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

Kseniya Yurkova
Kseniya Yurkova
 and 
Tomasz Krykowski
Tomasz Krykowski
   | Dec 31, 2023
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Published Online: Dec 31, 2023
Page range: 109 - 123
Received: Apr 28, 2023
Accepted: Jun 27, 2023
DOI: https://doi.org/10.2478/acee-2023-0055
Keywords
© 2023 Kseniya Yurkova et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Description Value
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]

Description M1 M2 M3 M4 M5 M6 M7 M8
D/D* 4 4 4 1 8 1 1 1
γc0/γc0* {\gamma _{{\rm{c}}0}}/\gamma _{{\rm{c}}0}^* 1 1 1 1 1 0.7 1 1.3
βc/βc* {\beta _{\rm{c}}}/\beta _{\rm{c}}^* 1 2 3 2 2 2 2 2
βt/βt* {\beta _{\rm{t}}}/\beta _{\rm{t}}^* 1 2 3 2 2 1.33 1.33 1.33

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

Description of the variable Value
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

Description Value
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

Parameter Value
Coefficient of friction, μ (1) 1.0 0.2 0.2 0.2
Cohesion coefficient, ch(MPa) 0.0 0.375 0.375 0.375
Normal contact stiffness, Kn/Kn0 {{\rm{K}}_{\rm{n}}}/{\rm{K}}_{\rm{n}}^0 1.0 1.0 1.0 1.0
Tangent contact stiffness, Kt/Kt0 {{\rm{K}}_{\rm{t}}}/{\rm{K}}_{\rm{t}}^0 1.0 2.0 5.0 5.0
Maximum allowable shear stress, τmax (MPa) 1E20 18.77 18.77 18.77
Contact Type B NSS CZM S

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

Model LAB (mm) |ΔAB|(mm) ΔLAB%% \left| {\Delta {\rm{L}}_{{\rm{AB}}}^\% } \right|\left( \% \right)
EX1 101.22 - -
EDM E1 100.94 0.27 29
EDM E2 100.96 0.25 26
EDM E3 101.01 0.20 20
EDM E4 100.98 0.23 24
CDPM C1 101.22 0.01 1
CDPM C2 101.20 0.02 2
CDPM C3 101.20 0.02 2
CDPM C4 101.20 0.02 2
MW M1 101.29 0.07 6
MW M2 101.26 0.04 3
MW M3 101.31 0.09 7
MW M4 101.30 0.08 6

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

Contact Type MW with HSD2 EDM CDPM
B M1 E1 C1
NSS M2 E2 C2
S M3 E3 C3
CZM M4 E4 C4

Supplementary parameters of the cohesive model (CZM)

Parameter Value
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]

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

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

Description N1 N2 N3 N4
βt 2000 2000 2000 3000
c (mm2) 12 8 5 5
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