This research presents a new mathematical framework for the optimal design of elliptical isolated footings under vertical load and two orthogonal moments. The suggested method considers the spatial variation of contact pressure between the footing and the supporting soil, facilitating an accurate representation of structural requirements. New formulations for bending moment, unidirectional shear, and punching shear are generated using volume integration, accurately representing the complex stress distribution beneath elliptical foundations. Lagrange multipliers are utilized to identify the crucial points of maximum and minimum contact stresses for elliptical and circular footing shapes. A thorough numerical analysis illustrates the benefits of the suggested strategy by contrasting its results with those of a conventional design methodology. The findings demonstrate that the newly created model produces more cost-effective designs while maintaining structural integrity and performance, underscoring its potential as a significant asset in engineering practice. A MATLAB code for design using new formulas is programmed and results obtained to those from literature and were more efficient and economic.

This paper presents a reliability analysis of circular footings on unsaturated soils. Two methods were used to capture the unsaturated soil behavior: implementing two elastoplastic constitutive models, including the Barcelona Basic Model (BBM) and the Sun Model (SM), which are explicitly proposed for unsaturated soils, and incorporating the apparent cohesion in the Mohr-Coulomb Model (MCM). The effect of soil suction on the bearing capacity of circular footings was investigated. It was shown that for low values of suction, the bearing capacities obtained from MCM were higher than those obtained from BBM and SM. However, as suction increased, MCM tended to predict lower bearing capacities. In practice, geotechnical engineers are still concerned with the measurement and determination of suction as a key stress state variable of unsaturated soils. In this context, the Monte Carlo simulation technique has been incorporated into numerical modeling for the investigation of the effect of suction uncertainties on the bearing capacity. Uncertainties associated with the suction value were modeled as normally and log-normally distributed random variables. It was shown that assuming a normal distribution for suction resulted in slightly lower probabilistic bearing capacity values (i.e., more conservative design) compared to the log-normal distributions. The results emphasized the important role of the coefficient of variation (COV) of suction in determining the probabilistic bearing capacity. A negative linear correlation was observed between the COV of suction and the probabilistic bearing capacity. Finally, a simple relationship was proposed to estimate the probabilistic bearing capacity of the circular footing in an unsaturated soil when its deterministic value and the COV of suction are known.

Environmental vibrations produced often by industrial and construction processes can affect adjacent soils and structures, sometimes resulting in foundation failure and structural damage. The application of confined cells under foundations as a mitigation technique against dynamic sources, such as generators, is investigated in this study. Numerical models were developed using Plaxis 3D software to simulate the effect of a vibrating source on a circular footing, both with and without confined cells filled with sand soil at varying depths and diameters. In these cells, the soil modeling considered compaction loads typical in actual construction conditions. Results indicate that placing a minimum-diameter cell closer to the foundation with adequate penetration depth can significantly enhance dynamic response and reduce subgrade deformation. The effectiveness of confined soil in minimizing displacement amplitude in the foundation is evaluated, revealing an impressive 86% reduction with specific cell dimensions (Hc/D = 0.50 and Dc/D = 1.15). Moreover, peak particle velocity and excess pore water pressure at monitored points in the surrounding environment experience reductions of 62% and 87%, respectively, demonstrating substantial vibration attenuation. The study does effectively highlight the novelty of the confined sand cell approach, positioning it as a more targeted, efficient, and cost-effective alternative to existing methods, especially for conditions where large-scale, deep vibrations are a concern.