# Strength Correlation and Prediction of Engineered Cementitious Composites with Microwave Properties
## 1 Introduction
This is attributed to the high magnetization reactance and high core loss of the transformer at high frequencies. In this paper, the authors propose a microwave near-field detecting approach to monitor the development of microstructure of CBM via the change of effective conductance during early-age hydration, where the degree of hydration relates to concrete's temperature response [17]. Moreover, the changes in the conductivity of hardening CBM are known to be the outcomes of microstructure development in the hydrating CBM. The CBM can be considered as a homogenous dielectric slab with an effective complex permittivity (\(\varepsilon_{c}=\varepsilon^{\prime}-j\varepsilon^{\prime\prime}\)). Dispersion in CBM is mainly due to the presence of liquid phase, which is actually a water solution of salts and chemical compounds sourcing from the cement components. According to the extended Debye model of dielectric materials, the imaginary part takes account of the energy losses due to the dielectric relaxation and the effective electrical conductivity (\(\sigma_{eff}\)) of CBM, and is given by [18]  
\[\varepsilon_{eff}^{\prime\prime}(\omega)=\frac{\sigma_{eff}(\omega)}{\omega}= \frac{\sigma_{dc}}{\omega}+\frac{\omega\tau\Delta\varepsilon}{1+\omega^{2} \tau^{2}}, \tag{1}\]  
where \(\sigma_{dc}\) is the dc conductivity, and \(\Delta\varepsilon=\varepsilon_{dc}-\varepsilon_{\infty}\) is the difference between values of the real part of the complex relative permittivity at very low and very high frequency, respectively, and \(\tau\) is the relaxation time in second (s) whereas \(\omega\) is the angular frequency in s\({}^{-1}\). From (1), it is known that the four-probe direct resistivity measurement method may only account for part of bulk conductivity, namely, the dc conductivity of CBM during hydration. Moreover, the losses due to dielectric relaxation and dipole polarization are not to be included in the transformer non-contact measurement method because a low frequency (10 kHz) was used [14; 15]. Nondestructive microwave near-field detecting techniques have remarkable applications, such as estimating compressive strength [19] and cure-state monitoring of CBM [20; 21]. The chosen microwave frequency allows electromagnetic (EM) energy to penetrate deeper into the specimen [21; 22], and hence a near-field technique at a microwave frequency of 2 GHz was used in this study. The goal was to measure the bulk effective conductance that accounted for all types of loss in order to monitor the development of microstructure of CBMs under the influence of various water-to-cement ratios [21; 23]. The objectives and applications of the aforementioned studies were to make compressive strength of CBM predictable and improve monitoring efficiency at early ages of the materials. However, these studies were largely focused on the traditional materials like concrete, mortar, and or cement paste, with less attention on the new type of cement composites. With the advent of ultra-ductile fiber-reinforced composites like engineered cementitious composite (ECC) [24; 25], substantial developments in commercialization and research of ECC technologies have materialized both in the academic and industrial communities [26; 27; 28]. ECC uses moderate amount of polyvinyl alcohol (PVA) fiber in volume fraction of 2%, but offers tensile ductility several hundred times higher than the conventional CBMs [25]. The present study developed two correlation models between compressive strength and effective electrical conductance measured at early ages. The goal was to monitor the strength evolution by means of early-age conductance and hence to predict the final compressive strength under influence of initial water-to-binder (\(w/b\)) ratios. It is known that compressive and flexural strengths of ECC are sensitive to initial water content at all ages. However, PVA fibers are hydrophilic material so they absorb water and provide a strong interfacial bond with the cementitious matrix and thereby have a favorable effect on strength development.