Structural performance evaluation of an aged structure using a modified plasticity model in inverse solution method

Figures & data

Figure 1. Uniaxial compressive stress–strain model presented by Hsu and Hsu [23].

Figure 2. Biaxial strength of concrete – Kupfer and Hilsdorf [25].

Figure 3. ‘Tensile behaviour’ for CDP model – Enochsson et al. [27].

Figure 4. Hyperbolic Drucker–Prager flow potential function-Abaqus theory manual, 6.11 [28].

Figure 5. ‘Tensile behaviour’ for CDP model – Wahalathantri et al. [24].

Figure 6. Flowchart of performance of CDP model.

Table 1. Variables used in inverse analyses.

Plastic input parameters			Elastic input parameters
Name	Value		Name	Value
ψ = Dilatation angle (degrees)	35		E H = Out-of-plane Young’s Modulus (MPa)	Variable
e = Eccentricity (dimensionless)	0.1		E v = In-plane Young’s Modulus (MPa)	Variable
F = σ bo/σ co (dimensionless)	1.16		υHV = Out-of-plane Poisson’s ratio	Variable
$K_{\text{c}}=\frac{{\overline{q}}_{\text{TM}}}{{\overline{q}}_{\text{CM}}}$ (dimensionless)	0.778		υV = In-plane Poisson’s ratio	Variable
			G H = Shear modulus (MPa)	Variable
Compressive behaviour			Tensile behaviour
Stress (MPa) variable	Strain (%)	d c = Compressive damage parameter	Stress (MPa) variable	Strain (%)	d t = Tensile damage parameter
0.3 f c	3.90E-04	0	0.08 f c	0	0
0.6 f c	1.00E-03	0	0.1 f c	3.333E-005	0
1.0 f c	1.90E-03	0	0.67 f c	0.00016042	0.342
0.8 f c	3.00E-03	0.2	0.3 f c	0.00027976	0.696
0.5 f c	4.00E-03	0.487	0.08 f c	0.00068459	0.920
0.3 f c	5.00E-03	0.671	0.01 f c	0.00108673	0.980

Figure 7. Solution procedure.

Figure 8. Dez Dam subdivisions separated by contraction joints.

Figure 9. Dez Dam section.

Figure 10. FE Model of the Dez Dam and its support.

Table 2. Element library of the dam–reservoir–foundation model.

Part	Number	Element type	FEM part
Arch dam	4672	C3D4
Foundation	853	C3D4
Reservoir	8503	Fluid- 8node
Total	14,028

Table 3. Long-term elastic stiffness components of the Dez Dam.

Year	E H (GPa)			E v (GPa)			υV	υHV	G H (GPa)
	Zone			Zone					Zone
	1	5	9	1	5	9			1	5	9
2007s	25	32	26	29	32	31	0.150	0.190	13	14	13.5
2005s	25	32	27	29	32	31	0.155	0.185	13	14	13.5
2001s	25.5	32	27	29	32	31	0.155	0.185	13	14	14
1999s	26	32	28.5	29.5	32	31	0.165	0.18	13.5	14	14
1995s	27.5	32	29	29.5	32	31	0.170	0.175	13.5	14	14
1991s	28	32	29.5	30	32	31	0.170	0.175	14	14	14
1987s	30	32	30.5	31	32	31	0.170	0.170	14	14	14
1980s	30.5	32	30.5	31	32	31	0.170	0.170	14	14	14
1976s	31	32	31	31	32	31	0.170	0.170	14	14	14
1973s	31.5	32	31.5	31.5	32	31.5	0.170	0.170	14	14	14
1970s	32	32	32	32	32	32	0.170	0.170	14	14	14
1965s	32	32	32	32	32	32	0.170	0.170	14	14	14

Figure 11. Long-term variations of the out-of-plane elastic modulus.

Figure 12. Long-term variations of the in-plane elastic modulus.

Figure 13. Long-term variations of the compressive strength of Dez Dam’s concrete.

Figure 14. Change of Young’s moduli over time at top and bottom of the dam in zone 1.

Figure 15. Change of Young’s moduli over time at top and bottom of the dam in zone 9.

Figure A1. Variations of water level of reservoir and temperature throughout the Year 1965 – blue line denotes water levels of reservoir, red line indicates temperature values at downstream face, green line shows temperature values at upstream face of the Dez Dam and two dotted vertical lines present two days selected for performing thermal inverse analysis.

Figure A2. Variations of water level of reservoir and temperature throughout the Year 1970 – blue line denotes water levels of reservoir, red line indicates temperature values at downstream face and green line shows temperature values at upstream face of the Dez Dam and two dotted vertical lines present two days selected for performing thermal inverse analysis.

Figure A3. Variations of water level of reservoir and temperature throughout the Year 1973 – blue line denotes water levels of reservoir, red line indicates temperature values at downstream face and green line shows temperature values at upstream face of the Dez Dam and two dotted vertical lines present two days selected for performing thermal inverse analysis.

Figure A4. Variations of water level of reservoir and temperature throughout the Year 1976 – blue line denotes water levels of reservoir, red line indicates temperature values at downstream face and green line shows temperature values at upstream face of the Dez Dam and two dotted vertical lines present two days selected for performing thermal inverse analysis.

Figure A5. Variations of water level of reservoir and temperature throughout the Year 1980 – blue line denotes water levels of reservoir, red line indicates temperature values at downstream face and green line shows temperature values at upstream face of the Dez Dam and two dotted vertical lines present two days selected for performing thermal inverse analysis.

Figure A6. Variations of water level of reservoir and temperature throughout the Year 1987 – blue line denotes water levels of reservoir, red line indicates temperature values at downstream face and green line shows temperature values at upstream face of the Dez Dam and two dotted vertical lines present two days selected for performing thermal inverse analysis.

Figure A7. Variations of water level of reservoir and temperature throughout the Year 1991 – blue line denotes water levels of reservoir, red line indicates temperature values at downstream face and green line shows temperature values at upstream face of the Dez Dam and two dotted vertical lines present two days selected for performing thermal inverse analysis.

Figure A8. Variations of water level of reservoir and temperature throughout the Year 1995 – blue line denotes water levels of reservoir, red line indicates temperature values at downstream face and green line shows temperature values at upstream face of the Dez Dam and two dotted vertical lines present two days selected for performing thermal inverse analysis.

Figure A9. Variations of water level of reservoir and temperature throughout the Year 1999 – blue line denotes water levels of reservoir, red line indicates temperature values at downstream face and green line shows temperature values at upstream face of the Dez Dam and two dotted vertical lines present two days selected for performing thermal inverse analysis.

Figure A10. Variations of water level of reservoir and temperature throughout the Year 2001 – blue line denotes water levels of reservoir, red line indicates temperature values at downstream face and green line shows temperature values at upstream face of the Dez Dam and two dotted vertical lines present two days selected for performing thermal inverse analysis.

Figure A11. Variations of water level of reservoir and temperature throughout the Year 2005 – blue line denotes water levels of reservoir, red line indicates temperature values at downstream face and green line shows temperature values at upstream face of the Dez Dam and two dotted vertical lines present two days selected for performing thermal inverse analysis.

Figure A12. Variations of water level of reservoir and temperature throughout the Year 2007 – blue line denotes water levels of reservoir, red line indicates temperature values at downstream face and green line shows temperature values at upstream face of the Dez Dam and two dotted vertical lines present two days selected for performing thermal inverse analysis.

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