Terahertz Time-Domain Spectroscopy for Non-Contact Porosity Estimation and Hydration Assessment of Hardened Cement Paste

This study presents a systematic terahertz time-domain spectroscopy (THz-TDS) investigation of hardened cement paste, framed as a complex-optical measurement in which the real and imaginary parts of the response probe distinct microstructural attributes. Transmission-mode measurements were made on pastes with water-to-cement (w/c) ratios of 0.3, 0.4, and 0.5 at curing ages of 7, 14, 28, and 56 days. The effective refractive index, obtained from the time-domain pulse delay (7, 28, and 56 days, paired with mercury intrusion porosimetry), correlates strongly and linearly with porosity over nine porosity-paired conditions spanning 15.1–30.4% (pooled R2 = 0.94, p < 0.001). In a quasi-static effective-medium framework—where the pores a re far smaller than the THz wavelength—this reflects the dependence of the effective permittivity on the solid volume fraction: the Bruggeman model outperforms the Maxwell–Garnett model, and all data fall within the Wiener bounds, lying close to the upper bound, indicating a continuously connected solid matrix with isolated pores. Cross-validated porosity estimation is reliable to within about ±2 percentage points (refractive-index uncertainty ±0.02–0.04). The absorption follows a power law (β ≈ 1.0–1.3) characteristic of disorder-activated vibrational absorption, in which the loss of long-range order in the amorphous C–S–H relaxes the crystalline selection rules and couples the THz field to the full vibrational density of states. The refractive index (structure-sensitive, governed by volume fraction) and the absorption (material-sensitive, governed by solid disorder; estimated loss tangent of order 0.1) thus form two complementary channels. Combining the THz-derived porosity with the Powers hydration model gives a degree of hydration consistent with literature ranges—an indirect comparison rather than direct validation. These results establish THz-TDS as a non-contact, non-ionizing technique for rapid porosity estimation and hydration assessment of cementitious materials.