Abstract
The force-measuring rock bolt instrumented with bare fiber Bragg grating (FBG) sensors are generally factory-fabricated. To enable users to fabricate a force-measuring rock bolt by themselves, the microclamped FBG sensor is proposed to replace the encapsulated bare FBG sensor. A theoretical formula of strain sensitivity is also established. The strain sensibility measured by indoor calibration is consistent with the theoretical one, indicating that the microclamped FBG sensor can measure strain accurately. Besides, the measured strain sensibility coefficient (wavelength difference/strain) matches the theoretical values, making the installed microclamped sensor free from the need for recalibration and proving the installation method to be reliable. Also, the test sensitivity can be adjusted as needed. The instrumented rock bolt with microclamped FBG sensors shows great mechanical performance in the field test, awaiting further usage in applications.
1. Introduction
Bolt supporting technology with simple structure, timely prestress, and small volume has been widely used in geotechnical engineering [1, 2]. The amount of rock bolt used worldwide in 2011 reached 500 million [3]. However, it is difficult to accurately monitor the bolting system hidden in complex geological conditions and the adverse construction environment. How to properly and accurately monitor a bolt supporting system is still under further research [4, 5].
The conventional measurement techniques, such as vibrating wire sensor [6] and electrical-resistance strain gauge [7], are widely used to test the axial stress distribution and the force transfer mechanism of rock bolt. However, some problems were encountered during the in situ applications, including (i) easily getting wet, (ii) difficult to get connected, (iii) unable to meet the requirements of the intelligent test, and (iv) low survival rate and poor durability [8]. In the recent two decades, the development of fiber Bragg grating (FBG) technology has provided a new method for test in geotechnical engineering [9]. Besides the advantages of the conventional fiber grating sensor, the small FBG sensor is easy to get connected with high stability, sensitivity, and resolution [10, 11].
Rock bolt is one popular geotechnical structure monitored using FBG sensors. The bare FBG sensor with a diameter of 125 μm is very fragile and can be easily damaged in practical engineering application, and the encapsulating process of bare FBG sensors is essential and requires careful design and protection [12]. There are three main encapsulating types of FBG sensors, including the embedded encapsulating type, substrate encapsulating type, and clamped (tube) encapsulating type [13–15]. The embedded encapsulating type means to directly embed bare FBG sensors into structure. For the rock bolt, a small groove is engraved along the bolt shaft, in which the sensors are later embedded and, finally, the groove is filled with adhesive material. Li et al. [16] analyzed the creep behavior of GFRP in concrete by embedding bare FBG sensors in groove with 2 mm width, 2 mm depth, and 15 mm length. Chai el al. [17] glued three FBG sensors in the 1 mm deep and 30 mm long groove of a bolt and used them to record axial stresses and strains along the bolt during a pull-out test. However, this type of encapsulating needs high requirements of the encapsulating condition, equipment, and technology. Li [18] used a self-fabricated force-measuring rock bolt instrumented with bare FBG sensors for indoor pull-out tests, and it was not until the sixth test that the axial force of rock bolt was successfully collected. The embedded place of bare FBG sensors and the use of adhesive material also have a great impact on the ultimate strain transition. So, the force-measuring rock bolt instrumented with bare FBG sensors is generally factory-fabricated, unable to meet the requirement of self-fabricated in in situ monitoring. The substrate encapsulating type of the FBG sensor is not suitable for slender component, such as rock bolt. Among the three encapsulating types, the clamped encapsulating type of the FBG sensor is the most suitable for rock bolt.
Therefore, authors have designed and produced a microclamped FBG sensor based on the fact that the bolt shaft is a slender bar. Also, a force-measuring rock bolt instrumented with microclamped FBG sensors is fabricated. The strain sensitivities of microclamped FBG sensors obtained from the theoretical formula and indoor calibration are compared to evaluate the applicability of the force-measuring rock bolt. Finally, it is applied to monitor the axial stress of rock bolts at the Muzhailing tunnel (in China), achieving timely, quick, and accurate test of in situ mechanical states of rock bolts.
2. Working Principle of FBG
Optical fiber is a waveguide medium mainly composed of a core, a cladding layer, and a coating layer, which works in the optical wave band. The electromagnetic energy in the form of light is reflected inside the core, and the light wave is conducted in axial direction. Fiber grating is a waveguide device with a specific waveguide structure written into optical fiber by ultraviolet light. A narrow band wave filter or mirror is formed in the core. When a light beam of wide spectrum enters the FBG, part of the spectrum produces an effective reflection under Bragg conditions. The peak wavelength of the reflected light is called the Bragg wavelength λ, as shown in Figure 1, which satisfies the following equation [19, 20]:where is the effective refractive index of the fiber core and Λ is the grating period (nm).
Any physical process that changes the abovementioned two parameters will cause a drift in the reflection and transmission wavelength. Stress and temperature are the physical quantities that most directly and greatly change the wavelength of fiber gratings. The drift of the center wavelength Δλ caused by axial stress and the axial strain of grating satisfies the following equation:where is the elasto-optical coefficient.
It can be seen from the abovementioned equation that the wavelength of the FBG has a good linear relationship with the strain, indicating that the linear transmission characteristics of FBG are great. However, the sensitivities of FBG sensors with different types of optical fibers or grating fabrication technologies vary a lot. To obtain the actual strain of structures, various types of FBG sensors should be calibrated before in situ monitoring [4, 21, 22].
3. Structure and Working Principle of the Microclamped FBG Sensor
In the microclamped FBG sensor, a small diameter casing is used to protect the fiber grating. Only both ends of the FBG are connected with the casing by adhesive material. In this way, the whole length of the FBG does not contact adhesive material, avoiding impacts of adhesive material on strain transfer. The microclamped FBG sensor is composed of the steel capillary tube, FBG, transmission fiber, and clamping components (Figure 2). This kind of sensor can be directly stuck, welded, or reverted to the surface of structures, which can be easily and conveniently set and replaced with great durability.
The working principle of the microclamped FBG sensor is shown in Figure 3. The clamping component is a steel tube with diameter of d, which is stuck to the basement. The equivalent distance between two fixed ends is L, while the fiber grating is Lf in length. From this, it follows that , in which refers to the length of clamping component between two fixed fulcrums. The axial deformation of the clamping component and the FBG is defined as ΔLs and ΔLf, respectively. The impact of the inner and outer adhesive layers of the clamped steel tube and the transmission fiber is ignored. Based on the material mechanics, the following equations can be obtained:where and refer to the axial load of the clamping component and the FBG, respectively. According to the load transfer mechanism, it can be assumed that , and in combination with equations (3) and (4), the following equations can be derived:and the parameters of the sensor are shown in Table 1.
Substituting the parameters into (6), the following equation can be obtained:and it can be seen from the abovementioned equation that the strain of the clamped steel tube can be ignored compared to that of the whole sensor. That is to say, the deformation between two clamped ends is approximately that of the FBG. The theoretical relationship between the strain of the basement and the FBG is as follows:and the theoretical relationship between the loading force of the basement F and the strain of the basement is as follows:where is the modulus of elasticity of the basement and is the cross-sectional area of the basement.
The test sensitivity coefficient is defined as . Substituting it into equation (8), the following equation is obtained:and it can be seen from equation (10) that the test sensitivity will change as K changes. The test sensitivity increases when K is above 1, while it decreases when K is below 1.
4. Calibration of the Rock Bolt Instrumented with the Microclamped FBG Sensor
4.1. Test System
There are three microclamped FBG sensors used in the test, named, FBG1, FBG2, and FBG3, the center wavelength of which are 1559.7915 nm, 1535.1585 nm, and 1525.0652 nm. The FBG is 8 mm in length with the initial calibration distance (factory calibration) of 12 mm (Figure 4), and the measurement range is between −1500 με to 1500 με. The corresponding sensitivity coefficients of sensors are 1.40088 pm/με, 1.38563 pm/με, and 1.33676 pm/με, respectively.
A universal testing machine, as shown in Figure 5, is used for the tensile test of the force-measuring rock bolt. An Sm125 static FBG demodulator produced by Micron Optic is used to acquire and identify FBG wavelength. The elastic modulus and Poisson ratio of the epoxy resin adhesive used in the test are 3.5 GPa and 0.32, respectively.
4.2. The Force-Measuring Rock Bolt
Based on regulations of the specimen size [23], the bolt shaft is made of Q420 and 60 cm in length with an outer diameter of 32 mm, wall thickness of 6 mm, and sectional area of 490.0 mm2.
There are two main methods to test the strain of the bolt shaft. One is to first polish the surface of bolt shafts and, then, directly stick the sensors to it. The other is to slot the bolt shaft first and, then, embed the sensors in the groove. To enable the sensors to survive in the tough construction environment of tunnels, the second method is adopted in this test.
Fabrication of the force-measuring rock bolt: firstly, a rectangle groove of 3 mm in width and 2 mm in depth is slotted on the surface of the bolt shaft; secondly, the coarse sandpaper is used to polish the groove surface to remove rust, oil, and uneven bumps after that the alcohol is used to clean the groove; thirdly, FBG sensors are prefixed at the predetermined position (fixed fulcrum) in the groove with 502 glue, and the sensors are prestretched by 0.2∼0.8 nm during the prefixing process; fourthly, the white pigtails on both sides of the sensor are fixed in the groove to prevent them from being pulled which will impact the stress of the sensor; fifthly, the two sides of each fixed fulcrum are fixed and encapsulated with epoxy resin glue, and after 24 hours, with the glue completely solidificated, the fabrication is down, and a force-measuring rock bolt instrumented with one microclamped FBG sensor, as shown in Figure 6.
Three force-measuring rock bolts are fabricated in this test, an FBG1 force-measuring rock bolt, FBG2 force-measuring rock bolt, and FBG3 force-measuring rock bolt, whose installation parameters are shown in Figures 7–9. Based on the initial calibration distance, the theoretical installed strain sensitivity coefficients of FBG1, FBG2, and FBG3 are obtained, respectively: 1.86784 (=1.40088 16/12) pm/με, 2.30938 (=1.38563 20/12) pm/με, and 2.67352 (=1.33676 24/12) pm/με.
4.3. Testing Method and Result Analysis
Since this test is carried out in the laboratory with short duration, the variation in temperature can be ignored. That is to say, the wavelength variation of FBG sensors is considered to be completely derived from strain change in ignorance of temperature change. The test is carried out under isocratic load from 0 to 100 kN at constant speed. The center wavelength of FBG sensors is recorded every 10 kN during the loading process. Each bolt shaft is cyclically loaded 3 times, and the average center wavelength is taken. The calibration data are shown in Table 2.
A scatter of load-wavelength drift is plotted based on the experimental results, as shown in Figure 10. The linear fit relationships of FBG1, FBG2, and FBG3 are given aswhere refers to the load acting on the bolt, i.e., the “Load” in Table 2 and Figure 10. The corresponding R2 are 0.9969, 0.9945, and 0.9978, all above 0.99, indicating that the above-installed microclamped FBG sensors have good stabilities to test the stress state of rock bolts.
The load sensitivity coefficients (wavelength drift/load) of FBG1, FBG2, and FBG3 are 0.0194 nm/kN, 0.0231 nm/kN, and 0.0286 nm/kN, respectively. Based on the equation , where the elastic modulus E is 200 GPa and the cross-sectional area A of the bolt shaft is 490 mm2, the corresponding measured strain sensitivity coefficients (wavelength drift/strain) are 1.9012 pm/με, 2.2638 pm/με, and 2.8028 pm/με, respectively. The corresponding theoretical strain sensitivity coefficients are 1.8678 pm/με, 2.3094 pm/με, and 2.6735 pm/με, matching the measured ones well. The comparison of the theoretical and measured strain sensitivity coefficients is shown in Figure 11. It can be seen that the maximum difference is only 0.1293 pm/με, which appears at FBG3.
Summing up these experimental results, it is found that the microclamped FBG sensor has high measuring accuracy. The load and wavelength drift have a great linear relationship with linearity over 0.99. Meanwhile, the force-measuring rock bolt has great measuring stability. The measured and theoretical strain sensitivities of installed FBG sensors match well. Also, there is no need for calibration of installed FBG sensors, allowing for direct application of the force-measuring rock bolt instrumented with microclamped FBG sensors in the field engineering with high reliability.
5. Field Tests
5.1. Ground Condition
The Muzhailing tunnel crosses the Muzhailing Mountain, spanning Zhang County and Min County in China, as shown in Figure 12. The surrounding rock is mainly carbonaceous slate with a saturated uniaxial compressive strength of no more than 30 MPa. The tunnel is located in the Qinling-Kunlun latitudinal tectonic area with high geostress and large stress intensity ratio, where large deformation issue is the major issue.
The conventional solutions such as to encrypt steel frames, thicken the shotcrete, and immediately install the secondary are of poor effect. These methods aim to resist large deformation by strengthening support structures. However, large deformation cannot get controlled by these methods with subsequent structures failure, as shown in Figure 13.
(a)
(b)
In this situation, new methods aiming to release deformation energy using yielding rock bolts are proposed. In the preparation to apply the yielding rock bolt in the Muzhailing tunnel, it is necessary to study the working performance of it in the specific geological conditions of the Muzhailing tunnel. Since the traditional force-measuring rock bolt instrumented with vulnerable strain gauges obtains data with large deviation, the FBG is proposed. Besides, to meet requirements of integrating different size rock bolts, the force-measuring rock bolt instrumented with microclamped FBG sensors can be self-fabricated.
5.2. Testing Method
The test site was located at a depth of about 521 m below the surface, and the cavern was excavated by the three-step method with an excavation span of 13.4 m. The measuring point was arranged on the middle step, and the test was carried out about 20 days after the excavation of the upper step. The force-measuring rock bolt used in the field test was fabricated from YR25-5 bolts, whose yield load and ultimate bearing capacity are greater than 151 kN and 205 kN, respectively. Figure 14 shows a 3 m force-measuring rock bolt instrumented with four microclamped FBG sensors.
In the test, the force-measuring rock bolt is firstly inserted into the hole drilled by using a YT28 Rock Drill. Then, the anchor plate is installed, and the P. O 42.5 cement slurry with a water vapor ratio of 1 : 0.4, which could provide an excellent premature strength to withstand the load that grew rapidly at the early stage, was, then, injected. After that, the initial data of the force-measuring rock bolt were obtained by using the FBG demodulator. The data were recorded once a day during the test. The force-measuring rock bolt installed in field is shown in Figure 15. Figure 16 is a schematic diagram of the field test, which contains the installation parameters of FBGs.
5.3. Data Analysis
The data obtained by FBG1 to FBG4 from Nov. 1 to Nov. 6 are extracted to calculate the axial force of rock bolt at the corresponding measuring points. The relationship between the axial force of the bolt shaft and the distance from the measuring points to the wall is shown in Figure 17. The measured horizontal displacement and the displacement difference of the wall at the 3 m force-measuring rock bolt from Nov. 1 to Nov. 6 are shown in Figure 18.
As shown in Figure 17, with the increase of the bolt shaft depth into rock, the axial force of the shaft increases first and, then, decreases with the peak at FBG2. On the second day after installation, the measured maximum axial force is 45 kN, showing great support effects of the rock bolt. It can be seen in Figure 18 that the displacement of the wall at the force-measuring rock bolt increases from 203 mm on Nov. 2 to 230 mm on Nov. 6, showing rock plastic flow under high ground stress. Therefore, the measured varying axial force of the rock bolt matches with the theoretical one. It can be seen in Figure 18 that the displacement difference between Nov. 2 and Nov. 3 is obviously larger than that of the subsequent days. The corresponding part in Figure 17 shows that the axial force of the shaft on Nov. 3 increases a lot from that on Nov. 2 and the increment is larger than that of the subsequent days. It can be concluded from the abovementioned data that this instrumented rock bolt with microclamped FBG sensors can accurately measure the varying axial force, and results were well with the limits as theoretical calculation.
6. Conclusions and Future Work
In this paper, a microclamped FBG sensor is proposed to replace an encapsulated bare FBG sensor in a rock bolt, and through the analysis of the experimental data of indoor calibration and filed test, the following conclusions are obtained:(1)The microclamped FBG sensor can be integrated with rock bolts by users. Besides, the wavelength drift and applied load show great linear correlation ( > 0.99), allowing for acceptable performance of the strain measurement system.(2)The strain sensitivities from the indoor calibration match the theoretical formula. Therefore, the strain sensitivity can be derived from the distance. That is to say, the encapsulated FBG sensor does not need recalibration.(3)The field studies at the Muzhailing tunnel have shown that the force-measuring rock bolt instrumented with the microclamped FBG sensors is suitable for field monitoring of tunnel constructions. This type of rock bolt can accurately measure the varying axial force, and results were well with the limits as theoretical calculation.
The primary support of tunnels mainly includes the rock bolt, the shotcrete, and the steel arch. In the future, the microclamped FBG sensors can be applied to test the force on the shotcrete and the steel arch, leading to the ability for intelligent monitoring of the primary support.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare no conflicts of interest.
Acknowledgments
The authors gratefully acknowledge the support provided by the National Natural Science Foundation of China (No. 51878571 and 51578456) and the Gansu Science and Technology Program (19ZD2GA005).