Mechanical Characterization of Anchor under Uniaxial Compression Loading Conditions

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Introduction
Rock bolting support can improve the strength and shear resistance of the rock, making the rock bear greater cooperation, and improving the stability of an engineering rock tunnel [1,2]. e use of anchor bolt makes the rock bear greater cooperation, and therefore improves the stability of a layered rock tunnel [3]. For this reason, many types of anchor bolts are used in mine and tunnel construction, and the waveform anchor bolt technology is used in the support of underground phosphate rock [4]. Lei et al. [5] studied the uniaxial compression test of fractured rock specimens without anchorage, full-length bonded anchorage, and prestressed anchorage. e results showed that the length of the crack had little e ect on the anchorage specimen, and full-length bonded anchorage and prestressed anchorage could signi cantly improve the strength of the anchor and restrain the deformation of the fractured rock mass. Kan et al. [6] pointed out that the anchoring e ect of anchor solid was related to the parameters of the anchoring agent used and the mixing speed applied in anchoring installation. e anchoring agent and the mixing speed would a ect the anchoring strength. Sakhno et al. [7] adopted the full-length drilling self-extending mixture anchoring technology developed in the Wieliczka mine to improve the maximum anchoring capacity of the anchor and the elastic deformation bearing capacity of the anchor. Wu et al. [8] studied the uniaxial compression mechanical behavior of prestressing anchors in coal mining by numerical simulation and considered that the bolt had the function of absorbing and storing energy. Ren et al. [9] conducted a uniaxial compression test on the anchorage column of a weak interlayer in the laboratory and found that the existence of anchor rod improved the ductility of the stress-strain curve of the specimen. Xiao et al. [10] used a compression shear test to study the mechanical properties of CFRC composite grouting materials under long-term water immersion conditions. Zhu et al [11] established the coupling effect model of equal creep deformation and stress and verified the model by a uniaxial creep test. It was found that there was a nonlinear relationship between prestress loss and the increase in stress level. With the increase of axial load, the specimen produced compression deformation and transverse expansion. e first mock exam was carried out by Zhu and others [11], and the model of creep deformation and stress was established. Zhao et al. [12] studied the creep deformation characteristics of red sandstone under uniaxial compression and multi-stage loading. sun et al. [13] studied the failure characteristics of anchors under multi-stage loading and corrosion by indoor test. Zheng et al. [14] conducted a uniaxial compression test on fiber reinforced concrete, and discussed the influence of fiber type and fiber content on the uniaxial compressive strength of fiber reinforced concrete, showing nonuniformity and nonlinearity. Different fiber content would also change the failure mode of the specimen. Algburi et al. [15] studied the relationship between axial load and axial strain of composite reinforced concrete by uniaxial compression. Zainal et al. [16] studied the experimental mechanical properties of hybrid fiber reinforced wonton materials with super-plasticizer by unidirectional loading.
Electrochemical impedance spectroscopy (EIS) is a multi-purpose and destructive testing technology [17]. Electrochemical impedance spectroscopy is also widely used in the research of nanocomposite preparation [18], carbon steel corrosion [19], lithium-ion battery [20], and metal oxide electrode [21]. Viacheslav et al. [22] believed that electrochemical impedance spectroscopy could reveal the dynamic characteristics of local heterogeneous interfaces. Ribeiro and Abrantes [23] used electrochemical impedance spectroscopy to monitor the corrosion state of reinforced concrete. Peng et al. [24] characterized the permeability of grouted fractured rocks by electrochemical impedance spectroscopy. Electrochemical impedance spectroscopy was used to monitor the corrosion state of reinforced concrete. Song [25] constructed the equivalent circuit model of the AC chemical impedance spectrum of concrete and pointed out that water-cement ratio and hydration time will affect the equivalent circuit. Dhouibi et al. [26] used electrochemical impedance spectroscopy to determine the effect of corrosion inhibitors on the corrosion resistance of reinforcement. Deus et al. [27] studied the corrosion rate of the reinforcement in concrete under the influence of chloride and temperature by electrochemical impedance spectroscopy. e results showed that the corrosion rate was dependent on temperature. e electrochemical analysis method was used in the experimental measurement of anchor under osmotic pressure [28]. Sohail et al. [29] conducted electrochemical test research on different types of reinforcement under corrosion conditions. He et al. [30] studied the electrochemical impedance spectrum characteristics of X70 pipeline steel corroded by saline sandy soil by electrochemical method and scanning electron microscope. It was considered that when the water content exceeds 18%, the main corrosion process was point corrosion or local corrosion.
e Nyquist curve of the electrochemical test can reflect the development of cracks in mudstone under the condition of the freeze-thaw cycle [31,32]. Li et al. [33] studied the change of resistivity of coal under different loading modes. e results showed that the resistivity of coal would change with different loading modes, which may be related to the change in pore structure and stress state of coal.
In conclusion, the above-related research methods, research results, and engineering applications provided a meaningful reference for the further study of anchor characteristics. e study of this article focused on the behavior characteristics of anchor under uniaxial loading.
Anchor specimens were made and tested in the laboratory. e tests included a uniaxial compression test, multi-stage loading test, and electrochemical impedance spectroscopy test. e structure of the rest of the article is as follows. e second section introduces the test materials and methods.
e third section provides the test results and discussion. Lastly, the fourth part presents the conclusions of the study.

Specimen Preparation.
e general idea of specimen making is to select the mold with the appropriate size, next arrange the anchor rod simulation device in the mold, and then pour the mold, vibrate, compact, and maintain. e specific process can be divided into the following six steps.
(1) In the laboratory of Zhongyuan University of Technology, internal size 150 mm × 150 mm × 150 mm mold was selected, and the release agent was evenly applied on the inner side of the mold.
(2) en, the threaded rod with a diameter of 5 mm, gasket, and nut were used to simulate the anchor bolt, the anchor agent was applied on the surface of the anchor bolt, and then the anchor bolt was arranged at the geometric center of the mold. (3) One solid steel bar with a diameter of 1 cm was arranged on the other four geometric center points of the mold, and the surface of each solid steel bar was coated with a release agent. (4) Cement, gypsum, quartz sand, water, and boron were mixed according to the mass ratio of 1 : 0.25 : 0.25 : 0.12. en, the mixture was thoroughly stirred in the mixer. After mixing evenly, the mixture was poured into the mold. en, the test block was placed on the shaking table for vibration and compaction. (5) After the sample was cured at room temperature for 24 h, demoded and taken out of the embedded solid rigid bar, and inserted the steel porous water pressure pipe coated with anchoring agent into the reserved hole. A conductive electrode sheet was pasted in the middle of the porous steel pipe. (6) Placed the anchored rock specimen at room temperature and in a naturally dry environment for 28 days. e fabricated specimen can prepare for the unidirectional compression test of the specimen in the next step. e schematic diagram of the test specimen is shown in Figure 1. (1) According to the preparation method of experimental specimens, four specimens for test shall be prepared in the laboratory. (2) ree of the four specimens (GA, GB, GC) were used to carry out the uniaxial compression test without permeability. en, the stress-strain curve of each sample was analyzed. e force applied by the testing machine to the specimen is F. e stress of the test specimen is σ. e contact area between the test specimen and the testing machine is S. e stress of the test specimen can be calculated by the following formula:

Test
(3) e remaining specimen GD was used to carry out a uniaxial multi-stage loading test without penetration. en, its multi-stage loading mechanical characteristics and electrochemical impedance spectroscopy characteristics were analyzed.

Uniaxial Compression Test.
In order to accurately obtain the uniaxial compressive strength of the test specimens, the method of taking the average value of multiple groups of tests was adopted. e uniaxial compression tests on n specimens in total were carried out and each of the n test specimens was taken and named as i. rough the uniaxial compression test, the uniaxial compressive strength of the specimen i is σ ci . e uniaxial compressive strength of these test specimens is recorded as σ c . en the relationship between σ c and σ ci can be expressed by the following formula: First, the three test specimens were numbered GA, GB, and GC, respectively. Secondly, the three specimens were subjected to uniaxial compression test, and the stress-strain curves of each specimen were obtained. e peak compressive strength of GA, GB, and GC test specimens were 8.31 MPa, 8.4 MPa, and 8.23 MPa, respectively. Using the formula (2), the average uniaxial compressive strength of the tested specimens is σ c � 8.31 MPa. e shape of the uniaxial compression stress-strain curve of GA, GB, and GC was similar. In order to study the characteristics of the uniaxial compression test process of the Advances in Materials Science and Engineering specimen in detail, the GA specimen was taken as an example for analysis. According to the curve variation law, the stress-strain curve of specimen GA was divided into four different stages.
(1) Stage I: Gap compaction stage. e stress-strain curve formed at this stage shows an upward concave curve. ere were different volumes of pores in the fabricated specimen GA. When subjected to external force, the pores' volume in the anchor specimen GA gradually decreased.
(2) Stage II: Elastic deformation stage. e main reason for the deformation at this stage was that when the specimen was subjected to external stress, friction will occur between the internal cracks of the specimen, and there will be force and reaction force between the pores. Ideally, the deformation at this stage will recover with the disappearance of external force, and the stress-strain curve of the specimen at this stage basically presented the characteristics in a straight line. Under the continuous action of gradually increasing external stress, new cracks began to form in the specimen. e stress-strain curve formed in this stage showed a relatively gentle shape. e overall curve at this stage had a downward trend, indicating that the microcracks in the specimen were developing and changing. (4) Stage IV: Unstable development stage of microfracture. At this stage, the crack development speed of the specimen accelerated rapidly and gradually developed into a macrofracture surface. In this process, the specimen's bearing capacity decreased rapidly, but the specimen will still maintain a certain bearing capacity.

Multistage Loading Test.
e test specimen was loaded in stages. e loading process was divided into six different levels and the loading sizes at all levels are shown in Table 3. e test machine's loading speed to the specimen GD was 1 kN/min. e holding time of each constant pressure level stage was about 8 hours. e specimen's change process of strain during multi-stage loading levels is shown in Figure 2. For each loading stage, the strain of the specimen will increase with the increase of the load on the specimen. At the moment after the failure of the specimen, the strain of the specimen increased rapidly. e characteristics of the specimen GD after failure are shown in Figure 3. ere were longitudinal cracks on the four sides of the specimen. Some surface materials even separated and fell off.
It can be seen from Table 4 that the elastic strain value and creep strain value of test specimen GD increased with the progress of loading. Furthermore, it was found that the elastic strain value of the test specimen GD at each stage was greater than its creep strain value. According to the details of Table 4, the increase of elastic strain was gradually reduced with the increase of the load grade, while the increase of creep strain was increased with the subsequent increase of the load level at most of the load levels. e variation law of elastic strain and creep strain reflects that the elastic strain    and creep strain of anchor specimen were jointly controlled by the value of the loading process and the length of loading time. In addition, the proportion of elastic strain value and creep strain value in the total strain value was shown in Table 4. In the first loading stage, the elastic strain of the specimen accounted for 55.21% of the total strain, 55.82% of the total strain for the second loading stage, 54.04% of the total strain for the third loading stage, 52.61% of the total strain for the fourth loading stage and 51.90% of the total strain for the fifth loading stage. e increase of elastic strain of loading stages 2 to 6 was 0.074, 0.067, 0.062, 0.053, and 0.040, respectively. e increase ratio of elastic strain at each stage was 41.11%, 26.38%, 19.31%, 13.84%, and 9.17%, respectively. On the other hand, the proportion of creep strain in the total strain for the loading stages 1 to 6 was 44.79%, 44.18%, 45.96%, 47.39%, and 48.10%, respectively. e increase of creep strain of loading stages 2 to 5 was 0.055, 0.072, 0.072, and 0.059, respectively. e increase ratio of creep strain at each stage was 37.67%, 35.82%, 26.37%, and 17.10%, respectively. e results showed that the proportion of creep strain in total strain showed a slight upward trend. During the whole loading process, the elastic strain of the specimen accounted for more than 50% of the total strain, and the elastic strain produced by the specimen was greater than the creep strain of the specimen.

Electrochemical Test.
e changes in microstructure in specimen GD were monitored by the electrochemical method in real-time. A total of seven sampling monitoring operations were conducted. e first sampling operation shall be carried out before the multi-stage loading test. e time point of the other 6 sampling operations was 10 minutes before the end of each step loading. e data obtained from these seven sampling operations were numbered from A to G in chronological order.
Assuming that the test frequency was expressed in ω, then the impedance expression in electrochemistry can be expressed as follows: where Z is impedance, Z ′ is the real part of the impedance, Z ″ is the imaginary part of the impedance. e values of impedance Z, real part of the impedance Z ′ and imaginary part of impedance Z ″ change with frequency ω. erefore, the electrochemical Nyquist impedance spectrum curves

Advances in Materials Science and Engineering
and Bode diagram curves of the tested specimen can be obtained by changing the test frequency. Figure 4 plotted the seven Nyquist curves of specimen GD at different sampling times. rough the comparative analysis of these seven groups of curves, it can be found that: (1) Generally, the geometric shapes of Nyquist curves measured for specimen GD at different times are similar, but the geometric dimensions of these curves were different. On the one hand, the first 4 test curves A ∼ D were closer in space in the three-dimensional coordinate axis, while the last 3 test curves E ∼ G are more dispersed in space in the three-dimensional coordinate axis. On the other hand, with the loading time of the specimen, compared with the data curve measured at the previous time, the Nyquist curve obtained at the latter time showed the characteristic that the length gradually becomes shorter. (2) With the change of test frequency, the real part Z ′ and imaginary part Z ″ of the impedance of the tested specimen were also changing. In the lower frequency band of the frequency, with the increasing frequency, the real part of the impedance Z ′ and imaginary part of the impedance Z ″ of each test curve had an overall trend of decreasing. In the higher frequency band of the frequency, the variation law of the real part Z ′ and imaginary part Z ″ of the impedance gradually did not tend to be unified. (3) e morphological changes of electrochemical curves and the changes in impedance at different test times were analyzed. It was found that when the load increased and the loading time became longer, the pores in the specimen were gradually compressed and the volume of the specimen became smaller. Consequently, cracks in the specimen developed and finally the specimen was damaged. e test curve law reflected the development and inoculation of pores and cracks in the specimen to a certain extent.
By analyzing each area curve in Figure 5(a), it can be seen that the impedance value decreases with the increase of detection frequency. From the shape of the test line, the cumulative detection value of the low-frequency phase was greater than that of the high-frequency phase. e total area accumulation chart showed the characteristics of high first and then low. Comparing the characteristics of each area curve, it can be found that the larger the stress loading value and the longer the time for the specimen, the faster the impedance value decreases. Except for the last group of G area curve, the cross-sectional areas of the other six groups had a relatively small intercept along the vertical direction. e reason was that the test time of group G data was obtained in the sixth loading level stage, in which cracks and even damage appear in the specimen. e crack and  failure had a great influence on the test results of electrochemical impedance. e variation area curves of phase angle with frequency at different times of specimen GD are shown in Figure 5(b). In the ln ω − φ coordinate axis, the distribution of A ∼ F area curves had differential characteristics, and the area curve G was independent of them. A ∼ F area curve showed the characteristics of upward convexity. With the increasing detection frequency, the phase angle values of the seven curves were increasing. Among the seven groups of curves, the phase angle of group G was the fastest to increase. e test results showed that the more serious the internal damage of the specimen is, the greater the influence on the phase angle is obtained by the electrochemical test.

Conclusions
In this study, four groups of anchor specimens GA ∼ GD were made in the laboratory. en, uniaxial compression tests were carried out on three groups of specimens GA ∼ GC, and a multi-stage loading test was carried out on specimen GD. Specimen GD's elastic strain, creep strain and total strain of under each loading stage were analyzed. e electrochemical test characteristics of specimen GD at 7 different loading stages were studied. e test process was tested and analyzed, and the experimental method in this paper can also be used in similar research work. e following main conclusions can be obtained from the experimental work.
(1) In order to obtain the uniaxial compressive strength value of the anchor specimen accurately, three groups of specimens GA ∼ GC were used for the uniaxial compression test. eir uniaxial compression process included four stages, stage I to stage IV. en, the average method was used to get the average compressive strength of the three specimens. Finally, the average uniaxial compressive strength of the specimens was 8.31 MPa.
(2) e specimen GD was damaged during the 6th stage of loading. e total strain of specimen GD during loading was composed of elastic strain and creep strain. During the whole loading process, the proportion of elastic strain in the total strain was greater than that of creep strain, and the proportion of elastic strain was between 51.90% and 55.82%. (3) During the test, the electrochemical workstation was used to collect the data of specimen GD seven times. e Nyquist curve and Bode curve obtained at each detection time were analyzed. It was proved that the electrochemical test results had a certain correlation with the damage degree of the specimen. In particular, the electrochemical test curves at the failure stage showed more significant differences.

Data Availability
e data used to support the findings of the study are included within the article.

Conflicts of Interest
e authors declare no conflict of interest.