**1. Introduction**

The prestressed concrete bridge is widely used in bridge construction because of its advantages of sizeable structural stiffness, smooth driving, and low maintenance cost [1]. Vertical prestressed rebar is used to provide vertical compressive stress to the reinforcement by post-tensioned method. The effect of vertical prestressed rebar can make the shear load capacity of the structure significantly increase by 95% [2]. However, the elongation of vertical prestressed rebar is slight during vertical prestressing tensioning in construction. Therefore, the prestress loss caused by rebar retraction is significant [3]. Furthermore, the loss of vertical prestress has an important influence on the principal tensile stress of the box girder web [4]. Once the vertical prestress is lost and the web cracks, the bridge structure's safety and durability will be affected [5–7]. Therefore, the vertical prestressed rebar working stress must be accurately monitored to ensure the structure's safety.

To avoid prestress detection affecting the structure's durability, nondestructive testing methods are usually used [8]. Commonly used methods are the strain method, electromagnetic resonance method, the stiffness method, the ultrasonic guided wave method, the eddy current method, and the magnetoelastic method. The strain method is based on the stress–strain relationship. The test is carried out by pasting electronic strain gauges or embedded sensors, and then converting the stress. Sawicki [9] successfully identified

**Citation:** Xia, J.; Zhang, S.; Liao, L.; Liu, H.; Sun, Y. Working Stress Measurement of Prestressed Rebars Using the Magnetic Resonance Method. *Buildings* **2023**, *13*, 1416. https://doi.org/10.3390/ buildings13061416

Academic Editor: Roberto Capozucca

Received: 21 April 2023 Revised: 24 May 2023 Accepted: 29 May 2023 Published: 30 May 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the stress of rebars by using strain gauges installed on rebars and distributed optical fiber sensors for strain detection. However, this method is susceptible to temperature and has low durability. The electromagnetic resonance method connects the steel strand analog inductor to the oscillation circuit and calculates the stress by measuring the oscillation frequency of the circuit with a frequency meter. Cui [10] measured the stress of prestressed concrete beams by the electromagnetic resonance method and obtained the functional relationship between resonance frequency increment and stress increment. However, rebars cannot simulate the inductance due to their different configurations, so this method is unsuitable for rebar stress monitoring. The stiffness method measures the frequency of the anchorage zone of the exposed section of the rebar and then infers the magnitude of the prestress [11]. Zhong has conducted much research on the measurement of rebar tension by the stiffness method and achieved specific results [12,13]. However, this method is susceptible to boundary conditions and is only suitable for stress measurement during construction [14]. The ultrasonic guided wave method measures stress by the acoustoelastic effect. Chen [15] used single-source high-frequency cylindrical guided waves to improve the accuracy of the ultrasonic guided wave method. The ultrasonic guided wave method has a rapid energy attenuation rate due to the bonding between rebar and concrete, so the method's reliability needs to be improved. It can be seen that the existing methods are not suitable for rebar stress monitoring, or the detection accuracy needs to be further improved. Therefore, the monitoring of working stress of rebar still needs further study.

The magnetoelastic effect indicates that the magnetism of ferromagnetic material changes with its stress. Based on the magnetoelastic effect, scholars have conducted much research and proposed the eddy current and magnetoelastic methods. The eddy current method realizes stress monitoring through the relationship between sensor impedance and stress [16]. To improve the eddy current sensor's performance, Xiu [17] designed a sleeve structure to reduce the loss of magnetic field and provide a higher permeability path. Alonso [18] used an eddy current sleeve structure and phase shift measurements to detect the stress in iron-based materials. Liang [19] found that the magnetoelastic method is more suitable for stress monitoring than the eddy current method.

The magnetoelastic method uses the magnetoelastic effect to monitor the change of magnetization intensity to obtain the magnitude of stress. Due to its advantages of noncontact, high sensitivity, and robustness, the method is considered a promising nondestructive stress monitoring method [20]. According to their different structural forms, magnetoelastic sensors can be divided into U-type sensors, permanent magnet magnetization sensors, and sleeve sensors. Joh [21] designed a U-shaped sensor to measure the magnitude of prestress. Deng [22] used the static magnetization of the permanent magnet to replace the magnetization of the coil. However, the U-shaped sensor and the permanent magnet magnetization sensor are unsuitable for monitoring vertical prestress due to the irregular excitation structure and large size. The sleeve magnetoelastic sensor uses the coil as the excitation element and the sensing element. The monitoring object is used as the coil core. This method has the advantages of a clear magnetic circuit and less magnetic field leakage [23]. To optimize the sleeve sensor, Duan [24] proposed an intelligent elastomagnetic (EME) sensor by replacing the secondary coil with a laminated composite magnetic sensor. Due to its large size and high functional requirements, the sensor is mainly used for cable force detection. Zhang [25] simplified the primary coil and induction unit of the EM sensor into self-inductive coils, then proposed a magnetoelastic inductance method using weak magnetic excitation. The magnetoelastic inductance method has the advantages of reducing the sensor size and reducing the power supply demand. However, the low sensitivity of this method affects the accuracy of stress monitoring. Therefore, the sensor needs to be optimized.

Kurs [26] first proposed the magnetic resonance theory, which improves the transmission efficiency of the coil-based energy transmission system. To improve the working performance of the sensor, magnetic resonance theory is introduced into the sensor field. Hughes [27] studied the enhancement effect of resonant coupling on eddy current sensors

and improved the sensitivity of corrosion damage detection. The magnetoelastic sensor is also composed of the coil as the main component. To improve the sensor's sensitivity, Zhang [28] introduced the magnetic resonance theory into the magnetoelastic effect method. He proposed the resonance enhanced magnetoelastic method (REME) and verified the feasibility of this method for monitoring the stress of steel strands. However, as a hotrolled low-carbon steel structure, the rebar's section form, initial magnetization state, and stress–strain relationship differ from those of the steel strand, resulting in different stress identification. In addition, the advantage of small size of the magnetic resonance sensor meets the pre-embedded requirement of vertical prestressed rebar and can be applied in post-tensioned pipeline [29]. Therefore, monitoring the working stress of the rebar by REME needs further study.

Based on the existing research, this paper combined the magnetoelastic effect, electromagnetic induction law, and magnetic resonance effect. A working stress monitoring method for vertical prestressed rebar was proposed using the magnetic resonance sensor. Firstly, the relationship between sensor induced voltage and rebar stress was analyzed. Then, working stress monitoring experiments under different working conditions were carried out on rebars with different diameters. According to the experiment results, the nonlinear relationship between the induced voltage peak-to-peak values and the prestress was analyzed. Based on the experiment data, the correlation between the characteristic indicator and the rebar working stress was obtained by nonlinear fit and linear fit. According to the relationship, the working stress was accurately evaluated, and the feasibility of the proposed method was verified.
