# Dynamic Behavior of Concrete and Seismic Engineering

The obtained results indicate that aftershocks can have considerable effect on dynamic behaviour of concrete structures in terms of enlarging zones affected by irreversible strains or additional damage evolution. The analysis revealed that aftershocks, which are usually not as strong as mainshocks, may result even in total loss of concrete material strength while performing in mainshock—aftershock seismic sequences.

Large seismic mainshocks are usually followed by numerous aftershocks within a short period of time. Aftershocks can have a significant effect on the dynamic behaviour of a structure in terms of irreversible plastic strains and accumulated damage, as they affect a structure already weakened during a mainshock. The dynamic response of structures subjected to a mainshock—aftershock seismic sequence has been extensively studied recently. Representative examples of damages of buildings, observed under multiple earthquakes, can be found in current studies Abdelnaby Abdelnaby A.

Response of reinforced concrete structures under multiple earthquakes [PhD thesis]. Response of degrading RC frames under replicate motions. London UK : Oxford Abstracts. Aftershock response of RC buildings in Santiago, Chile, succeeding the magnitude 8. Eng Struct. Seismic analyses of a RCC building under mainshock—aftershock seismic sequences.

Soil Dyn Earthq Eng. Structures may go plastic or even collapse during aftershocks, since they are already degraded and cracked during mainshocks. Only advanced constitutive models of a concrete material, which include damage and failure phenomena, are advisable for examining the dynamic behaviour of concrete structures under mainshock—aftershock sequences. In the paper, the dynamic responses of a concrete building subjected to a mainshock—aftershock seismic sequence are investigated.

In order to compare damages under repeated earthquakes and to assess the impact of both shocks on the analyzed structure, the concrete damage plasticity CDP model, which describes multi-hardening plasticity and damage cracking , was implemented. The dynamic analysis of a concrete structure under multiple earthquakes was carried out for a one-story engine shed located in an industrial area. Dassault systemes ; [cited May 25].

The model of the concrete engine shed with monitoring points. Figure 1. The windows of the object are strengthened by concrete heads.

The structural roof system consists of steel trusses. The roof is covered by a steel sheeting. A plastic-damage model for concrete. Int J Solids Struct. Plastic-damage model for cyclic loading of concrete structures. J Eng Mech. The model is specially recommended for calculations of concrete structures subjected to dynamic loadings, like earthquakes Simulia Simulia ABAQUS. Performance of steel pipeline with concrete coating modeled with concrete damage plasticity under seismic wave passage. Appl Mech Mater.

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The CDP model consists of the combination of nonassociated multi-hardening plasticity and scalar damaged elasticity to describe the irreversible damage that occurs during the fracturing process. The yield surface is controlled by two variables representing equivalent plastic strains: and , associated with failure mechanisms under tension and compression loading, respectively.

The concrete damage is characterized by two different damage variables: for tension and for compression. These variables are functions of equivalent plastic strains.

They can take values from zero, which represents undamaged material, to one, which denotes total loss of strength. The CDP model assumes that the reduction of the elastic modulus E is given in terms of a scalar degradation variable d function of the stress state and the uniaxial damage variables d t and d c as: 1 where is the initial elasticity modulus of the undamaged material.

Experimental and numerical analysis of fracture processes in concrete. Delft : Delft University of Technology. Identification of parameters of concrete damage plasticity constitutive model. Found Civ Environ Eng.

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These properties were obtained through laboratory tests. Constitutive parameters of the concrete damage plasticity model Schlangen Schlangen E. Other parameters of the concrete material were taken as follows: the elasticity modulus In the dynamic analysis of the concrete structure, two earthquakes registered in Nocera Umbra central Italy were applied as kinematic excitations of the structure ITACA Time histories of the mainshock accelerations: a west—east direction, b north—south direction and c vertical direction. Figure 2.

## Behavior Of Concrete And Seismic Engineering

Figure 3. Time histories of the aftershock accelerations: a west—east direction, b north—south direction and c vertical direction. Table 2. The peak ground accelerations PGAs of the mainshock and the aftershock. The dynamic response of the concrete structure to both shocks was calculated using full time history analysis. As the damage and failure model of concrete implements strong material nonlinearity, a step of numerical integration was not fixed. The geometric nonlinearity of the problem was also taken into account.

For the dynamic analysis, the Rayleigh model of mass and stiffness proportional damping was applied. The damping ratio of 3. The dynamic analysis was performed for the selected mainshock—aftershock sequence. The observed evolution of plastic and damage measures, incorporated into the CDP model of the material, allowed to assess the impact of both shocks on the structure.

Distribution of plastic strain magnitude PEMAG on the front wall resulted from: a the mainshock, b the aftershock. Figure 4. Figure 5. The aftershock resulted only in a slight growth of the area affected by the plastic strains see points B and D.

## Dynamic Behavior of Concrete Structures, Volume 44 - 1st Edition

The level of plastic strains at some points increased considerably see point A after the second seismic event. However, at the vast majority of analyzed points, the level of plastic strains did not undergo noticeable changes see point C. The subsequent shock caused additional cracking in zones which did not undergo any damages during the first shock. The value of tensile damage variable reached 0. Time history of plastic , and tensile damage measures of the concrete material at point C due to the mainshock and the aftershock.

Figure 6. The following time histories of plastic and damage measures were examined: logarithmic maximal principal strains , equivalent plastic strains and tensile damage parameter. Logarithmic strain shows the dependence of total strain on time. Volume 49 Volume 48 Volume 47 Volume 46 Issue 2 Summer and Autumn , Page Issue 1 Winter and Spring , Page Bozorgmehrnia, S. Civil Engineering Infrastructures Journal , 46 2 , Civil Engineering Infrastructures Journal , 46, 2, , Civil Engineering Infrastructures Journal , ; 46 2 : These structures have various types and are constructed in a way that a greater portion of their weight is concentrated at an elevation much about the base.

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Damage to these structures during strong ground motions may lead to fire or other hazardous events. The liquid mass of the tank was modeled as lumped mass known as sloshing mass, or impulsive mass. The corresponding stiffness constants associated with the lumped mass were determined depending upon the properties of the tank wall and liquid mass.

Tank responses including base shear, overturning moment, tank displacement, and sloshing displacement were also calculated. Obtained results revealed that the system responses are highly influenced by the structural parameters and the earthquake characteristics such as frequency content. Dogangun, A. Donea, J. Dutta, S. Haroun, M. Housner, G. Kwak, H. Livaoglu, R.