As materials degrade over time and traffic loads increase, monitoring the structural health of concrete infrastructures has become crucial. Structural health monitoring (SHM) and non-destructive evaluation (NDE) techniques are gaining attention for their role in maintaining the functionality and safety of these structures. One of the most effective methods is tracking stress changes in concrete, as it allows engineers to detect potential weaknesses and address them proactively, thus preventing catastrophic failures and improving safety. To monitor these changes, bulk wave-based acoustoelasticity is chosen for its promise in long-term monitoring and tracking of internal stress distributions.

However, applying bulk wave-based acoustoelasticity to concrete presents significant challenges. These challenges arise from three main areas: data processing techniques, acoustoelastic theory, and heterogeneity of concrete. First, there is limited research on data processing techniques for extracting bulk wave properties specific to concrete, resulting in a gap in understanding how these techniques apply to this material. Second, the existing acoustoelastic theory is primarily developed for scenarios where bulk waves propagate parallel or orthogonal to the principal deformation directions. This focus limits its applicability to concrete, where the principal deformation directions often vary under different loading conditions. Third, the meso-scale heterogeneity of concrete causes strong interactions between bulk waves, at frequencies of around a hundred kilohertz, and heterogeneities within the concrete. These interactions, known as scattering, significantly impact the propagation and spatial distribution of bulk waves, making interpretation challenging. This dissertation explores solutions to these challenges and offers a theoretical framework for engineers and researchers to monitor stress and strain changes in concrete using acoustoelasticity.

Our investigation into data processing techniques focuses on retrieving two categories of bulk wave properties from experiments: travel time changes and diffusive properties. We use wave interferometry techniques to measure travel time changes resulting from stress changes, comparing the wavelet cross-spectrum (WCS) technique and the stretching technique. The results show consistency in the velocity changes retrieved by both techniques. For diffusive properties like diffusivity and dissipation, we fit these proper-ties through the diffusion equation. Adjustments are made to account for boundary effects by incorporating reflected energy from so-called image sources.

We further revisit the current acoustoelastic theory to address bulk waves propagating at angles to the principal deformation directions. Our findings reveal that while shear strains have a minimal impact on longitudinal wave velocities, they significantly affect transverse wave velocities. Based on this, we propose a simplified acoustoelastic ex-pression for inclined propagating ballistic waves, primarily longitudinal, in a plane stress state, and validate it experimentally.

Understanding acoustoelastic theory alone is insufficient for interpreting travel time changes of diffuse waves in concrete; the energy ratio between longitudinal and trans-verse waves is also crucial. To address this, we propose a bulk wave energy transport model to estimate this energy ratio based on the angular frequency of bulk waves, the volume fraction of coarse aggregates, and the characteristic radius of these aggregates. The validity of the proposed model is confirmed by comparing theoretical diffusivities with experimental values, which are fitted from the diffusion equation while accounting for boundary reflections.

To investigate travel time changes of diffuse bulk waves, we integrate the previously discussed acoustoelastic theory with the bulk wave energy transport model. The energy transport model estimates the energy ratio between longitudinal and transverse waves and the time required for this ratio to equilibrate. Using Monte Carlo simulations in conjunction with acoustoelastic theory, we estimate the travel time changes for diffuse longitudinal and transverse waves. These estimates are then weighted by the energy ratio to predict travel time changes, which are compared with experimental observations retrieved using the WCS techniques.

This dissertation provides a theoretical foundation for applying bulk wave-based acoustoelasticity to concrete. Additionally, the revisited acoustoelastic theory may be applicable to other compressible, statistically isotropic solids, such as metals. The scattering theory-based model also offers a valuable tool for investigating scatterer proper-ties in concrete.