Structural Response of A Slotted Bridge Pier Under Blast Loading Using Finite Element Analysis

Abstract: Bridge pier is a crucial part for the transportation in marine structures. Scouring is a major cause for the failure of the pier. slot among the other countermeasures increases the efficiency of scour reduction and minimizes the failure due to scour.as we provide the slot; the strength of the pier reduces compared to the conventional pier. change in reinforcement pattern in slotted bridge pier changes the behavior of the pier under similar loading conditions. blast occurrence has increased in recent times and rehabilitation of a structure and improvement of strength against explosion is necessary in structure. this paper studies the behavior of slotted bridge pier under blast loading and compares theoretical and analytical aspects for the same. Design criteria for blast load according to NCHRP 12-72 are followed to carry out theoretical load response of the pier under blast loading. Analytically the behavior of pier is checked using coupled eulerian lagrangian approach using ABAQUS software. a detailed eulerian domain and slotted pier with reinforcement is assembled in ABAQUS to analyze the behavior of pier under explosion using TNT of 100kg at a scaled distance of 4ft for the period of 0.02seconds. this design gave better result in terms of mitigating effects of blast on slotted bridge pier.


Introduction
Bridge is widely used structure as a hydraulics structure in river. As the water passes in the river, the pier becomes an obstruction to the current. The current velocity will reach stagnation point at pier surface and the following water will push down the stagnant water. As an effect of that horse shoe vortex will generate at the base of pier and scouring will occur Figure 1 (W. .Scouring around the bridge pier is considered to be the major cause of failure of the pier. Provision of slot with the combination of collar proves to be most effective to reduce the scouring around the pier but slot provision reduces the strength of the pier as volume and reinforcement is reduced in the conventional pier (Heidarnejad et al., 2010).
An external blast wave is a phenomenon where surrounding atmosphere gets compressed due to the outward effect of the explosion and gets pushed back (Ibrahim and Nabil, 2019). As the wave propagates, the front portion is known as shock front and it has more pressure compare to the back region of the wave(El-Ghorab, 2013). As the wave propagates it decays with respect to time. As the pressure decays it can get decrease below surrounding pressure and thus creating suction in surrounding region (Ding et al., 2018). An ideal explosion has both the region, one being overpressure also known as positive phase and the other being under pressure also known as negative phase as shown in Figure 2 (Wu et al., 2018). ta is the wave arrival time, to + is the duration of the positive phase, tois the total duration of the negative phase, P is the peak overpressure, P a is the ambient atmospheric pressure, P is the peak under pressure(Blast-Resistant Highw. Bridg. Des. Detailing Guidel., 2010) (Jin et al., 2020).
In blast explosion scaling is an important parameter to measure the factor of damage induced. Scaling of the explosion as suggested by Hopkinson's Law can be considered. The law states that pressure induced at a distance R1 with explosive weight of W1 will induce same effect as pressure induced at distance R2 with explosive weight as W2 (Sabuwala et al., 2005).

Figure 2 Ideal Blast Wave
The parameter λ is referred to as the explosive yield factor. We can also use scaled distance for the explosion as below(C. Zhang   Here ρs is greater than the minimum ρs required, thus the pier with this dimension will withstand the explosion with this standoff distance and weight of TNT(Moussa et al., 2018).

Theoretical load development and response prediction
We also have to calculate pressure intensity and impulse for the same case. We can get these values from the graph shown in Figure 3 by calculating the value of scaling distance Z(Syed et al., 2016).
In our case Z=0.26 thus from the graph we get,

Po=9500 MPa
Is=350MPa m-s and To= 3.6 ms or 0.0036 s

Analytical approach
Use of ABAQUS software was selected for this study. Due to the use of explosion in analysis the time duration of analysis is of fraction of seconds and thus the element type used in this analysis is 8-noded continuum (brick) elements with reduced integration (C3D8R) for air blast and EC3D8R for coupled eulerian lagrangian domain analysis(Ibrahim and Nabil, 2019). The comparison of blast impact on a pier is observed in two different cases, both for air blast and for partially submerged pier under the effect of blast loading. Critical loading will be found in second analysis as damage done due to blast is much more worst in water than in air. As to create an assembly of partially submerged pier in water, and to create an EoS of a TNT we have to work in eulerian domain in which we can predefine the volumetric fraction and fill the volume with material such as water, air and TNT and analysis the model for that loading (Selvakumaran et al., 2018). To observe the damage in concrete and reinforcement after the failure or blast loading impact we have to provide the material properties for them accordingly. Here in this case material property used for concrete and steel are listed in the Figure 4 below(Hafezolghorani et al., 2017).

Figure 3 Shock Wave Parameters For Spherical TNT Explosion In Free Air At Sea Level
The assembly of domain containing water, air, TNT and pier is shown in figure. Eulerian domain can be assigned volume fraction to fill the predefined material in the domain(Jin et al., 2020).

Figure 6 Eulerian Domain, TNT And Pier Assembly
In field output options we have to select few extra entities such as SDV (solution dependent stress variable), UVARM (user defined output variables), STATUS (failure in plastic model), DMIERT (damage initiative criteria), EVF (volume fraction eulerian model), etc. interaction that need to be defined in this case will be a general contact for all the surface as domain and pier is in contact and interact with each other and embedded region for reinforcement and concrete. In loading portion, we have to predefine the material water and air that we have to fill in volume fraction of the domain region (Sabuwala et al., 2005)(Ibrahim and Nabil, 2019).

Result
As the blast occurs wave takes few milliseconds of time to reach the pier surface. Explosion wave travels much faster in air than in water and does more damage in water than in air. Water provides damping effect to the pier and thus reduces the damage done due to blast. Figure 7shows the initial domain ODB view for the analysis. Figure 8 shows the final representation of a domain after the analysis is over in 0.02seconds. as from the figure we can say that blast wave has travelled more in air domain.

Figure 8 After Blast Representation Of Domain
As we have analyzed the pier keeping the TNT at the middle of the domain, the majority of explosion takes place in air region and damage done due to that is more in that region.          Table 2 represents the comparison of theoretical and analytical entities required to analyze the blast.

Conclusion
Provision of slot increases the chances of scour reduction and thus increases the scour efficiency and minimize the failure due to scouring. On the same hand it reduces the strength of the pier. change in reinforcement patterns changes the behavior of the slotted pier. blast waves travel much faster in air than in water but does more damage in water than in air.
• Based on the results obtained from theoretical and analytical approach and as per the design suggested in NCHRP 12-72. • As per NCHRP 12-72 structural member is design appropriately for the blast load values given in this case for the displacement and rotation that occurs in the member. • The slotted pier is observed to reduce in strength than conventional pier under blast loading, exhibiting lower values of rotation and deformation. • The bottom fixed part and the area near the blast, which is middle part of the pier are the area of concern.
Middle portions forms a plastic hinge and fails abruptly after the blast. Bottom portion fails in shear after the blast.