In this study, the quantitative effect of the random distribution of the soil material properties to the probability density functions of the failure load and displacements is presented. A modified Cam-Clay failure criterion is embedded into a stochastic finite element numerical tool for this purpose. Various assumptions for the random distribution of the compressibility factor $$\kappa$$κ , of the constitutive relation, the critical state line inclination c of the soil, and the permeability k have been tested and assessed with Latin hypercube sampling followed by Monte Carlo simulation. It is confirmed that both failure load and displacements follow Gaussian normal distribution despite the nonlinearity of the problem. Moreover, as the soil depth increases the mean value of failure load decreases and the failure displacement increases. Consequently, failure mechanism of clays can be determined in this work within an acceptable variability, taking into account the soil depth and nonlinear constitutive relations which in the analytical solutions is not feasible as it is assumed the Meyerhoff theory which considers the elastic halfspace.

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 $$10^{-5}$$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.

In this article, a set of neural networks for the prediction of the stresses and the corresponding strains at failure of cohesive soils when subjected to a load of a shallow foundation are presented. The data are acquired via Monte Carlo analyses for different types of loadings and stochastic input material variabilities, and by adopting the clayey soil domain and modified Cam Clay material yield function. The mathematical functions for the estimation of the failure stresses and strains are computed with the feed forward neural network method (FNN). It is demonstrated that the accuracy of the derived relations is in the order of a maximum relative error of ${10}^{-5}$ in all monitored output variables. In addition, the number of training epochs required for convergence is relatively low and this means that the computational and data costs for the construction of the FNN are low. The critical input variable for the estimation of the most unfavorable situations is the Karhunen Loeve series expansion for porous analyses, while for non-porous analyses the constant distribution over depth is the one that provides more critical estimations for the monitored output variables of stresses and strains at failure. This set of functions can estimate the aforementioned variables of the footing settlement in clays with high accuracy; consequently, it can be an important tool for geotechnical engineering design, especially in providing the largest stress allowed from the foundation.

In this article, a quantitative numerical study of the random distribution of the soil material parameters to the probability density functions of the failure load and failure displacements of a shallow foundation is presented. A modified Cam-Clay yield function is used for this scope into a stochastic finite element numerical formulation. Several hypotheses for the random distribution of the compressibility factor $\kappa$, of the material constitutive relation, the critical state line inclination c of the soil, as well as of the permeability k of the continuum, have been tested and assessed with Monte Carlo simulation accelerated with Latin hypercube sampling. It is validated that both failure load and failure displacements follow Gaussian normal distribution despite the non-linear behaviour of the soil. Furthermore, as the soil depth increases, the mean value of failure load decreases and the failure displacement increases. The failure mechanism of clays can be determined with accuracy using this numerical implementation, without the restrictions imposed by analytical solutions, taking into consideration the eccentricity of the load in combination with non-linear constitutive relations.

Non-destructive testing (NDT) is a crucial method for detecting damages in concrete structures. Structural damage can lead to functional changes, necessitating a range of damage detection techniques. Non-destructive methods enable the pinpointing of the location of the damage without causing harm to the structure, thus saving both time and money. Damaged structures exhibit alterations in their static and dynamic properties, primarily stemming from a reduction in stiffness. Monitoring these changes allows for the determination of the failure location and severity, facilitating timely repairs and reinforcement before further deterioration occurs. A systematic approach to damage detection and assessment is pivotal for fortifying structures and preventing structural collapse, which can result in both financial and human losses. In this study, we employ image processing to categorize damaged beams based on their crack growth and propagation patterns. We also utilize support vector machine (SVM) and k-nearest neighbor (KNN) methods to detect the type, location, and extent of failures in reinforced concrete beams. To provide context and relevance for the laboratory specimens, we will compare our findings to the results from controlled experiments in a controlled laboratory setting.

Rock mechanics and the estimation of their material properties through field tests are important aspects and challengees in civil and geotechnical engineering. However, this procedure is expensive and difficult to attain, while the machine learning and neural network theory provide a computational tool for estimating the material properties with limited data. In this work, an estimation of the Young Modulus and the cohesion of a clayey-originated rock through feed-forward neural networks constructed from in situ data measurements is given. The input values come from the Geological Strength Index (GSI) proposed values of the point load index $I_{s50}$, the uniaxial compression strength ${\sigma }_s$, as well as the specific gravity $\gamma$ of the rock mass. The convergence analysis revealed that the convergence occurs at approximately 2000 epochs, with the largest $L_2$ mean square error norm being no greater than ${10}^{-5}$. In addition, it is demonstrated that augmenting $\gamma$ results in the estimation of rock that is stiffer and stronger. The aforementioned increase in the specific site may be up to 20% for the stiffness and up to 25% for the cohesion. This model, aside from readability and accuracy, offers the convenience of enriching it with more in situ data, thereby enhancing the flexibility of the proposed numerical tool proposed. However, its applicability is limited to the specific data acquired from the particular site, so a more general estimation requires a substantially larger dataset. Finally, the justification of the proposed model has been carried out based on suggestions from the literature for common values of clayey-oriented rock, which is fairly disintegrated as seen in the field.