^{1}

^{1}

^{2}

^{1}

^{2}

Most of the recent studies focus on the progressive collapse of ordinary structures due to gravity and blast loads. A few focus on studying progressive collapse due to seismic actions, especially of bridge structures. The past major earthquakes have shown that it is possible to develop improved earthquake-resistant design techniques for new bridges if the process of damage from initial failure to ultimate collapse and its effects on structural failure mechanisms could be analyzed and monitored. This paper presents a simulation and analysis of bridge progressive collapse behavior during seismic actions using the Applied Element Method (AEM) which can take into account the separation of structural components resulted from fracture failure and falling debris contact or impact forces. Simple, continuous, and monolithic bridges’ superstructures were numerically analyzed under the influence of the severe ground motions not considering the live loads. The parameters studied were the superstructure redundancy and the effect of severe ground motion such as Kobe, Chi-Chi, and Northridge ground motions on different bridge structural systems. The effect of reducing the reinforcement ratio on the collapse behavior of RC box girders and the variation of columns height were also studied. The results showed that monolithic bridge models with reduced reinforcement to the minimum reinforcement according to ECP 203/2018 showed a collapse behavior under the effect of severe seismic ground motions. However, changing the bridge structural system from monolithic to continuous or simple on bearing bridge models could prevent the bridge models from collapse.

Progressive collapse phenomenon is defined as the global damage or collapse behavior of a large part of the structural system that is caused by a failure of a relatively small or localized part of the structure. Structural progressive collapse occurs as a result of failure of one or more structural members or components. The load is transferred in the structural system due to changes in the distribution of stiffness, the pattern of the stress behavior, and/or the structural boundary conditions [

Seible et al. [

Previous studies on the progressive collapse of structures gave insights into the effect of strengthening on improving the structural capacity to prevent progressive collapse due to seismic and blast loads. Those studies have shown that such detailing and strengthening against the earthquake could enhance buildings’ progressive collapse resistance to such load effects [

Wibowo et al. [

In a similar vein, Salem et al. [

Domaneschi et al. [

Bridges could be in several structural forms, i.e., simple on bearings, continuous on bearings, and monolithic with column bridge structures. There are no sufficient studies on the effect of severe seismic ground motions for such different bridges’ structural systems; especially, most researchers studied bridges’ models, either continuous or simple bridges. In the current study, Wibowo’s Bridge is modeled and verified using the applied element method. Also, the effect of the reduction in reinforcement quantity on the collapse of RC box girder bridges under Kobe ground motion is investigated. Several bridges’ models with different structural systems such as simple on bearings, continuous on bearings, and monolithic with column bridges are analyzed under severe seismic ground motions: Kobe, Chi-Chi, and Northridge earthquakes.

The Extreme Loading for Structures (ELS) program, developed by ASI-2018 [

Modeling of a structure with AEM [

Different types of element contacts. (a) Corner-to-face or corner-to-ground contact. (b) Edge-to-edge contact [

Maekawa and Okamura's model [

An interface material is used to model bearings. The interface material model is a precracked element where the material is initially cracked and cannot bear tensile stresses. As for compression, the stress–strain relation is linear up to compression failure stress (Figure

Modeling of a bearing interface with AEM [

During progressive collapse analysis, the failure, separation, contact, and falling debris of elements must be traced. Using FEM, it is very difficult to model progressive collapse. On the other hand, using AEM, to analyze these processes is made easy and effective taking into consideration all the analysis stages until collision (Figure

Scope of FEM and AEM.

The selected numerical example was previously investigated experimentally by Guedes [

Layout of the bridge structural elements [

Reinforcement details of the numerical study [

Material properties of the numerical model.

Parameter | Pier 2 | Pier 3 | Pier 4 | Box girder | R. Steel | Unit |
---|---|---|---|---|---|---|

Compressive strength | 3.212 | 3.569 | 4.375 | 3 | 3.6 | kg/m^{2} |

Tensile strength | 3.212 | 3.569 | 4.375 | 3 | 3.6 | kg/m^{2} |

Strain at unconfined peak stress | 0.002 | 0.002 | 0.002 | 0.002 | — | m/m |

Young’s modulus | 2.55 | 2.55 | 2.55 | 2.55 | 2.0389 | kg/m^{2} |

Shear modulus | 1.062 | 1.062 | 1.062 | 1.062 | 8.155 | kg/m^{2} |

Specific weight | 2549.291 | 2549.291 | 2549.291 | 2549.291 | 7840 | kg/m^{3} |

Separation strain | 0.1 | 0.1 | 0.1 | 0.1 | 0.2 | — |

Friction coefficient | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 | — |

Postyield stiffness ratio | — | — | — | — | 0.01 | — |

The used earthquake ground motion was artificial; it followed the work of Guedes [

Artificial earthquake ground motion [

Hereby, the analysis is performed twice. The first assumes that the box girder is elastic, and the piers are assumed to be nonlinear, while the second considers the nonlinear behavior of the box girder and the piers. The top displacement of the piers is compared by that obtained from Wibowo et al. [

As shown in Figure

Comparison between the displacement time history of the top end of the piers of the numerical study and the research of Wibowo et al. [

Analyzing the nonlinear model, the top displacements of the piers were compared by those obtained by Wibowo et al. [

Comparison between the displacement time history of the top end of the piers of the numerical study and the research of Wibowo et al. [

Throughout the analysis of the nonlinear model, the collapse mechanism was monitored (Figure

Collapse mechanism of the nonlinear bridge model during the time history.

Through these results, it can be concluded that ELS can correctly model the bridge linear and nonlinear behavior, including various structural elements such as piers, bridge superstructure, reinforcement details, and material properties, and thus can provide reliable results.

RC box girder bridges were modeled 3 × 25000 millimeters bays (Figure

Layout of the box girder bridges. (a) Monolithic with columns; (b) continuous on bearing; and (c) simple box girder bridges on bearing.

Dimensions of the box girder and reinforcement details of the bridge elements.

Bridge models and box girder reinforcements (unit: mm).

Model | Ground motion | Bridge system | Sec. | Reinforcement of the box girder | Reinforcement ratio (%) | |||
---|---|---|---|---|---|---|---|---|

Ø (mm)/spacing (mm) | No. of bars Ø (mm) | |||||||

A1-M-K | Kobe | Monolithic | 1 | Ø16/125 | Ø18/125 | 16Ø32 | 10Ø32 | 100 |

2 | 34Ø32 | |||||||

A2-M-K | Kobe | Monolithic | 1 | Ø10/125 | Ø10/125 | 16Ø18 | 10Ø18 | 35 |

2 | 34Ø18 | |||||||

A3-M-K | Kobe | Monolithic | 1 | Ø10/125 | Ø8/125 | 16Ø16 | 10Ø16 | 25 |

A3-M-C | Chi-Chi | |||||||

A3-M-N | Northridge | 2 | 34Ø16 | |||||

A3-C-K | Kobe | Continuous | 1 | Ø10/125 | Ø8/125 | 16Ø16 | 10Ø16 | |

A3-C-C | Chi-Chi | |||||||

A3-C-N | Northridge | 2 | 34Ø16 | |||||

A3-S-K | Kobe | Simple | 1 | Ø10/125 | Ø8/125 | 30Ø16 | 10Ø16 | |

A3-S-C | Chi-Chi | |||||||

A3-S-N | Northridge |

∗-M-∗: monolithic; ∗-C-∗: continuous; and∗-S-∗ simple bridges. ∗-∗-C: Chi-Chi; ∗-∗-K: Kobe; and ∗-∗-N: Northridge.

The material properties adopted in AEM analysis are presented in Table

Properties of the bridge materials.

Parameter | Concrete | Steel reinforcement and plates | Bearing interface | Unit |
---|---|---|---|---|

Compressive strength | 4 | 3.6 | 5.51 | kg/m^{2} |

Tensile strength | 4 | 3.6 | — | kg/m^{2} |

Young’s modulus | 2.213 | 2.0389 | 2.0389 | kg/m^{2} |

Shear modulus | 984297 | 8.1556 | 203943 | kg/m^{2} |

Specific weight | 2500 | 7840 | 7840 | kg/m^{3} |

Separation strain | 0.2 | 0.12 | 1 | — |

Friction coefficient | 0.8 | 0.8 | 0.6 | — |

Ultimate strength/tensile stress | — | 1.4444 | — | — |

Normal contact stiffness factor | 0.0001 | 0.0001 | 0.0001 | — |

Shear contact stiffness factor | 1.00 | 1.00 | 1.00 | — |

Contact spring unloading stiffness factor | 2 | 2 | 2 | — |

Postyield stiffness ratio | — | 0.01 | — | — |

Kobe, Chi-Chi, and Northridge ground accelerations were used in the progressive collapse analysis of the bridge models, as there was some bridge collapse during these earthquakes [

Seismic ground motions.

Earthquake | Year of occurrence | Record station | PGA in X-Dir. (g) | Moment magnitude | Original duration | Reduced duration |
---|---|---|---|---|---|---|

Kobe | Jan 1995 | KJMA | 0.834 | 6.9 | 90 | 20 |

Chi-Chi | Sep 1999 | CWB | 0.63 | 7.6 | 90 | 15 |

Northridge | Jan 1994 | CDMG | 1.585 | 6.7 | 40 | 15 |

(a) Original and reduced 1995 Kobe earthquake ground motion. (b) Original and reduced 1999 Chi-Chi earthquake ground motion. (c) Original and reduced 1994 Northridge earthquake ground motion.

A mesh sensitivity analysis was carried out to obtain a suitable mesh size that would be used in all the analysis cases for columns and bridge superstructure. Horizontal and vertical concentrated loads were used for the column and the box girder, respectively. Figure

Mesh sensitivity of the column and the box girder. (a) Column. (b) Box girder.

The analysis was carried out on two stages; the first was static to take into account the gravity loads and original deformations of the bridge, whereas the second was a dynamic analysis, implementing the different seismic ground motions. For more details about how the analysis was carried out, please refer to ELS theoretical manual, ASI [

Figure

Displacements–time history of the right column of models “A1-M-K, A2-M-K, and A3-M-K.”

Figure

(a) Axial force–time history of the right column of models “A1-M-K, A2-M-K, and A3-M-K.” (b) Moment–time history of the right column of models “A1-M-K, A2-M-K, and A3-M-K.” (c) Base shear–time history of the right column of models “A1-M-K, A2-M-K, and A3-M-K.”

Figure

Displacements–time history of the right column of models “A3-M-K, A3-C-K, and A3-S-K.”

Figure

(a) Axial force–time history of the right column of models “A3-M-K, A3-C-K, and A3-S-K.” (b) Moment–time history of the right column of models “A3-M-K, A3-C-K, and A3-S-K.” (c) Base shear–time history of the right column of models “A3-M-K, A3-C-K, and A3-S-K.”

Cracks are represented through the principal strains. A comparison between models A1-M-K, A2-M-K, and A3-M-K is presented in Figures

Principal normal strain of model “A1-M-K.”

Principal normal strain of model “A2-M-K.”

(a) 2D view of the principal normal strain during the time history “model A3-M-K.” (b) 3D view of the principal normal strain during the time history “model A3-M-K.”

In the monolithic bridge models, the seismic ground motions brought about cracks at the upper and lower ends of the columns in the plastic hinge zones, since they are the areas of stress concentration. It should be noted that the cracks did not spread along with the column height, as the column dimensions were very large (1 × 2.5 meters), and the amount of reinforcing steel, either stirrups or longitudinal reinforcement, was very high. Also, in Figure

Figures

Principal normal strain during the time of “model A3-C-K.”

Principal normal strain during the time of “model A3-S-K.”

Kobe, Chi-Chi, and Northridge ground motions were used to analyze monolithic, simple, and continuous bridge models to determine the effect of severe ground motions on the collapse behavior of these bridge models. From models A3-M-K, A3-M-C, and A3-M-N, it is noted that the monolithic bridge model always had a collapse behavior once the reinforcement ratio of the superstructure has been reduced below the minimum reinforcement ratio (Figures

Principal normal strain at the end of the analysis, “model A3-M-C.”

Principal normal strain at the end of the analysis, “model A3-M-N.”

Principal normal strain at the end of the analysis, “model A3-C-C.”

Principal normal strain at the end of the analysis, “model A3-C-N.”

Principal normal strain at the end of the analysis, model “A3-S-C.”

Principal normal strain at the end of the analysis, model “A3-S-N.”

In model A3-M-K, it is noted that the monolithic bridge model collapsed by Kobe ground acceleration, while by analyzing the same bridge configuration it showed a partial collapse by Chi-Chi and Northridge ground accelerations, as in models A3-M-C and A3-M-N. Thus, the collapse of the structures did not depend on the largest value of the peak ground acceleration; yet it depended on the number of cyclic reversal accelerations.

In the current study, the seismic progressive collapse behavior and analysis of reinforced concrete bridges were analyzed. Various bridge configurations: monolithic with columns, continuous on bearings, and simple on bearings bridge models were analyzed. The bridge models and selected earthquake excitations used in the study were discussed. A summary of the findings is presented herein.

Progressive collapse will not occur unless the reinforcement ratio of the bridge superstructure is reduced to the minimum reinforcement ratio according to the ECP 203-2018.

Monolithic bridge models with reduced reinforcement ratio always show a collapse behavior during the analysis using severe ground motions. However, changing the bridge structural system from monolithic to continuous or simple on bearing bridge models prevented the bridge models from collapse.

The total collapse of the structures does not depend on the largest value of the peak ground acceleration as in Northridge, and it depends on the number of reversal cycles of reversal waves as in Kobe.

In reinforced bridge models that are designed according to “The Egyptian Code of Practice 203-2018,” the reinforcement ratio in the bridge prevents any bridges from collapsing even under the influence of the severe ground motions, but it may show some cracks both at the bridge superstructure and at the column bases.

Similar progressive collapse phenomenon is observed in the collapse of bridge structures caused by blast or abnormal loads and is also observed in the failures of structures during earthquakes even although the damage and propagation characteristics are more universal in nature, as can be detected in the analysis and simulation results in this study.

ELS program can be a means to predict the behavior of ordinary and special structures against abnormal events during the design, construction, and service loads.

Sufficient ductility capacity in bridge columns or piers can help ensure ductile behavior and higher deformation capability of the structure that leads to better performance against seismic progressive collapse.

The datasets used to support the findings of this study are incorporated into the article.

The authors declare that that there are no conflicts of interest regarding the publication of this paper.