# Assessment of the Bearing Capacity of Bridge Foundation on Rock Masses
## 4 Results and Discussion
### The Influence of the Self-Weight on Bearing Capacity
It is emphasized that the value of 25 MPa is the average value of the compressive strength of concrete, as well as the limit to define the soft and hard rock according to ISRM [52]. Thus, the cases where the self-weight present more influence on the bearing capacity are the same that the bearing capacity can condition the completion of the project. Figure 14: Correlation between \(P_{hSW}\) and \(P_{hWL}\), depending on \(P_{hWL}\). Figure 13: Correlation between \(P_{hSW}\) and \(P_{hWL}\) depending on _GSI_ and _UCS_. Self-Weight Correction Factor (W\({}_{\text{F}}\))  
The analysis of the results obtained numerically for \(P_{hSW}\) and \(P_{hWL}\) demonstrated that the correlation of the bearing capacity presents a great dispersion depending on the state of the rock mass (_GSI_), _UCS_, and the footing width (\(B\)). In addition, the rock type (\(m_{i}\)) has very little effect on the correlation of results for \(P_{hSW}\) and \(P_{hWL}\). In many cases, notably with the combination of high values of \(GSI\) and _UCS_, the increase in load due to the consideration of the self-weight of material was less than 5% (Figure 13). Consequently, it is not useful to perform a detailed numerical calculation to estimate the increase in bearing capacity because the self-weight is too small. For this reason, and to allow for a better adjustment of \(W_{F}\), the cases in which the load increase was less than 5% are represented in the graph of the Figure 15.  
From Figure 15, knowing the \(GSI\) and the _UCS_ of the rock mass, depending on \(B\), we can know whether the consideration of the self-weight of material increases the bearing capacity by more than 5%. This is because the lines for different \(B\) values delimit the differences smaller than 5% for the combination of \(GSI\) and _UCS_ above each line for each of the \(B\) values studied. For example, for a footing width of \(B=10\) m, all combinations of _UCS_ and _GSI_ that are below the line corresponding to \(B=10\) m show an increase in the bearing capacity, due to the self-weight of material, that exceeds 5%. If the footing has the width of \(B=12\) m, a line between \(B=10\) m and \(B=15\) m should be interpolated, and the points resulting from the combination of \(GSI\) and _UCS_ that are below the line present an increase in the bearing capacity due to the self-weight of the material greater than 5%. Once we separated the case studies with an increase lower than 5%, we then developed the correction coefficient taking into account the self-weight (\(W_{F}\)). To make the equation dimensionless, it was divided by the lower value of the ultimate bearing capacity correspondent to the case weightless (\(P_{hWL}\)) and therefore it is proposed in the present research:  
\[\frac{P_{h_{SW}}}{P_{h_{WL}}}=1+\frac{\Delta P_{h}}{P_{h_{WL}}}=1+W_{F} \tag{13}\]  
Figure 16 represents the correction coefficient (\(W_{F}\)) divided by \(\sqrt{B}\) versus the _UCS_, obtaining the fitting equations (also shown in Table 4) with high correlation coefficients. In  
Figure 15: Limit of 5% increase in the bearing capacity due to the self-weight of the material. the graph corresponding to \(GSI\) = 85 in Figure 16 there are no equivalent columns to the _UCS_ of 50 and 100 MPa, because for these combinations of parameters the variation of the bearing capacity with and without the self-weight of the material is less than 5%. Since the equations in Table 4 have the same structure, a single equation can be generalized (14) as a function of the \(GSI\), that allows to obtain a new coefficient as a result of this study.