It is usual to adopt the seismic force acting as an additional body force, employing the pseudo-static hypothesis, when considering earthquakes in the estimation of the bearing capacity of foundations. A similar approach in seepage studies can be applied for the pore pressure’s consideration as an external force. In the present study, the bearing capacity of shallow foundations on rock masses considering the presence of the pseudo-static load was developed by applying an analytical solution for the Modified Hoek and Brown failure criterion. Calculations were performed adopting various inclinations of the load and the slope on the edge of the foundation, as well as different values of the vertical and horizontal components of the pseudo-static load. The results are presented in the form of charts to allow an affordable and immediate practical application for footing problems in the event of seismic loads or seepages. Finally, and to validate the analytical solution presented, a numerical study was developed applying the finite difference method to estimate the bearing capacity of a shallow foundation on a rock mass considering the presence of an additional horizontal force that could be caused by an earthquake or a seepage.
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.
The discontinuity layout optimization (DLO) method is applied to obtain the bearing capacity of rock masses where it is necessary to consider a non‐linear resistance law. In rock mechanics, it is widely accepted the modified Hoek & Brown failure criterion, developed for homogeneous and isotropic rock masses. The results obtained with the DLO method are compared with those obtained from the analytical solution and using the finite differences method (FDM). To validate the DLO numerical method, the same hypotheses of the analytical solution are adopted: plane strain conditions, associated flow rule, Hoek & Brown material, and weightless rock. The research analyses the results of a numerical and analytical study based on a sensitivity study varying the three parameters that characterize the rock mass (rock type, uniaxial compressive strength, and geological strength index) and shows the need to adopt an adequate linearization of the non‐linear failure criterion in the numerical calculations. Furthermore, numerical results are obtained considering the self‐weight of the rock mass, using both DLO, considering the intermediate secant linearization proposed in this investigation, and FDM, implemented in a widely accepted geotechnical software. After comparing the results, the advantages and limitations of the DLO method are pointed out.
The presence of the groundwater level (GWL) at the rock mass may significantly affect the mechanical behavior, and consequently the bearing capacity. The water particularly modifies two aspects that influence the bearing capacity: the submerged unit weight and the overall geotechnical quality of the rock mass, because water circulation tends to clean and open the joints. This paper is a study of the influence groundwater level has on the ultimate bearing capacity of shallow foundations on the rock mass. The calculations were developed using the finite difference method. The numerical results included three possible locations of groundwater level: at the foundation level, at a depth equal to a quarter of the footing width from the foundation level, and inexistent location. The analysis was based on a sensitivity study with four parameters: foundation width, rock mass type (mi), uniaxial compressive strength, and geological strength index. Included in the analysis was the influence of the self-weight of the material on the bearing capacity and the critical depth where the GWL no longer affected the bearing capacity. Finally, a simple approximation of the solution estimated in this study is suggested for practical purposes.
The influence of the non-associative flow law on the bearing capacity of shallow foundations on rock masses is, in general, a subject that is not discussed in the field of rock mechanics. The calculation methods of bearing capacity usually do not define which flow law is adopted and, in some methods, the associative flow rule is assumed without knowing how that hypothesis influences the bearing capacity of the rock mass. In this paper, the study of the influence of the dilatancy angle on the bearing capacity of shallow foundations on rock masses is presented. The variation of the bearing capacity with the associative flow law and the non-associative flow law with zero dilatancy angle is studied using the finite difference method and by considering the influence of the self-weight of rock material. The calculations confirm the great influence of the flow law on the bearing capacity and a correction coefficient is proposed, which makes it possible to estimate the variation of the bearing capacity of the rock mass in terms of the function of the flow law for the hypothesis of weightless rock masses.
This paper aims to study the bearing capacity of a shallow foundation on rock mass, considering the most usual bridge footing width and adopting a Hoek–Brown material. The dimension of the foundation has been shown to be very significant in soils with linear failure criteria (Mohr–Coulomb envelope), and its study is necessary in the case of non-linear failure criteria, typical of rock masses. Analytical solutions do not allow incorporating this effect. A parametric study by a finite difference method was carried out, studying a wide variety of rock mass through sensitivity analysis of three geotechnical parameters: geological origin of the rock mass (mi), uniaxial compressive strength, and geological strength index. The results obtained by the numerical solution for the Hoek–Brown failure criterion were compared with the analytical results by adopting the classical hypotheses of plane strain conditions, associated flow rule, and weightless rock mass. The variation of the numerical bearing capacity due to the consideration of the self-weight of the rock mass was also analyzed since its influence is conditioned by the volume of ground mobilized and therefore by the width of the foundation. Considering the similarities observed between the numerical and analytical results, a correlation factor function of the self-weight is proposed. It can be used in conjunction with the analytical method, to estimate in a semi-analytical way the bearing capacity of a bridge foundation.
Svetlana Melentijevic was not included as an author in the original publication [...]
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