The Application of Monte Carlo Method …
85
Table 3 Parameters of
concrete for FEM
calculations [11]
Modulus of elasticity, E (GPa)
38.28
Poisson’s ratio, v (1)
0.2
Average tensile strength, f ctm (MPa)
3.99
Average compressive strength, f cm (MPa)
56.4
Fracture energy, G F (kN/m)
0.151
Maximum diameter of aggregate particles d max (mm) 8
Active shear factor (1)
20
Table 4 Material parameters
for interface elements
(steel-concrete interface
transition zone)
Normal stiffness, k nn (MN/m 3 )
2 · 10 8
Tangential stiffness, k tt (MN/m 3 )
2 · 10 8
Cohesion, c (MPa)
1
Friction coefficient, φ (1)
0.1
Tension strength, f t (MPa)
0.3
Table 5 Parameters of steel
for FEM calculations [11]
Modulus of elasticity, E (GPa)
200
Poisson’s ratio, v (1)
0.3
Yield strength of steel, f y (N/mm 2 )
235
Values showing the width of cracks in the reinforced concrete specimen were
determined in the next stage. Calculations were made for the adopted MontereyWillam and Rankine-Fracturing material model for concrete and perfectly elastic
-plastic model by Huber-Misses-Hencky for steel. Material parameters for concrete
and steel are shown in Tables 3 and 4. Parameters necessary for defining the interfacial
transition zone are shown in Table 5.
As a result of the calculations, the courses of changes in the crack opening width
in the sample as a function of time were determined for the lower in f
ε
V
and
upper sup
ε
V
limits of the volume increase of corrosion products. The results of
the crack opening width were determined at the Gauss points of the finite element
(at the Gauss point located closest to the point measuring the crack opening A). The
calculation results obtained for both considered load cases and the graphic image
visualizing the way the sample is scratched assuming the visibility of the scratches
meeting the criterion w min ≥ 0.1 mm is presented in Fig. 6.
5 Summary and Final Conclusions
The proposed calculation approach is useful in estimating intervals, within which
damage to reinforced concrete elements in structures are observed under the corrosion
85
Table 3 Parameters of
concrete for FEM
calculations [11]
Modulus of elasticity, E (GPa)
38.28
Poisson’s ratio, v (1)
0.2
Average tensile strength, f ctm (MPa)
3.99
Average compressive strength, f cm (MPa)
56.4
Fracture energy, G F (kN/m)
0.151
Maximum diameter of aggregate particles d max (mm) 8
Active shear factor (1)
20
Table 4 Material parameters
for interface elements
(steel-concrete interface
transition zone)
Normal stiffness, k nn (MN/m 3 )
2 · 10 8
Tangential stiffness, k tt (MN/m 3 )
2 · 10 8
Cohesion, c (MPa)
1
Friction coefficient, φ (1)
0.1
Tension strength, f t (MPa)
0.3
Table 5 Parameters of steel
for FEM calculations [11]
Modulus of elasticity, E (GPa)
200
Poisson’s ratio, v (1)
0.3
Yield strength of steel, f y (N/mm 2 )
235
Values showing the width of cracks in the reinforced concrete specimen were
determined in the next stage. Calculations were made for the adopted MontereyWillam and Rankine-Fracturing material model for concrete and perfectly elastic
-plastic model by Huber-Misses-Hencky for steel. Material parameters for concrete
and steel are shown in Tables 3 and 4. Parameters necessary for defining the interfacial
transition zone are shown in Table 5.
As a result of the calculations, the courses of changes in the crack opening width
in the sample as a function of time were determined for the lower in f
ε
V
and
upper sup
ε
V
limits of the volume increase of corrosion products. The results of
the crack opening width were determined at the Gauss points of the finite element
(at the Gauss point located closest to the point measuring the crack opening A). The
calculation results obtained for both considered load cases and the graphic image
visualizing the way the sample is scratched assuming the visibility of the scratches
meeting the criterion w min ≥ 0.1 mm is presented in Fig. 6.
5 Summary and Final Conclusions
The proposed calculation approach is useful in estimating intervals, within which
damage to reinforced concrete elements in structures are observed under the corrosion