Seismic Damage Evaluation of Reinforced Concrete Structures Using 3D Lattice Model
Department of Civil Engineering, Kobe University
Mauro Ricardo SIMÃO (Student ID: 120T147)
Supervisor: Dr. Tomohiro Miki
1. INTRODUCTION
On the scope of the Hyogo-Ken Nanbu Earthquake, a big degree of destruction was registered on RC urban elevatedviaducts; causing a re-evaluation of seismic performance assessment. On that note, the objective of this study is topropose means of seismic damage assessment of RC structures using a 3D lattice model with an actual geometricalconfiguration discretization of the target structure to perform nonlinear static and dynamic analysis and propose energy
dissipation as a valid measurement for seismic damage range evaluation.
2. ANALYTICAL MODEL
The analytical system of lattice model divides the concrete in truss members and arch members. For a 2D represented
RC column, the concrete is modelled into flexural compression members, horizontal members, diagonal compression
members, diagonal tension members, horizontal members and two arch members (Miki et al.2004) according to Fig. 1.
Ratio of the width of the arch part to the cross section b is defined as index t. Based on the 2D model lattice model, a 3Dmodel, as presented in Fig. 2, is developed where the analytical model is assumed to be equivalent. In the 3D latticemodel, the assumption of global stiffness being equivalent to 2D lattice model allows the estimation of the crosssectional area of the arch and truss members (Miki et al. 2004).

Fig. 1 2D lattice model (Miki et al. 2004)

Fig. 2 3D lattice model for a RC column (Miki et al. 2004)

3. NONLINEAR ANALYSIS FOR RC VIADUCT COLUMN
3.1 Outline of target structure modelling and analysis
The target structure C1-5 is a reinforced concrete column tested in E-Defence (Kawashima et al. 2010).as shown inFig. 3, with diameter of 2000 mm and 7500 mm tall, where the design concrete strength is 27 MPa and the longitudinal
and transverse bars have a nominal strength of 345 MPa subjected to E-Takatori input ground motion, which is 80% oforiginal JR Takatori Station ground motion.
The column has been modelled into the 3D lattice model presented in Fig. 4. The particularity of this modelling isthe change in geometry of the target structure, where different from the study presented by Miki et al. (2003), the crosssection is circular which introduced a need for readjustments on the analytical model, where a circular 16 peripheral
nodes model based in equivalence in area moment of inertia between the model and the target has been used to estimate
both mesh size, as well as arch and truss members cross section. Although it proved difficult to accurately estimate thecross section of concrete members, which ultimately was subjected to sensitivity analysis, the analysis was performed inorder to produce results as accurate as possible, which was verified by comparing analytical and experimental results.
The model itself is 8000 mm tall with a mesh size of 810 mm defined as half of the analytical diameter, which in the caseis 1620 mm. Because of its geometry; it has been discretized with 8 arch members to seek improvement in accuracy. It isdifficult to obtain an exact matching model of the target structure, due to differences in discretization based on the meshsize and the actual size of the structure, therefore the main aim is to come as close as possible.
In the pre-analysis, the values of index t for both width and effective depth are assumed as 0.35 and 0.25 (Miki et al.
2004), for simplification, and are based on the principle of minimum total potential energy. The loading point is
considered to be at the top of the column, and thus the shear span as shown by the experimental program presented byKawashima et al (2010). C1-5 was subjected to the 100% E-Takatori ground motion (C1-5(1)) and after the mass wasincreased by 21 % from 307 t to 372 t, C1-5 was subjected to the 100% E-Takatori ground motion (C1-5(2)).Then C1-5
was subjected to the 125% E-Takatori ground motion (C1-5(3)). Dynamic analysis has been performed using
DYNALLAT 1.1.4, in-house developed software based on nonlinear finite elements analysis.

1

1500

D35@36bars

9300

6000

D22@150mm

150 100
1800

1800

56@150=8400

27@300=8100

D35@36bars

7000

Fig. 3 Target structure details

Fig 4. Column discretization model

3.2 Energy dissipation on RC column
The results from dynamic analysis are used to propose the amount of energy dissipated under seismic loading as ameasurement of damage range. To do that, the energy inside the pier is addressed in terms of the elemental energy where
it’s assumed that the average stress-strain relationships govern each element after cracking occurs and used for
estimation of strain energy as presented in Eq. (1). The energy dissipation presented in Eq. (2) is used, where it will be
the total sum of the product between strain energy and volume for each element. The energy dissipation has been
calculated for the three C1-5 targets for total size and bottom part of the columns corresponding to 1620 mm.

STRAIN  ENERGY 1 i   11  i   i1 2(1)

ENERGY  DISSIPATION  i 1 STRAIN  ENERGY  Vi n(2)1000Energy Dissipation (kN-m)

900

800
700
600

Bottom Layers Energy
Dissipation (kN-m)

500

Total Energy Dissipation(kN-m)

400
300
200
100

0C1-5(1)C1-5(2)
TargetC1-5(3)Fig. 5 Energy dissipation in three cases of C1-5 during excitations
4. CONCLUSIONSThe study presented 3D lattice model analysis of RC column, in order to grasp seismic behaviour. An actual
circular cross section target model has been developed for analysis using circular 16 peripheral nodes approach. Basedon dynamic analysis of cyclic loading, energy dissipation has been proposed for the evaluation of damage range in RCstructures. From the analytical results, the level of damage increases from case C1-5(1), to C1-5(2) and finally C1-5(3).
Furthermore the results suggest that about 50% of damage is concentrated at the bottom of the piers. The concept ofdamage evaluation using energy dissipation allows the expansion of scope to full framed RC viaducts.
REFERENCES
Kawashima, K., Sasaki, T., Ukon, H., Kajiwara, K., Unjoh, S., Sakai, J., Kosa, k., Takahashi, Y., Yabe, M., andMatsuzaki, H.: Evaluation of Seismic Performance of a Circular Reinforced Concrete Bridge Column Designed inAccordance With the Current Design Code Based on E-Defence Excitation, Journal of JSCE, vol.66, no.2, 2010, 324343.(in Japanese)Miki, T., and Niwa, J.: Analytical Evaluation of Seismic Performance For reinforced Concrete Bridge Piers, TechnicalReport, no.67, Department of Civil Engineering, Tokyo institute of Technology, March 2003, Tokyo, Japan.
Miki, T., and Niwa, J.: Nonlinear Analysis of RC Structural Members using 3D Lattice Model, Journal of Advanced
Concrete Technology, Japan Concrete Institute, vol.2, No. 3, 2004, Japan, 345-358.

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