PSI - Issue 64

Mehdi Aghabagloo et al. / Procedia Structural Integrity 64 (2024) 1516–1523 Mehdi Aghabagloo/ Structural Integrity Procedia 00 (2019) 000 – 000

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of the bonded joint, with maximum load of HB specimen almost tripling that of the EBR specimen (an increase of 186% is obtained). Black solid line in Fig. 3 corresponds to the load-slip curve of the second test performed to the HB specimen, conducted to analyze the effect of compressive stresses exerted by the metal plate. In this second test (referred to as HB post-failure), the slope of the ascending branch is lower than that of the HB test, indicating less stiffness. This discrepancy arises because the test was conducted relying solely on friction and interlock between the sand substrate provided by the compressive stress due to the metallic plate. After attaining a maximum load of P max =64.37 kN, a constant horizontal stage follows. As observed in the plot, the maximum load of the HB post-failure specimen is lower than that of the horizontal stage in the HB specimen (around P =73 kN), possibly due to the transition from dense sand to loose sand in the post-test phase (Das., 1990).

Fig. 3 Experimental load-slip curves for EBR, HB, and HB post-failure

3. Prediction of bond-slip laws In this section, a novel methodology to obtain the local bond-slip law is employed, enabling flexibility to avoid pre-defining a shape for the bond-slip law calibration (Aghabagloo et al., 2024). This flexibility permits the adoption of a multi-linear form ( n -line segments bond-slip law), offering a unique advantage, where n is a user-defined parameter. This methodology requires a load-slip curve as an input parameter, for which the experimental load-slip curves obtained from the single shear tests and presented in Fig. 3 are utilized. In this study, n is fixed to 15, so that the parameters to be fitted by the methodology correspond to fourteen values of stresses ( τ 1 , τ 2 , …, τ 14 ) and two values of slips ( s 1 and s final ; being s 2 , s 3 , ..., s final equally spaced). For the application of the numerical methodology, a range of possible values for shear and slip needs to be defined. Table 2 provides details on the variable limits and the teaching-learning-based optimization (TLBO) control parameters for applying the TLBO algorithm. The upper limits of slips ( s final-max ) were selected to be higher than the maximum slip of experimental load-slip curves in case the bonded length of specimens is less than the effective bond length.

Table 2. Variable limits and TLBO Control parameters Method P TLBO N Iter τ max (MPa)

s 1-max (mm)

s final-min (mm)

τ min (MPa)

s 1-min (mm)

s final-max (mm)

EBR

350 300 300

200 200 200

25 20 20

0.1 0.1 0.1

0.3

0.001 0.01 0.01

Max a +2 Max a +2 Max a +2

0.1 0.1 0.1

HB

1 1

HB post-failure

a corresponding to the maximum slip of the load-slip curve input

3.1. Numerical predictions Predictions of the aforementioned methodology are presented in this section. The accuracy of the predictions is later assessed by comparing them with experimental data obtained from DIC (for the case of EBR specimens) and