Influence of Axial Load on Electromechanical Impedance (EMI) of Embedded Piezoceramic Transducers in Steel Fiber Concrete

With the advantages of high tensile, bending, and shear strength, steel fiber concrete structures have been widely used in civil engineering. The health monitoring of concrete structures, including steel fiber concrete structures, receives increasing attention, and the Electromechanical Impedance (EMI)-based method is commonly used. Structures are often subject to changing axial load and ignoring the effect of axial forces may introduce error to Structural Health Monitoring (SHM), including the EMI-based method. However, many of the concrete structure monitoring algorithms do not consider the effects of axial loading. To investigate the influence of axial load on the EMI of a steel fiber concrete structure, concrete specimens with different steel fiber content (0, 30, 60, 90, 120) (kg/m3) were casted and the Lead Zirconate Titanate (PZT)-based Smart Aggregate (SA) was used as the EMI sensor. During tests, the step-by-step loading procedure was applied on different steel fiber content specimens, and the electromechanical impedance values were measured. The Normalized root-mean-square deviation Index (NI) was developed to analyze the EMI information and evaluate the test results. The results show that the normalized root-mean-square deviation index increases with the increase of the axial load, which clearly demonstrates the influence of axial load on the EMI values for steel fiber concrete and this influence should be considered during a monitoring or damage detection procedure if the axial load changes. In addition, testing results clearly reveal that the steel fiber content, often at low mass and volume percentage, has no obvious influence on the PZT’s EMI values. Furthermore, experiments to test the repeatability of the proposed method were conducted. The repeating test results show that the EMI-based indices are repeatable and there is a great linearity between the NI and the applied loading.


Introduction
Distributed short steel fibers in concrete hinder the expansion of microcracks and the formation of macroscopic cracks [1], enhancing the crack resistance of concrete. Steel fiber concrete has been widely used in important projects, such as tunnels, subways, airports, and seismic engineering. The health monitoring of steel fiber concrete structures, like that of other concrete structures, is receiving increasing attention. evaluate the degradation level of the rock bolt pre-stress. Bhalla et al. [41] proposed a new approach for fatigue life assessment of bolted steel joints using the equivalent stiffness determined by surface-bonded piezo-impedance transducers. Previously developed impedance models were revisited by Yun et al. [42] to investigate the effects of sensor and/or bonding defects on the admittance measurement. The feasibility of the modified impedance model for sensor self-diagnosis using the admittance measurements was demonstrated by a series of parametric studies using a simple example of PZT-driven single-degree-of-freedom spring-mass-damper system. Yang et al. [43] presented an electromechanical impedance (EMI) model for health monitoring of cylindrical shell structures to investigate the interaction between the PZT transducers and a typical cylindrical shell structure.
The influence of axial force on piezoceramic-transducer-based monitoring is crucial for evaluation the health status of structures. The pitch-catch method was employed by Liu et al. [44] to measure the amplitude and velocity of active sensing signals during the loading process. The experimental results demonstrated that the load variation within elastic range still has a significant effect on monitoring signals using an SA-based monitoring system. However, the influence of the axial load on the commonly used EMI-based approach for steel fiber concrete structures has not been studied, to the authors' best knowledge.
In this paper, the authors proposed to experimentally study the influence of the axial load on EMI-based damage or SHM of steel fiber structures. In addition, the influence of steel fiber content on the EMI values will also be experimentally studied. Standard concrete cube specimens (150 mm × 150 mm × 150 mm) with five different steel fiber contents (0, 30, 60, 90, 120) (kg/m 3 ) were casted. For each fiber content, three specimens were fabricated. The strength of the concrete specimens is 50 Mpa. The EM impedance signals were recorded at the axial force values of 0, 20, 40, 60, 80, and 100 kN, which ensured the specimens deformed within the elastic range of strains. The elastic loading range prevents damage to the steel fiber concrete specimens and narrows the influencing factor to only the axial load for a test period when the load is increased from 0 to 100 kN. A smart aggregate with a 15 mm × 15 mm × 1 mm PZT patch as its sensing core was embedded in each specimen for the EMI measurement. During each test period, the PZT EMI measurements were acquired through an impedance analyzer. Testing results clearly demonstrated that the axial load greatly influences the EMI value and the effect of axial load should be considered for EMI-based structural health monitoring of concrete structures. Experimental results also clearly revealed that the fiber content, normally at a small mass and volume percentage, has no obvious effect on the EMI values.

Smart Aggregate (SA)
Shown in Figure 1a is the configuration of a PZT-based smart aggregate (SA). The core of the SA is a waterproofed PZT patch with electrical connecting wires. The dimension of the PZT patch is 15 mm × 15 mm × 1 mm. The PZT patch is sandwiched between two marble blocks, which offer protection to the fragile PZT patch. The height and diameter of the smart aggregates are 20 mm and 25 mm, respectively. Figure 1b shows a photo of the fabricated SA with the connecting wire and a connector. With this configuration, SA can be embedded into a concrete structure and survive the harsh vibration process. The direct and converse piezoelectric effect make the PZT-based smart aggregate suitable for sensing and actuation applications, including active sensing and impedance-based for concrete structure health monitoring. For example, Kong et al. [45] presented research on very-early-age concrete hydration characterization by using piezoceramic-based smart aggregates. Du et al. [46] used SA to monitor quartz Sand-Filled Steel Tube Column (SFSTC) internal stress during impacts.

Electromechanical Impedance (EMI) Method
For EMI-based damage detection, a PZT transducer is often embedded in or surface-bonded to a structure. Damage to a structure will often cause the change of its physical properties, such as mass, stiffness, damping, and boundary conditions, and this change will alter the energy transfer between the PZT and host structure [37]. The coupling effect between the host structure and the PZT transducer can be detected by the PZT's electromechanical impedance (EMI) in the high-frequency range (typically >20 kHz). In this study, the PZT-based Smart Aggregate was embedded into the steel fiber concrete specimen. As shown in Figure 2, a one-degree-of-freedom spring-mass-damper electromechanical system is used to illustrate the coupling effect between the PZT transducer and the steel fiber concrete specimen. The electromechanical impedance (EMI) and the electric admittance are reciprocal to each other. In the PZT-transducer-driven, single-degree-of-freedom mass-stiffness-damping system, the Z(ω), which is the impedance of the piezo-transducer coupled to the host structure, is given by where  is the angular frequency of excitation; i is the imaginary unit; wA, hA, and lA are the width, thickness, and length of the PZT patch, respectively;  33 is the complex permittivity when the PZT stress is zero or a constant; d32 is the piezoelectric constant; and 22 E Y is the complex Young's modulus at zero or constant electric field. Please note that the complex Young's modulus includes a real part that is called the elastic Young's modulus, and an imaginary part that is called the loss Young's modulus. ZA and ZS represent the electromechanical impedance of PZT and the structure, respectively. Assuming that the mechanical properties of the PZT patch do not vary during the

Electromechanical Impedance (EMI) Method
For EMI-based damage detection, a PZT transducer is often embedded in or surface-bonded to a structure. Damage to a structure will often cause the change of its physical properties, such as mass, stiffness, damping, and boundary conditions, and this change will alter the energy transfer between the PZT and host structure [37]. The coupling effect between the host structure and the PZT transducer can be detected by the PZT's electromechanical impedance (EMI) in the high-frequency range (typically >20 kHz). In this study, the PZT-based Smart Aggregate was embedded into the steel fiber concrete specimen. As shown in Figure 2, a one-degree-of-freedom spring-mass-damper electromechanical system is used to illustrate the coupling effect between the PZT transducer and the steel fiber concrete specimen.

Electromechanical Impedance (EMI) Method
For EMI-based damage detection, a PZT transducer is often embedded in or surface-bonded to a structure. Damage to a structure will often cause the change of its physical properties, such as mass, stiffness, damping, and boundary conditions, and this change will alter the energy transfer between the PZT and host structure [37]. The coupling effect between the host structure and the PZT transducer can be detected by the PZT's electromechanical impedance (EMI) in the high-frequency range (typically >20 kHz). In this study, the PZT-based Smart Aggregate was embedded into the steel fiber concrete specimen. As shown in Figure 2, a one-degree-of-freedom spring-mass-damper electromechanical system is used to illustrate the coupling effect between the PZT transducer and the steel fiber concrete specimen. The electromechanical impedance (EMI) and the electric admittance are reciprocal to each other. In the PZT-transducer-driven, single-degree-of-freedom mass-stiffness-damping system, the Z(ω), which is the impedance of the piezo-transducer coupled to the host structure, is given by where  is the angular frequency of excitation; i is the imaginary unit; wA, hA, and lA are the width, thickness, and length of the PZT patch, respectively;  33 is the complex permittivity when the PZT stress is zero or a constant; d32 is the piezoelectric constant; and 22 E Y is the complex Young's modulus at zero or constant electric field. Please note that the complex Young's modulus includes a real part that is called the elastic Young's modulus, and an imaginary part that is called the loss Young's modulus. ZA and ZS represent the electromechanical impedance of PZT and the structure, respectively. Assuming that the mechanical properties of the PZT patch do not vary during the The electromechanical impedance (EMI) and the electric admittance are reciprocal to each other. In the PZT-transducer-driven, single-degree-of-freedom mass-stiffness-damping system, the Z(ω), which is the impedance of the piezo-transducer coupled to the host structure, is given by where ω is the angular frequency of excitation; i is the imaginary unit; w A , h A , and l A are the width, thickness, and length of the PZT patch, respectively; ε 33 is the complex permittivity when the PZT stress is zero or a constant; d 32 is the piezoelectric constant; and Y E 22 is the complex Young's modulus at zero or constant electric field. Please note that the complex Young's modulus includes a real part that is called the elastic Young's modulus, and an imaginary part that is called the loss Young's modulus. Z A and Z S represent the electromechanical impedance of PZT and the structure, respectively. Assuming that the mechanical properties of the PZT patch do not vary during the measurement procedure, Equation (1) shows that the electrical impedance of the PZT patch is directly related to the structure's impedance [47]. Axial force causes changes in the structure's mechanical impedance, thus changing local dynamic features. Based on the EMI information measured by the impedance analyzer, the root-mean-square deviation of the impedance real part (RMSD R ) is used in this paper, as indicated by where Z R i is the ith measurement of the EMI real part signal at a certain frequency range, and Z R N is the real part of the EMI signal under the same frequency range in the nondestructive state.

Steel Fiber Concrete Specimens
The cube specimens were composed of 50 MPa strength concrete with different steel fiber content (0, 30, 60, 90, 120) (kg/m 3 ). The stress wave propagation velocity in the 50 MPa strength concrete structure is about 4000 m/s. The concrete mix proportion is shown in Table 1. End-hook-type steel fibers, as shown in Figure 3, were used in this research, and the detailed technical information of the steel fibers is shown in Table 2. The content of the concrete specimens and the groups of specimens are shown in Table 3. The dimension of the specimens was 150 mm × 150 mm × 150 mm. The steel fiber concrete specimens were fabricated in the lab in accordance with the fiber concrete specimen mixing standards: "Technology specification for application of fiber-reinforced concrete and steel-fiber-reinforced concrete". For each specimen, one smart aggregate was embedded in the steel fiber concrete specimen, as shown in Figure 4. The SA is located along the center line of the specimen, 25 mm below the top surface. All test specimens were cured in a standard condition for 28 days and then moved into the lab for testing.  (1) shows that the electrical impedance of the PZT patch is directly related to the structure's impedance [47]. Axial force causes changes in the structure's mechanical impedance, thus changing local dynamic features. Based on the EMI information measured by the impedance analyzer, the root-mean-square deviation of the impedance real part (RMSDR) is used in this paper, as indicated by where R i Z is the ith measurement of the EMI real part signal at a certain frequency range, and R N Z is the real part of the EMI signal under the same frequency range in the nondestructive state.

Steel Fiber Concrete Specimens
The cube specimens were composed of 50 MPa strength concrete with different steel fiber content (0, 30, 60, 90, 120) (kg/m 3 ). The stress wave propagation velocity in the 50 MPa strength concrete structure is about 4000 m/s. The concrete mix proportion is shown in Table 1. End-hook-type steel fibers, as shown in Figure 3, were used in this research, and the detailed technical information of the steel fibers is shown in Table 2. The content of the concrete specimens and the groups of specimens are shown in Table 3. The dimension of the specimens was 150 mm × 150 mm × 150 mm. The steel fiber concrete specimens were fabricated in the lab in accordance with the fiber concrete specimen mixing standards: "Technology specification for application of fiber-reinforced concrete and steel-fiber-reinforced concrete". For each specimen, one smart aggregate was embedded in the steel fiber concrete specimen, as shown in Figure 4. The SA is located along the center line of the specimen, 25 mm below the top surface. All test specimens were cured in a standard condition for 28 days and then moved into the lab for testing.

Experimental Setup
The instrumentation setup, mainly including the impedance analyzer, is shown in Figure 5. The entire test setup is shown is Figure 6, which shows that an electric universal loading machine with a capacity of 100 kN was used to load the concrete specimens. A step-by-step load was used in this study to increase the axial load to the specimens. The Agilent 4294A (Agilent Technologies, Santa Clara, CA, USA) precision impedance analyzer produced by Agilent Technologies, was used to measure the impedance signals, the frequency range of which is from 40 Hz to 110 MHz. The excitation frequency in the range of 10 kHz to 500 kHz was chosen in the test. Too low a frequency range is not sensitive to tiny damages in the structures, while too high a frequency range causes PZT to be too sensitive to temperature and boundary conditions, which can affect the judgment of damage information [48].

Experimental Setup
The instrumentation setup, mainly including the impedance analyzer, is shown in Figure 5. The entire test setup is shown is Figure 6, which shows that an electric universal loading machine with a capacity of 100 kN was used to load the concrete specimens. A step-by-step load was used in this study to increase the axial load to the specimens. The Agilent 4294A (Agilent Technologies, Santa Clara, CA, USA) precision impedance analyzer produced by Agilent Technologies, was used to measure the impedance signals, the frequency range of which is from 40 Hz to 110 MHz. The excitation frequency in the range of 10 kHz to 500 kHz was chosen in the test. Too low a frequency range is not sensitive to tiny damages in the structures, while too high a frequency range causes PZT to be too sensitive to temperature and boundary conditions, which can affect the judgment of damage information [48].
The baseline impedance signals of all steel fiber concretes were recorded before applying any load. The load was applied on each specimen according to the designed step-by-step load schedule. As shown in Figure 7, the step loads include 0, 20, 40, 60, 80, and 100 kN, and the largest loading value of 100 kN is less than 10% of the failure load of 50 MPa concrete cube specimens; therefore, the strain is within the elastic range. During each load increasing stage, the loading rate was taken as 100 N/s. During this load increasing stage, three EMI measurements were taken at the beginning, the middle, and the end of each stage. Then, the load was kept at a constant for 600 s, during which there are seven measured points and 100 s delay between each measured point. The step-by-step loading strategy is shown in Figure 7.
Clara, CA, USA) precision impedance analyzer produced by Agilent Technologies, was used to measure the impedance signals, the frequency range of which is from 40 Hz to 110 MHz. The excitation frequency in the range of 10 kHz to 500 kHz was chosen in the test. Too low a frequency range is not sensitive to tiny damages in the structures, while too high a frequency range causes PZT to be too sensitive to temperature and boundary conditions, which can affect the judgment of damage information [48].  The baseline impedance signals of all steel fiber concretes were recorded before applying any load. The load was applied on each specimen according to the designed step-by-step load schedule. As shown in Figure 7, the step loads include 0, 20, 40, 60, 80, and 100 kN, and the largest loading value of 100 kN is less than 10% of the failure load of 50 MPa concrete cube specimens; therefore, the strain is within the elastic range. During each load increasing stage, the loading rate was taken as 100 N/s. During this load increasing stage, three EMI measurements were taken at the beginning, the middle, and the end of each stage. Then, the load was kept at a constant for 600 s, during which there are seven measured points and 100 s delay between each measured point. The step-by-step loading strategy is shown in Figure 7.  The baseline impedance signals of all steel fiber concretes were recorded before applying any load. The load was applied on each specimen according to the designed step-by-step load schedule. As shown in Figure 7, the step loads include 0, 20, 40, 60, 80, and 100 kN, and the largest loading value of 100 kN is less than 10% of the failure load of 50 MPa concrete cube specimens; therefore, the strain is within the elastic range. During each load increasing stage, the loading rate was taken as 100 N/s. During this load increasing stage, three EMI measurements were taken at the beginning, the middle, and the end of each stage. Then, the load was kept at a constant for 600 s, during which there are seven measured points and 100 s delay between each measured point. The step-by-step loading strategy is shown in Figure 7.

Experimental Results and Discussion on Influence of Axial Load on EMI
The step-by-step loading schedule was applied to steel fiber concrete specimens within the elastic range. We purposely chose step-by-step loading so that we could measure the impedance value at a steady state to minimize the dynamic effect. For each loading value, the impedance information of the smart aggregate was directly acquired by the impedance analyzer. The real parts of the impedance for Specimens 1-1, 2-1, 3-1, 4-1, and 5-1 over the frequency range of 10 kHz to 500 kHz were recorded and plotted in Figure 8, which clearly shows that with the increase of the axial

Experimental Results and Discussion on Influence of Axial Load on EMI
The step-by-step loading schedule was applied to steel fiber concrete specimens within the elastic range. We purposely chose step-by-step loading so that we could measure the impedance value at a steady state to minimize the dynamic effect. For each loading value, the impedance information of the smart aggregate was directly acquired by the impedance analyzer. The real parts of the impedance for Specimens 1-1, 2-1, 3-1, 4-1, and 5-1 over the frequency range of 10 kHz to 500 kHz were recorded and plotted in Figure 8, which clearly shows that with the increase of the axial load, the EMI value increases. Therefore, the axial load has an influence on the EMI value. Specifically, the central frequencies of Specimens 1-1, 2-1, 3-1, 4-1, and 5-1 are 175 kHz, 174 kHz, 178 kHz, 175 kHz, and 170 kHz, respectively. With the increasing axial forces, the central frequencies shift little. This is caused by the high stiffness and small geometric size. On the other hand, with the increase of the steel fiber content (0, 30, 60, 90, 120) (kg/m 3 ), as shown in Figure 8a-e, no clear trend of change of the EMI can be observed. Hence, the steel fiber content has no clear impact on the EMI value, which is reasonable since the steel fiber content in terms of mass or volume percentage is very small. In addition, the steel fibers have very small cross-sectional area.   In all cases in Figure 9, the normalized RMSD indices (NI) increase with the loading value, which is consistent with the finding from Figure 8. It should be noted that the normalized RMSD index in the same mix seems to vary to some degree at the same load level, as shown in Figure 9. There are two main reasons for this: (1) concrete is notorious for its inconsistent properties and uncertainties; and (2) the steel fiber concrete is an anisotropic material. In this research, for each case of fiber content, we have three specimens. It is not surprising for us to see differences among the specimens for each case. The important observation is that all specimens show a clear and similar trend. As an important finding of this research, if an impedance-based index is used for structural health monitoring, the index should be corrected by subtracting the increase caused by the applied load. To address the issue of discrepancy, for practice, we will calculate the mean value of the specimens with the same fiber content, and this mean value will be used for the correction. A future work will be the study of the discrepancy among the specimens with the same fiber content. where i denotes the ith loading condition in the experiment; I w RMSD is the RMSD index of the specimen without loading applied; I l RMSD is the RMSD index with the largest load applied; and I i RMSD is the RMSD index at the ith loading condition. The normalized results are shown in Figure 9.
In all cases in Figure 9, the normalized RMSD indices (NI) increase with the loading value, which is consistent with the finding from Figure 8. It should be noted that the normalized RMSD index in the same mix seems to vary to some degree at the same load level, as shown in Figure 9. There are two main reasons for this: (1) concrete is notorious for its inconsistent properties and uncertainties; and (2) the steel fiber concrete is an anisotropic material. In this research, for each case of fiber content, we have three specimens. It is not surprising for us to see differences among the specimens for each case. The important observation is that all specimens show a clear and similar trend. As an important finding of this research, if an impedance-based index is used for structural health monitoring, the index should be corrected by subtracting the increase caused by the applied load. To address the issue of discrepancy, for practice, we will calculate the mean value of the specimens with the same fiber content, and this mean value will be used for the correction. A future work will be the study of the discrepancy among the specimens with the same fiber content.  In addition, as shown in Figure 9, there is no clear trend in how the fiber content impacts the normalized RMSD index. It is clear that the steel fiber content has no clear impact on the EMI value. In this research, the excitation frequency is in the range of 10 kHz to 500 kHz. The 500 kHz wave has the shortest wave length, 0.008 m or 8 mm, which is obtained by dividing the wave velocity of 4000 m/s by the frequency of 500,000 Hz. We used the fact that the stress wave propagation velocity in the 50 MPa strength concrete structure is about 4000 m/s. Since the profile of the fiber is very small (0.75 mm in diameter) as compared with the shortest wave length of the stress wave (8 mm), the fiber content will have very little impact on the stress wave propagation.
It should be noticed that in Figure 9h,k, the normalized RMSD index (NI) was missing for 40 kN and 20 kN, respectively. The reason for this is that these two impedance signals were acquired during the unstable axial loading stages. Severe drift of impedance signals occurred at 40 kN and 20 kN. Therefore, the two curves cannot be used in calculating the normalized RMSD index (NI).

Observations and Discussions
Experimental results clearly demonstrated that the axial load greatly influences the EMI value and the effect of axial load should be considered for EMI-based structural health monitoring of concrete structures. Experimental results also clearly revealed that the fiber content, normally at a small mass and volume percentage, has no obvious effect on the EMI values.
To investigate the influence of axial load on concrete, Liu et al. [44] proposed the pitch-catch method to measure the voltage amplitude and the velocity of the monitoring signals during the loading steps. In their experiments, there was no consistent relationship between amplitudes and unloading steps for different specimens or monitoring signals when step-by-step loads were applied on the specimens. However, as shown in Figure 9, the normalized RMSD index (NI)-based impedance method can monitor the loading process well with different steel fiber content (0, 30, 60, 90, 120) (g/m 3 ). Therefore, it is more reasonable to use electrical impedance to study the influence of axial force on the voltage amplitude. In this research, the loading is along the axial direction and the loading level is relatively small to ensure the elastic response of the specimen. In reality, the loading may be complex and loading levels may be large and sometimes damage the steel fiber structures. For the next step, we will investigate the feasibility of electromechanical impedance (EMI)-based damage monitoring of steel fiber concrete structures. In addition, we will study the effectiveness of SA-enabled EMI in a complex state of stresses.

Additional Experiments to Study Repeatability of the Proposed Method
In order to demonstrate the repeatability and reliability of the proposed technique, additional experiments were conducted. A new specimen with 90 kg/m 3 steel fiber content was casted, as shown in Figure 10. It was cured in a standard condition for 28 days and then moved into the lab for testing. In addition, as shown in Figure 9, there is no clear trend in how the fiber content impacts the normalized RMSD index. It is clear that the steel fiber content has no clear impact on the EMI value. In this research, the excitation frequency is in the range of 10 kHz to 500 kHz. The 500 kHz wave has the shortest wave length, 0.008m or 8 mm, which is obtained by dividing the wave velocity of 4000 m/s by the frequency of 500,000 Hz. We used the fact that the stress wave propagation velocity in the 50 MPa strength concrete structure is about 4000 m/s. Since the profile of the fiber is very small (0.75 mm in diameter) as compared with the shortest wave length of the stress wave (8 mm), the fiber content will have very little impact on the stress wave propagation.
It should be noticed that in Figure 9h and Figure 9k, the normalized RMSD index (NI) was missing for 40 kN and 20 kN, respectively. The reason for this is that these two impedance signals were acquired during the unstable axial loading stages. Severe drift of impedance signals occurred at 40 kN and 20 kN. Therefore, the two curves cannot be used in calculating the normalized RMSD index (NI).

Observations and Discussions
Experimental results clearly demonstrated that the axial load greatly influences the EMI value and the effect of axial load should be considered for EMI-based structural health monitoring of concrete structures. Experimental results also clearly revealed that the fiber content, normally at a small mass and volume percentage, has no obvious effect on the EMI values.
To investigate the influence of axial load on concrete, Liu et al. [44] proposed the pitch-catch method to measure the voltage amplitude and the velocity of the monitoring signals during the loading steps. In their experiments, there was no consistent relationship between amplitudes and unloading steps for different specimens or monitoring signals when step-by-step loads were applied on the specimens. However, as shown in Figure 9, the normalized RMSD index (NI)-based impedance method can monitor the loading process well with different steel fiber content (0, 30, 60, 90, 120) (g/m 3 ). Therefore, it is more reasonable to use electrical impedance to study the influence of axial force on the voltage amplitude. In this research, the loading is along the axial direction and the loading level is relatively small to ensure the elastic response of the specimen. In reality, the loading may be complex and loading levels may be large and sometimes damage the steel fiber structures. For the next step, we will investigate the feasibility of electromechanical impedance (EMI)-based damage monitoring of steel fiber concrete structures. In addition, we will study the effectiveness of SA-enabled EMI in a complex state of stresses.

Additional Experiments to Study Repeatability of the Proposed Method
In order to demonstrate the repeatability and reliability of the proposed technique, additional experiments were conducted. A new specimen with 90 kg/m 3 steel fiber content was casted, as shown in Figure 10. It was cured in a standard condition for 28 days and then moved into the lab for testing.   The test procedure was the same as that detailed in Section 3.2. Nine repeated experiments were conducted and the impedance-based normalized RMSD index was also calculated according to Equation (2). The impedance-based normalized RMSD index is shown in Figure 11. The test procedure was the same as that detailed in Section 3.2. Nine repeated experiments were conducted and the impedance-based normalized RMSD index was also calculated according to Equation (2). The impedance-based normalized RMSD index is shown in Figure 11. As shown in Figure 11, the repeated testing results demonstrate that the normalized RMSD indices vary within a small range for different loading cases. The largest discrepancy is no more than 10%, which is in the loading case of 60 kN. The repeated experimental results clearly show the repeatability of the proposed method.
In order to demonstrate the reliability of the proposed method, data fitting was conducted for the nine repeated experimental results as shown in Figure 12. The linear fitting formula f(x) = 0.009854x + 0.04817 can be obtained. The R-squared value is 0.9919, which means that there is a good linearity between the normalized RMSD index and loading value. These results can be good evidence for the good reliability of the proposed method.
It should be noted that the distribution of steel fibers in steel fiber concrete is uneven [49]. The uneven distribution of steel fiber may cause the RMSD value discrepancy of different specimens with same steel fiber content. In addition, the proprieties of dielectricity and piezoelectricity of each smart aggregate are not the same. Therefore, although with the same steel fiber content, the sensibility of each smart aggregate is different. The above experimental results demonstrated that, for one specific smart aggregate, the stability and good linearity show that the proposed technique has good repeatability and reliability. For field implementation, each smart aggregate will be individually calibrated to obtain the relationship between the EMI value and the applied load. As shown in Figure 11, the repeated testing results demonstrate that the normalized RMSD indices vary within a small range for different loading cases. The largest discrepancy is no more than 10%, which is in the loading case of 60 kN. The repeated experimental results clearly show the repeatability of the proposed method.
In order to demonstrate the reliability of the proposed method, data fitting was conducted for the nine repeated experimental results as shown in Figure 12. The test procedure was the same as that detailed in Section 3.2. Nine repeated experiments were conducted and the impedance-based normalized RMSD index was also calculated according to Equation (2). The impedance-based normalized RMSD index is shown in Figure 11. As shown in Figure 11, the repeated testing results demonstrate that the normalized RMSD indices vary within a small range for different loading cases. The largest discrepancy is no more than 10%, which is in the loading case of 60 kN. The repeated experimental results clearly show the repeatability of the proposed method.
In order to demonstrate the reliability of the proposed method, data fitting was conducted for the nine repeated experimental results as shown in Figure 12. The linear fitting formula f(x) = 0.009854x + 0.04817 can be obtained. The R-squared value is 0.9919, which means that there is a good linearity between the normalized RMSD index and loading value. These results can be good evidence for the good reliability of the proposed method.
It should be noted that the distribution of steel fibers in steel fiber concrete is uneven [49]. The uneven distribution of steel fiber may cause the RMSD value discrepancy of different specimens with same steel fiber content. In addition, the proprieties of dielectricity and piezoelectricity of each smart aggregate are not the same. Therefore, although with the same steel fiber content, the sensibility of each smart aggregate is different. The above experimental results demonstrated that, for one specific smart aggregate, the stability and good linearity show that the proposed technique has good repeatability and reliability. For field implementation, each smart aggregate will be individually calibrated to obtain the relationship between the EMI value and the applied load. The linear fitting formula f(x) = 0.009854x + 0.04817 can be obtained. The R-squared value is 0.9919, which means that there is a good linearity between the normalized RMSD index and loading value. These results can be good evidence for the good reliability of the proposed method.
It should be noted that the distribution of steel fibers in steel fiber concrete is uneven [49]. The uneven distribution of steel fiber may cause the RMSD value discrepancy of different specimens with same steel fiber content. In addition, the proprieties of dielectricity and piezoelectricity of each smart aggregate are not the same. Therefore, although with the same steel fiber content, the sensibility of each smart aggregate is different. The above experimental results demonstrated that, for one specific smart aggregate, the stability and good linearity show that the proposed technique has good repeatability and reliability. For field implementation, each smart aggregate will be individually calibrated to obtain the relationship between the EMI value and the applied load.

Conclusions and Future Work
This paper addressed two important issues related to PZT-enabled electromechanical impedance (EMI)-based structural health monitoring of steel fiber concrete structures. The first is how the axial load affects the EMI values and the second is how the steel fiber content impacts the EMI values. To address these two issues, 50 MPa strength concrete cube specimens (150 mm × 150 mm × 150 mm) with different steel fiber content (0, 30, 60, 90, 120) (kg/m 3 ) were fabricated and tested under the axial loads of 0, 20, 40, 60, 80, and 100 kN, which ensured the specimens deformed within the elastic range of strains. The elastic loading range prevents damage to the steel fiber concrete specimens and narrows the influencing factor to only the axial load for a test period when the load is increased from 0 kN to 100 kN. Each specimen was equipped with an embedded smart aggregate with a 15 mm × 15 mm × 1 mm PZT patch as its core. During each test period, the PZT EMI measurements were acquired through an impedance analyzer. Experimental results clearly demonstrated that the axial load greatly influences the EMI value and the effect of axial load should be considered for EMI-based structural health monitoring of concrete structures. Experimental results also clearly revealed that the fiber content, normally at a small mass and volume percentage, has no obvious effect on the EMI values. Experiments to test the repeatability of the proposed method were conducted. The repeating test results show that the EMI-based indices are repeatable and there is a great linearity between the NI and the applied loading. As an important finding of this research, if an impedance-based index is used for structural health monitoring, the index should be corrected by subtracting the increase caused by the applied load. To address the issue of discrepancy in practice, we will calculate the mean value of the specimens with the same fiber content, and this mean value will be used for the correction. Future work will be the study of the discrepancy among specimens with the same fiber content. For the next step, we will investigate the feasibility of electromechanical impedance (EMI)-based steel fiber concrete structure damage monitoring. It will be an interesting topic for future work to study the effect of loading rate or unloading rate on the impedance response. In addition, we will study the effectiveness of SA-enabled EMI in a complex state of stresses.