## 1 Introduction  
Reinforced concrete (RC) is one of the most widely used modern building materials. Natural disasters, such as earthquakes or strong ground motions, degrade RC column members. The health of a structure that includes such members must be evaluated immediately following an extreme event to provide fundamental structural information regarding building safety. Throughout the service life of a building, its structural performance must be monitored and its residual seismic or serviceability capacity must be measured. Structural health monitoring (SHM) for RC column members is part of these processes. Generally, confirmation of the safety and integrity of building structures depends on the accuracy and precision of nondestructive testing (NDT) methods, such as visual inspection (VT), acoustic emission (AE), ultrasonic testing (UT), infrared and thermal testing (IR), and others. Although NDT is practical, it has some limitations, such as the impossibility of testing a dangerous structure or one close to failure, dependence on the skills of the operator of the test instruments, and the prohibitive time required for large-scale building evaluations. In recent decades, piezoelectric sensors have become popular SHM instruments for use in concrete buildings because of their low cost, responsiveness, active/passive sensing, ease of use, and versatility ([PERSON] and [PERSON] [1]). [PERSON] et al. [2] grouped piezoelectric materials into four categories based on their structural characteristics: ceramic, single crystal, polymer, and composite (combining a polymer with a single crystal or ceramic). The traditionally used piezoelectric compound is barium titanate (BaTiO\({}_{3}\)), which has been replaced by PZT (Lead Zirconate Titanate), which have greater sensitivity and a higher operating temperature. An interesting phenomenon that arises from the accumulation of electric charge in certain solid materials under applied mechanical stress is the reversible piezoelectricity. Generally, the piezoelectric effect means that when PZT ceramic is deformed, an internal measurable electric charge is generated. Conversely, the dimensions of this material are changed by applying an external electric field; this behavior is called the inverse piezoelectric effect. Equation (1) describes the positive piezoelectric effect of a sensor and Equation (2) describes the inverse piezo-effect of the actuator. Equations (1) and (2) are the fundamental equations for piezoelectric materials. \[D=d^{T}+\varepsilon^{T}E \tag{1}\]  
\[S=s^{E}T+dE \tag{2}\]  
where \(D\) is the electrical displacement; \(d\) is the piezoelectric deformation constant; \(T\) is the stress field; \(\varepsilon^{T}\) is the dielectric permittivity; \(E\) is the electrical field; \(S\) is the strain field; and \(s^{E}\) is the elastic coefficient. [PERSON] et al. [3] studied the monitoring of the health of circular concrete columns to determine their structural performance under earthquake loading by analyzing the responses of piezoelectric ceramic transducers. [PERSON] et al. [4] observed the structural damage status, including the degree and location of cracking damage, of in situ SHM using post-embedded piezoelectric sensors on RC bridge piers in Taiwan under reversed cyclic excitation. [PERSON] et al. [5] investigated the effectiveness of piezoceramic transducers for monitoring structural health and developed a damage level index for multi-story RC frame structures in a shake table test. [PERSON] and [PERSON] [1] studied the properties of structurally damaged RC shear walls with shear failure using the receptivity of piezoceramic transducers under reversed cyclic loading. Recently, [PERSON] et al. [6] applied the SHM method to post-installed shear walls in an RC frame under seismic excitation, and they used post-embedded piezoelectric sensors to identify surface deterioration around the boundary connections among structural elements of retrofitted walls, columns, beams, and foundations.