Modeling of alkali-silica reaction in concrete: a review
J.W. PAN, Y.T. FENG, J.T. WANG, Q.C. SUN, C.H. ZHANG, D.R.J. OWEN
Modeling of alkali-silica reaction in concrete: a review
This paper presents a comprehensive review of modeling of alkali-silica reaction (ASR) in concrete. Such modeling is essential for investigating the chemical expansion mechanism and the subsequent influence on the mechanical aspects of the material. The concept of ASR and the mechanism of expansion are first outlined, and the state-of-the-art of modeling for ASR, the focus of the paper, is then presented in detail. The modeling includes theoretical approaches, meso- and macroscopic models for ASR analysis. The theoretical approaches dealt with the chemical reaction mechanism and were used for predicting pessimum size of aggregate. Mesoscopic models have attempted to explain the mechanism of mechanical deterioration of ASR-affected concrete at material scale. The macroscopic models, chemo-mechanical coupling models, have been generally developed by combining the chemical reaction kinetics with linear or nonlinear mechanical constitutive, and were applied to reproduce and predict the long-term behavior of structures suffering from ASR. Finally, a conclusion and discussion of the modeling are given.
alkali-silica reaction (ASR) / modeling / concrete / mesoscopic / macroscopic
[1] |
Stanton T E. Expansion of concrete through reaction between cement and aggregate. Proceeding American Society of Civil Engineers, 1940, 66: 1781–1811
|
[2] |
Fernandes I, Noronha F, Teles M. Microscopic analysis of alkali-aggregate reaction products in a 50-year-old concrete. Materials Characterization, 2004, 53(2-4): 295–306
CrossRef
Google scholar
|
[3] |
Ramyar K, Çopuroglu O, Andiç Ö, Fraaij A L A. Comparison of alkali-silica reaction products of fly-ash- or lithium-salt-bearing mortar under long-term accelerated curing. Cement and Concrete Research, 2004, 34(7): 1179–1183
CrossRef
Google scholar
|
[4] |
Peterson K, Gress D, Vandam T, Sutter L. Crystallized alkali-silica gel in concrete from the late 1890s. Cement and Concrete Research, 2006, 36(8): 1523–1532
CrossRef
Google scholar
|
[5] |
1260-94 AC. Standard test method for determining the potential alkali reactivity of combinations of cementious materials and aggregate (accelerated mortar-bar method). Annual Book of ASTM Standards 2002, American Society for Testing and Materials, 1916 Race Street, Philadelphia, PA 19103. 2002; 04.02
|
[6] |
A23.2-25A-00 C. Detection of alkali-silica reactive aggregate by accelerated expansion of mortar bars. CSA A23.2-00: Methods of Test for Concrete, Canadian Standards Association, Mississauga
|
[7] |
TC191-ARP-AAR02 R. Detection of potential alkali-reactivity of aggregates-the ultra-accelerated mortar-bar test. Materials and Structures, 2000, 33: 283–293
|
[8] |
A23. 2-14A-00 C. Potential expansivity of aggregates (procedure for length change due to alkali-aggregate reaction in concrete prisms). CSA A23.2-00: Methods of Test for Concrete, Canadian Standards Association, Mississauga (ON), 2000, 207–216
|
[9] |
1293-01 AC. Standard test method for concrete aggregates by determination of length change of concrete due to alkali-silica reaction. Annual Book of ASTM Standards, vol. 04.02 (Concrete and Aggregates), Philadelphia (PA), 2002
|
[10] |
Hobbs D W. Alkali-silica reaction in concrete. London: Thomas Telford, 1988
|
[11] |
Swamy R N, Al-Asali M M. Engineering properties of concrete affected by alkali-silica reaction. ACI Materials Journal, 1988, 85: 367–374
|
[12] |
Swamy R N, Al-Asali M M. Effect of alkali-silica reaction on the structural behavior of reinforced concrete beams. ACI Materials Journal, 1989, 86: 451–459
|
[13] |
Clark L A. Modeling the structural effects of alkali-silica reac-tions on reinforced concrete. ACI Materials Journal, 1991, 88: 271–277
|
[14] |
Ahmed T, Burley E, Rigden S, Abu-Taira A I. The effect of alkali reactivity on the mechanical properties of concrete. Construction & Building Materials, 2003, 17(2): 123–144
CrossRef
Google scholar
|
[15] |
Fan S F, Hanson J M. Length expansion and cracking of plain and reinforced concrete prisms due to alkali-silica reaction. ACI Materials Journal, 1998, 95: 480–487
|
[16] |
Monette L J, Gardner N J, Grattan-Bellew P E. Re-sidual strength of reinforced concrete beams damaged by alkali-silica reaction—Examination of damage rating index method. ACI Materials Journal, 2002, 99: 42–50
|
[17] |
Multon S, Multon S, Seignol J F, Toutlemonde F. Structural behavior of concrete beams affected by alkali-silica reaction. ACI Materials Journal, 2005, 102: 67–76
|
[18] |
Giaccio G, Zerbino R, Ponce J, Batic O. Mechanical behavior of concretes damaged by alkali-silica reaction. Cement and Concrete Research, 2008, 38(7): 993–1004
CrossRef
Google scholar
|
[19] |
Marzouk H, Langdon S. The effect of alkali-aggregate reactivity on the mechanical properties of high and normal strength concrete. Cement and Concrete Composites, 2003, 25(4-5): 549–556
CrossRef
Google scholar
|
[20] |
Berra M, Mangialardi T, Paolini A E. Rapid evaluation of the threshold alkali level for alkali-reactive siliceous aggregates in concrete. Cement and Concrete Composites, 1999, 21(4): 325–333
CrossRef
Google scholar
|
[21] |
Smaoui N, Berube M, Fournier B, Bissonnette B, Durand B. Effects of alkali addition on the mechanical properties and durability of concrete. Cement and Concrete Research, 2005, 35(2): 203–212
CrossRef
Google scholar
|
[22] |
Multon S, Toutlemonde F. Effect of applied stresses on alkali-silica reaction-induced expansions. Cement and Concrete Research, 2006, 36(5): 912–920
CrossRef
Google scholar
|
[23] |
Multon S, Cyr M, Sellier A, Leklou N, Petit L. Coupled effects of aggregate size and alkali content on ASR expansion. Cement and Concrete Research, 2008, 38(3): 350–359
CrossRef
Google scholar
|
[24] |
Puertas F, Palacios M, Gil-Maroto A, Vázquez T. Alkali-aggregate behaviour of alkali-activated slag mortars: Effect of aggregate type. Cement and Concrete Composites, 2009, 31(5): 277–284
CrossRef
Google scholar
|
[25] |
Berra M, Faggiani G, Mangialardi T, Paolini A E. Influence of stress restraint on the expansive behaviour of concrete affected by alkali-silica reaction. Cement and Concrete Research, 2010, 40(9): 1403–1409
CrossRef
Google scholar
|
[26] |
Multon S, Cyr M, Sellier A, Diederich P, Petit L. Effects of aggregate size and alkali content on ASR expansion. Cement and Concrete Research, 2010, 40(4): 508–516
CrossRef
Google scholar
|
[27] |
Multon S, Toutlemonde F. Effect of moisture conditions and transfers on alkali silica reaction damaged structures. Cement and Concrete Research, 2010, 40(6): 924–934
CrossRef
Google scholar
|
[28] |
Smaoui N, Bissonnette B, Bérubé M A, Fournier B. Stresses induced by alkali-silica reactivity in prototypes of reinforced concrete columns incorporating various types of reactive aggregates. Canadian Journal of Civil Engineering, 2007, 34(12): 1554–1566
CrossRef
Google scholar
|
[29] |
Steffens A, Li K, Coussy O. Aging approach to water effect on alkali-silica reaction degradation of structures. Journal of Engineering Mechanics of Materials, 2003, 129: 50–59
|
[30] |
Poyet S, Sellier A, Capra B, Thèvenin-Foray G, Torrenti J M, Tournier-Cognon H, Bourdarot E. Influence of water on alkali-silica reaction: Experimental Study and Numerical Simulations. Journal of Materials in Civil Engineering, 2006, 18(4): 588–596
CrossRef
Google scholar
|
[31] |
Bazǎnt Z P, Steffens A. Mathematical model for kinetics of alkali-silica reaction in concrete. Cement and Concrete Research, 2000, 30(3): 419–428
CrossRef
Google scholar
|
[32] |
Suwitoa A, Jinb W, Xia Y, Meyerc C. A Mathematical Model for the Pessimum Effect of ASR in Concrete. 2000
|
[33] |
Multon S, Sellier A, Cyr M. Chemo-mechanical modeling for prediction of alkali silica reaction (ASR) expansion. Cement and Concrete Research, 2009, 39(6): 490–500
CrossRef
Google scholar
|
[34] |
Vivian H E. The effects on mortar expansion of reactive component in the aggregate. Studies in cement-aggregate reactions, part 10. CSIRO Bull, 1947, 256: 13–20
|
[35] |
Mather B. How to make concrete that will not suffer deleterious alkali-silica reaction. Cement and Concrete Research, 1999, 29(8): 1277–1280
CrossRef
Google scholar
|
[36] |
Alasali M M, Malhotra V, Soles J A. Performance of various test methods for assessing the potential alkali reactivity of some Canadian aggre-gates. ACI Materials Journal, 1991, 88: 613–619
|
[37] |
Shehata M H, Thomas M D A. The effect of fly ash composition on the expansion of concrete due to alkali-silica reaction. Cement and Concrete Research, 2000, 30(7): 1063–1072
CrossRef
Google scholar
|
[38] |
Bleszynski R F, Thomas M D A. Microstructural Studies of Alkali-Silica Reaction in Fly Ash Concrete Immersed in Alkaline Solutions. Advanced Cement Based Materials, 1998, 7(2): 66–78
CrossRef
Google scholar
|
[39] |
Karakurt C, Topçu İ B. Effect of blended cements produced with natural zeolite and industrial by-products on alkali-silica reaction and sulfate resistance of concrete. Construction & Building Materials, 2011, 25(4): 1789–1795
CrossRef
Google scholar
|
[40] |
Comby-Peyrot I, Bernard F, Bouchard P O, Bay F, Garcia-Diaz E. Development and validation of a 3D computational tool to describe concrete behaviour at mesoscale. Application to the alkali-silica reaction. Computational Materials Science, 2009, 46(4): 1163–1177
CrossRef
Google scholar
|
[41] |
Dunant C F, Scrivener K L. Micro-mechanical modelling of alkali-silica-reaction-induced degradation using the AMIE framework. Cement and Concrete Research, 2010, 40(4): 517–525
CrossRef
Google scholar
|
[42] |
Amberg F. Performance of Dams affected by Expanding Concrete. V-0009401EN/1021-R-237, 2011
|
[43] |
Léger P, Côté P, Tinawi R. Finite element analysis of concrete swelling due to alkali-aggregate reactions in dams. Computers & Structures, 1996, 60(4): 601–611
CrossRef
Google scholar
|
[44] |
Pietruszczak S. On the mechanical behaviour of concrete subjected to alkali-aggregate reaction. Computers & Structures, 1996, 58(6): 1093–1097
CrossRef
Google scholar
|
[45] |
Ulm F J, Coussy O, Kefei L, Larive C. Thermo-chemo-mechanics of ASR expansion in concrete structures. Journal of Engineering Mechanics, 2000, 126(3): 233–242
CrossRef
Google scholar
|
[46] |
Huang M, Pietruszczak S. Modeling of Thermomechanical Effects of Alkali-Silica Reaction. Journal of Engineering Mechanics, 1999, 125(4): 476–485
CrossRef
Google scholar
|
[47] |
Comi C, Fedele R, Perego U. A chemo-thermo-damage model for the analysis of concrete dams affected by alkali-silica reaction. Mechanics of Materials, 2009, 41(3): 210–230
CrossRef
Google scholar
|
[48] |
Comi C, Perego U. Anisotropic Damage Model for Concrete Affected by Alkali-Aggregate Reaction. International Journal of Damage Mechanics, 2011, 20(4): 598–617
CrossRef
Google scholar
|
[49] |
Grimal E, Sellier A, Pape Y L, Bourdarot E. Creep, Shrinkage, and Anisotropic Damage in Alkali-Aggregate Reaction Swelling Mechanism-Part I: A Constitutive Model. ACI Materials Journal, 2008, 105: 227–235
|
[50] |
Grimal E, Sellier A, Pape Y L, Bourdarot E. Creep, Shrinkage, and Anisotropic Damage in Alkali-Aggregate Reaction Swelling Mechanism-Part II: Identification of Model Parameters and Application. ACI Materials Journal, 2008, 105: 236–242
|
[51] |
Larive C. Apports Combin'es de l’Experimentation et de la Modélisation à la Comprehension del Alcali-Réaction et de ses Effets Mécaniques. Dissertation for the Doctoral Degree, Laboratoire Central des Ponts et Chaussées, Paris (in France). 1998
|
[52] |
Dent Glasser L S, Kataoka N. N. K. The chemistry of alkali-aggregate reaction. Cement and Concrete Research, 1981, 11(1): 1–9
CrossRef
Google scholar
|
[53] |
Dent Glasser L S, Kataoka N. On the role of Calcium in the Alkali-aggregate reaction. Cement and Concrete Research, 1982, 12(3): 321–331
CrossRef
Google scholar
|
[54] |
Deschenes D J, Bayrak O, Folliard K J. ASR/DEF-damaged bent caps: shear tests and field implications. Technical Report No 12-8XXIA006, Texas Department of Transportation. 2009
|
[55] |
Dron R, Brivot F. Thermodynamic and kinetic approach to the alkali-silica reaction. Part 1: Concepts. Cement and Concrete Research, 1992, 22(5): 941–948
CrossRef
Google scholar
|
[56] |
Dron R, Brivot F. Thermodynamic and kinetic approach to the alkali-silica reaction. Part 2: Experiment. Cement and Concrete Research, 1993, 23(1): 93–103
CrossRef
Google scholar
|
[57] |
Diamond S. Chemistry and Other Characteristics of ASR Gels. Proceedings of the 11th International Conference on Alkali-Aggregate Reaction in Concrete, Quebec City, Canada. 2000, 31–40
|
[58] |
Knudsen T, Thaulow N. Quantitative microanalyses of alkali-silica gel in concrete. Cement and Concrete Research, 1975, 5(5): 443–454
CrossRef
Google scholar
|
[59] |
Thaulow N, Jakobsen U H, Clark B. Composition of alkali silica gel and ettringite in concrete railroad ties SEM-EDX and X-ray diffraction analyses. Cement and Concrete Research, 1996, 26(2): 309–318
CrossRef
Google scholar
|
[60] |
Regourd M, Hornain H, Poitevin O. Alkali-aggregate reaction-concrete microstructural evolution. Proceedings of the 5l International Conference on Alkali-Aggregate Reaction in Concrete, Cape Town, South Africa. 1981, S252/35
|
[61] |
Fernandes I. Composition of alkali-silica reaction products at different locations within concrete structures. Materials Characterization, 2009, 60(7): 655–668
CrossRef
Google scholar
|
[62] |
Šachlová Š, Přikryl R, Pertold Z. Alkali-silica reaction products: Comparison between samples from concrete structures and laboratory test specimens. Materials Characterization, 2010, 61(12): 1379–1393
CrossRef
Google scholar
|
[63] |
Kawamura M, Arano N, Terashima T. Composition of ASR gels and expansion of mortars. In: Cohen M, Mindess S, Skalny J, editors Materials Science of Concrete: Special Volume-The Sidney Diamond Symposium Westerville, OH: American Ceram-ic Society. 1998, 261–76
|
[64] |
Thomas M. The role of calcium in alkali -silica reaction. In: Cohen M, Mindess S, Skalny J, editors Materials Science of Concrete — The Sidney Diamond Symposium Westerville, OH: American Ceramic Society Bulletin. 1998, 325–37
|
[65] |
Powers T C, Steinour H H. An interpretation of some published researchers on alkali-aggregate reaction. Part 1-the chemical reactions and mechanism of expansion. ACI Journal Proceedings., 1955, 51: 497–516
|
[66] |
Powers T C, Steinour H H. An interpretation of some published researchers on alkali-aggregate reaction. Part 2-a hypothesis concerning safe and unsafe reactions with reactive silica in concrete. ACI Journal Proceedings, 1955, 51: 785–812
|
[67] |
Helmuth R, Stark D. Alkali-silica reactivity mechanisms. Ed Skalny, J. Materials Science of Concrete, 1992, III: 131–208
|
[68] |
Jun S S, Jin C S. ASR products on the content of reactive aggregate. KSCE Journal of Civil Engineering, 2010, 14(4): 539–545
CrossRef
Google scholar
|
[69] |
Scrivener K L, Monteiro P J M. The alkali-silica reaction in a monolithic opal. Journal of the American Ceramic Society, 1994, 77(11): 2849–2856
CrossRef
Google scholar
|
[70] |
Fernandes I, Noronha F, Teles M. Examination of the concrete from an old Portuguese dam: Texture and composition of alkali-silica gel. Materials Characterization, 2007, 58(11-12): 1160–1170
CrossRef
Google scholar
|
[71] |
Hansen W C. Studies relating to the mechanism by which the alkali-aggregate reaction produces expansion in concrete. Journal of the American Concrete Institute, 1944, 15: 213–227
|
[72] |
Dent Glasser L S. Osmotic pressure and the swelling of gels. Cement and Concrete Research, 1979, 9(4): 515–517
CrossRef
Google scholar
|
[73] |
Poole A B. Alkali-silica reactivity mechanisms of gel formation and expansion. In: Proceedings of the 9th International Conference on Alkali-Aggregate Reaction, London (England). 1992, 104: 782–9
|
[74] |
McGowan J K, Vivian H E. Studies in cement-aggregate reaction: correlation between crack development and expansion of mortars. Australian Journal of Applied Science, 1952, 3: 228–232
|
[75] |
Ponce J, Batic O. Different manifestations of the alkali-silica reaction in concrete according to the reaction kinetics of the reactive aggregate. Cement and Concrete Research, 2006, 36(6): 1148–1156
CrossRef
Google scholar
|
[76] |
Idorn G M. A discussion of the paper 'Mathematical model for kinetics of alkali-silica reaction in concrete' by Zdenek P. Bazant and Alexander Steffens. Cement and Concrete Research, 2001, 31(7): 1109–1110
CrossRef
Google scholar
|
[77] |
Garcia-Diaz E, Riche J, Bulteel D, Vernet C. Mechanism of damage for the alkali-silica reaction. Cement and Concrete Research, 2006, 36(2): 395–400
CrossRef
Google scholar
|
[78] |
Ichikawa T, Miura M. Modified model of alkali-silica reaction. Cement and Concrete Research, 2007, 37(9): 1291–1297
CrossRef
Google scholar
|
[79] |
Bazant Z P, Zi G, Meyer C. Fracture mechanics of asr in concretes with waste glass particles of different sizes. Journal of Engineering Mechanics, 2000, 126(3): 226–232
CrossRef
Google scholar
|
[80] |
Hobbs D W. The alkali-silica reaction—a model for predicting expansion in mortar. Magazine of Concrete Research, 1981, 33(117): 208–220
CrossRef
Google scholar
|
[81] |
Groves G W, Zhang X. A dilatation model for the expansion of silica glass/OPC mortars. Cement and Concrete Research, 1990, 20(3): 453–460
CrossRef
Google scholar
|
[82] |
Furusawa Y, Ohga H, Uomoto T. An analytical study concerning prediction of concrete expansion due to alkali-silica reaction. Third International Conference on Durability of Concrete, Nice, France. 1994, 757–80
|
[83] |
Meyer C, Baxter S. Use of recycled glass and fly ash for precast concrete. Report NYSERDA 98-18 (4292-IABR-IA-96) to New York State Energy Research and Developement Authority, Department of Civil Engineering and Engineering Mechanics, Columbia University. 1998
|
[84] |
Suwito A, Jin W, Xi Y, Meyer C. A mathematical model for the pessimum effect of ASR in concrete. Concrete Science and Engineering, RILEM., 2002, 4: 23–34
|
[85] |
Xi Y, Suwito A, Wen X, Meyer C, Jin W. Testing and modeling alkali-silica reaction and the associated expansion of concrete. Mechanics of Quasi-Brittle Materials and Structures, Proceedings of International Workshop in honor of Prof ZP Bazant 60th birthday, Hermes Science Publications, Paris. 1998
|
[86] |
Xi Y, Jennings H M. Shrinkage of cement paste and concrete modelled by a multiscale effective homogeneous theory. Materials and Structures, 1997, 30(6): 329–339
CrossRef
Google scholar
|
[87] |
Fick A. Ueber Diffusion. Annalen der Physik., 1855, 170(1): 59–86
CrossRef
Google scholar
|
[88] |
Wang Z M, Kwan A K H, Chan H C. Mesoscopic study of concrete I: generation of random aggregate structure and finite element mesh. Computers & Structures, 1999, 70(5): 533–544
CrossRef
Google scholar
|
[89] |
Riche J, Garcia-Diaz E, Bulteel D, Siwak J M. Mechanism of damage for the alkali-silica reaction: relationship between swelling and reaction degree. in: Dhir R, Roderick Jones M, Li Z (Eds), Repair, Rejuvenation and Enhancement of Concrete, Proceedings of International Conference of Dundee. 2002, 94–102
|
[90] |
Haha M B, Gallucci E, Guidoum A, Scrivener K L. Relation of expansion due to alkali silica reaction to the degree of reaction measured by SEM image analysis. Cement and Concrete Research, 2007, 37(8): 1206–1214
CrossRef
Google scholar
|
[91] |
Moës N, Cloire M, Cartra P, Remacle J. A computational approach to handle complex microstructure geometries. Communications in Numerical Methods in Engineering, 2003, 192: 3163–3177
|
[92] |
Ben Haha M. Mechanical effects of alkali silica reaction in concrete studied by SEM-image analysis. DissertationTip. 2006
|
[93] |
Shin J h, Struble L J, Kirkpatrick R J. Modeling alkali-silica reaction using image analysis and finite element analysis. Proceedings of the 6th International Symposium on Cement & Concrete and Canmet/Aci International Symposium on Concrete Technology for Sustainable Development, 2006, 3: 1669–75
|
[94] |
Shin J h. Modeling alkali-silica reaction using image analysis and finite element analysis. DissertationTip, University of Illinois at Urbana-Champaign. 2009
|
[95] |
Struble L J, Diamond S. Swelling properties of synthetic alkali silica gels. Journal of the American Ceramic Society, 1981, 64(11): 652–655
CrossRef
Google scholar
|
[96] |
Charlwood R G, Solymar S V, Curtis D D. A review of alkali aggregate reactions in hydroelectric plants and dams. Proceedings of the International Conference of Alkali-Aggregate Reactions in Hydroelectric Plants and Dams, Fredericton, Canada. 1992, 129
|
[97] |
Thompson G, Charlwood R, Steele R, Curtis D. Mactaquac generating station Intake and spillway remedial measures. Proceedings for the Eighteenth International Congress on Large Dams, Durban, South Africa. 1994, V. 1, Q-68, R.24: 347–68
|
[98] |
Engineering IoS. Effects of alkali-silica reaction SETO, London. 1992
|
[99] |
Herrador M F, Martínez-Abella F, Hoyo Fernández-Gago R. Mechanical behavior model for ASR-affected dam concrete under service load: formulation and verification. Materials and Structures, 2009, 42(2): 201–212
CrossRef
Google scholar
|
[100] |
Saouma V, Xi Y. Literature review of alkali aggregate reactions in concrete dams. Swiss Federal Office for Water and Geology, Bienne Switzerland, Report No CU/SA-XI-2004/001. 2004
|
[101] |
Huang M, Pietruszczak S. Numerical analysis of concrete structures subjected to alkali-aggregate reaction. Mechanics of Cohesive-Frictional Materials, 1996, 1(4): 305–319
CrossRef
Google scholar
|
[102] |
Parvini M, Pietruszczak S, Gocevski V. Seismic analysis of hydraulic structures affected by alkali-aggregate reaction: a case study. Canadian Journal of Civil Engineering, 2001, 28(2): 332–338
CrossRef
Google scholar
|
[103] |
Winnicki A, Pietruszczak S. On mechanical degradation of reinforced concrete affected by alkali-silica reaction. Journal of Engineering Mechanics, 2008, 134(8): 611–627
CrossRef
Google scholar
|
[104] |
Coussy O. Mechanics of porous continua. Wiley, Chichester, UK. 1995
|
[105] |
Atkins P W. Physical Chemistry. 5th ed, Oxford: Oxford University Press, 1994
|
[106] |
Farage M, Alves J L D, Fairbairn E M R. Macroscopic model of concrete subjected to alkali-aggregate reaction. Cement and Concrete Research, 2004, 34(3): 495–505
CrossRef
Google scholar
|
[107] |
Fairbairn E M R, Ribeiro F L B, Lopes L E, Toledo-Filho R D, Silvoso M M. Modelling the structural behaviour of a dam affected by alkali-silica reaction. Communications in Numerical Methods in Engineering, 2005, 22(1): 1–12
CrossRef
Google scholar
|
[108] |
Saouma V, Perotti L. Constitutive Model for Alkali-Aggregate Reactions. ACI Materials Journal, 2006, 103: 194–202
|
[109] |
Multon S, Seignol J F, Toutlemonde F. Chemomechanical assessment of beams damaged by alkali-silica reaction. Journal of Materials in Civil Engineering, 2006, 18(4): 500–509
CrossRef
Google scholar
|
[110] |
Newell V A, Wagner C D. Fontana Dam A Crack in the Curve. Waterpower, 1999, 1–10
|
[111] |
Bangert F, Kuhl D, Meschke G. Chemo-hygro-mechanical modelling and numerical simulation of concrete deterioration caused by alkali-silica reaction. International Journal for Numerical and Analytical Methods in Geomechanics, 2004, 28(78): 689–714
CrossRef
Google scholar
|
[112] |
Poyet S, Sellier A, Capra B, Foray G, Torrenti J M, Cognon H, Bourdarot E. Chemical modelling of Alkali Silica reaction: Influence of the reactive aggregate size distribution. Materials and Structures, 2007, 40(2): 229–239
CrossRef
Google scholar
|
[113] |
Grimal E, Sellier A, Multon S, Le Pape Y, Bourdarot E. Concrete modelling for expertise of structures affected by alkali aggregate reaction. Cement and Concrete Research, 2010, 40(4): 502–507
CrossRef
Google scholar
|
[114] |
Capra B, Sellier A. Orthotropic modelling of alkali-aggregate reaction in concrete structures: numerical simulations. Mechanics of Materials, 2003, 35(8): 817–830
CrossRef
Google scholar
|
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