环境和疲劳荷载作用下开裂混凝土寿命预测研究进展

摘要/Abstract

摘要： 混凝土是一种准脆性材料,大量混凝土结构在设计使用寿命期间会不可避免地出现裂缝并带着裂缝工作。裂缝的存在会直接影响到混凝土结构使用寿命,特别是在侵蚀性环境因素或疲劳荷载作用下。本文对钢筋混凝土裂缝扩展过程进行了分析,对不同侵蚀环境作用下开裂混凝土结构劣化机制、寿命预测研究方法及预测模型等进行了系统的梳理和对比。阐述了疲劳裂纹扩展理论在开裂混凝土结构疲劳寿命预测中的应用现状与优势,并归纳了基于该理论的部分寿命预测方法及预测模型。此外,还对侵蚀环境与疲劳荷载耦合作用下开裂混凝土结构寿命预测方法进行了总结与讨论,指出了现有开裂混凝土结构寿命预测研究尚存在的问题,并对今后的研究方向提出了建议。

关键词: 开裂混凝土, 裂缝, 侵蚀性环境, 疲劳荷载, 寿命预测

Abstract: Concrete is a quasi brittle material, and a large number of concrete structures inevitably experience cracks and work with them during their designed service life. The existence of cracks directly affects the service life of concrete structures, especially under erosion environmental factors or fatigue loads. The crack propagation process of reinforced concrete is analyzed. The deterioration mechanism, life prediction methods and prediction models of cracked concrete structures under different erosion environments are systematically reviewed and compared. The application status and advantages of fatigue crack propagation theory in fatigue life prediction of cracked concrete structures are described, and some life prediction methods and prediction models based on this theory are summarized. In addition, the life prediction methods of cracked concrete structures under the coupling action of erosion environment and fatigue load are summarized and discussed. In the end, the existing problems in the field of life prediction of cracked concrete structures are pointed out and some suggestions for future research are put forward.

Key words: cracked concrete, crack, erosion environment, fatigue load, life prediction

中图分类号:

TU528.01

司秀勇, 高青宇, 潘慧敏, 赵庆新. 环境和疲劳荷载作用下开裂混凝土寿命预测研究进展[J]. 硅酸盐通报, 2024, 43(1): 1-15.

SI Xiuyong, GAO Qingyu, PAN Huimin, ZHAO Qingxin. Research Progress on Life Prediction of Cracked Concrete under Environment and Fatigue Load[J]. BULLETIN OF THE CHINESE CERAMIC SOCIETY, 2024, 43(1): 1-15.

参考文献

[1] 李克非, 廉慧珍, 邸小坛. 混凝土结构耐久性设计原则、方法与标准[J]. 土木工程学报, 2021, 54(10): 64-71+96.
LI K F, LIAN H Z, DI X T. Durability design of concrete structures: principle, method and standard[J]. China Civil Engineering Journal, 2021, 54(10): 64-71+96 (in Chinese).
[2] BOGAS J A, CARRIÇO A, PONTES J. Influence of cracking on the capillary absorption and carbonation of structural lightweight aggregate concrete[J]. Cement and Concrete Composites, 2019, 104: 103382.
[3] 韦建刚, 陈荣, 黄伟, 等. 静水压力下超高性能混凝土的抗氯离子渗透性能[J]. 硅酸盐通报, 2022, 41(8): 2706-2715+2747.
WEI J G, CHEN R, HUANG W, et al. Chloride penetration resistance of ultra-high performance concrete under hydrostatic pressure[J]. Bulletin of the Chinese Ceramic Society, 2022, 41(8): 2706-2715+2747 (in Chinese).
[4] BELTRAME N A M, DIAS R L, WITZKE F B, et al. Effect of carbonation curing on the physical, mechanical, and microstructural properties of metakaolin-based geopolymer concrete[J]. Construction and Building Materials, 2023, 406: 133403.
[5] GHANTOUS R M, POYET S, L’HOSTIS V, et al. Effect of crack openings on carbonation-induced corrosion[J]. Cement and Concrete Research, 2017, 95: 257-269.
[6] 贡力, 梁颖, 宫雪磊, 等. 硫酸盐环境下再生混凝土抗冻耐久性及界面微观结构研究[J]. 应用基础与工程科学学报, 2023, 31(4): 1006-1017.
GONG L, LIANG Y, GONG X L, et al. Study on frost resistance durability and interface microstructure of recycled concrete in sulfate environment[J]. Journal of Basic Science and Engineering, 2023, 31(4): 1006-1017 (in Chinese).
[7] WANG Y, XIE M, ZHANG J, Mechanical properties and damage model of modified recycled concrete under freeze-thaw cycles[J]. Journal of Building Engineering, 2023, 78: 107680.
[8] GUO Y C, PAN H M, SHEN A Q, et al. Fracture properties of basalt-fiber-reinforced bridge concrete under dynamic fatigue loading[J]. Structures, 2023, 56: 105018.
[9] FREDDI F, MINGAZZI L. A predictive phase-field approach for cover cracking in corroded concrete elements[J]. Theoretical and Applied Fracture Mechanics, 2022, 122: 103657.
[10] 商怀帅, 柴鑫. 往复荷载下锈蚀钢筋与混凝土粘结性能的试验研究[J]. 材料导报, 2023, 37(1): 133-138.
SHANG H S, CHAI X. Experimental study on bond performance between corroded steel bars and concrete under reciprocating load[J]. Materials Reports, 2023, 37(1): 133-138 (in Chinese).
[11] KOREC E, JIRÁSEK M, WONG H S, et al. A phase-field chemo-mechanical model for corrosion-induced cracking in reinforced concrete[J]. Construction and Building Materials, 2023, 393: 131964.
[12] ZHU X J, ZI G. A 2D mechano-chemical model for the simulation of reinforcement corrosion and concrete damage[J]. Construction and Building Materials, 2017, 137: 330-344.
[13] CHENG X D, SU Q Z, MA F L, et al. Investigation on crack propagation of concrete cover induced by non-uniform corrosion of multiple rebars[J]. Engineering Fracture Mechanics, 2018, 201: 366-384.
[14] BUI H T, TAN K H. Time-dependent nonuniform numerical model of corrosion process and consequent corrosion-induced concrete cracking under chloride attack[J]. Structures, 2023, 52: 332-347.
[15] WANG T, LI C H, ZHENG J J, et al. Consideration of coupling of crack development and corrosion in assessing the reliability of reinforced concrete beams subjected to bending[J]. Reliability Engineering & System Safety, 2023, 233: 109095.
[16] KIM H, SHARMA R, PEI J J, et al. Effect of carbonation curing on physicochemical properties of mineral admixture blended belite-rich cement[J]. Journal of Building Engineering, 2022, 56: 104771.
[17] CAREVIĆ V, IGNJATOVIĆ I. Influence of loading cracks on the carbonation resistance of RC elements[J]. Construction and Building Materials, 2019, 227: 116583.
[18] ALAHMAD S, TOUMI A, VERDIER J, et al. Effect of crack opening on carbon dioxide penetration in cracked mortar samples[J]. Materials and Structures, 2009, 42(5): 559-566.
[19] ZHANG S P, ZONG L, DONG L F, et al. Influence of cracking on carbonation of cement-based materials[J]. Advanced Materials Research, 2011, 261/262/263: 84-88.
[20] WANG X H, VAL D V, ZHENG L, et al. Influence of loading and cracks on carbonation of RC elements made of different concrete types[J]. Construction and Building Materials, 2018, 164: 12-28.
[21] JIANG C, GU X L, ZHANG W P, et al. Modeling of carbonation in tensile zone of plain concrete beams damaged by cyclic loading[J]. Construction and Building Materials, 2015, 77: 479-488.
[22] ANN K Y, PACK S W, HWANG J P, et al. Service life prediction of a concrete bridge structure subjected to carbonation[J]. Construction and Building Materials, 2010, 24(8): 1494-1501.
[23] 中国气象局. 中国温室气体公报——截至2021年底中国和全球大气温室气体观测结果[EB/OL]. https://www.cma.gov.cn/.
China Meteorological Administration. China greenhouse gas bulletin—Observations of greenhouse gases in the atmosphere of China and the world as of the end of 2021[EB/OL]. https://www.cma.gov.cn/(in Chinese).
[24] CUI H Z, TANG W, LIU W, et al. Experimental study on effects of CO₂ concentrations on concrete carbonation and diffusion mechanisms[J]. Construction and Building Materials, 2015, 93: 522-527.
[25] CAO Y, GEHLEN C, ANGST U, et al. Critical chloride content in reinforced concrete: an updated review considering Chinese experience[J]. Cement and Concrete Research, 2019, 117: 58-68.
[26] WANG Y Z, LIU C X, WANG Y C, et al. Investigation on chloride threshold for reinforced concrete by a test method combining ANDT and ACMT[J]. Construction and Building Materials, 2019, 214: 158-168.
[27] LI C Z, JIANG L H, LI S S. Effect of limestone powder addition on threshold chloride concentration for steel corrosion in reinforced concrete[J]. Cement and Concrete Research, 2020, 131: 106018.
[28] MANERA M, VENNESLAND Ø, BERTOLINI L. Chloride threshold for rebar corrosion in concrete with addition of silica fume[J]. Corrosion Science, 2008, 50(2): 554-560.
[29] MEIRA G R, ANDRADE C, VILAR E O, et al. Analysis of chloride threshold from laboratory and field experiments in marine atmosphere zone[J]. Construction and Building Materials, 2014, 55: 289-298.
[30] ANGST U M, ELSENER B, LARSEN C K, et al. Chloride induced reinforcement corrosion: electrochemical monitoring of initiation stage and chloride threshold values[J]. Corrosion Science, 2011, 53(4): 1451-1464.
[31] 张倩倩, 孙伟, 施锦杰. 矿物掺合料对钢筋锈蚀临界氯离子含量的影响[J]. 硅酸盐学报, 2010, 38(4): 633-637.
ZHANG Q Q, SUN W, SHI J J. Influence of mineral admixtures on chloride threshold level for corrosion of steel in mortar[J]. Journal of the Chinese Ceramic Society, 2010, 38(4): 633-637 (in Chinese).
[32] THOMAS M. Chloride thresholds in marine concrete[J]. Cement and Concrete Research, 1996, 26(4): 513-519.
[33] CHEEWAKET T, JATURAPITAKKUL C, CHALEE W. Initial corrosion presented by chloride threshold penetration of concrete up to 10 year-results under marine site[J]. Construction and Building Materials, 2012, 37: 693-698.
[34] YANG D Q, YAN C W, ZHANG J, et al. Chloride threshold value and initial corrosion time of steel bars in concrete exposed to saline soil environments[J]. Construction and Building Materials, 2021, 267: 120979.
[35] 孙丛涛, 刘诗群, 牛荻涛, 等. 干湿循环条件下钢筋锈蚀的临界氯离子浓度[J]. 建筑材料学报, 2016, 19(2): 385-389.
SUN C T, LIU S Q, NIU D T, et al. Critical chloride concentration of rebar corrosion under dry-wet cycles[J]. Journal of Building Materials, 2016, 19(2): 385-389 (in Chinese).
[36] 卢金马, 黄俊铭, 余波, 等. 电极工作面积和孔隙液pH值对钢筋脱钝临界氯离子浓度的影响[J]. 建筑材料学报, 2021, 24(5): 994-1001.
LU J M, HUANG J M, YU B, et al. Influence of working area of electrode and pH value of pore solution on critical chloride concentration for steel bar depassivation[J]. Journal of Building Materials, 2021, 24(5): 994-1001 (in Chinese).
[37] LU Z H, ZHAO Y G, YU Z W, et al. Probabilistic evaluation of initiation time in RC bridge beams with load-induced cracks exposed to de-icing salts[J]. Cement and Concrete Research, 2011, 41(3): 365-372.
[38] AUDENAERT K, MARSAVINA L, DE SCHUTTER G. Influence of cracks on the service life of concrete structures in a marine environment[J]. Key Engineering Materials, 2008, 399: 153-160.
[39] PARK S S, KWON S J, JUNG S H. Analysis technique for chloride penetration in cracked concrete using equivalent diffusion and permeation[J]. Construction and Building Materials, 2012, 29: 183-192.
[40] KWON S J, NA U J, PARK S S, et al. Service life prediction of concrete wharves with early-aged crack: probabilistic approach for chloride diffusion[J]. Structural Safety, 2009, 31(1): 75-83.
[41] 鞠学莉, 吴林键, 刘明维, 等. 考虑氯离子侵蚀维度的钢筋混凝土码头服役寿命预测[J]. 材料导报, 2021, 35(24): 24075-24080+24087.
JU X L, WU L J, LIU M W, et al. Service life prediction for reinforced concrete wharf considering the influence of chloride erosion dimension[J]. Materials Reports, 2021, 35(24): 24075-24080+24087 (in Chinese).
[42] JAMALI A, ANGST U, ADEY B, et al. Modeling of corrosion-induced concrete cover cracking: a critical analysis[J]. Construction and Building Materials, 2013, 42: 225-237.
[43] 金伟良, 王晓舟. 基于锈胀开裂路径的混凝土构件耐久性能概率预测模型及应用[J]. 建筑结构学报, 2011, 32(1): 95-104.
JIN W L, WANG X Z. Corrosion-crack path based probabilistic prediction model on durability behavior of reinforced concrete elements and application[J]. Journal of Building Structures, 2011, 32(1): 95-104 (in Chinese).
[44] YÜZER N, AKÖZ F, KABAY N. Prediction of time to crack initiation in reinforced concrete exposed to chloride[J]. Construction and Building Materials, 2008, 22(6): 1100-1107.
[45] ZHANG X G, LI M H, TANG L P, et al. Corrosion induced stress field and cracking time of reinforced concrete with initial defects: analytical modeling and experimental investigation[J]. Corrosion Science, 2017, 120: 158-170.
[46] 李金玉, 曹建国, 徐文雨, 等. 混凝土冻融破坏机理的研究[J]. 水利学报, 1999, 30(1): 41-49.
LI J Y, CAO J G, XU W Y, et al. Stydy on the mechanism of concrete destruction under frost action[J]. Journal of Hydraulic Engineering, 1999, 30(1): 41-49 (in Chinese).
[47] 陈有亮, 刘明亮, 蒋立浩. 含宏观裂纹混凝土冻融的力学性能试验研究[J]. 土木工程学报, 2011, 44(增刊2): 230-233.
CHEN Y L, LIU M L, JIANG L H. Experimental study on mechanical properties of concrete with cracks after freeze-thaw cycles[J]. China Civil Engineering Journal, 2011, 44(supplement 2): 230-233 (in Chinese).
[48] 高矗, 申向东, 王萧萧, 等. 应力损伤轻骨料混凝土抗冻融性能[J]. 硅酸盐学报, 2014, 42(10): 1247-1252.
GAO C, SHEN X D, WANG X X, et al. Freeze-thaw resistance of lightweight aggregate concrete with stress damage[J]. Journal of the Chinese Ceramic Society, 2014, 42(10): 1247-1252 (in Chinese).
[49] ZHANG W H, PI Y L, KONG W P, et al. Influence of damage degree on the degradation of concrete under freezing-thawing cycles[J]. Construction and Building Materials, 2020, 260: 119903.
[50] 王兰. 荷载损伤混凝土抗冻性能的退化机理[D]. 大连: 大连理工大学, 2021.
WANG L. Degradation mechanism of frost resistance of concrete damaged by load[D]. Dalian: Dalian University of Technology, 2021 (in Chinese).
[51] LOTHENBACH B, BARY B, BESCOP P L, et al. Sulfate ingress in Portland cement[J]. Cement and Concrete Research, 2010, 40(8): 1211-1225.
[52] 赵庆新, 李东华, 闫国亮, 等. 受损混凝土抗硫酸盐腐蚀性能[J]. 硅酸盐学报, 2012, 40(2): 217-220.
ZHAO Q X, LI D H, YAN G L, et al. Corrosion resistance of damaged concrete exposed to sulphate attack[J]. Journal of the Chinese Ceramic Society, 2012, 40(2): 217-220 (in Chinese).
[53] 刘娟红, 赵力, 纪洪广. 初始损伤对混凝土硫酸盐腐蚀劣化性能的影响[J]. 工程科学学报, 2017, 39(8): 1278-1287.
LIU J H, ZHAO L, JI H G. Influence of initial damage on degradation and deterioration of concrete under sulfate attack[J]. Chinese Journal of Engineering, 2017, 39(8): 1278-1287 (in Chinese).
[54] 杨永敢, 康子豪, 詹炳根, 等. 初始损伤混凝土的抗硫酸盐侵蚀性能[J]. 建筑材料学报, 2022, 25(12): 1255-1261.
YANG Y G, KANG Z H, ZHAN B G, et al. Sulfate corrosion resistance of initial damage concrete[J]. Journal of Building Materials, 2022, 25(12): 1255-1261 (in Chinese).
[55] PAN H M, SI X Y, ZHAO Q X. Damage evolution model of early disturbed concrete under sulfate attack and its experimental verification[J]. Dyna, 2018, 93(1): 52-59.
[56] ZHOU C L, ZHU Z M, WANG Z H, et al. Deterioration of concrete fracture toughness and elastic modulus under simulated acid-sulfate environment[J]. Construction and Building Materials, 2018, 176: 490-499.
[57] YANG S Y, CHEN X L, HAN M, et al. Effect of sulfate attack, drying-wetting cycles and freezing-thawing cycles on reinforced concrete columns under eccentric loads[J]. Structures, 2022, 45: 1864-1877.
[58] 王鹏刚, 莫芮, 隋晓萌, 等. 混凝土中氯盐-硫酸盐耦合侵蚀的化学-损伤-传输模型研究进展[J]. 硅酸盐学报, 2022, 50(2): 512-521.
WANG P G, MO R, SUI X M, et al. Chemo-damage-transport model of combined chloride-sulfate attack in concrete[J]. Journal of the Chinese Ceramic Society, 2022, 50(2): 512-521 (in Chinese).
[59] 张成琳, 刘清风. 钢筋混凝土中氯盐和硫酸盐耦合侵蚀研究进展[J]. 材料导报, 2022, 36(1): 69-77.
ZHANG C L, LIU Q F. Coupling erosion of chlorides and sulfates in reinforced concrete: a review[J]. Materials Reports, 2022, 36(1): 69-77 (in Chinese).
[60] LIU G Y, MU S, CAI J S, et al. Influence of crack on concrete damage in salt-freezing environment[J]. Advances in Materials Science and Engineering, 2021, 2021: 1-13.
[61] 徐存东, 程昱, 王荣荣, 等. 带初始冻融损伤的混凝土材料受盐冻作用下性能劣化分析[J]. 工程科学与技术, 2019, 51(1): 17-26.
XU C D, CHENG Y, WANG R R, et al. Analysis of performance deterioration of concrete material with initial freeze-thaw damage under salt-freezing condition[J]. Advanced Engineering Sciences, 2019, 51(1): 17-26 (in Chinese).
[62] ZHOU H, ZHANG S S, FERNANDO D, et al. The bond-behaviour of CFRP-to-concrete bonded joints under fatigue loading: a damage accumulation model[J]. Engineering Fracture Mechanics, 2023, 284: 109272.
[63] KORTE S, BOEL V, DE CORTE W, et al. Behaviour of fatigue loaded self-compacting concrete compared to vibrated concrete[J]. Structural Concrete, 2014, 15(4): 575-589.
[64] TEPFERS R, KUTTI T. Fatigue strength of plain, ordinary, and lightweight concrete[J]. ACI Journal Proceedings, 1979, 76(5): 635-652.
[65] MINER M A. Cumulative damage in fatigue[J]. Journal of Applied Mechanics, 1945, 12(3): A159-A164.
[66] MIARKA P, SEITL S, BÍLEK V, et al. Assessment of fatigue resistance of concrete: S-N curves to the Paris’ law curves[J]. Construction and Building Materials, 2022, 341: 127811.
[67] 张劲泉, 宋紫薇, 韩冰, 等. 车辆荷载作用下公路混凝土桥梁疲劳问题研究进展[J]. 土木工程学报, 2022, 55(12): 65-79.
ZHANG J Q, SONG Z W, HAN B, et al. Research progress on fatigue problem of highway concrete bridge under vehicle load[J]. China Civil Engineering Journal, 2022, 55(12): 65-79 (in Chinese).
[68] SUN J Z, DING Z H, HUANG Q. Corrosion fatigue life prediction for steel bar in concrete based on fatigue crack propagation and equivalent initial flaw size[J]. Construction and Building Materials, 2019, 195: 208-217.
[69] PARIS P, ERDOGAN F. A critical analysis of crack propagation laws[J]. Journal of Basic Engineering, 1963, 85(4): 528-533.
[70] BALUCH M H, QURESHY A B, AZAD A K. Fatigue crack propagation in plain concrete[C]//SHAH S P, SWARTZ S E. Fracture of Concrete and Rock. New York: Springer, 1989: 80-87.
[71] BAZANT Z P, SCHELL W F. Fatigue fracture of high-strength concrete and size effect[J]. ACI Materials Journal, 1993, 90(5): 472.
[72] LE J L, MANNING J, LABUZ J F. Scaling of fatigue crack growth in rock[J]. International Journal of Rock Mechanics and Mining Sciences, 2014, 72: 71-79.
[73] KIRANE K, BAŽANT Z P. Size effect in Paris law and fatigue lifetimes for quasibrittle materials: modified theory, experiments and micro-modeling[J]. International Journal of Fatigue, 2016, 83: 209-220.
[74] WALKER K. The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7075-T6 aluminum[M]//Effects of Environment and Complex Load History on Fatigue Life. 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959: ASTM International, 2009: 1.
[75] FORMAN R G, KEARNEY V E, ENGLE R M. Numerical analysis of crack propagation in cyclic-loaded structures[J]. Journal of Basic Engineering, 1967, 89(3): 459-463.
[76] KUMAR B, RAY S. Nano-mechanics based crack growth characterization of concrete under fatigue loading[J]. Procedia Structural Integrity, 2022, 39: 222-228.
[77] BHOWMIK S, RAY S. An improved crack propagation model for plain concrete under fatigue loading[J]. Engineering Fracture Mechanics, 2018, 191: 365-382.
[78] PERVAIZ FATHIMA K M, CHANDRA KISHEN J M. A thermodynamic framework for fatigue crack growth in concrete[J]. International Journal of Fatigue, 2013, 54: 17-24.
[79] SIMON K M, CHANDRA KISHEN J M. A multiscale approach for modeling fatigue crack growth in concrete[J]. International Journal of Fatigue, 2017, 98: 1-13.
[80] GAEDICKE C, ROESLER J, SHAH S. Fatigue crack growth prediction in concrete slabs[J]. International Journal of Fatigue, 2009, 31(8/9): 1309-1317.
[81] 栾利强. 半刚性基层沥青路面疲劳裂缝扩展与寿命预估研究[J]. 土木工程学报, 2017, 50(9): 118-128.
LUAN L Q. Research on fatigue crack propagation and fatigue life prediction of semi-rigid base asphalt pavement[J]. China Civil Engineering Journal, 2017, 50(9): 118-128 (in Chinese).
[82] 李进洲, 余志武, 宋力. 重载铁路桥梁疲劳变形和裂缝扩展规律研究[J]. 土木工程学报, 2013, 46(9): 72-82.
LI J Z, YU Z W, SONG L. Study on fatigue deflection and crack propagation laws of heavy-haul railway bridges[J]. China Civil Engineering Journal, 2013, 46(9): 72-82 (in Chinese).
[83] 刘问, 徐世烺, 李庆华. 超高韧性水泥基复合材料疲劳裂缝扩展公式的理论与试验研究[J]. 工程力学, 2013, 30(11): 67-74.
LIU W, XU S L, LI Q H. Theorical and experimental study on fatigue crack propagation law of ultra-high toughness cementitious composite[J]. Engineering Mechanics, 2013, 30(11): 67-74 (in Chinese).
[84] 王彦鹏, 李杰. 混凝土疲劳理论研究进展[J]. 同济大学学报(自然科学版), 2021, 49(5): 617-623.
WANG Y P, LI J. A review of theoretical study of concrete fatigue[J]. Journal of Tongji University (Natural Science), 2021, 49(5): 617-623 (in Chinese).
[85] CHAUSSUMIER M, SHAHZAD M, MABRU C, et al. A fatigue multi-site cracks model using coalescence, short and long crack growth laws, for anodized aluminum alloys[J]. Procedia Engineering, 2010, 2(1): 995-1004.
[86] 罗大明, 牛荻涛, 苏丽. 荷载与环境共同作用下混凝土耐久性研究进展[J]. 工程力学, 2019, 36(1): 1-14+43.
LUO D M, NIU D T, SU L. Research progress on durability of stressed concrete under environmental actions[J]. Engineering Mechanics, 2019, 36(1): 1-14+43 (in Chinese).
[87] MIURA T, SATO K, NAKAMURA H. Influence of primary cracks on static and fatigue compressive behavior of concrete under water[J]. Construction and Building Materials, 2021, 305: 124755.
[88] 张秋宇, 王立成. 基于能量法的水环境混凝土疲劳裂缝扩展模型[J]. 水利水运工程学报, 2020(3): 106-113.
ZHANG Q Y, WANG L C. Fatigue crack propagation model of concrete under water pressure based on energy approach[J]. Hydro-Science and Engineering, 2020(3): 106-113 (in Chinese).
[89] 蒋金洋, 孙伟, 金祖权, 等. 疲劳载荷与碳化耦合作用下结构混凝土寿命预测[J]. 建筑材料学报, 2010, 13(3): 304-309.
JIANG J Y, SUN W, JIN Z Q, et al. Service life prediction of structural concrete under coupled interactions of fatigue loading and carbonation factor[J]. Journal of Building Materials, 2010, 13(3): 304-309 (in Chinese).
[90] 覃潇, 申爱琴, 郭寅川, 等. 多场耦合下路面混凝土细观裂缝的演化规律[J]. 华南理工大学学报(自然科学版), 2017, 45(6): 81-88+102.
QIN X, SHEN A Q, GUO Y C, et al. Evolution rule of microcosmic cracks in pavement concrete under multi-field coupling[J]. Journal of South China University of Technology (Natural Science Edition), 2017, 45(6): 81-88+102 (in Chinese).
[91] 郭寅川, 申爱琴, 何天钦, 等. 疲劳荷载和冻融循环耦合作用下路面混凝土微裂缝扩展行为[J]. 交通运输工程学报, 2016, 16(5): 1-9.
GUO Y C, SHEN A Q, HE T Q, et al. Micro-crack propagation behavior of pavement concrete subjected to coupling effect of fatigue load and freezing-thawing cycles[J]. Journal of Traffic and Transportation Engineering, 2016, 16(5): 1-9 (in Chinese).
[92] FU C Q, YE H L, JIN X Y, et al. Chloride penetration into concrete damaged by uniaxial tensile fatigue loading[J]. Construction and Building Materials, 2016, 125: 714-723.
[93] 刘荣桂, 付凯, 颜庭成, 等. 预应力混凝土结构在冻融损伤条件下的疲劳寿命预测模型研究[J]. 建筑结构学报, 2009, 30(3): 79-86.
LIU R G, FU K, YAN T C, et al. Durability life prediction of prestressed concrete structures in an erosive environment with fatigue subjoining freezing-thawing circle[J]. Journal of Building Structures, 2009, 30(3): 79-86 (in Chinese).