain position on the optical fiber to be 165 tested and the simulation function is shown in Equation 1.
To facilitate the simulation calculations, the amplitude I(t) is taken as 1. During the simulation, I(t) needs to be discretized; the sampling rate is set to 1 MS/s and the sampling time is 1 s. Additionally, it is assumed that the position of the strong reflection point along the optical fiber to be measured is at 20.55 m, and the corresponding group delay is τ = 2 × 10 −7 s. 170 According to the magnitude of the nonlinear effect, it is discussed as follows: (1) let A n = 5 × 10 6 , f n = 25 Hz and the group delay τ is still 6 × 10 −7 s, corresponding to the fiber position 61.65 m; at this time the K value is still 0.2 and the other parameters are unchanged. The effect of the one-dimensional interpolation method before and after compensation is shown in Figure 7. Comparing Figures 7(a) and (b), it can be seen that the reflection peak broadens considerably when it is not compensated, and its interval is approximately 49.5~73.5 m. However, the reflection 175 peak after compensation is extremely sharp, indicating that the spatial resolution of the system has been greatly improved. (2) To test the compensation effect of the one-dimensional interpolation method for multiple reflection points, a second strong reflection peak position is added, namely τ 1 = 4 × 10 −7 s and τ 2 = 6 × 10 −7 s. At this time, the preset reflection point For the case of the same simulation model, in the face of more severe nonlinear frequency sweeping effects of the light source, the one-dimensional interpolation method greatly improves the spatial resolution of the system, narrows the width of 195 the reflection peaks significantly, and obtains the position information of the reflection points. As with single-point compensation, one-dimensional interpolation is performed on the same set of experimental data. Figure 9 shows the effects before and after compensation.  There is an extremely sharp reflection peak at 56 m, the energy is concentrated, and the system spatial resolution is greatly   Due to the stress application, a reflection peak appears at this position, the loss difference can be obtained by averaging the amplitudes of the 100 points to the left and right of the reflection peak and subtracting them. The figure shows that with the continuous increase of the mass of the weight, the fiber is squeezed more by the pressing teeth, the larger the bending curvature radius generated, the more the Rayleigh scattering signal decreases. Simultaneously, greater stresses produce higher peak values for the reflection peak caused by the bending, which reduces the optical power received by the 235 subsequent optical fiber and causes the overall reflection peak generated at the end of the fiber to decrease in amplitude. It can also be seen from Figure 11(g) that when the mass of the weight reaches 77.5 kg, the amplitude of the Rayleigh scattering spectrum after the stress application point is still greater than the noise amplitude, indicating that the measurement range of the system has not reached its limit. As the mass of the weight continues to increase, the Rayleigh scattering https://doi.org/10.5194/gi-2020-6 Preprint.    Table 2 shows that there are six stress sensors along the testing fiber, and the measured positions and pressure values for each sensor are shown in Table   2.
Table2    one-dimensional interpolation method discussed in Section 3. During the simulation process, I(t) needs to be discretized 345 while considering the size of the nonlinear effect.

Data analysis of the TK-02 monitoring site
(1) When the short-distance measurement is in the range 0-40 m, the nonlinear frequency sweep effect of the light source becomes larger without compensation as shown in Figure 21(a). When the NUFFT method is used for compensation, Figure   21(b) shows that broadening phenomenon of the reflection peak owing to the nonlinear effect is greatly improved and there is a significant reflection peak at 20.55 m. Therefore, under short-range measurement conditions, the NUFFT method can 350 effectively compensate for the nonlinear frequency sweep effect of the light source and improve the spatial resolution of the system. (2) When the measurement distance increases to 80 m, a comparison of Figure 21(a) and Figure 22(a) shows that the width of the broadened reflection peak (with no compensation) further increases, indicating that when the measurement distance increases, the linear effect grows stronger. Figure 22(b) shows the result after NUFFT compensation. It can be seen that NUFFT effectively eliminates the phase noise of the light source and can clearly distinguish a strong reflection point around 360 61.65 m. https://doi.org/10.5194/gi-2020-6 Preprint. Discussion started: 26 March 2020 c Author(s) 2020. CC BY 4.0 License. However, Figure 22(b) shows that the light source signal exhibits drastically changing noise after 76 m that may indicate the need for deconvolution when performing NUFFT operations. As shown in Figure 23, the Gaussian function spectrum W(z n ) is the dividend in Equation (2) that shows a good concentration. Therefore, its value is small and is close to zero at long distances (e.g., after 76 m) and the divisor X G (z n ) in Equation (2) is also close to zero at this distance. When two extremely small numbers are divided, this operation may cause major errors and even exceed the actual nonlinear phase noise. 370 Similarly, the NUFFT method is used to compensate for the single and double reflection points. From the simulation results, we know that within a short measurement range (generally no greater than 40 m), the main interferometer shows a narrow reflection peak in the distance domain signal, which means the system spatial resolution has greatly improved. However, 375 when the measurement distance exceeds 40 m, two minimal vectors, W(z n ) and X G (z n ), will occur for division when the NUFFT is deconvolved. There will be side-lobes around the reflection peak indicating that the phase noise has not been completely eliminated; therefore, using the NUFFT method for light source compensation will generate larger errors and risks in the long-distance measurements.
Both the NUFFT and one-dimensional interpolation algorithms are resampling methods. These methods can achieve high 380 spatial resolution for measurements over short distances. However, when the test distance increases, the difference between the test point delay on the main interferometer and the auxiliary interferometer delay becomes too large. Compared with the dechirp filter algorithm, the compensation effect is not as effective. When using the dechirp filter algorithm, the spatial resolution cannot be as high as when using resampling at short distances. Therefore, a compensation method combining a resampling method and de-slope filtering algorithm should be studied in the future work to improve the nonlinear 385 compensation effects for the OFDR light source that can achieve higher spatial resolutions for both short and long-distance measurements.

Conclusions
This paper proposes a quasi-distributed thrust measurement system based on OFDR. By designing an optical fiber stress sensor based on the optical micro-bending effect, combined with a high-resolution and high-precision OFDR demodulator, 390 and after a field engineering application on a landslide in the Three Gorges Dam area, quasi-distributed stress monitoring is accomplished with long measurement distances, high spatial resolutions, high sensitivities, and rapid responses. This paper provides a new concept and method for inner stress testing of rock and soil masses and can be extended to such safetyrelated monitoring fields as unstable slopes, slope engineering, water conservation and hydropower dams, and tunnel chambers that have great practical value and application prospects.