Discussion of “Numerical Investigation of Connection Forces of a Coastal Bridge Deck Impacted by Solitary Waves” by Yalong Cai, A. Agrawal, Ke Qu, and H. S. Tang

The discussed paper has novel features in analyzing the resultant forces due to solitary waves at the connections between the bridge superstructure (bridge deck) and substructure by fluid–structure interaction (FSI) simulations. ANSYS Fluent and Mechanical packages were coupled in a numerical wave tank, where two full-scale bridge models, a fixed deck and a flexible deck with respect to the vertical direction (in both models it is flexible in the horizontal direction), were parametrically studied. An empirical relationship between the vertical resultant force and overturning moment for the fixed deck was proposed in order to facilitate engineering analysis. This work should be complimented for these novel features, which can advance the understanding and knowledge regarding the bridge deck–wave interaction topic. The discusser would like to thank the authors for their substantial efforts for presenting this superior paper and also would like to put forward some comments and questions, which will hopefully enhance the current understanding on this specific topic. These comments and questions are mainly related to the vertically flexible deck model, the contribution of the horizontal forces to the overturning moment, and comparisons made with AASHTO (2008) for the relationship between the vertical resultant force and the overturning moment.

Fig. 12 in the original paper shows the vertically flexible deck model, where only the most onshore connection is treated as a linear vertical spring with a high stiffness. The other five connections cannot provide resistant forces when the resultant vertical force at the connection is larger than 0, i.e., the vertical wave load surpasses the distributed dead load at these connections. In other words, the deck can rotate around the most onshore connection for certain large waves, where the only resistance is from this connection. The authors address that Fig. 12 only shows one possible unseating behavior of the bridge deck in a hurricane event. The discusser would comment that this unseating model is not the critical one, but can be deemed as the last failure in the progressive failure of connections, triggered by the critical one. In the hours-long wave train in one hurricane event, a certain large wave, riding on the storm surge, should initiate the first failure among the connections, probably the most onshore or offshore connection (Yuan et al. 2018), which is the critical unseating of the deck. Theoretically, all six connections provide resistance to the first fail, whereas only the most onshore connection functions in the model depicted in Fig. 12.

Fig. 13 in the original paper defines the transferred force components from the superstructure, where Point O is chosen as the reference point for this force system. The overturning moment on the bent only includes the contributions from the vertical forces; however, the contribution of the horizontal force is neglected. The authors present reasons for this negligence: the magnitude of the vertical force is much larger than the horizontal force, and the moment arm for the vertical force is relatively larger. The discusser believes there are conceptual differences between the definitions of the force components ($F_h$, $F_v$, and $M_o$) for the bent, as shown in Fig. 13, and for the superstructure such that the preceding reasons should not be used for explaining this negligence. In Fig. 13, the contribution of the horizontal force to the moment is clearly 0 for the vertically fixed deck case. Even for the unseating behavior in the vertically flexible deck model, the bent would not rotate along the detached bridge deck. Therefore, based on the specific definitions of the force components, this contribution is still 0. However, regarding the force definitions for the superstructure, it would be another story. Case S3 ($Z_c/d_b=0.0$, $H=2.58\mathrm{m}$) with the vertically fixed deck model is thus demonstrated as one example. It is noted in Fig. 22 that the positive peak horizontal force is around 150 kN and in Fig. 25 that the maximum overturning moment is around $200\mathrm{kN}·\mathrm{m}$. In Case S3, the bottom of the bridge deck is just level to the still water level (SWL) and the wave height is much higher than the top of the deck. Therefore, it is reasonable to set the moment arm for the horizontal force as half the height of the bridge deck, i.e., 0.65 m. As such, the moment due to the horizontal force is $150\times 0.65=97.5\mathrm{kN}·\mathrm{m}$, which occupies almost half of the total overturning moment, indicating that the contribution from the horizontal force should not be ignored. The preceding calculation is based on the assumption that the positive peak vertical and horizontal forces occur at the same instance (AASHTO 2008; Xu et al. 2015). The moment in Fig. 13 is defined for the bent and connections such that this moment value may be smaller than the moment value defined for the superstructure. This is closely related to the chosen reference point. Nevertheless, the negligence of the contribution of the horizontal force to the overturning moment depends on the analyzed force system with a specified reference point.

Fig. 24 shows that the overturning moment does not necessarily reach the maximum at the same time for the resultant vertical force and the negative peak moment is larger than the positive peak moment. The authors compare these observations with AASHTO (2008). However, there are two apparent differences with AASHTO (2008) such that the comparisons may not be well justified. One difference is that in Scenarios I and II in AASHTO (2008), the reference point is defined at the bottom of the landward girder; this is the reason the calculated moments in this code usually have positive values. Another difference is that the equations provided by AASHTO (2008) are purposely for the superstructure rather than the bent; as discussed previously, there are conceptual differences between these two force systems. As such, the comparisons made by the authors seem unnecessary.

The empirical relationship between the vertical resultant force and overturning moment is helpful for engineering practice. However, the missing information on the horizontal forces constrains the appropriate design of the connections. Therefore, in light of this significance, the discussers encourage the authors to extend this empirical model by including the horizontal forces.