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

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

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