Computational study of impact fracture of concrete structures
R.R. Pedersen, L.J. Sluys and J. Weerheijm
Delft University of Technology Faculty of Civil Engineering and Geosciences P.O. Box 5048, 2600 GA Delft phone +31 15 278 8075, email: r.pedersen@citg.tudelft.nl
Introduction
For protective buildings, reinforced concrete is commonly used. Design against fragment penetration and blast loadings is an important issue for these structures. However, current knowledge on cracking patterns, and ultimate failure as a function of the explosive loading is insufficient to accurately predict the resistance.
Results
The coupled viscoplastic damage model shows promise for simulating the fracture process of the SHB test. (Figure 3).
Figure 3: Left: Crack pattern from tests. Right: Final damage state in numerical models. Figure 1: Explosion in tunnel.
Objective
Concrete structures exposed to impact loading respond differently than under static loading. Compressive and tensile strengths increase due to the loading rate effects. (Figure 2). Initial stiffness increases, and moreover the concrete strain capacity is increased in dynamic loading. The objective of this research is to develop a physically realistic model for concrete under high loading rates based on micro-mechanic considerations to account for the mechanisms that cause the strength increase.
6
The effect and physical interpretation of the model parameters are not sufficiently understood. In Figure 4 the effect of chosen model parameters on the localisation width is reported.
250
Influence of relaxation time
200
Influence of yield stress
τ=10.0 s β=10000 α=1.0 b=10000 a=1.0
Width of localisation [mm]
200
150
σ=3.0MPa y β=10000 α=1.0 b=10000 a=1.0
100
Width of localisation [mm]
20
150
100
50
50 0
Relaxation time [s] Influence of β
5
10
15
0 0
5
σ [MPa]
10
15
20
200
Influence of relaxation time
16 14 12 Stress [MPa] 10 8 6 4 2
4
Loading rate effect on concrete tensile strength
Width of localisation [mm]
150
3s 5s 10 s 15 s 20 s
5
Experiment D ata fit
100
σ=3.0 MPa y τ=10.0s α=1.0 b=10000 a=1.0
fd / fs
4
50
3
0 0
0.5
β [−]
1
1.5
2
0 0
0.001
x 10
0.002 Strain
0.003
0.004
2
Figure 4: Computational responses.
10
− 4
1 −5 10
10
− 3
10 10 10 10 Loading rate [GPa/s]
− 2
− 1
0
1
10
2
10
3
Future research
Development of a coupled hygromechanical model since moisture on a micromechanical level contributes to the strengthing effect.
Acknowledgements
Financial support from the Netherlands Technology Foundation (STW) and Prins Maurits Laboratory (TNO-PML) is gratefully acknowledged.
Figure 2: Rate effect in concrete.
Methods
A coupled experimental and numerical research program is defined. A modified Split Hopkinson Bar, SHB, test is used to determine the material properties in tension at high loading rates, which will be used in numerical models. In the numerical simulations a local damage model and a viscoplastic damage model are used.