# Assessment of the Bearing Capacity of Bridge Foundation on Rock Masses
## 6 Conclusions  
Existing analytical solutions [15] allow to obtain particular configurations and cannot consider the influence of the foundation dimension. To overcome this limitation, the solutions accepted and widely used in Soil Mechanics contemplate introducing empirical coefficients to improve the real estimate. Similarly, and since there are no such factors in the literature in the field of Rock Mechanics, in this research the correction factor (\(W_{F}\)) obtained by numerical experimentation is proposed to offer a complete semi-empirical formulation that considers the dimension of the foundation in the analytical formulation of the bearing capacity of the rock masses.  
Based on the comparison of the numerical and analytical results of bearing capacity for conventional foundation widths in bridge construction, the need to consider the influence of the self-weight on the bearing capacity in this type of foundation on rock masses is concluded.  
In general, regarding the correction coefficient due to the self-weight (\(W_{F}\)) proposed based on the results obtained in 192 cases studied by numerical analysis through FDM, the following can be concluded:  
* The parameters that have most impact on the value of the bearing capacity are \(GSI\) and \(UCS\), observing an exponential influence with increasing values of those parameters.
* Depending on the combination of the \(GSI\), the \(UCS\) and the footing width (\(B\)), the influence of the self-weight of the material may be less than 5% on the value of the bearing capacity in cases with high \(UCS\) and \(GSI\) or may exceed as much as 400% for very low values of \(GSI\) (\(GSI=10\)) and \(UCS\) (\(UCS=5\) MPa).
* Medium or high values of the ultimate bearing capacity (\(\geq\)25 MPa) are not significantly influenced by the material's self-weight component; the difference being lower than 20%. These case studies correspond to medium or high \(GSI\) values, as already indicated by [PERSON] et al. [7] and [PERSON] [55].
* The rock type (\(m_{i}\)) and the foundation width (\(B\)) influence the correlation of the results obtained with and without self-weight, however, depending on the combination of the \(UCS\) and the \(GSI\).
* Through the classical soil mechanics self-weight coefficient, the increase in the bearing capacity differs considerably from the estimated using the proposed coefficient for rock masses based on the numerical calculations through the finite difference method. This happens because the rock mass does not have a constant angle of friction, thus depending on the value of the self-weight factor (\(W_{F}\)) on \(UCS\) and \(GSI\).
* Based on the numerical and analytical results, the \(W_{F}\) coefficient can be used in conjunction with the analytical method, to estimate in a semi-analytical way the bearing capacity of a bridge foundation, once, due to the foundation size, a great contribution of the self-weight on the bearing capacity is expected.  
Conceptualization, A.A.; R.G.; C.O.M. and S.M.; Data curation, A.A. and R.G.; Funding acquisition, R.G. and C.O.M.; Investigation, A.A. and R.G.; Methodology, A.A., R.G. and S.M.; Project administration, A.A. and R.G.; Resources, A.A.; Software, A.A.; Supervision, R.G. and C.O.M.; Validation, A.A. and R.G.; Visualization, A.A.; Writing--original draft, A.A.; Writing--review & editing, R.G. and C.O.M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Universidad Politecnica de Madrid.  
**Acknowledgments:** The research described in this paper was financially supported by the Universidad Politecnica de Madrid from the grant with reference VMENTORUPM21 RAGA of the university's own program to carry out research and innovation projects.  
**Conflicts of Interest:** The authors declare no conflict of interest.