A time−space porosity computational model for concrete under sulfate attack
Hui SONG1,2, Jiankang CHEN2,3()
1. Jiangxi Provincial Key Laboratory of Hydraulic & Civil Engineering Infrastructure Security, Nanchang Institute of Technology, Nanchang 330099, China 2. Zhejiang Provincial Engineering Research Center for the Safety of Pressure Vessel and Pipeline, Ningbo University, Ningbo 315211, China 3. Ningbo University Donghai Academy, Ningbo 315211, China
The deterioration of the microscopic pore structure of concrete under external sulfate attack (ESA) is a primary cause of degradation. Nevertheless, little effort has been invested in exploring the temporal and spatial development of the porosity of concrete under ESA. This study proposes a mechanical–chemical model to simulate the spatiotemporal distribution of the porosity. A relationship between the corrosion damage and amount of ettringite is proposed based on the theory of volume expansion. In addition, the expansion strain at the macro-scale is obtained using a stress analysis model of composite concentric sphere elements and the micromechanical mean-field approach. Finally, considering the influence of corrosion damage and cement hydration on the diffusion of sulfate ions, the expansion deformation and porosity space−time distribution are obtained using the finite difference method. The results demonstrate that the expansion strains calculated using the suggested model agree well with previously reported experimental results. Moreover, the tricalcium aluminate concentration, initial elastic modulus of cement paste, corrosion damage, and continuous hydration of cement significantly affect concrete under ESA. The proposed model can forecast and assess the porosity of concrete covers and provide a credible approach for determining the residual life of concrete structures under ESA.
K X Liao, Y P Zhang, W Zhang, Y Wang, R L Zhang. Modeling constitutive relationship of sulfate-attacked concrete. Construction & Building Materials, 2020, 260: 119902 https://doi.org/10.1016/j.conbuildmat.2020.119902
2
Z Y Zhang, X G Jin, W Luo. Long-term behaviors of concrete under low-concentration sulfate attack subjected to natural variation of environmental climate conditions. Cement and Concrete Research, 2019, 116: 217–230 https://doi.org/10.1016/j.cemconres.2018.11.017
Q J Ding, J Yang, D S Hou, G Zhang. Insight on the mechanism of sulfate attacking on the cement paste with granulated blast furnace slag: An experimental and molecular dynamics study. Construction & Building Materials, 2018, 169: 601–611 https://doi.org/10.1016/j.conbuildmat.2018.02.148
6
R Ragoug, O O Metalssi, F Barberon, J M Torrenti, N Roussel, L Divet, de Lacaillerie J B d’Espinose. Durability of cement pastes exposed to external sulfate attack and leaching: Physical and chemical aspects. Cement and Concrete Research, 2019, 116: 134–145 https://doi.org/10.1016/j.cemconres.2018.11.006
7
D J Zou, S S Qin, T J Liu, A Jivkov. Experimental and numerical study of the effects of solution concentration and temperature on concrete under external sulfate attack. Cement and Concrete Research, 2021, 139: 106284 https://doi.org/10.1016/j.cemconres.2020.106284
8
X Liu, P Feng, W Li, G Geng, J Huang, Y Gao, S Mu, J Hong. Effects of pH on the nano/micro structure of calcium silicate hydrate (C−S−H) under sulfate attack. Cement and Concrete Research, 2021, 140: 106306 https://doi.org/10.1016/j.cemconres.2020.106306
9
M G Sohail, R Kahraman, N Al Nuaimi, B Gencturk, W Alnahhal. Durability characteristics of high and ultra-high performance concretes. Journal of Building Engineering, 2021, 33: 101669 https://doi.org/10.1016/j.jobe.2020.101669
10
Z Y Zhang, J T Zhou, J Yang, Y Zou, Z Wang. Understanding of the deterioration characteristic of concrete exposed to external sulfate attack: Insight into mesoscopic pore structures. Construction & Building Materials, 2020, 260: 119932 https://doi.org/10.1016/j.conbuildmat.2020.119932
11
Q Huang, L Zhao, C G Zhao, D Liu, C Wang. Microstructure change of nanosilica-cement composites partially exposed to sulfate attack. International Journal of Concrete Structures and Materials, 2020, 14(1): 1–11 https://doi.org/10.1186/s40069-020-00401-4
12
R El-Hachem, E Rozière, F Grondin, A Loukili. Multi-criteria analysis of the mechanism of degradation of Portland cement based mortars exposed to external sulphate attack. Cement and Concrete Research, 2012, 42(10): 1327–1335 https://doi.org/10.1016/j.cemconres.2012.06.005
13
M Sahmaran, O Kasap, K Duru, I O Yaman. Effects of mix composition and water−cement ratio on the sulfate resistance of blended cements. Cement and Concrete Composites, 2007, 29(3): 159–167 https://doi.org/10.1016/j.cemconcomp.2006.11.007
14
D Rajaram, D A T Michael, J F Kevin, D Thano. Chemical and physical sulfate attack on fly ash concrete mixtures. ACI Materials Journal, 2019, 116(4): 31–42
15
M B Bankir, U Korkut Sevim. Performance optimization of hybrid fiber concretes against acid and sulfate attack. Journal of Building Engineering, 2020, 32: 101443 https://doi.org/10.1016/j.jobe.2020.101443
16
Y W Zhou, M L Li, L L Sui, F Xing. Effect of sulfate attack on the stress−strain relationship of FRP-confined concrete. Construction & Building Materials, 2016, 110: 235–250 https://doi.org/10.1016/j.conbuildmat.2015.12.038
17
B A Tayeh, M W Hasaniyah, A M Zeyad, M M Awad, A Alaskar, A M Mohamed, R Alyousef. Durability and mechanical properties of seashell partially-replaced cement. Journal of Building Engineering, 2020, 31: 101328 https://doi.org/10.1016/j.jobe.2020.101328
18
F Bellmann, B Möser, J Stark. Influence of sulfate solution concentration on the formation of gypsum in sulfate resistance test specimen. Cement and Concrete Research, 2006, 36(2): 358–363 https://doi.org/10.1016/j.cemconres.2005.04.006
19
P Liu, Y Chen, Z W Yu, Z Lu. Effect of sulfate solution concentration on the deterioration mechanism and physical properties of concrete. Construction & Building Materials, 2019, 227: 116641 https://doi.org/10.1016/j.conbuildmat.2019.08.022
20
R S Gollop, H F W Taylor. Microstructural and microanalytical studies of sulfate attack III. Sulfate-resisting portland cement: Reactions with sodium and magnesium sulfate solutions. Cement and Concrete Research, 1995, 25(7): 1581–1590 https://doi.org/10.1016/0008-8846(95)00151-2
21
B TianM D Cohen. Does gypsum formation during sulfate attack on concrete lead to expansion? Cement and Concrete Research, 2000, 30(1): 117–123
22
H Song, J K Chen, J Y Jiang. An Internal expansive stress model of concrete under sulfate attack. Acta Mechanica Solida Sinica, 2016, 29(6): 610–619 https://doi.org/10.1016/S0894-9166(16)30331-7
23
J K Chen, C Qian, H Song. A new chemo-mechanical model of damage in concrete under sulfate attack. Construction & Building Materials, 2016, 115: 536–543 https://doi.org/10.1016/j.conbuildmat.2016.04.074
24
J W Yao, Y Z Yang, J K Chen. A novel chemo-mechanical model for fracture toughness of mortar under sulfate attack. Theoretical and Applied Fracture Mechanics, 2020, 109: 102762 https://doi.org/10.1016/j.tafmec.2020.102762
25
X Zhang, C X Qian, H C Chen, C Liang, W Kang. Calculation of expansion stresses and strains in concrete under sulfate crystallization attack in dry–wet cycles environments. Journal of Materials in Civil Engineering, 2021, 33(3): 04020479 https://doi.org/10.1061/(ASCE)MT.1943-5533.0003499
26
G J Yin, X B Zuo, X H Sun, Y J Tang. Numerical investigation of the external sulfate attack induced expansion response of cement paste by using crystallization pressure. Modelling and Simulation in Materials Science and Engineering, 2019, 27(2): 025006 https://doi.org/10.1088/1361-651X/aaf76a
27
T Ikumi, I Segura. Numerical assessment of external sulfate attack in concrete structures: A review. Cement and Concrete Research, 2019, 121: 91–105 https://doi.org/10.1016/j.cemconres.2019.04.010
28
C Yu, W Sun, K Scrivener. Mechanism of expansion of mortars immersed in sodium sulfate solutions. Cement and Concrete Research, 2013, 43: 105–111 https://doi.org/10.1016/j.cemconres.2012.10.001
29
M F Najjar, M L Nehdi, A M Soliman, T M Azabi. Damage mechanisms of two-stage concrete exposed to chemical and physical sulfate attack. Construction & Building Materials, 2017, 137: 141–152 https://doi.org/10.1016/j.conbuildmat.2017.01.112
30
B Bary, N Leterrier, E Deville, P Le Bescop. Coupled chemo-transport-mechanical modelling and numerical simulation of external sulfate attack in mortar. Cement and Concrete Composites, 2014, 49: 70–83 https://doi.org/10.1016/j.cemconcomp.2013.12.010
31
M Santhanam, M D Cohen, J Olek. Mechanism of sulfate attack: A fresh look: Part 1: Summary of experimental results. Cement and Concrete Research, 2002, 32(6): 915–921 https://doi.org/10.1016/S0008-8846(02)00724-X
32
E Rozière, A Loukili, Hachem R El, F Grondin. Durability of concrete exposed to leaching and external sulphate attacks. Cement and Concrete Research, 2009, 39(12): 1188–1198 https://doi.org/10.1016/j.cemconres.2009.07.021
33
D Krajcinovic, M Basista, K Mallick, D Sumarac. Chemo-micromechanics of brittle solids. Journal of the Mechanics and Physics of Solids, 1992, 40(5): 965–990 https://doi.org/10.1016/0022-5096(92)90058-A
34
R Tixier, B Mobasher. Modeling of damage in cement-based materials subjected to external sulfate attack. I: Formulation. Journal of Materials in Civil Engineering, 2003, 15(4): 305–313 https://doi.org/10.1061/(ASCE)0899-1561(2003)15:4(305
35
R Tixier, B Mobasher. Modeling of damage in cement-based materials subjected to external sulfate attack. II: Comparison with experiments. Journal of Materials in Civil Engineering, 2003, 15(4): 314–322 https://doi.org/10.1061/(ASCE)0899-1561(2003)15:4(314
36
S S Qin, D J Zou, T J Liu, A Jivkov. A chemo-transport-damage model for concrete under external sulfate attack. Cement and Concrete Research, 2020, 132: 106048 https://doi.org/10.1016/j.cemconres.2020.106048
37
J P Li, F Xie, G W Zhao, L Li. Experimental and numerical investigation of cast-in-situ concrete under external sulfate attack and drying−wetting cycles. Construction & Building Materials, 2020, 249: 118789 https://doi.org/10.1016/j.conbuildmat.2020.118789
38
W Kunther, B Lothenbach, K L Scrivener. On the relevance of volume increase for the length changes of mortar bars in sulfate solutions. Cement and Concrete Research, 2013, 46: 23–29 https://doi.org/10.1016/j.cemconres.2013.01.002
39
F L Qu, W G Li, W K Dong, V W Y Tam, T Yu. Durability deterioration of concrete under marine environment from material to structure: A critical review. Journal of Building Engineering, 2021, 35: 102074 https://doi.org/10.1016/j.jobe.2020.102074
40
S Multon, A Sellier. Expansion modelling based on cracking induced by the formation of new phases in concrete. International Journal of Solids and Structures, 2019, 160: 293–306 https://doi.org/10.1016/j.ijsolstr.2018.11.001
41
R D Gao. Micro−macro degradation regularity of sulfate attack on concrete under complex environments. Dissertation for the Doctoral Degree. Beijing: Tsinghua University, 2010 (in Chinese)
42
L O Höglund. Some notes of ettringite formation in cementitous materials: Influence of hydration and thermodynamic constraints for durability. Cement and Concrete Research, 1992, 22(2−3): 217−228
43
L Z Yu, J K Chen. A new evolution model of concrete porosity under continuous hydration. International Journal of Modelling Identification and Control, 2016, 26(4): 345–352 https://doi.org/10.1504/IJMIC.2016.081147
C S Lu, R Danzer, F D Fischer. Fracture statistics of brittle materials: Weibull or normal distribution. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 2002, 65(6): 067102 https://doi.org/10.1103/PhysRevE.65.067102
49
C S Lu, R Danzer, F D Fischer. Scaling of fracture strength in ZnO: Effects of pore/grain-size interaction and porosity. Journal of the European Ceramic Society, 2004, 24(14): 3643–3651 https://doi.org/10.1016/j.jeurceramsoc.2003.12.001
50
E J Garboczi, D P Bentz. Computer simulation of the diffusivity of cement-based materials. Journal of Materials Science, 1992, 27(8): 2083–2092 https://doi.org/10.1007/BF01117921
51
C F FerrarisJ R CliftonP E StutzmanE J Garboczi. Mechanisms of degradation Portland cement-based systems by sulfate attack. In: Young J F, eds. Materials Research Society’s Symposium on Mechanisms of Chemical Degradation of Cement-based Systems. Boston: Materials Research Society’s Symposium on Mechanisms of Chemical Degradation of Cement-based Systems, 1997
52
B Lagerblad. Long term test of concrete resistance against sulphate attack. In: Marchand J, Skalny J, eds. Materials Science of Concrete: Sulfate Attack Mechanisms. Ohio: American Ceramic Society, 1999, 325–336
53
M C Martins, E A Langaro, G Macioski, M H F Medeiros. External ammonium sulfate attack in concrete: Analysis of the current methodology. Construction & Building Materials, 2021, 277: 122252 https://doi.org/10.1016/j.conbuildmat.2021.122252
54
S Boudache, A Loukili, E Rozière, L Izoret. Influence of initial material properties on the degradation of mortars with low expansion cements subjected to external sulfate attack. Materials and Structures, 2021, 54(3): 104 https://doi.org/10.1617/s11527-021-01709-7
55
N N Naik, A C Jupe, S R Stock, A P Wilkinson, P L Lee, K E Kurtis. Sulfate attack monitored by microCT and EDXRD: Influence of cement type, water-to-cement ratio, and aggregate. Cement and Concrete Research, 2006, 36(1): 144–159 https://doi.org/10.1016/j.cemconres.2005.06.004
56
X T Yu, D Chen, J R Feng, Y Zhang, Y Liao. Behavior of mortar exposed to different exposure conditions of sulfate attack. Ocean Engineering, 2018, 157: 1–12 https://doi.org/10.1016/j.oceaneng.2018.03.017