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Accurate characterization of the response of coastal structures when subjected to tsunami-like waves is important for structural engineering assessment and design. The weakly-compressive Smoothed Particle Hydrodynamic (SPH) model can theoretically investigate such phenomena in both horizontal and vertical directions. Yet, the convergence of the solutions is sensitive to physical and numerical parameters used in the modeling. In this paper, multiple three- and two-dimensional SPH models are used to study the numerical convergence of free-surface elevation solutions for various initial inter-particle distances, domain locations along the flume and vicinity of the structure, and unbroken and broken wave flow conditions. The results are used to infer on the trade-offs between the accuracy of the SPH solutions and computational costs of the simulations, including computing time and data storage requirements. Two-dimensional models and an approximate ratio of ten particles per wave height can reasonably predict the nonturbulent unbroken wave case. The broken wave case requires three-dimensional models and four times the ratio of particles per wave height. A correlation between experimental and numerical results is then performed, showing adequacy of the free-surface elevation converged SPH models to capture global force responses. The distribution of horizontal and vertical pressures exerted on the elevated structure are characterized and compared with an analytical equation derived from the experimental dataset, highlighting the symbiotic relationship between experimental data, for calibration of the models, and numerical insights, for physical setup design. For example, additional instruments should be placed at strategic locations in future experimental programs to further validate numerical local responses, such as pressures near the edges and corners of structures. Such insights are important to support future work and development of updated US and European guidelines for the design of overland built infrastructures.