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Analysis of Application of Gradient Concrete Models to Assess Concrete Cover Degradation Under Reinforcement Corrosion Cover

Analysis of Application of Gradient Concrete Models to Assess Concrete Cover Degradation Under Reinforcement Corrosion

Architecture, Civil Engineering, Environment
Volume 16 (2023): Issue 4 (December 2023)
By: Kseniya Yurkova and  Tomasz Krykowski  
Open Access
|Dec 2023

Figures & Tables

Figure 1.

Model of the test element subject to accelerated reinforcement corrosion: a) FEM model; b) steel-concrete contact zone model, description in the text
Model of the test element subject to accelerated reinforcement corrosion: a) FEM model; b) steel-concrete contact zone model, description in the text

Figure 2.

Functions of the intensity of the current and equivalent increments of volumetric strains in the plane perpendicular to the reinforcing bar axis, Δɛ (description in the text)
Functions of the intensity of the current and equivalent increments of volumetric strains in the plane perpendicular to the reinforcing bar axis, Δɛ (description in the text)

Figure 3.

Test model: a) notched tensile sample and b) cyclically compressed sample
Test model: a) notched tensile sample and b) cyclically compressed sample

Figure 4.

Response of the system and maps of principal tensile strains ɛ1 (model EDM, variables c, β): a) response of the system; b) c = 5 mm2, β = 50; c) c = 5 mm2, β = 100; d) c = 5 mm2, β= 300, e) c = 8 mm2, β= 50; f) c = 8 mm2, β = 100; g) c = 8 mm2, β= 300
Response of the system and maps of principal tensile strains ɛ1 (model EDM, variables c, β): a) response of the system; b) c = 5 mm2, β = 50; c) c = 5 mm2, β = 100; d) c = 5 mm2, β= 300, e) c = 8 mm2, β= 50; f) c = 8 mm2, β = 100; g) c = 8 mm2, β= 300

Figure 5.

Change of the σ-ɛ relationship in a cyclically compressed and tensiled sample (description in the text)
Change of the σ-ɛ relationship in a cyclically compressed and tensiled sample (description in the text)

Figure 6.

Relationship between the force and displacement of the system with a variable value of the βt parameter and the gradient parameter c (description in the text)
Relationship between the force and displacement of the system with a variable value of the βt parameter and the gradient parameter c (description in the text)

Figure 7.

Maps of the main tensile strains ɛ1 of the notched element (CDPM model, variable parameters βt and c): a) N1, βt = 2000, c = 12; b) N2, βt = 2000, c = 8; c) N3, βt = 2000, c = 5; d) N4, βt = 3000, c =5
Maps of the main tensile strains ɛ1 of the notched element (CDPM model, variable parameters βt and c): a) N1, βt = 2000, c = 12; b) N2, βt = 2000, c = 8; c) N3, βt = 2000, c = 5; d) N4, βt = 3000, c =5

Figure 8.

The evolution of changes in the elongation of the edges of elements of reinforced concrete samples ΔLAB as a result of reinforcement corrosion/calculation model (cf. Fig. 1)
The evolution of changes in the elongation of the edges of elements of reinforced concrete samples ΔLAB as a result of reinforcement corrosion/calculation model (cf. Fig. 1)

Figure 9.

Maps of total and principal strains, ɛ1, with the CDPM gradient model, time t=388 h
Maps of total and principal strains, ɛ1, with the CDPM gradient model, time t=388 h

Figure 10.

Maps of total and principal strains, ɛ1, with the EDM gradient model, time t=388 h
Maps of total and principal strains, ɛ1, with the EDM gradient model, time t=388 h

Figure 11.

Maps of the total and principal strains, ɛ1, model MW with HSD2, time t=388 h
Maps of the total and principal strains, ɛ1, model MW with HSD2, time t=388 h

Initial elastic and strength material parameters of concrete

DescriptionValue
Modulus of elasticity, E (GPa)38.28
Poisson’s ratio, ν (−)0.2
Uniaxial tensile strength, ft (MPa)3.99
Uniaxial compressive strength, fc (MPa)56.4
Biaxial compressive strength, fbc=1.15 fc (MPa)64.86

Variable material parameters of the CDPM model assumed for the cyclic compression test to determine the value D, βc, γc0, [30]

DescriptionM1M2M3M4M5M6M7M8
D/D*44418111
γc0/γc0* {\gamma _{{\rm{c}}0}}/\gamma _{{\rm{c}}0}^* 111110.711.3
βc/βc* {\beta _{\rm{c}}}/\beta _{\rm{c}}^* 12322222
βt/βt* {\beta _{\rm{t}}}/\beta _{\rm{t}}^* 123221.331.331.33

The material parameters of the CDPM model assumed in the cyclic compression test to determine the values D, βc, γc0, [30]

Description of the variableValue
Abscissa of the intersection point between the compression cap and the Drucker-Prager yield function, σVc \sigma _{\rm{V}}^{\rm{c}} (MPa)−50
The ratio between the major and minor axes of the cap, R (−)2
Tension cap hardening constant, RT (−)1
Tension damage thresholds, γt0 · 105 (−)9.38
Nonlocal interaction range parameter, c (−)10
Over-nonlocal averaging parameter, m (−)2.5
Tension damage evolution constant, βt*− \beta _{\rm{t}}^*\left( - \right) βt*=1.5 βc* \beta _{\rm{t}}^* = 1.5\;\beta _{\rm{c}}^*
Hardening material constant, D* (MPa)10000
Compression damage thresholds, γc0*− \gamma _{{\rm{c}}0}^*\left( - \right) 0.0001
Compression damage evolution constant, βc*− \beta _{\rm{c}}^*\left( - \right) 1000

Initial elastic and strength material parameters of steel

DescriptionValue
Modulus of elasticity, Es (GPa)200
Poisson’s ratio, νs (1)0.3
Yield strength, fy (MPa)235

Contact model parameters: bonded, no separation with sliding, CZM, standard

ParameterValue
Coefficient of friction, μ (1)1.00.20.20.2
Cohesion coefficient, ch(MPa)0.00.3750.3750.375
Normal contact stiffness, Kn/Kn0 {{\rm{K}}_{\rm{n}}}/{\rm{K}}_{\rm{n}}^0 1.01.01.01.0
Tangent contact stiffness, Kt/Kt0 {{\rm{K}}_{\rm{t}}}/{\rm{K}}_{\rm{t}}^0 1.02.05.05.0
Maximum allowable shear stress, τmax (MPa)1E2018.7718.7718.77
Contact TypeBNSSCZMS

Comparison of the calculation results and the percentage deviation from the results obtained for the MW model with HSD2

ModelLAB (mm)|ΔAB|(mm) ΔLAB%% \left| {\Delta {\rm{L}}_{{\rm{AB}}}^\% } \right|\left( \% \right)
EX1101.22--
EDM E1100.940.2729
EDM E2100.960.2526
EDM E3101.010.2020
EDM E4100.980.2324
CDPM C1101.220.011
CDPM C2101.200.022
CDPM C3101.200.022
CDPM C4101.200.022
MW M1101.290.076
MW M2101.260.043
MW M3101.310.097
MW M4101.300.086

List of materials and contact models analysed in the paper, along with denotations

Contact TypeMW with HSD2EDMCDPM
BM1E1C1
NSSM2E2C2
SM3E3C3
CZMM4E4C4

Supplementary parameters of the cohesive model (CZM)

ParameterValue
Maximum normal contact stress, σmax (MPa)3.99
Critical crack energy in the normal direction, Gcn (N/m)151
Maximum tangential contact stress, τt,max (MPa)2.26
Critical fracture energy in the tangential direction, Gct (N/m)113
Artificial damping parameter, η (1)0.0001

Inelastic parameters of the MW model with HSD2 [21]

DescriptionValueDescriptionValue
Fracture energy, Gft (N/m)151Ωci (1)*)0.33
Dilation angle, ψ (Deg)20Ωcu (1)*)0.85
κcm (1)*)0.00151Ωcr (1)*)0.2
κcu (1)*)0.00175Ωtr (1)*)0.1

Variable material parameters of the CDPM model assumed for the tensile test to determine the values βt and c [30]

DescriptionN1N2N3N4
βt2000200020003000
c (mm2)12855
DOI: https://doi.org/10.2478/acee-2023-0055 | Journal eISSN: 2720-6947 | Journal ISSN: 1899-0142
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Language: English
Page range: 109 - 123
Submitted on: Apr 28, 2023
Accepted on: Jun 27, 2023
Published on: Dec 31, 2023
Published by: Silesian University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
Corrosion,
FEM,
Gradient methods,
Plasticity,
Cover degradation
Related subjects:
Architecture and design,
Architecture,
Architects, buildings

© 2023 Kseniya Yurkova, Tomasz Krykowski, published by Silesian University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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