An Internal Stress Detection Technology of Concrete Based on Displacement Current

Abstract

Existing testing methods inadequately capture the internal stress state of concrete, a vital structural safety metric, resulting in a divergence between measured and actual internal stress states, especially in larger structures. There is an urgent need for innovative theoretical and technical approaches that can directly, accurately, and instantly reflect the internal stress state of concrete, meeting the growing demand for such detection. This paper conducts experimental research on the internal stress detection of concrete based on the principle of displacement current. Firstly, the theoretical relationship between the internal stress and oscillation frequency of concrete is established. Secondly, two dielectric plates are embedded in the concrete specimen as a sensing unit, and an LC oscillation circuit is connected externally to express the internal stress state of the concrete in the form of oscillation frequency. The research findings suggest that there is a decrease in the oscillation frequency as the dielectric constant of the concrete increases. Additionally, a significant change in the oscillation frequency is observed because of the dielectric polarization effect that takes place during the pouring and curing of the concrete specimen. The concrete age starts from about 25 days, and its oscillation frequency gradually stabilizes; the internal stress of the concrete is proportional to the oscillation frequency, and they show a good correlation in the experiment.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Concrete structures, prevalent in infrastructure construction, necessitate regular testing and long-term health monitoring of their load-bearing performance for practical engineering applications [1, 2]. Therefore, the academic community has shown increasing interest in the detection technology and methods of stress states in concrete structures, a crucial evaluation indicator of their safety level [3–6].

The current research primarily focuses on optical fiber sensing technology and vibrating wire sensing technology for detecting internal stress in concrete [7]. Fiber optic sensing technology measures the stress state inside a structure by observing changes in optical properties as a laser propagates through a fiber [8]. This technology has yielded significant results in concrete structure applications. For instance, Kim et al. [9] utilized long-volume optical fiber sensors for the long-term monitoring of stress states in prestressed concrete beam bridges, while Minutolo et al. [10] employed embedded optical fiber sensors to investigate the strain distribution within structures. Overall, optical fiber sensors offer the benefits of high precision and mature technology [11]. However, due to the high requirements of optical fiber sensors for the construction process and the elevated cost of the necessary detection equipment, optical fiber strain sensing technology is typically reserved for the detection and monitoring of critical parts or structures, such as large-span bridges and high-rise buildings [12–14]. Vibrating wire sensing technology, in contrast to optical fiber sensing, leverages the relationship between the natural frequency and tension of a stretched steel wire to detect internal stress in concrete [15, 16]. With the advantages of controllable cost and mature technology, this method has seen widespread use in recent years [17–20]. For instance, Lee et al. [17] employed this technology for the long-term continuous monitoring of operational concrete structures, while Biswal and Ramaswamy [18] used it to measure the existing prestress in concrete structures. However, this technology has certain limitations, including significant susceptibility to concrete hydration heat, as well as issues with frequency drift [20, 21]. A combination of the above two detection technologies reveals that these sensing methods cannot concurrently fulfill the requirements of accurate measurement of internal stress in concrete, cost-effectiveness, long-term usability, and sensor stability. Therefore, it is imperative to find new breakthroughs in the detection technology and theoretical methods of internal stress in concrete, aiming for accuracy, cost-effectiveness, and long-term performance [20–22].

In fact, in the realm of electromagnetic applications, Shao et al. [23, 24], Wang [25], and Chen et al. [26] have demonstrated that technologies based on the principle of displacement current hold promising application prospects in research areas such as wireless power transmission and friction nanogenerators. Shao et al. [23] starting from Maxwell’s displacement current proposed a predictable method for understanding current and power behavior and used this to standardize the charging characteristics of friction nanogenerators. Wang [25] introduced a nonelectric field-induced polarization term into the Maxwell equation group, derived a system theory that describes the electromagnetic dynamics of nanogenerators from first principles, and used this to quantify the output power of nanogenerators. Chen et al. [26] investigated the propagation characteristics of wireless power transmission based on spherical high-frequency electric field displacement current, finding that spheres with the same center radius exhibit equal electric field strength. It becomes apparent that their research is grounded in the polarization term of displacement current [27]. Therefore, drawing inspiration from these scholars, this research endeavors to apply this principle to the detection of the internal stress state in concrete. The displacement current, determined by the position field strength and polarization intensity of the medium, is the integral of the rate of change of electric displacement flux over time on a surface [28, 29]. Theoretically, the displacement current can resemble the current flowing through concrete materials [30]. It is associated with factors like the vacuum dielectric constant, electric field strength, and polarization intensity, which are closely tied to the properties of concrete materials [30–33]. From an implementation perspective, materials with good electrical conductivity need only be embedded into concrete as sensing probes, followed by connecting the resonant circuit outside the concrete structure [31, 33]. The sensing probe, capable of direct contact with the concrete material, inevitably shortens the transmission path. The externally connected resonant circuit, including LC and LRC circuits, represents more mature measurement and control equipment. If technical methods based on this principle are applied to concrete structure detection, they should offer advantages such as wide range, low cost, convenient construction, and stable performance. This is attributed to numerous parallel studies in other fields based on this principle, offering relatively mature theoretical and technical support. Simultaneously, the enclosed environment of concrete materials provides a singular medium for the passage of displacement current [32, 33].

This article, beginning with the nature of the displacement current principle and leveraging currently available mature technical advantages, conducts research on the detection technology of internal stress in concrete structures to meet the growing demand for such detection. The polarization effect of the concrete medium and stress state changes translate into displacement current changes. When combined with the LC oscillation circuit, the displacement current signal is represented as an electromagnetic resonance frequency, enabling the achievement of the method for detecting internal stress in concrete.

2. Basic Principle

2.1. Displacement Current Theory

The displacement current is essentially the changing electric field in the dielectric space, which can be expressed according to Maxwell’s equations as:$$\begin{array}{}\text{(1)}& I_{\mathrm{D}}={\iint }_{\mathrm{S}}\frac{\partial \mathit{D}}{\partial t}dS={\iint }_{\mathrm{S}}{\epsilon }_0\frac{\partial \mathit{E}}{\partial t}+\frac{\partial \mathit{P}}{\partial t}dS,\end{array}$$where ${\epsilon }_0$ is the vacuum permittivity, $E$ is the electric field intensity, $P$ is the electric polarization intensity, and $\partial D/\partial t$ is the displacement current density.

It can be shown by Equation (1) that the displacement current is determined by the electric field intensity in space and the polarization intensity of the dielectric.

In this study, concrete serves as the dielectric material between the plates, with the dielectric properties of its components dictating the overall dielectric characteristics. Following the pouring of concrete, the internal cement experiences ongoing hydration, resulting in a rise in hydration product content, which in turn modifies the structure’s overall dielectric properties. Consequently, the primary focus of analyzing the impact of concrete hydration is on its dielectric properties.

2.2. Dielectric Polarization of Concrete

Dielectric materials belong to insulating materials, and the polarization of the dielectric is that the surface of the material will show electrical properties under the action of an external electric field. Through the analysis of the microstructure of concrete, concrete is a polycrystalline and multiphase inorganic material, and there are common polarizations under the mixing of multiple dielectrics, mainly including electron and ion displacement polarization, relaxation polarization, and orientation polarization.

The polarization characteristics of the medium can be expressed by the relative permittivity.$$\begin{array}{}\text{(2)}& P={\epsilon }_{\mathrm{r}}-1{\epsilon }_{0}E,\end{array}$$where ${\epsilon }_{\mathrm{r}}$ is the relative permittivity of concrete, ${\epsilon }_0$ is the vacuum permittivity, and $E$ is the field strength at the location of the concrete.

2.3. The LC Electromagnetic Oscillation

To measure the internal stress of concrete, a sensing unit and circuit are designed based on the principle of displacement current. The sensing unit consists of two metal plates that form a capacitor. The purpose of this method is to apply an electric field to the concrete and detect changes in the internal electric field of the concrete when it is subjected to stress. The feedback information is processed through the LC electromagnetic resonance circuit.

According to the characteristics of the LC circuit, the energy loss during resonance can be ignored at low frequencies, and the resonance frequency can be expressed as$$\begin{array}{}\text{(3)}& f=\frac{1}{2\pi \sqrt{LC}}.\end{array}$$

The LC electromagnetic oscillation circuit is composed of an inductor and a capacitor in parallel. Upon connecting to the power supply, the capacitor starts to charge, and the field strength between the plates increases with the collection of charges. After completion, the capacitor begins to discharge due to the presence of the inductor. After the voltage across the inductor reaches the maximum, the capacitor discharge is completed, and the cycle repeats to form a resonance.

3. The Relationship Between Oscillation Frequency and Internal Stress

The schematic diagram of the buried sensing unit is illustrated in Figure 1. The sensing unit is regarded as a capacitive model and a fixed inductance in parallel to form an LC resonance circuit, as shown in Figure 2. Under the action of load, the displacement current between the two plates is influenced by the polarization and deformation of the concrete medium, and its effect appears as a frequency signal through the LC circuit.

[figure(s) omitted; refer to PDF]

After the circuit is energized, the charges on the two metal plates can be regarded as evenly distributed on the plates. Assuming that the electric field intensity on any plane parallel to the two metal plates is equal to the electric field intensity at the central axis of the metal plates, the microelement shown in Figure 3 is utilized. The method calculates the field strength at a distance $x$ from a single metal plate.

[figure(s) omitted; refer to PDF]

Divide the circular metal plate into a collection of several charged thin rings, and take charge elements on the rings.$$\begin{array}{}\text{(4)}& dq=\frac{q}{2\pi r}d\lambda ,\end{array}$$where $q$ is the amount of charge on the thin ring and $r$ is the radius of the ring.

The electric field intensity of the charge element on the axis of the point $A$ is$$\begin{array}{}\text{(5)}& d{E}_{\mathrm{x}}=\frac{dq}{4\pi a^2{\epsilon }_0{\epsilon }_{\mathrm{r}}}\cos \theta .\end{array}$$

The field strength of the ring at point $A$ is$$\begin{array}{}\text{(6)}& E_{\mathrm{A}}=\int d{E}_{\mathrm{x}}=\frac{q}{4\pi {\epsilon }_0{\epsilon }_{\mathrm{r}}}\cdot \frac{x}{{x^2+r^2}^{3/2}}.\end{array}$$

According to the equation, the electric field intensity of the micro ring in the circular metal plate at point $A$ is$$\begin{array}{}\text{(7)}& d{E}_{\text{plate}}=\frac{x}{4\pi {\epsilon }_0{\epsilon }_{\mathrm{r}}{x^2+r^2}^{3/2}}\frac{Q}{\pi R^2}2\pi r\cdot dr,\end{array}$$where $R$ is the radius of the circular metal pole plate, $Q$ is the amount of charge on the pole plate, and $r$ is the radius of the micro ring.

Then the field strength of the circular metal plate on the central axis is$$\begin{array}{}\text{(8)}& E_{\text{plate}}={\iint }_{\mathrm{S}}d{E}_{\text{plate}}=\frac{Q}{2\pi R^2{\epsilon }_0{\epsilon }_{\mathrm{r}}}gx,\end{array}$$where $gx=1-\frac{x}{\sqrt{x^2+R^2}}$.

Considering the two circular metal plates with equal charges shown in Figure 4, the total electric field at any position between the plates can be expressed as

[figure(s) omitted; refer to PDF]

$$\begin{array}{}\text{(9)}& E_{\text{Total}}=\frac{Q}{2\pi R^2{\epsilon }_0{\epsilon }_{\mathrm{r}}}gx+gd-x.\end{array}$$

The potential difference between the two metal plates are$$\begin{array}{}\text{(10)}& V={\int }_0^d{E}_{\text{Total}}dx.\end{array}$$

For the metal plate capacitance in the circuit,$$\begin{array}{}\text{(11)}& C=\frac{Q}{V}.\end{array}$$

When the concrete is under stress, substituting Equation (10) into Equation (11) results in a change in the distance between the plates from $d$ to $d+\Delta d$, yielding the capacitance between the plates as$$\begin{array}{}\text{(12)}& C=\frac{\pi R^2{\epsilon }_0{\epsilon }_{\mathrm{r}}}{d+\Delta d+R-\sqrt{{d+\Delta d}^2+R^2}}.\end{array}$$

According to Hooke’s law, the increase in the distance between the plates, $\Delta d$, in Equation (12) can be represented by the initial distance $d$ between the plates, the elastic modulus $Y$, and the stress $\sigma$, that is,$$\begin{array}{}\text{(13)}& \Delta d=\frac{\sigma }{Y}d.\end{array}$$

By substituting Equation (13) into Equation (12), the relationship between the capacitance and stress between the plates is obtained. Further, substituting this into Equation (3) yields the relationship between the stress of the concrete and the oscillation frequency. Note that once the parameters of the concrete material and the electrode are fixed, only two unknowns, $\Delta d$ and ${\epsilon }_{\mathrm{r}}$, remain in Equation (12), with all other physical quantities being constants. That is, Equation (3) can be expressed as$$\begin{array}{}\text{(14)}& f=f\sigma ,{\epsilon }_{\mathrm{r}}.\end{array}$$

To date, the relationship between the internal stress state of the concrete and the oscillation frequency has been established.

As the age increases, the free water inside the concrete structure is consumed, the degree of cement hydration in the concrete continues to increase, and the proportion of hydration products increases, resulting in changes in the dielectric constant and volume ratio of each component in the mixture. Since the dielectric constant of water is much larger than other media in concrete, according to the dielectric model of mixed media, the dielectric constant of concrete will continue to decrease until the hydration rate reaches a slow level or the hydration process ends, and the dielectric constant will stabilize [34].

4. Experiments

4.1. Experimental Preparation

4.1.1. Preparation of Sensing Unit

The sensor unit’s preparation process comprises two steps: assembly and insulation, depicted in Figures 5 and 6.

[figure(s) omitted; refer to PDF]

During assembly, a T2 copper plate, 1 mm thick and 17 mm in diameter, serves as the dielectric plate. As Figure 5a illustrates, the plate features five 1-mm diameter holes, four for securing the copper plate’s position and one for wiring. After soldering the lead to the copper plate, four insulating screws are used to maintain an 8 mm gap between the two copper plates. The contact position of the copper plate is temporarily secured with quick-drying glue, as shown in Figure 5b. Figure 5c displays the completed sensor unit assembly.

During the insulation process, each of the sensor unit’s two copper plates is sequentially wrapped with epoxy resin for insulation, as depicted in Figure 6a. After insulation, check the sensor unit, as shown in Figure 6b. Any uninsulated areas on the copper plate are addressed by adding more epoxy resin until the entire sensor unit is fully insulated. Figure 6c presents the final, fully insulated sensor unit.

4.1.2. Making Concrete Specimens

Prepare six C40 concrete cube specimens with dimensions of 150 mm × 150 mm × 150 mm, as shown in Figure 7. The mix ratio is cement: water: sand: gravel = 1 : 0.39 : 1.29 : 2.88, and the cement is enabled of No. 425 standard Portland cement, locally produced medium coarse sand, and gravel. When making the test piece, the sensing unit is vertically embedded in the center of the test block. For number 6 test pieces, 1#, 2#, and 3# test blocks are used for structural compression test, 1#–6# are used for monitoring test, and 3# test blocks are made with the same batch of concrete used to test the compressive strength experiment. Each concrete specimen underwent 7 days curing period under standard curing conditions.

[figure(s) omitted; refer to PDF]

4.2. Experimental Process

4.2.1. Experiments on Age and Frequency

The degree of hydration of cement is closely linked to age, and the degree of hydration determines the polarization of the concrete medium. The experiment reflects the effect of medium polarization on concrete monitoring by monitoring the relationship between age and frequency. During the experiment, record the monitoring frequency of the sensor unit before and on the 0, 2, 7, 10, 17, and 25 days after the concrete is embedded.

4.2.2. Experiment on Stress and Frequency

The purpose of the experiment is to explore the response relationship between the stress and frequency of the concrete after being stressed and test the feasibility of applying this technology to the internal stress monitoring of the concrete.

Take the specimens cured for 7 days for compressive test, as showed in Figures 8–10.

[figure(s) omitted; refer to PDF]

Perform a compressive strength test on three pieces of concrete to determine the standard compressive strength of this batch of specimens, and then take 1/3 of the standard compressive strength as the maximum compressive load strength of 1#, 2#, and 3# specimens to ensure that 1#–3# specimens are compressed in the elastic range. The test piece was preloaded in the elastic range for three times for a loading speed of 5 kN/s, before the formal experiment. In the test, the specimen was first preloaded to 5 kN. It was then loaded to 205 kN with a step size of 40 kN. Record the frequency of LC circuit under each force value. Perform three compression test cycles.

4.3. Experimental Data

To study the effect of the dielectric polarization of the concrete on the monitoring frequency, the recorded ages and corresponding circuit response frequencies are summarized in Table 1. Figure 11 shows the frequency changes with age.

[figure(s) omitted; refer to PDF]

Table 1

Monitoring frequency of specimens at different ages.

Age (d)	Frequency of each test piece (Hz)
	1#	2#	3#	4#	5#	6#
Before embedding	772,775	787,391	770,369	769,924	767,276	782,916
0	492,493	510,356	538,086	467,345	481,434	506,600
2	510,416	507,304	551,620	477,204	503,467	522,063
7	559,831	543,543	555,440	497,319	547,906	525,932
10	555,197	526,239	557,699	514,585	549,247	529,869
17	563,749	533,356	561,843	526,962	552,983	546,563
25	566,137	539,434	557,798	537,504	556,278	554,406

To explore the feasibility and practical effects of this monitoring technology, compression tests were carried out on the 1#, 2#, and 3# test blocks embedded with the sensing unit. The stress and response frequency data of each test piece obtained are shown in Tables 2–4. The stress and frequency data for the three specimens are plotted in Figure 12, and the data for each specimen are fitted. The fitting diagrams are shown in Figure 13.

[figure(s) omitted; refer to PDF]

Table 2

Experimental data-1#.

Stress (MPa)	Measuring frequency (Hz)						Standard deviation	Error (%)	Average (Hz)
	Load 1	Unload 1	Load 2	Unload 2	Load 3	Unload 3
0.22	553,278	552,998	553,127	552,968	552,947	552,868	134.73	0.0244	553,031
2.00	552,686	552,472	552,776	552,742	552,726	552,602	102.95	0.0186	552,667
3.78	552,558	552,416	552,684	552,576	552,311	552,526	119.45	0.0216	552,512
5.56	552,465	552,385	552,332	552,345	552,232	552,265	76.36	0.0138	552,337
7.33	552,215	552,237	552,240	552,190	552,100	552,160	48.88	0.0089	552,190
9.11	552,186	552,186	552,145	552,145	552,005	552,005	77.49	0.0140	552,112

Table 3

Experimental data-2#.

Stress (MPa)	Measuring frequency (Hz)						Standard deviation	Error (%)	Average (Hz)
	Load 1	Unload 1	Load 2	Unload 2	Load 3	Unload 3
0.22	520,232	520,208	520,295	520,247	520,431	520,352	77.01	0.0148	520,294
2.00	520,011	519,852	519,954	519,982	520,069	520,168	97.67	0.0188	520,006
3.78	519,883	519,661	519,758	519,912	519,997	519,926	112.75	0.0217	519,856
5.56	519,784	519,625	519,527	519,692	519,737	519,777	90.75	0.0175	519,690
7.33	519,576	519,585	519,545	519,484	519,619	519,669	57.62	0.0111	519,580
9.11	519,498	519,498	519,468	519,468	519,605	519,605	58.80	0.0113	519,524

Table 4

Experimental data-3#.

Stress (MPa)	Measuring frequency (Hz)						Standard deviation	Error (%)	Average (Hz)
	Load 1	Unload 1	Load 2	Unload 2	Load 3	Unload 3
0.22	554,802	554,705	555,051	554,966	554,898	554,854	111.31	0.0201	554,879
2.00	554,404	554,518	554,758	554,531	554,653	554,713	122.72	0.0221	554,596
3.78	554,302	554,239	554,402	554,494	554,596	554,474	119.96	0.0216	554,418
5.56	554,261	554,103	554,209	554,317	554,273	554,371	84.54	0.0153	554,256
7.33	554,002	554,062	554,127	554,236	554,167	554,319	105.20	0.0190	554,152
9.11	553,989	553,989	554,116	554,116	554,070	554,070	52.50	0.0095	554,058

5. Data Analysis

5.1. Analysis of Age-Frequency Data

Through the analysis of the age-frequency monitoring data, the frequency of the sensing unit is greatly reduced before and after being embedded in the concrete, as shown in the mutation segment of Figure 11. This is because the sensing unit is embedded with air as the dielectric between the plates. After filling the concrete between the plates, the medium polarization of the concrete has an obvious effect on the monitoring frequency.

As can be seen from Figure 11, from just after the concrete is poured to about 25 days of age, the monitoring frequency grows faster at the beginning and tends to level off at a later stage. Before the age of 10 days, the concrete has been curing, the water content in the structure is high, and the degree of hydration grows more, which leads to a greater change in the polarization characteristics of the concrete, and the dielectric constant decreases significantly, and the growth of the monitoring frequency is obvious. After the age of 10 days, the watering and curing are stopped, the outside world no longer provides water to the structure, the internal moisture content of the concrete decreases, the cement hydration rate slows down, the change in the dielectric constant of the concrete also decreases, and the monitoring frequency tends to stabilize.

5.2. Analysis of Stress and Frequency Data

As can be seen in Tables 2–4, the frequency repeatability errors measured from the start of loading to unloading to the initial stress are within 0.03% for all three sensing units. After each unloading, the frequency value is slightly lower than when loaded, as in Figure 12.

It can be observed in Figure 12 that as the stress increases, the output frequency of the monitoring circuit gradually decreases, and there is a good correlation between stress and frequency. Under the load, the concrete is deformed by compression. From Equation (13), the frequency decreases as the compressive stress increases. The theoretical analysis trend is consistent with the experimental results.

As shown by the force-frequency fitting diagrams in Figure 13, the actual amount of change in frequency during the experiments differs from that of the theoretical analysis. The reason for the analysis may be that the compression between the plates causes the tiny pores in the structure to close. The cement gel in the transition zone and the cement matrix are compressed, the volume of the concrete is reduced, and the change of the respective volume rate of the multiphase medium leads to the change of the polarization strength and dielectric constant of the concrete, resulting in this response to the monitoring frequency. This phenomenon will be further studied in the future.

5.3. Error Analysis

The data obtained from the three specimens were fitted, and the fitting formula was used as the core formula of the monitoring technique. The data calculated by the fitting formula were the monitored stress, the stress applied by the universal hydraulic press was the true stress, and the corresponding standard deviation was calculated and summarized in Table 5. To facilitate the comparison between the calculated stress and the true stress, the calculated stress and the true stress data are plotted in Figure 14.

[figure(s) omitted; refer to PDF]

Table 5

Comparison of true stress and calculated stress.

1#				2#				3#
Frequency (Hz)	True stress (MPa)	Calculated stress (MPa)	Standard deviation	Frequency (Hz)	True stress (MPa)	Calculated stress (MPa)	Standard deviation	Frequency (Hz)	True stress (MPa)	Calculated stress (MPa)	Standard deviation
553,031	0.2222	0.3840	0.08090	520,294	0.2222	0.4513	0.11455	554,879	0.2222	0.6073	0.19255
552,667	2.0000	2.2914	0.14570	520,006	2.0000	2.1397	0.06985	554,596	2.0000	2.2508	0.12540
552,512	3.7778	3.7107	0.03355	519,856	3.7778	3.7181	0.02985	554,418	3.7778	4.0205	0.12135
552,337	5.5556	5.7509	0.09765	519,690	5.5556	6.0231	0.23375	554,256	5.5556	6.1251	0.28475
552,190	7.3333	7.8234	0.24505	519,580	7.3333	7.8736	0.27015	554,152	7.3333	7.7242	0.19545
552,112	9.1111	9.0560	0.02755	519,524	9.1111	8.9146	0.09825	554,058	9.1111	9.3365	0.11270

By fitting the stress-frequency points for each sensing unit under three loading and unloading cycles, it can be found that the stress on the concrete has an exact function of the monitoring frequency. The stress-frequency equations of the three sensing units are approximately the same. R² of the fitted equations was 0.99323, 0.98748, and 0.99736, respectively, indicating that the sensing unit can output the stress information of concrete more stably under the load, and the correlation between stress and frequency is credible. The reason for some differences in the starting frequencies of each sensing unit in the equations is that the sensing unit is handmade and cannot achieve a high degree of uniformity. In the following research, this phenomenon can be avoided by using machined sensing units.

From the comparison chart of true stress and calculated stress, the calculated stress curves deviate from the true stress curve, indicating a certain error in the monitoring results. The smaller standard deviation in Table 5 indicates that the deviation between the true stress and the calculated stress is smaller. From a theoretical analysis point of view, the reason for the deviation of the calculated stress from the true stress may be that the uneven pores in the cement stone and the concrete transition zone are compressed and closed under the action of stress, which causes the change of the polarization effect of the concrete. In addition, due to the high sensitivity of the LC monitoring circuit, it does not rule out that external interference will affect the monitoring process.

6. Conclusions

This paper presents a method for detecting the internal stress of concrete structures based on the principle of displacement current, analyzes the dielectric polarization effect of concrete, combines the LC oscillation circuit to provide a method for detecting the internal stress of concrete, and carries out theoretical derivation and experimental analysis, reaching the following conclusions.

As the age of the concrete increases, the oscillation frequency first increases rapidly and then stabilizes, indicating that the faster the hydration rate, the smaller the dielectric constant of the concrete, and the growth of hydration changes the dielectric properties of the concrete. During the compression process of the specimen, the oscillation frequency decreases with the increase of compressive stress, and there is a good correlation between stress and oscillation frequency, which is consistent with the trend of the change in the oscillation frequency caused by the change of the stress in the theoretical analysis.

References

[1] F. P. Bos, C. Menna, M. Pradena, "The Realities of Additively Manufactured Concrete Structures in Practice," Cement and Concrete Research, vol. 156,DOI: 10.1016/j.cemconres.2022.106746, 2022.

[2] Y. Lecieux, E. Rozière, V. Gaillard, "Monitoring of a Reinforced Concrete Wharf Using Structural Health Monitoring System and Material Testing," Journal of Marine Science and Engineering, vol. 7 no. 4,DOI: 10.3390/jmse7040084, 2019.

[3] R. Davoudi, G. R. Miller, P. Calvi, J. N. Kutz, "Computer Vision–Based Damage and Stress State Estimation for Reinforced Concrete and Steel Fiber–Reinforced Concrete Panels," Structural Health Monitoring, vol. 19 no. 6, pp. 1645-1665, DOI: 10.1177/1475921719892345, 2020.

[4] P. A. Gaydeckp, F. M. Burdekin, "Nondestructive Testing of Reinforced and Pre-Stressed Concrete Structures," Nondestructive Testing and Evaluation, vol. 14 no. 6, pp. 339-392, DOI: 10.1080/10589759808953058, 1998.

[5] A. Castellano, A. Fraddosio, M. D. Piccioni, T. Kundu, "Linear and Nonlinear Ultrasonic Techniques for Monitoring Stress-Induced Damages in Concrete," Journal of Nondestructive Evaluation, Diagnostics and Prognostics of Engineering Systems, vol. 4 no. 4,DOI: 10.1115/1.4050354, 2021.

[6] Y. Xia, X. Lei, P. Wang, G. Liu, L. Sun, "Long-Term Performance Monitoring and Assessment of Concrete Beam Bridges Using Neutral Axis Indicator," Structural Control and Health Monitoring, vol. 27 no. 12,DOI: 10.1002/stc.2637, 2020.

[7] H. Zhu, Y. Hu, R. Ma, J. Wang, Q. Li, "Concrete Thermal Failure Criteria, Test Method, and Mechanism: A Review," Construction and Building Materials, vol. 283 no. 10,DOI: 10.1016/j.conbuildmat.2021.122762, 2021.

[8] I. Floris, J. M. Adam, P. A. Calderón, S. Sales, "Fiber Optic Shape Sensors: A Comprehensive Review," Optics and Lasers in Engineering, vol. 139,DOI: 10.1016/j.optlaseng.2020.106508, 2021.

[9] T. M. Kim, D.-H. Kim, M. K. Kim, Y. M. Lim, "Fiber Bragg Grating-Based Long-Gauge Fiber Optic Sensor for Monitoring of a 60m Full-Scale Prestressed Concrete Girder during Lifting and Loading," Sensors and Actuators A: Physical, vol. 252, pp. 134-145, DOI: 10.1016/j.sna.2016.10.037, 2016.

[10] V. M. Minutolo, L. Esposito, P. Ferla, S. Palladino, R. Zona, "Non Linear Strain Measures on Concrete Structures by Means of Embedded Optical Fiber Sensors," International Journal of Civil Engineering and Technology, vol. 10 no. 12, pp. 16-31, 2019.

[11] H. Wang, P. Xiang, L. Jiang, "Strain Transfer Theory of Industrialized Optical Fiber-Based Sensors in Civil Engineering: A Review on Measurement Accuracy, Design and Calibration," Sensors and Actuators A: Physical, vol. 285, pp. 414-426, DOI: 10.1016/j.sna.2018.11.019, 2019.

[12] J. Zhang, Y. Tian, C. Yang, "Vibration and Deformation Monitoring of a Long-Span Rigid-Frame Bridge With Distributed Long-Gauge Sensors," Journal of Aerospace Engineering, vol. 30 no. 2,DOI: 10.1061/(ASCE)AS.1943-5525.0000678, 2017.

[13] H.-N. Li, L. Ren, Z.-G. Jia, T.-H. Yi, D.-S. Li, "State-of-the-Art in Structural Health Monitoring of Large and Complex Civil Infrastructures," Journal of Civil Structural Health Monitoring, vol. 6 no. 1,DOI: 10.1007/s13349-015-0108-9, 2016.

[14] X. W. Ye, Y. Q. Ni, Y. X. Xia, "Distributed Strain Sensor Networks for in-Construction Monitoring and Safety Evaluation of a High-Rise Building," International Journal of Distributed Sensor Networks, vol. 8 no. 9, 2012.

[15] T. Wang, W. Zhou, "A Study on Dynamic Measurement Methods Based on Vibrating Wire Sensors," Measurement Science and Technology, vol. 30 no. 2, 2019.

[16] L. Peng, G. Jing, Z. Luo, X. Yuan, Y. Wang, B. Zhang, "Temperature and Strain Correlation of Bridge Parallel Structure Based on Vibrating Wire Strain Sensor," Sensors, vol. 20 no. 3,DOI: 10.3390/s20030658, 2020.

[17] H. M. Lee, J. M. Kim, K. Sho, H. S. Park, "A Wireless Vibrating Wire Sensor Node for Continuous Structural Health Monitoring," Smart Materials and Structures, vol. 19 no. 5,DOI: 10.1088/0964-1726/19/5/055004, 2010.

[18] S. Biswal, A. Ramaswamy, "Measurement of Existing Prestressing Force in Concrete Structures Through an Embedded Vibrating Beam Strain Gauge," Measurement, vol. 83, pp. 10-19, DOI: 10.1016/j.measurement.2016.01.031, 2016.

[19] S. Liu, Y. Sun, X. Jiang, Y. Kang, "A Review of Wire Rope Detection Methods, Sensors and Signal Processing Techniques," Journal of Nondestructive Evaluation, vol. 39 no. 4,DOI: 10.1007/s10921-020-00732-y, 2020.

[20] S. Hassani, U. Dackermann, "A Systematic Review of Advanced Sensor Technologies for Non-Destructive Testing and Structural Health Monitoring," Sensors, vol. 23 no. 4,DOI: 10.3390/s23042204, 2023.

[21] H. Shokravi, H. Shokravi, N. Bakhary, M. Heidarrezaei, S. S. Rahimian Koloor, M. Petrů, "Application of the Subspace-Based Methods in Health Monitoring of Civil Structures: A Systematic Review and Meta-Analysis," Applied Sciences, vol. 10 no. 10,DOI: 10.3390/app10103607, 2020.

[22] T. Zheng, M. Ardolino, A. Bacchetti, M. Perona, "The Applications of Industry 4.0 Technologies in Manufacturing Context: A Systematic Literature Review," International Journal of Production Research, vol. 59 no. 6, pp. 1922-1954, DOI: 10.1080/00207543.2020.1824085, 2021.

[23] J. Shao, M. Willatzen, T. Jiang, "Quantifying the Power Output and Structural Figure-of-Merits of Triboelectric Nanogenerators in a Charging System Starting From the Maxwell’s Displacement Current," Nano Energy, vol. 59, pp. 380-389, DOI: 10.1016/j.nanoen.2019.02.051, 2019.

[24] J. Shao, T. Jiang, W. Tang, X. Chen, L. Xu, Z. L. Wang, "Structural Figure-of-Merits of Triboelectric Nanogenerators at Powering Loads," Nano Energy, vol. 51, pp. 688-697, DOI: 10.1016/j.nanoen.2018.07.032, 2018.

[25] Z. L. Wang, "On the First Principle Theory of Nanogenerators From Maxwell’s Equations," Nano Energy, vol. 68,DOI: 10.1016/j.nanoen.2019.104272, 2020.

[26] Y. Chen, Y. Jie, N. Wang, Z. L. Wang, X. Cao, "Novel Wireless Power Transmission Based on Maxwell Displacement Current," Nano Energy, vol. 76,DOI: 10.1016/j.nanoen.2020.105051, 2020.

[27] G. Xu, X. Li, X. Xia, J. Fu, W. Ding, Y. Zi, "On the Force and Energy Conversion in Triboelectric Nanogenerators," Nano Energy, vol. 59, pp. 154-161, DOI: 10.1016/j.nanoen.2019.02.035, 2019.

[28] J. Roche, "The Present Status of Maxwell’s Displacement Current," European Journal of Physics, vol. 19 no. 2, pp. 155-166, DOI: 10.1088/0143-0807/19/2/009, 1998.

[29] J. D. Jackson, "Maxwell’s Displacement Current Revisited," European Journal of Physics, vol. 20 no. 6, pp. 495-499, DOI: 10.1088/0143-0807/20/6/315, 1999.

[30] A. P. French, J. R. Tessman, "Displacement Currents and Magnetic Fields," American Journal of Physics, vol. 31 no. 3, pp. 201-204, DOI: 10.1119/1.1969359, 1963.

[31] Y. Song, R. L. Lysak, "Displacement Current and the Generation of Parallel Electric Fields," Physical Review Letters, vol. 96 no. 14,DOI: 10.1103/PhysRevLett.96.145002, 2006.

[32] D. A. Koleva, O. Copuroglu, K. van Breugel, G. Ye, J. H. W. de Wit, "Electrical Resistivity and Microstructural Properties of Concrete Materials in Conditions of Current Flow," Cement and Concrete Composites, vol. 30 no. 8, pp. 731-744, DOI: 10.1016/j.cemconcomp.2008.04.001, 2008.

[33] T. Wu, R. Huang, M. Chi, T. Weng, "A Study on Electrical and Thermal Properties of Conductive Concrete," Computers and Concrete, vol. 12 no. 3, pp. 337-349, DOI: 10.12989/cac.2013.12.3.337, 2013.

[34] K. Roth, R. Schulin, H. Flühler, W. Attinger, "Calibration of Time Domain Reflectometry for Water Content Measurement Using a Composite Dielectric Approach," Water Resources Research, vol. 26 no. 10, pp. 2267-2273, DOI: 10.1029/WR026i010p02267, 1990.