PSI - Issue 78

Sabatino Di Benedetto et al. / Procedia Structural Integrity 78 (2026) 1697–1704

1702

4. Numerical activity To model the mechanical behaviour of the foundation footing with micropile in OpenSees, a simplified approach was adopted, aimed exclusively at representing the bond mechanism between a steel tube and the surrounding concrete. In this idealized representation, the footing and the reinforcement are not modelled explicitly, as the concrete is assumed to be perfectly rigid and resistant. The model is one-dimensional and represents the tube as a series of nodes connected by elastic beam elements, with a cross-sectional area equal to that of the tubular profile (3240 mm²) and an assumed width of b = π × 137 mm = 430.18 mm. The interaction between steel and concrete is modelled using zeroLength elements, which exhibit a nonlinear response characterized by an initial parabolic branch, consistent with the recommendations of the Model Code 1990, followed by a linear softening phase down to zero stress. This second branch does not strictly follow the Model Code 1990, as the authors assumed a slip value of s 3 = 0.2 mm and a final bond stress τ f = 0 MPa. This bond behaviour is implemented using the MultiLinear material, defined by a force – slip curve that reproduces the two aforementioned phases. The developed script allows customization of parameters such as tube length, number of nodes, and mechanical properties of the materials. Additionally, it automatically generates the model geometry and elements. A monotonically increasing imposed displacement is applied at the free end of the tube (Fig. 3). In summary, this model provides a simplified simulation of the bond behaviour of a smooth steel tube embedded in a concrete plinth, taking into account the nonlinear bond response at the steel – concrete interface. The proposed numerical model, calibrated using the geometric and mechanical properties of the tested specimen, predicts a bond resistance of 325 kN, underestimating the experimental value by only 2%. As shown in Fig. 3, the distribution of bond stresses along the embedded tube is non-uniform. Specifically, the nonlinear behaviour is primarily due to three factors: the use of two different concrete classes, which causes a discontinuity in the stress curve at an embedment depth of 300 mm; the parabolic shape of the stress – slip relationship; and the linear degradation observed in the final branch of the stress – slip curve.

Fig. 3. Simplified representation of the adopted mechanical model (left) and shear stress at the interface between the tube and the concrete

This outcome is significant for another reason: the bond resistance is strongly influenced by the shape of the bond stress – slip curve. Assuming a uniform distribution of the maximum bond stress (τ) along the steel – concrete interface, the bond resistance predicted by existing design codes does not capture the experimental value. Table 3 reports the bond stress values calculated according to different design provisions, distinguishing between the portions of the composite tube embedded in two types of concrete with different strength classes. Table 4, on the other hand, presents the bonding resistance of the tested specimen as determined by the same design provisions. In particular, the value of shown in Table 4 is computed using Eq. (3): , = . 50/60 , 50/60 + . 32/40 , 32/40 (3) In Eq. (3), = 137 denotes the external diameter of the tube, . 50/60 = 300 and . 32/40 = 200 represent the lengths of the tube segments embedded in concrete classes C50/60 and C32/40, respectively. Similarly, , 50/60 and , 32/40 are the corresponding bond stresses for concrete classes C50/60 and C32/40.