Literature review of modelling approaches for ASR in concrete: a new perspective

Figures & data

Table 1. Overview of modelling approaches for ASR in concrete.

Table 2. Models based on concrete expansion.

			No. input parameters
	Model type	Imposed strains dependent on	Mechanical	Temp.	RH	Stress state	Reactivity	Validation (V)/Demonstration (D)
Charlwood (1994); Thompson et al. (1994)	Phenomenological	Stress state	2	1	–	2	–	Powerhouse (V)
Léger et al. (1996)	Phenomenological with reduction of stiffness and tensile strength	Stress state, temperature, moisture, reactivity	6	2	2	2	1	2D FEA spillway pier (V)
Capra and Bournazel (1998)	Phenomenological with probabilistic fracture mechanics	Stress state, temperature, moisture, reactivity	1	2	1	2	3	Lab specimens (D)
Malla and Wieland (1999)	Phenomenological with linear elastic fracture mechanics	–	2	1	–	–	–	3D FEA arch-gravity dam (V)
Ulm et al. (2000)	Thermo-chemo-plastic with kinetics law	Temperature	5	7	–	–	1	2D FEA dam and bridge box girder (D)
Li and Coussy (2002, 2004)	Thermo-chemo-plastic with kinetics law	Temperature, moisture	5	4	1	–	1	2D FEA bridge pier (D), 3D FEA bridge pylon (D)
Capra and Sellier (2003)	Thermo-hygro-chemo-damage with kinetics law	Temperature, moisture, reactivity	11	1	1	–	–	2D FEA of lab specimens (V) and of RC beam (D)
Farage et al. (2004), Fairbairn et al. (2004)	Thermo-chemo-cracking with kinetics law	Temperature	8	2	–	–	1	3D FEA lab specimen (V) and 2D FEA dam (V)
Bangert et al. (2004)	Thermo-hygro-chemo-damage based on mixture theory	Temperature, moisture	10	3	2	–	–	2D FEA lab specimens and beam (D)
Saouma and Perotti (2006)	Thermo-hygro-chemo with kinetics law and reduction of stiffness and tensile strength	Stress state, temperature, moisture	8	5	–	1	1	2D FEA lab specimens (V) and dam (D)
Winnicki and Pietruszczak (2008), Winnicki et al. (2014)	Thermo-hygro-chemo-plastic for RC with kinetics law	Stress state, temperature, moisture	11	3	1	1	1	Lab specimens (V) and 2D FEA dam (V)
Comi et al. (2009)	Thermo-chemo-damage with kinetics law	Stress state, temperature	18	5	–	–	1	2D FEA lab specimens and dam (V)
Pesavento et al. (2012)	Thermo-hygro-chemo-damage based on mixture theory	Temperature, moisture	3	7	5	–	2	2D FEA lab specimens (V)
Esposito and Hendriks (2012)	Thermo-chemo-cracking rheological-based	Temperature	6	5	–	–	3	Lab specimens (V)

Table 3. Models based on internal pressure.

			No. input parameters
	Model type	Imposed	Microstucture	Mechanical	Reactivity	Validation (V)/Demonstration (D)
Bažant et al. (2000)	Linear fracture mechanics theory	Pressure in particle rim	3	3	2	Idealised one-particle cubic cell (D)
Dormieux et al. (2004)	Chemo-poro-micro-elastic	Pressure in porosity	2	2	1	Lab specimens (D)
Schlangen and Van Breugel (2005)	Lattice model with quasi-brittle aggregate, ITZ and matrix phase	Strain in aggregate and/or ITZ	4	6	–	2D FEA lab specimens (D)
Çopuroğlu and Schlangen (2007), Schlangen and Copuroğlu (2010), Anaç et al. (2012)	Lattice model with quasi-brittle aggregate, ITZ and matrix phase	Strain in aggregate and/or ITZ	4	6	–	2D and 3D FEA lab specimens (V)
Comby-Peyrot et al. (2009)	Particle model with linear elastic aggregate phase and elastic damage matrix phase	Strain at aggregates rim	4	11	–	3D FEA lab specimens (V)
Reinhardt and Mielich (2011)	Linear elastic fracture mechanics	Pressure in aggregates	2	1	1	Rock specimens (V)
Wu et al. (2014)	FE${}^2$ multiscale model	Strain in porosity at lower level	4	6	8	3D FEA lab specimens (D)
Esposito (2016), Esposito and Hendriks (2016)	Micro-poro-fracture	Pressure	4	6	–	Lab specimens (V)

Table 4. Models based on gel production.

			No. input parameters
	Model type	Variation of gel	Microstucture	Mechanical	Creep	Reactivity	Validation (V)/Demonstration (D)
Ulm et al. (2002)	Chemo-micro-poro-plastic	Mass	1	4	–	1	Lab specimens (V)
Lemarchand (2001), Lemarchand et al. (2003, 2005)	Chemo-micro-poro-elastic	Mass	6	3	–	1	Lab specimens (V)
Grimal et al. (2008a, b)	Thermo-hygo-chemo-damage rheological-based	Mass	1	8	4	4	lab specimens (V) and 3D FEA RC beams (V)
Dunant and Scrivener (2010)	XFEM with quasi-brittle aggregate and cement paste phases, elastic gel pockets	Surface	2	8	–	1	2D FEA lab specimens (V)
Giorla (2013), Giorla et al. (2015)	XFEM with quasi-brittle viscoelastic cement paste phase, quasi-brittle aggregates and elastic gel pockets	Surface	2	9	4	2	2D FEA lab specimens (V)
Pignatelli et al. (2013)	Chemo-micro-poro-damage	Mass	1	16	–	7	Lab specimens (V) and 2D FEA beams (V)
Charpin (2013), Charpin and Ehrlacher (2014)	Chemo-micro-poro-fracture	Volume	6	7	–	1	Lab specimens (V)

Table 5. Models based on ions diffusion–reaction mechanisms.

			No. input parameters
	Model type	Diffusion–reaction mechanism	Microstucture	Mechanical	Creep/Shrinkage	Reactivity	Validation (V)/Demonstration (D)
Bažant and Steffens (2000)	Mathematical	Dissolution silica, water diffusion within gel rim, water imbibation from porosity	1	1	–	4	Idealised one-particle cubic cell (D)
Suwito et al. (2002)	Chemo-micro-poro-elastic	Diffusion alkali ions, diffusion of gel in cement paste	3	5	–	5	Lab specimens (V)
Poyet et al. (2007)	Chemo-micro-poro-elastic	Diffusion–reaction of sodium and calcium ions within gel rim	3	2	–	6	Idealised one-particle cubic cell (V)
Multon et al. (2009), Sanchez et al. (2014)	Chemo-micro-poro-damage	Diffusion–reaction of sodium and calcium ions within gel rim	5	5	–	5	Lab specimens (V)
Puatatsananon and Saouma (2013)	Computational multiscale	Diffusion alkali ions, diffusion of gel in cement paste	3	12	–	3	Lab specimens (V)
Alnaggar et al. (2013)	Lattice discrete particle	Dissolution silica, water diffusion within gel rim, water imbibation from porosity	5	16	4	8	3D FEA lab specimens (V)
Liuaudat et al. (2014)	Mathematical model	Forward and backward diffusion–reaction of alkali and silica ions in the rim	4	6	–	9	1D interface system between aggregate and cement paste (D)
Nguyen et al. (2014)	Chemo-elastic	Diffusion–reaction of sodium ions	1	4	–	4	1D penetration of NaCl ions in concrete beam (D)
Bažant and Rahimi-Aghdam (2016), Rahimi-Aghdam, Bažant, and Caner (2016)	Diffusion-based and creep-based chemo-mechanical model	Dissolution silica, water diffusion in gel, water imbibation from porosity	1	28	–	13	3D FEA lab specimens (V)
Multon and Sellier (2016)	Poromechanical	Diffusion and fixation of alkali ions in gel and diffusion of alkali ions due to leaching	4	8	4	5	3D FEA lab specimens (V)
Alnaggar et al. (2017)	Lattice discrete particle	Dissolution silica, water diffusion in gel rim, water imbibation from porosity	8	12	13	9	3D FEA lab specimens (V)

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