PSI - Issue 70

Rachit Sharma et al. / Procedia Structural Integrity 70 (2025) 386–393 Sharma and Laskar/ Structural Integrity Procedia 00 (2025) 000 – 000

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In contrary to SHAP summary plot, the SHAP dependency plot highlights the interdependency of input features. Figure 4(a-d) illustrates critical features based on SHAP dependency plots. From Fig. 4(a), SHAP values consistent linear increment with increasing b suggesting that shear strength is positively correlated with width, b . For section depths (h < 300), SHAP values remain near zero to indicate insignificant effect of this parameter on predicted variable at lower depths. For higher section depth and lower a/d ratio (indicated in blue colour), a sharp increase in SHAP values suggest that the corresponding parameter has considerable effect on shear strength. This trend aligns well with the size effect where large section depth significantly influence the shear strength (Li et al. (2021)), (see Fig. 4(b)). The SHAP values were almost constant for f c from 20 MPa to almost 50 MPa, beyond which the SHAP values are almost non-linear (see Fig. 4(c)). This suggests that shear strength of FRP-RC beams exhibit greater variability when f c exceeds 50 MPa and it is advisable to employ different equation for f c > 50 MPa is the design of FRP-RC beams. Similar trend is observed for E f where there is a sharp increase in SHAP values for lower E f (< 50 GPa) to indicate lower stiffness of GFRP bar and for E f greater than 125 GPa indicating higher stiffness of CFRP bar influencing the shear strength due to dowel action (see Fig. 4(d)). This suggests that the omission of the FRP elastic modulus in current Indian Standard codes may compromise the model's efficiency. While these codes account for the percentage of reinforcement, they do not consider the elastic modulus of rebar, potentially leading to inaccuracies in structural assessments.

Fig. 4. Relative Importance of Parameters from SHAP Values.

6. Conclusions and Future Work This study establishes a comprehensive database of shear strength of 402 FRP-RC beams. A comparison is made between the shear strength predictions from typical empirical models and ML models and the advantages of ensemble model (XGBoost) is highlighted. Finally, the SHAP method is utilized to interpret the ensemble model and validate