PSI - Issue 78

1700 Sabatino Di Benedetto et al. / Procedia Structural Integrity 78 (2026) 1697–1704 splitting along the design anchorage length; 1 and 2 are the same parameters defined in Eq. (1); is the design tensile strength of the concrete. In the context of micropiles, pull-out resistance can be influenced by various factors. The quality of concrete plays a significant role, as higher compressive strength tends to improve the bond at the steel–concrete interface. The geometry of the steel tube, including surface roughness or the presence of ribs and other mechanical features, can increase the contact area and enhance bonding. Additionally, the application of high-pressure grouting during installation improves concrete compaction, which in turn contributes to greater bond strength. Technical standards such as the NTC2018 and Eurocode 2 provide detailed guidance on the bond between steel and concrete, primarily focusing on ribbed bars, for instance B450C. However, in the case of smooth steel structural tubes, the standards do not provide specific design indications. The bond between smooth steel surfaces and concrete is generally weaker than that achieved with ribbed bars, due to the absence of ribs or surface irregularities, which limits mechanical interlock between the two materials. As a result, the ability to transfer stresses from steel to concrete is reduced. The Model Code 1990 (Telford, 1993) offers useful guidance for defining the bond behaviour of both ribbed and smooth bars. The bond-slip relationship is described by an initial nonlinear ascending branch, followed by a plateau, and a final descending linear branch that approaches zero. The monotonic bond stress–slip curve is shown in Fig. 1. Additionally, the Model Code 1990 also provides a table that allows for the evaluation of the parameters in Fig. 1 based on the characteristics of the reinforcing bars. An example of this table, specific to the case of smooth bars, is presented in Table 1. It is worth noting that the peak bond stress varies with the square root of the characteristic compressive strength of the concrete.

Fig. 1. Analytical bond stress–slip relationship under monotonic loading as defined by the Model Code 90

Table 1. Parameters for defining the bond stress-slip relationship of smooth bars according to Eqs. (3-6) Cold drawn wire Hot rolled bars Good bond conditions All other conditions Good bond conditions All other conditions = = 0.01 mm 0.01 mm 0.1 mm 0.1 mm 0.5 0.5 0.5 0.5 = 0.1√ 0.05√ 0.3√ 0.15√ Eurocode 4 (EN 1994-1-1, 2004) provides guidance regarding bond stress in the case of steel–concrete composite sections. Specifically, it defines the design bond stress values between the steel element and the concrete. The values of τ Rd , provided that the steel surface in contact with the concrete is unpainted and free of oil, grease, scale, or rust, are given in Table 2 . Eurocode 4 specifies that the τ Rd value listed in Table 2 for fully encased steel sections applies to cases where the minimum concrete cover is 40 mm and where both transverse and longitudinal reinforcement meet the minimum requirements set by the code.

Table 2. Design shear strength (  Rd ) according to Eurocode 4

Type of cross section

Type of cross section

 Rd (N/mm

2 )

Rd (N/mm

2 )



Completely concrete encased steel sections Concrete filled circular hollow sections Concrete filled rectangular hollow sections

0.30 0.55 0.40

Flanges of partially encased sections Webs of partially encased sections

0.20 0.00