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In the construction of engineering structures, deep foundations, such as piles or wells, are commonly employed in continuous clayey soils at considerable depths. However, their utilization is often hindered by the associated high costs and time requirements. Shallow foundations are generally unsuitable due to substantial consolidation settlements. Ground improvement techniques, crucial in contemporary civil engineering projects, offer viable alternatives. Pre-Fabricated Vertical Drains (PVDs) expedite dewatering, accelerating the consolidation process in clayey soils. Additionally, stone columns enhance soil strength and expedite consolidation. This study explores the feasibility of shallow foundations like Isolated/Raft/box foundations employing ground improvement techniques such as PVDs and stone columns in clayey soils. Various properties of clayey soil, coupled with the impact on soil and Safe Bearing Capacity (SBC) at diverse depths utilizing PVDs and stone columns with distinct lengths and diameters, constitute the analytical focus. Numerical methods, specifically employing PLAXIS Software, facilitate a comprehensive examination. Results indicate that, for the prescribed settlement criteria, the Safe Bearing Capacity experienced a notable increase. This underscores the effectiveness of employing PVDs and stone columns as ground improvement techniques for enhancing the stability and performance of shallow foundations in clayey soils.

The bearing capacity of shallow foundation is significantly affected by stratum uncertainty, mainly including geological uncertainty and spatial variability of soil properties. This paper aims to develop a general framework of shallow foundation to characterize the influence of two types of uncertainties on bearing capacity quantitatively. The geological uncertainty is simulated by Markov random field with different borehole schemes. The spatial variability is characterized using random field theory considering variations of the vertical scale of fluctuation. The bearing capacity of shallow foundation analysis is then conducted based on the proposed calculation framework. Borehole data and soil properties collected from Shenzhen Mawan are adopted as an example to illustrate the proposed framework. A reduction factor is developed to reveal the relationship of two category uncertainties on bearing capacity. A contribution rate indicator is defined to quantitatively evaluate the impact of two category uncertainties. Results show that the geological uncertainty greatly influences the calculation results when boreholes are sparse. However, spatial variability dominates in two kinds of uncertainties when having relatively more boreholes.

Calculation of the bearing capacity of shallow foundations on rock masses is usually addressed either using empirical equations, analytical solutions, or numerical models. While the empirical laws are limited to the particular conditions and local geology of the data and the application of analytical solutions is complex and limited by its simplified assumptions, numerical models offer a reliable solution for the task but require more computational effort. This research presents an artificial neural network (ANN) solution to predict the bearing capacity due to general shear failure more simply and straightforwardly, obtained from FLAC numerical calculations based on the Hoek and Brown criterion, reproducing more realistic configurations than those offered by empirical or analytical solutions. The inputs included in the proposed ANN are rock type, uniaxial compressive strength, geological strength index, foundation width, dilatancy, bidimensional or axisymmetric problem, the roughness of the foundation-rock contact, and consideration or not of the self-weight of the rock mass. The predictions from the ANN model are in very good agreement with the numerical results, proving that it can be successfully employed to provide a very accurate assessment of the bearing capacity in a simpler and more accessible way than the existing methods.

A collection of feed forward neural networks (FNN) for estimating the limit pressure load and the according displacements at limit state of a footing settlement is presented. The training procedure is through supervised learning with error loss function the mean squared error norm. The input dataset is originated from Monte Carlo simulations for a variety of loadings and stochastic uncertainty of the material of the clayey soil domain. The material yield function is the Modified Cam Clay model. The accuracy of the FNN’s is in terms of relative error no more than 10 - 5 and this applies to all output variables. Furthermore, the epochs of the training of the FNN’s required for construction are found to be small in amount, in the order of magnitude of 90,000, leading to an alleviated data cost and computational expense. The input uncertainty of Karhunen Loeve random field sum appears to provide the most detrimental values for the displacement field of the soil domain. The most unfavorable situation for the displacement field result to limit displacements in the order of magnitude of 0.05 m, that may result to structural collapse if they appear to the founded structure. These series can provide an easy and reliable estimation for the failure of shallow foundation and therefore it can be a useful implement for geotechnical engineering analysis and design.

This study presents the prediction of bearing capacity factors for multiple square shallow foundations in cohesive-frictional soils, utilizing finite element limit analysis (FELA), and machine learning (ML) techniques. The footings are considered to be of equal spacing s , and constant width B . Results from FELA, based on upper and lower bound theorems, were presented in dimensionless charts, showing the correlation between three bearing capacity factors ( N c , N q , and N γ ), the angle of internal friction ( ϕ ), and the spacing ratio ( S/B ). ML techniques, namely ANN and XGBoost, were employed to estimate bearing capacity factors using ϕ and S/B as inputs. The developed models were assessed against FELA data through various metrics, with both ML models showing good agreement with FELA. Among the two models, XGBoost demonstrates slightly higher consistency with FELA data, with R 2 values exceeding 99.9% across all datasets. Besides, a feature importance analysis identified the friction angle as the dominant parameter with permutation importance of more than 85% in the estimation of three bearing capacity factors.

This paper describes an approach for utilizing in-situ measurements of shear wave velocity Vs to carry out preliminary and check design calculations for shallow and deep foundations. For estimates of foundation movements, Vs can be used directly to estimate the small-strain stiffness of the soil or rock strata, while for ultimate capacity calculations, use is made of empirical correlations between Vs and penetration resistance measures, which in turn are correlated to the foundation resistance characteristics. The approach is applied to a series of published tests on shallow footings, and on a series of pile load tests for a very tall building. For these cases, comparisons of the calculated with the measured load—settlement behaviour indicates that the suggested approach provides a reasonable, albeit somewhat conservative, level of agreement.

There exist many structures founded on unsaturated soil deposits. Shear strength augmentation due to the evolution of the matric suction within the unsaturated porous media enhances the bearing capacity of the overlying foundation. This paper presents the evaluation of the pseudo-static seismic bearing capacity of the shallow foundations resting on unsaturated soil deposits using limit equilibrium method. Adopting the Coulomb failure mechanism and Bishop effective stress concept, the bearing capacity equations are solved. The distribution of the matric suction beneath the footing is assumed to be linear. The results of the bearing capacity evaluation are validated against some experimental data found in literature for the static condition. For the seismic loading consideration, the pseudo-static method is utilized. The dual effect of the earthquake acceleration vertical component is thoroughly discussed and a suction transition point is introduced in which the minimum bearing capacity is observed to bear the same value for both upward and downward directions. The increase in the matric suction throughout the soil deposit leads to the increase in the soil shear strength, thus posing more resisting forces as well as higher ultimate bearing capacity. The offered solution is deemed a consistent and useful tool for the accurate prediction of the seismic bearing capacity of shallow footings resting on unsaturated soil deposits.

The investigation of the ultimate bearing capacity (UBC) of shallow foundations has consistently been a significant area of study within the realm of geotechnical engineering. Estimating the UBC is a challenging and intricate task due to the influence of various factors, including soil qualities, foundation depth, and shape. Consequently, this subject gained considerable interest from researchers during the past century. Due to the rapid advancement of AI techniques, numerous models have been effectively utilized in foundation engineering, resulting in a significant rise in the number of related research publications. Despite considerable advancement in recent years, there is still a lack of a comprehensive overview of this topic. In order to comprehensively summarize the most recent developments and offer insights into future investigations, the objective of this review is to present a detailed analysis of AI applications in the evaluation of UBC of shallow foundations. By analyzing the recently published articles concerning the application of AI techniques in UBC prediction, the advantages and disadvantages of the established techniques are clearly outlined. According to the investigation, the choice of input parameters and the quantity and types of datasets used in AI systems determine their accuracy and success. Upon analysis of the considered publications, it was observed that the utilization of AI techniques for evaluating the UBC of shallow foundations has produced acceptable and encouraging outcomes.

Rocking shallow foundations interrupt the seismic transmission path from the base of the structure and possess advantages, such as effective seismic isolation, self-resetting capabilities post-earthquake, and low costs. A numerical model of the rocking shallow foundation was developed in OpenSees (version: Opensees 3.5.0) based on field test data using numerical simulation. The effect of different parameters (column height, foundation sizes, top mass, and soil softness and stiffness) on the seismic response characteristics of rocking shallow foundations is investigated, and the seismic response characteristics of rocking shallow foundations are analyzed under the action of sinusoidal waves of different frequencies and various seismic wave types. The results of the study show that, as the height of the column increases, the bending moment decreases and settlement decreases; as the size of the foundation increases, the bending moment increases and settlement increases; as the mass of the top increases, the bending moment increases and settlement increases; and as the soil becomes softer, the bending moment decreases, and settlement increases. Inputting a sine wave that matches the structure’s natural oscillation frequency may induce resonance. This phenomenon can significantly amplify the structure’s vibrations; thus, it is essential to avoid external excitation frequencies that coincide with the foundation’s natural oscillation frequency. Under seismic loading, the rocking shallow foundation can mitigate the bending moment in the superstructure. When the displacement ratio remains within −0.5 to 0.5 percent, the foundation settlement is minimal. However, when the absolute displacement ratio exceeds 0.5 percent, the soil exhibits plastic deformation characteristics, resulting in increased foundation settlement. This study is an important contribution to the improvement of seismic performance of buildings and an important reference for improving seismic design standards and practices for buildings in earthquake-prone areas. In the future, the seismic response characteristics of rocking shallow foundations under bidirectional seismic action will be investigated.

This paper addresses the critical gap of uncertainty quantification in existing geotechnical models predicting bearing capacity for shallow foundations on cohesionless soils. The developed Bayesian regression model improves point estimate accuracy by 30% compared to traditional models while introducing a robust method for quantifying prediction uncertainty. Utilizing extensively studied literature data, we demonstrate the model’s closed-form structure, allowing the direct calculation of both the most probable bearing capacity and its uncertainty. This transparency distinguishes the proposed model from black-box machine learning alternatives. Furthermore, we illustrate its practical applicability by integrating it into reliability-based design, specifically showcasing its utility in incorporating applied load distributions. In essence, this research enhances predictive accuracy and establishes a comprehensive framework for addressing uncertainty in bearing capacity models, with direct implications for reliability-based design practices.