# Influence of Pile Foundation Stiffness on Column Design in One-Story Reinforced Concrete Frames
## 3 Method for Calculating Pile Foundation Settlement  
A foundation pile loaded by an axial force transmits a load to the surrounding soil medium due to shear resistance mobilized at the side of the pile and at the pile base resistance (Figure 2). The magnitude of resistance mobilized at the side of the pile in the individual layers and under the base of the pile can be related to the magnitude of the displacement (strain). This relationship is described by load transfer functions (\(\sigma-z;\tau-z\)), as shown in Figure 2. To date, many proposals for load transfer functions have been developed and described mathematically on the basis of empirical results and theoretical solutions [18; 19; 20; 21; 22; 23; 24]. Figure 2: Application of load transfer functions in axially loaded pile analysis. In numerical modeling, the load transfer functions represent the stiffness characteristics of the elastic support, which reflect the mobilized resistance of the surrounding subsoil (Figure 2). After discretization of the pile model, the values of the forces generated at the individual nodes and node displacements are obtained as a result of a numerical procedure. The calculations for successive load increments produce non-linear settlement (load) curves that characterize the behavior of the pile over the full range of its loading (Figure 3). According to the above scheme, the calculation represents an approach for the design of pile foundations that abandons the classic concept of pile bearing capacity expressed in terms of force and gives more weight to the amount of settlement by obtaining the load-settlement (\(Q\)-s) characteristics of the pile. This design concept is easier to apply than the classical approach. An example of such an approach is a method based on theoretical load transfer functions [20; 21] by [PERSON] et al. [25]. The empirical load transfer functions are of limited use, while the theoretical functions are more attractive because of the universality of the solution, which is the approach used in the method presented in [26; 27]. In foundations that are a group of piles, the interaction between the piles must additionally be taken into account. This is a significant issue in itself [28; 29; 30; 31], but with the use of the load transfer function method, it is reduced to a modification of the original function for a single pile. The settlement of adjacent piles is due to the settlement of a single pile loaded by an axial force and the interaction between the piles. This results in higher settlements of piles in a group (\(s_{ij}\)) compared to settlements of the same piles considered as single piles (\(s_{i}\), \(s_{j}\)), as shown in Figure 4.  
If the foundation rests on a group of \(n\) piles, the settlement of the \(i\)-th pile, taking into account the interaction between the piles, is calculated according to the following formula:  
\[s_{G,i}=s_{i}+\sum_{j=1}^{n}\bigl{(}s_{ij}-s_{i}\bigr{)}\text{ for }j\
eq i \tag{7}\]  
where  
\(s_{i}\)--settlement of the single pile \(i\) under the load \(Q_{i}\);  
\(s_{ij}\)--settlement of the pile pair \(i\) and \(j\) loaded with the forces \(Q_{i}\) and \(Q_{j}\). Figure 3: Example of settlement curves for a single pile. It follows that the multiple pile settlement will be greater than that of a single pile settlement if more piles interact with each other; see the example in Figure 5.  
To calculate the settlement of piles in a group, a method is proposed [26; 27], which is based on the idea of the hybrid method presented by [PERSON] [32]. For single piles, the method uses a solution to create non-linear foundation pile settlement curves. The method was developed and improved on the basis of analyses of the results of studies on non-linear soil behavior and test loads on piles under field conditions. In the single pile analysis method, a non-linear elastic-plastic model was used to reflect the non-linear behavior of the pile before reaching the ultimate bearing capacity in the pile-soil contact zone.