冻融作用下混凝土的损伤与断裂研究
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摘要
我国大部分地区处于寒冷地带,低温和冻融循环作用往往是导致混凝土性能劣化的主要原因。研究混凝土在低温和冻融循环环境下的断裂损伤性能和材料断裂的微观机理,具有重要的理论研究价值及现实指导意义。
本文针对寒冷地区混凝土长期经受冻融作用的断裂损伤问题,分别从微观显微结构、机理分析、宏观力学性能及冻融后断裂面分形特征等方面进行细致研究,旨在应用断裂及损伤力学评价混凝土的冻融作用,揭示冻融损伤发展规律,为实现寒冷地区混凝土结构的抗冻耐久性设计、评估及寿命预测提供理论依据。
对冻融作用后混凝土进行断裂试验,探讨冻融作用对混凝土断裂行为的影响,揭示混凝土断裂参数劣化特征;应用断裂力学的原理和方法推导了四点弯曲方法进行混凝土断裂韧度测试的计算公式以及断裂韧度测试的其他参数计算方法,对混凝土段韧度测试应用四点弯曲方法进行测试,对冻融作用下不同水灰比、引气剂、不同掺合料混凝土的断裂韧度、断裂能及劣化趋势进行了分析和探讨,混凝土的断裂韧度与相对动弹性模量之间具有良好的线性关系。
利用显微观测技术,观察冻融前后混凝土内部微观裂纹及损伤特征,对比混凝土内部显微结构变化趋势,阐明冻融作用对内部结构的损伤机理;通过对混凝土断裂试验结果对比分析,确定改善混凝土冻融损伤的优化方案,利用显微观测方法分析各种掺合料对冻融耐久性的影响,并提出了合理化建议。利用损伤理论对冻融后混凝土导致的冻融损伤问题展开研究,建立混凝土冻融损伤的演化方程。
用高强石膏直接在混凝土断裂试件的表面复型,短时间内即可准确取出相应三维形貌的断裂表面,便于高精度分割和无破损直接测试,。应用数字图像方法处理进行混凝土的宏观裂缝以及微裂纹的分维计算,相对于传统的测量方法具有精度高、速度快的优点。此方法可以用于混凝土的分形计算中。
混凝土断裂面具有很好的自相似特征,可以用分形几何的理论和方法指导其分形特征的测试和评价。对冻融前后混凝土断裂面进行分形特征研究,将分形理论应用于混凝土冻融损伤研究中,为探索混凝土断裂面分形特征与断裂行为之间的内在规律以及建立相关的数学模型提供了重要的依据。混凝土断裂面具有良好的分形特点,冻融后混凝土断裂面断裂表面进行分维计算表明,其分形维数的方差非常小,线性回归的相关系数也非常好,测试精度比较高。可以将分形理论与混凝土的断裂理论结合起来,评价混凝土在冻融作用下的断裂行为。
利用最小二乘支持向量机模型进行冻融作用下混凝土的断裂韧度和断裂能预测,不需建立方程式,模型的建立和修改容易,可处理被干扰的数据,具有较强的概括性,比较适合小样本状态现的机器学习问题。LS-SVM模型是通过对数据文件的自学习获得规律,进行趋势预测,但这种规律具有特殊性,会随着影响因素变化而发生变化,所以,需要在模型中添加数据更新的性能,使之进行不断重新学习获得符合实际条件的规律,使预测模型保持较高精度。
Most of the territory of China locate in cold region, therefore, actions due to low temperature and freeze-and-thaw cycle become the main reason of deterioration of concrete properties. It has significant theoretical and practical meaning to study the fracture damage behavior and the micro mechanism of material fracture under low temperature and freeze-and-thaw cycle
In this paper, the fracture damage problem of concrete in cold region subjected to long term freeze-and-thaw actions is studied from aspects as micro-structure, mechanism analysis, macro mechanics properties and fractal features of fracture plane after freeze-and-thaw etc. The purpose is to discover the freeze-and-thaw damage development regularities by assessing the freeze-and-thaw actions by application of fracture and damage mechanics to provide theoretical basis for the design of anti-freeze durability, assessment and service period prediction of concrete structure in cold region.
Fracture tests of concrete after freeze-and-thaw were carried out to discuss the influence of freeze-and-thaw action to concrete fracture behavior and to discover deterioration features of concrete fracture parameters. The calculation formulae of concrete fracture toughness test using four point bending method, as well as calculation method of other parameters are derived by fracture mechanics principles. Under action of freeze-and-thaw, the fracture toughness, fracture energy and deterioration tendency of concrete with various water to cement ratio, air entraining agent and admixture are analyzed and discussed.There are very well linear relationship between relative dynamic elastic modulus of concrete and fracture toughness.
By utilizing micro observation technology, the inner micro crack and damage features of concrete before and after freeze-and-thaw are observed. By comparison of change tendency of concrete inner micro structure, the damage mechanism of inner structure due to freeze-and-thaw action is illuminated. The optimization plan of improving concrete damage due to freeze-and-thaw is determined by comparative analysis of concrete fracture test results. The influence of various admixture on freeze-and-thaw durability is analyzed by micro observation method, and reasonable suggestion is put forward. The freeze-and-thaw damage problem is studied by damage theory and the evolution equation of concrete is established.
The three-dimensional fracture surface can be precisely obtained in very short time by pasting high-strength gypsum directly on broken concrete specimen surface to facilitate high-precision segmentation and unbroken test. Fractal calculation of concrete macro and micro crack are performed by digital image process, which is better than traditional measurement method by high precision and fast calculation. This method can be applied in fractal calculation of concrete.
Concrete fracture surface features very good self-resemblance, therefore, fractal theory and method can be applied to guide the test and assessment of fractal characteristics. The fractal characteristics study on concrete fracture surface before and after freeze-and-thaw provides important basis for exploring the inner regularities between fractal characteristics and fracture behavior on concrete fracture surface and establishing related mathematical models. Concrete fracture surface possesses good fractal characteristics. Fractal dimension calculation of concrete surface showes that Fractal dimension variance is very small; the relativity coefficient of linear regression is also good; and the test precision is high. So, fractal theory and fracture theory of concrete can be combined to evaluate fracture behavior of concrete under freeze-and-thaw actions.
Using LS-SVM to predict fracture toughness and fracture energy of concrete under freeze-and-thaw actions doesn’t need to establish equations. It is easy to build the model and modify the model. The disturbed data can be processed and it has strong summarize. Therefore, it is suitable for small sample mechine study problem. LS-SVM model obtain regularity by self learning of data files to predict tendency; however, the regularity is special and it changes with influence factors. For this reason, it is necessary to add data updating function in the model to make it possible learning new regularities that are suitable for the real condition, which keeps the high precision of the prediction model.
本文针对寒冷地区混凝土长期经受冻融作用的断裂损伤问题,分别从微观显微结构、机理分析、宏观力学性能及冻融后断裂面分形特征等方面进行细致研究,旨在应用断裂及损伤力学评价混凝土的冻融作用,揭示冻融损伤发展规律,为实现寒冷地区混凝土结构的抗冻耐久性设计、评估及寿命预测提供理论依据。
对冻融作用后混凝土进行断裂试验,探讨冻融作用对混凝土断裂行为的影响,揭示混凝土断裂参数劣化特征;应用断裂力学的原理和方法推导了四点弯曲方法进行混凝土断裂韧度测试的计算公式以及断裂韧度测试的其他参数计算方法,对混凝土段韧度测试应用四点弯曲方法进行测试,对冻融作用下不同水灰比、引气剂、不同掺合料混凝土的断裂韧度、断裂能及劣化趋势进行了分析和探讨,混凝土的断裂韧度与相对动弹性模量之间具有良好的线性关系。
利用显微观测技术,观察冻融前后混凝土内部微观裂纹及损伤特征,对比混凝土内部显微结构变化趋势,阐明冻融作用对内部结构的损伤机理;通过对混凝土断裂试验结果对比分析,确定改善混凝土冻融损伤的优化方案,利用显微观测方法分析各种掺合料对冻融耐久性的影响,并提出了合理化建议。利用损伤理论对冻融后混凝土导致的冻融损伤问题展开研究,建立混凝土冻融损伤的演化方程。
用高强石膏直接在混凝土断裂试件的表面复型,短时间内即可准确取出相应三维形貌的断裂表面,便于高精度分割和无破损直接测试,。应用数字图像方法处理进行混凝土的宏观裂缝以及微裂纹的分维计算,相对于传统的测量方法具有精度高、速度快的优点。此方法可以用于混凝土的分形计算中。
混凝土断裂面具有很好的自相似特征,可以用分形几何的理论和方法指导其分形特征的测试和评价。对冻融前后混凝土断裂面进行分形特征研究,将分形理论应用于混凝土冻融损伤研究中,为探索混凝土断裂面分形特征与断裂行为之间的内在规律以及建立相关的数学模型提供了重要的依据。混凝土断裂面具有良好的分形特点,冻融后混凝土断裂面断裂表面进行分维计算表明,其分形维数的方差非常小,线性回归的相关系数也非常好,测试精度比较高。可以将分形理论与混凝土的断裂理论结合起来,评价混凝土在冻融作用下的断裂行为。
利用最小二乘支持向量机模型进行冻融作用下混凝土的断裂韧度和断裂能预测,不需建立方程式,模型的建立和修改容易,可处理被干扰的数据,具有较强的概括性,比较适合小样本状态现的机器学习问题。LS-SVM模型是通过对数据文件的自学习获得规律,进行趋势预测,但这种规律具有特殊性,会随着影响因素变化而发生变化,所以,需要在模型中添加数据更新的性能,使之进行不断重新学习获得符合实际条件的规律,使预测模型保持较高精度。
Most of the territory of China locate in cold region, therefore, actions due to low temperature and freeze-and-thaw cycle become the main reason of deterioration of concrete properties. It has significant theoretical and practical meaning to study the fracture damage behavior and the micro mechanism of material fracture under low temperature and freeze-and-thaw cycle
In this paper, the fracture damage problem of concrete in cold region subjected to long term freeze-and-thaw actions is studied from aspects as micro-structure, mechanism analysis, macro mechanics properties and fractal features of fracture plane after freeze-and-thaw etc. The purpose is to discover the freeze-and-thaw damage development regularities by assessing the freeze-and-thaw actions by application of fracture and damage mechanics to provide theoretical basis for the design of anti-freeze durability, assessment and service period prediction of concrete structure in cold region.
Fracture tests of concrete after freeze-and-thaw were carried out to discuss the influence of freeze-and-thaw action to concrete fracture behavior and to discover deterioration features of concrete fracture parameters. The calculation formulae of concrete fracture toughness test using four point bending method, as well as calculation method of other parameters are derived by fracture mechanics principles. Under action of freeze-and-thaw, the fracture toughness, fracture energy and deterioration tendency of concrete with various water to cement ratio, air entraining agent and admixture are analyzed and discussed.There are very well linear relationship between relative dynamic elastic modulus of concrete and fracture toughness.
By utilizing micro observation technology, the inner micro crack and damage features of concrete before and after freeze-and-thaw are observed. By comparison of change tendency of concrete inner micro structure, the damage mechanism of inner structure due to freeze-and-thaw action is illuminated. The optimization plan of improving concrete damage due to freeze-and-thaw is determined by comparative analysis of concrete fracture test results. The influence of various admixture on freeze-and-thaw durability is analyzed by micro observation method, and reasonable suggestion is put forward. The freeze-and-thaw damage problem is studied by damage theory and the evolution equation of concrete is established.
The three-dimensional fracture surface can be precisely obtained in very short time by pasting high-strength gypsum directly on broken concrete specimen surface to facilitate high-precision segmentation and unbroken test. Fractal calculation of concrete macro and micro crack are performed by digital image process, which is better than traditional measurement method by high precision and fast calculation. This method can be applied in fractal calculation of concrete.
Concrete fracture surface features very good self-resemblance, therefore, fractal theory and method can be applied to guide the test and assessment of fractal characteristics. The fractal characteristics study on concrete fracture surface before and after freeze-and-thaw provides important basis for exploring the inner regularities between fractal characteristics and fracture behavior on concrete fracture surface and establishing related mathematical models. Concrete fracture surface possesses good fractal characteristics. Fractal dimension calculation of concrete surface showes that Fractal dimension variance is very small; the relativity coefficient of linear regression is also good; and the test precision is high. So, fractal theory and fracture theory of concrete can be combined to evaluate fracture behavior of concrete under freeze-and-thaw actions.
Using LS-SVM to predict fracture toughness and fracture energy of concrete under freeze-and-thaw actions doesn’t need to establish equations. It is easy to build the model and modify the model. The disturbed data can be processed and it has strong summarize. Therefore, it is suitable for small sample mechine study problem. LS-SVM model obtain regularity by self learning of data files to predict tendency; however, the regularity is special and it changes with influence factors. For this reason, it is necessary to add data updating function in the model to make it possible learning new regularities that are suitable for the real condition, which keeps the high precision of the prediction model.
引文
1邓敏,唐明述.混凝土的耐久性与建筑业的可持续发展.混凝土. 1999, 2(2):8~12
2 Kaplan. M. F. Crack propagation and the fracture of concreteACI Journal. 1961, 3(11):591~610
3于骁中,谯常忻.岩石和混凝土断裂力学.中南工业大学出版社. 1998:67~69
4潘家铮.岩石混凝土损伤力学.中国矿业大学出版社. 1990:124~129
5杨延毅,周维垣.岩石与混凝土类材料断裂过程研究.水利学报. 1992, 5(11):69~74
6 RSM(Ouchterlong, F. Coordinator). Suggested methods for determining the fracture toughness of rock. International Journal of Rock Mechanics and Mining Science and Geomechanical Abstract. 1988,25:71~96
7王水林,葛修润.流形元方法在模拟裂纹扩展中的应用.岩石力学与工程学报. 1997,3(5):405~410
8周维垣,寇晓东.无单元法及其在岩土工程中的应用.岩土工程学报. 1998,6(1):18~20
9 Kesler, C. Naus, D. J. Lott, et al.Behavior of materials. In Proceedings of the International Conference on Mechanical Behavior of Materials Kyoto. 1971,7(4):231~255
10 Z. bazant, E. P. Chen. Scaling of structural failure. Applied Mechanical Review. 1997,11(10):593~627
11 J.Glucklich. The Structure of Concrete. Cement and Concrete Association. 1968, 7(4):176~189
12于骁中,居襄.断裂力学在水工结构设计中的应用.水利学报. 1980,8(5):86~87
13 F. H. Wuttmann. Structure of concrete with respect to crack formation. Fracture Mechanics of Concrete. Eds.Elsevier Science Publishers. 1989:257~262
14于骁中,居襄,曹建国.试件厚度对砂浆、混凝土断裂韧度的影响和缝端微裂纹区的形状和大小.水利学报. 1983,10(9):20~28
15 A. M. Neville. Properties of Concrete. London: Pitman Publishing limited.1981:193~196
16杨庆生,杨卫.断裂过程的有限元模拟.计算力学学报. 1997,5(4):407~412
17宋玉普.钢筋混凝土构件非线性有限单元法分析.大连理工大学学报. 1984,8(4):32~36
18 Z. P. Bazant,F.B.Liu. Nonlocal smeared cracking model for concrete fracture. Journal of Engineering Mechanics, ASCE. 1988,20(11):2493~2689
19 A. Hillerborg,M. Modeer, P. E. Peterson. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research. 1976,7(6):773~782
20用带切口的三点弯曲梁确定砂浆和混凝土的断裂能.RILEM试验标准.岩石、混凝土断裂与强度,1985
21 A. Hillerborg. Numerical method to simulate softening and fracture of concrete.Structural Application and Numerical Calculation.ed.George, C.sih and Ditommaso, A. Martinus Nijhoff Publishers.1985
22 Carmeliet, J. And Borst, R. D. Nonlocal damage and random fields.Computer Modelling of concrete Structures,Proceedings of EURO-C International Conference held in Innsbruck. Austria. 1994:63-72
23 A.Vervuurt, E.Schlangen, J. G.M.Van Mier,Tensile cracking in concrete and sandstone; part 1-basic instruments.Materials and structures. 1996,(29):9-18.
24 Z. P. bazantm, B. H. oh. Crack band model for concrete. Materials and Structures(RILEM). 1983,(16):155-177
25张东,吴科如.模拟混凝土断裂过程的影响因子矩阵法.同济大学学报. 1999,9(4):427~431
26 C. A. Brebbia, J. J. Connor. Crack growth in concrete using boundary elements. Computational,Mechanics Publications, Southampton UK and Boston USA
27谢和平.岩石、混凝土损伤力学.中国矿业大学出版社. 1990:243~248
28蔡四维,蔡敏.混凝土的损伤断裂.人民交通出版社. 1999:148-155
29 J. W. Dougil, et al. Journal of Engineering Mechanics, ASCE. 1976,(1):102-333
30 K. E. Loland. Continuous damage models for load-response estimation of concrete. Cement and Concrete Resrarch. 1980,5(10):392~492
31 J. Mazars. Application de le mecanique de lendonnagement an comportement non lineaire de structure. These de doctorat detat, Univ. Pris 6, Enset, Mai.1980 :122~134
32余天庆.混凝土的分段线性损伤模型.岩石、混凝土断裂与强度. 1985,11(2) :4~16
33钱济成,周建方.混凝土的两种损伤模型及其应用.河海大学学报. 1989,1(3):40~47
34 F. Supartono, F. Sidoroff. Anisotropic damage modeling for brittle elastic materials. Symposium of France-Poland. 1984:369~377
35 D. Krajcinovic, G. U. Fonseka. Continuous damage theory of brittle materials. Journal of applied Mechanics. 1981,21(48):809~824
36余天庆.损伤理论及其应用.国防工业出版社.1993:354~366
37 J. Kaufmann. Experimental Identification of Damage Mechanisms in Cementitious Porous Materials on Phase Transition of Pore Solution under Frost Deicing Salt Attack. thesis EPF Lausanne No 2037(1999)
38 M. A. Oritiz. constitutive theory for the inelastic behavior of concrete. Mechanics of Materials. 1985,5(4):67~93
39 M. Oritiz. An analysis study the localized failure models of concrete. Mechanics of Materials. 1987,7(6):159~174
40 H. Mihashi, M.A.Izumi. stochastic theory of concrete fracture. Cement and Concrete Research. 1977,9(7):411~422
41 N. J. Burt, J. W. Diygukk. Progressive failure in a heterogeneous medium. Journal of Engineering Mechanics, ASCE. 1977,24(13):365~376
42徐世烺.混凝土断裂韧度的概率统计分析.水利学报. 1984,9(10):23~27
43徐世琅,赵国藩.混凝土断裂韧度的概率模型研究.土木工程学报. 1988,11(11):9~23
44李平先,赵国藩,张雷顺.受冻融损伤混凝土与新混凝土的粘结剪切性能试验研究.建筑结构学报. 2004,25(5):111~117
45 T. C. Powers. Freezing Effect in Concrete. Durability of Concrete. 1975,9(2):47~10
46施士升.冻融循环对混凝土力学性能的影响.土木工程学报. 1997,30(4):35~42
47 Zou Chaoying, Zhao Juan, Liang Feng. Experimental Study on Stress-Strain Relationship of Frost-Resistant Concrete.Proceeding of The Eighth International Symposium on Structural Engineering for Young Exports. Xi’an, Science Press. 2004:1038~1042.
48 Chao-Ying Zou, Juan Zhao, Jian-Lin Luo, et al. Experimental Studies on Mechanical Properties of Concrete under Freeze-ThawAction.Proceeding of the Ninth International Symposium on Structural Engineering for Young Exports. Fuzhou, Science Press.2006:1759~1764
49 Chao-Ying Zou, Jian-Lin Luo, Juan Zhao, et al. Experimental Study on the Mechanical Behavior of Frost-Resistant Concrete under the Repetitive Load Action.Proceeding of the Ninth International Symposium on Structural Engineering for Young Exports. Fuzhou, Science Press. 2006:1955-1961
50覃丽坤,宋玉普,陈浩然.冻融循环对混凝土力学性能的影响.岩石力学与工程学报. 2005,8(1):5049~5053
51宋玉普,于长江,覃丽坤.冻融环境下混凝土双向受压强度与变形特性试验研究.大连理工大学学报. 2004,44(4):545~549
52于长江,宋玉普.冻融环境下混凝土双向拉压强度与变形特性的试验研究.混凝土. 2004,175(5):12~16
53商怀帅,宋玉普,覃丽坤.冻融循环后在三向受压荷载下混凝土性能的试验研究.水利学报. 2006,37(7):874~880
54覃丽坤,宋玉普,王玉杰.冻融环境对海水中混凝土抗压性能的影响.混凝土. 2004,171(1):16~18
55 W. Sun, Y. M. Zhang, H. D. Yan. Damage and Damage Resistance of High Strength Concrete under the Action of Load and Freeze-Thaw Cycles. Cement and Concrete Research. 1999,1(29):1519~1523
56 W. Sun, Y. M. Zhang, H. D. Yan,et al.Damage and its Restraint of Concrete with Different Strength Grades under Double Damage Factors. Cement & Concrete Composites. 1999,21:439~442
57邹超英,徐天水,胡琼.应力状态对抗冻混凝土力学性能的影响.低温建筑技术. 2005,108(6):6~8
58周圣斌,侯建国,杨小兵.钢筋混凝土结构冻融破坏的随机模糊可靠度分析.武汉大学学报. 2004,37(3):70~73
59 Zongjin Li, C. K. Chau, Xiangming Zhou. Accelerated Assessment and Fuzzy Evaluation of Concrete Durability. Journal of Materials in Civil Engineering. 2005,24(5-6):257~263
60刘远.基于损伤理论的混凝土抗冻耐久性随机预测方法研究.浙江大学硕士论文. 2006
61巩妮娜,刘西拉.从结构工程的角度看混凝土在冻融循环中的破坏标准.四川建筑科学研究. 2005,31(6):144~148
62 ACI 201.2R-92. Guide to Durable Concrete. Committee201, ACI. 1992
63 CEB/FIP Mode Code 1990.CEB/FIP Design Guide to Durable Concrete Structures.1990
64 BS 8110-1985. British Standards Institution. 1985
65 SL/T 5057-96水工混凝土结构设计规范. 1996
66 JTJ267-98港口工程混凝土结构设计规范. 1998
67中国工程院土木水利与建筑学部工程结构安全性与耐久性研究咨询项目组.混凝土结构耐久性设计及施工指南.中国建筑工业出版社. 2004
68 M. J. Setzer, R.Auberg . Frost Resistance of Concrete.Proceeding of the International RILEM Workshop on Resistance of Concrete to Freezing and Thawing with or without De-Icing Chemicals. New York. 1997
69黄士元.混凝土结构抗冻融(包括盐冻)侵蚀耐久性设计的建议.混凝土结构耐久性及耐久性设计会议.北京, 2002
70 M. Pigeon, J. Marchand , R. Pleau. Frost Resistance Concrete. Construction and Building Materials. 1996,10(5):339~348
71 J. Stefan, M. Jacques, H. Hugues. SEM Observations of the Microstructure of Frost Deteriorated and Self-Healed Concretes. Cement and Concrete Research. 1995,25(8):1781~1790
72 T. C. Powers. A Working Hypothesis for Further Studies of Frost Resistance of Concrete. Journal of ACI. 1945, 16(4):245~272
73 T. C. Powers. Freezing Effects in Concete. Durability of Concrete. 1975,1(2):332~338
74 A. M. Neville. Properties of Concrete. Pitman Publishing Ltd. 1995
75 P. K. Mihta, P.Schiessl,M.Raupach. Performance and Durability of Concrete systems.Proceedings of 9th International Congress on the Chemistry of Cement. 1992, 1(2):571~659
76 J. S. Ma. Mechanical Stability Criterion,Triple-Phase Condition,and Pressure Differences of Matter Condensed in a Porous Matrix. Journal of Colloid and Interface Science. 2001,(235):170~182
77 J. S. Max. Micro-Ice-Lens Formation in Porous Solid. Journal of Colloid andInterface Science. 2001,243:193~201
78 J. S. Max. Mechanisms of Frost Action.Proceedings of an International Workshop on Durability of Reinforced Concrete under Combined Mechanical and Climatic Loads. QingDao, 2005:263~274
79李金玉,曹建国,徐文雨.混凝土冻融破坏机理的研究.水利学报. 1999,5(1):41~49
80 G?ran Fagerlund. Mechanical Damage and Fatigue Effects Associated with Freeze-Thaw of Materials.Proceedings of the International RELEM Workshop. Essen,Germany. The Publishing Company of RELEM. 2002:117~132
81 P. Josef Kaufmann. Experimental Identification of Ice Formation in Small Concrete Pores. Cement and Concrete Research. 2004,34:1421~1427
82 Stefan Jacobsen. Calculating Liquid Transport into High-Performance Concrete during Wet Freeze-Thaw. Cement and Concrete Research. 2005,(35):213~219
83 D. Bager, S. Jacobsen. A Model for the Destructive Mechanism in Concrete Caused by Freeze-Thaw. Proceedings of the International RELEM Workshop(PRO25). Cachan,France. 2002:17~40
84李守巨,刘迎曦,陈昌林.混凝土大坝冻融破坏问题的数值计算分析.岩土力学. 2004,25(2):189~190
85 S. Kasparek, M.J.Setzer.Analysis of Heat Flux and Moisture Transport in Concrete during Freezing and Thawing.Proceedings of the International RELEM Workshop. Essen, Germany. The Publishing Company of RELEM. 2002:187~196
86 R. E. Beddoe. Low-Temperature Phase Transitions of Pore Water in Hardened Cement Paste.Proceedings of the International RELEM Workshop. Essen, Germany. The Publishing Company of RELEM. 2002:161~168
87 A. O. Mohamed, L. R. Kevin, J. J. stalnaker. Factors Affecting Resistance of Concrete to Freezing and Thawing Damage. Journal of materials in civil engineering. 2000,(2):26~32
88 P. E. Grattan-Bellew. Microstructural Investigation of Deteriorated Porland Cement Concretes. Construction and Building Materials. 1996,10(1):3~16
89 P. K. Mehta, P. J. M. Monterio. Concrete Structure,Propertied and Materials. New Jersey: Prentice Hall. 1993,(2):548~560
90 G. Nerbeck. Pore Structure-Significance of Tests and Properties of Concrete andConcrete and Concrete Making Materials. ASTM Special Technical Publication. 1982:211~219
91赵霄龙,卫军,黄玉盈.混凝土冻融耐久性劣化与孔结构变化的关系.武汉理工大学学报. 2002,6(12):14~17
92罗晓辉,卫军,罗昕.混凝土劣化与有害孔洞的物理关系.华中科技大学学报. 2006,34(3):94~96
93 A. O. Mohamed. Factors Affecting Resistance of Concrete to Freezing and Thawing Damage. Journal of Materials in Civil Engineering. 2000,(2):26~32
94 M. J. Setzer, R. Auberg. Frost Resistance of Concrete: Proceedings of the International RELEM Workshop on Resistance of Concrete to Freezing and Thawing with or without De-icing Chemicals[J].Journal of Cold Regions Engineering. 1999,(3):56~58
95谭克锋.水灰比和掺合料对混凝土抗冻性的影响.武汉理工大学学报. 2006,28(3):58~60
96 T. C. Powers. The Air-Requirement of Frost-Resistant Concrete. Proceedings of Highway Research Board 29. 1949:184~211
97 M. Pigeon, R. Pleau.Durability of Concrete in Cold Climates. London: Chapman & Hall, 1995
98 G. Pardini, G. Vigna Guidi, R. Pini. Structure and Porosity of Smectitic Mudrocks as Affected by Experimental Wetting-Drying Cycles and Freezing-Thawing Cycles. Catena. 1996,(27):149~165
99 S. Perron, J. J. Beaudoin. Freezing of Water in Portland Cement Paste- An Ac impedance Spectroscopy Study. Cement & Concrete Composites. 2002,(24):467~475
100 L. Basheer, P. A. M. Basheer, A.E. Long.Influence of Coarse Aggregate on the Permeation Durability and the Microstructure Characteristics of Ordinary Proland Cement Concrete. Construction and Building Materials. 2005,(19):682~690
101 Gao Peiwei, Deng Min, Feng Naiqian. The Influence of Superplasticizer and Superfine Mineral Powder on the Flexibility. Strength and Durability of HPC. Cement and Concrete Research. 2001,31:703~706
102 S. Chatterji. Freezing of Air-Entrained Cement-Based Materials and Specific Actions of Air-Entraning Agents[J].Cement & Concrete Composites. 2003,25:759~765
103 Lianxiang Du, J. F. Kevin. Mechanisms of Air Entraiment in Concrete. Cement and Concrete Research. 2005,(35):1463~1471
104 ASTM-C666,混凝土快速冻融试验方法.美国材料与试验协会,1986.
105 JIS-85,混凝土冻融试验方法.日本工业标准, 1985
106 GB J82-1985,混凝土长期性能和耐久性试验方法. 1985
107 RILEM TC 176 IDC: CIF-Test Test Method of Frost Resistance of Concrete. 2001
108孙振平,蒋正武,金慧忠. RILEM混凝土抗冻融性推荐测试方法CIF及评述.混凝土. 2006,197(3):15~21
109赵霄龙,卫军,黄玉盈.混凝土冻融耐久性劣化的评价指标对比.华中科技大学学报. 2003,31(2):103~105
110罗昕,卫军.冻融条件下混凝土劣化陡劣点的探讨.混凝土. 2005,193(11):14~17
111刘卫东,张东芹,刘胜利.超声波检测混凝土结构抗冻性的方法研究.无损检测. 2002,24(5):196~199
112税国双,汪越胜,曲建民.材料力学性能退化的超声波无损检测与评价.力学进展. 2005,35(1):52~68
113 Stefan Jacobsen, Jacques Marchand,Hugues Hornain. SEM Observations of the Microstructure of Frost Deteriorated and Self-Healed Concretes. Cement and Concrete Research. 1995,25(8):1781~1790
114韩继红,张雄.冻融破坏混凝土红外热象特征及损伤程度评定.无损检测. 1998,20(12):346~347
115 P. J. Prado, B. J. Balcom, S. D. Beyea. Concrete Freeze/Thaw as Studied by Magnetic Resonance Imaging. Cement and Concrete Research. 1998,28(2):261~270
116 Tetsuya Suzuki, Masayasu Ohtsu. Quantitative Damage Evaluation of Structural Concrete by a Compression Test Based on AE Rate Process Analysis. Construction and Building Materials. 2004,18:197~202
117 L. B. Wang, J. D. Frost, G. Z. Voyiadjis. Quantification of Damage Parameters Using X-ray Tomography Images. Mechanics and Materials. 2003,35:777~790
118 Z. P. Bazant. Mathematical Model for Freeze-Thaw Durability of Concrete. Journal of the American Ceramic Society. 1988.71(9):776~783
119 B. Zuber. Modeling the Mechanisms of Frost Degradation of Hydrated CementSystem. UniversitéLaval/Ecole Normale Supérieure de Cachan, 2000
120 B. Zuber, J. Marchand. Modeling the Deterioration of Hydrated Cement System Exposed to Frost action.Part 1: Description of the Mathematical Model. Cement and Concrete Research. 2000,(3):1929~1939
121 Mamoru Matsumoto, Shuichi Hokoi, Masanori Hatano. Model for Simulation of Freezing and Thawing Processes in Building Materials[J].Building and Environment. 2001,36:733~742
122 P. H?upl, J. Grunewald, H. fechner. Coupled Heat Air and Moisture Transfer in Building Structure. International Journal of Heat and Mass transfer. 1997,40(7):1633~1642
123 T. Lucas, J. M. Chourot, P. h. Bohuon. Freezing of a Porous Medium in Contact with a Concentrated Aqueous Freezant: Numerical Modeling of Coupled Heat and Mass Transport. International Journal of Heat and Mass transfer. 2001,(44):2093~2106
124 Muneo Hori. Micromechanical Analysis on Deterioration due to Freezing and Thawing in Porous Brittle Materials. International Journal of Engineering Science. 1998,36(4):511~522
125 M. J. Setzer. Development of the Micro-Ice-Lens Model. Proceedings of the International RILEM Workshop: Frost Resistance of Concrete. Essen, Germany. The Publishing Company of RELEM. 2002:133~145
126 M. J. Setzer. Modeling of Frost-Attack on HPC with CIF Test. Proceedings of International Conference on Durability of High-Performance Concrete and final workshop of CONlife. AEDIFICATIO Publishers. Freiburg. 2004:179~196
127蔡昊.混凝土抗冻耐久性预测模型.清华大学博士论文. 1998
128许丽萍,吴学礼,黄士元.抗冻耐久性设计.上海建材学院学报. 1993,6(2):112~123
129李金玉,邓正刚,曹建国.混凝土抗冻性的定量化设计.重点工程混凝土耐久性研究与工程应用.中国建材工业出版社. 2001
130陈宁,朱伟勇. M-J混沌分形图谱.东北大学出版社. 1998:1~14
131吴彤.自组织方法论研究.清华大学出版社. 2001:3~14
132王东生,曹磊.混沌、分形及其应用.中国科学技术大学出版社. 1995:93~103
133 B. B. Mandelbrot. How Long is the Coast of Britain, Statistical Self Similarityand Fractional Dimension. Science. 1967,(155):636-638
134 B. B. Mandelbrot. Fractals: Form Chance and Dimension. Freeman, SanFrancisco. 1977:7~20
135 B. B. Mandelbrot. The Fractal Geometry of Nature. New York, W. H. Freeman. 1982:1~25
136张济忠.分形.清华大学出版社. 1995:1~18
137敖力布,林鸿溢.分形学导论.内蒙古人民出版社. 1996:1~32
138 B. B. Mandelbrot. Fractal character of fracture surfaces of metals of metals. Nature, 1984, (308):72-723
139谢和平.分形一岩石力学导论.科学出版社. 1997:168-257
140 V. C. Saouma. Fractal characterization of concrete crack surfaces. Engng, Fracture Mech. 1990,35(1):25~28
141 A. B. Molosov, F.M.Borodich.Fractal fracture of brittle bodies undercompression(in Rassian). Doklady Akademii Nauk. 1992,324(3):546~549
142 F. M. Borodich. Fracture energy of fractal crack, propagation in concrete and rock(in Rassian). Doklady Akademii Nauk. 1992,325(6):1138~1141
143 D. A. Lange. Relationship between fracture surface roughness and fracture behavior of cement paste and mortar. J. of Am. Ceramic Soc. 1993,76(3):589~597
144 V. C. Saouma, C. C. Barton. Fractals, fracture and size efect in concrete. J. of Engng Mechanics ASCE. 1994,120(4):835~854
145 Keru Wu. Efect of metallica ggregate on strength and fracture properties of HPC. Cement and Concrete Reseach. 2001,(31):113~118
146 AnYan, Keru Wu. Effect of fracture path on the fracture energy of high-strength concrete. Cement and Concrete Research. 2001,(31):1601~1606
147董毓利.混凝土非线性力学基础.中国建筑工业出版社. 1997:173~-181
148 M. B. Feodor. Fractals and fractal scaling in fracture mechanics. International Journal of Fracture. 1999,(95):239-259
149 A. Carpinteri. Fractal nature of material microstructure and size efects on apparent mechanical properties. Mechanics of M aterials. 1994,(18):89~101
150 A. Carpinteri, B. Chiaia. Crack-resistance behavior as a consequence of self-similar fracture topologies. I ntenational Journal of Fracture. 1996,(76):327~340
151 M. B. Bruneto. Scaling phenomena due to fractal contact in concrete and rock fractures. Intenational Journal of Fracture. 1999,(95):221~238
152康光宗,湛君毅.混凝土结构裂缝宽度尺寸效应的分形行为.湖南城建高等专科学校学报. 1999,(2):1~3
153周克荣,肖小松,吴晓涵.混凝土立方体抗压强度尺寸效应中的分形行为.福州大学学报. 1996,(supp):63~68
154周克荣,肖小松,吴晓涵.混凝土轴心抗压强度尺寸效应中的分形行为.福州大学学报. 1996,(supp):58~62
155周瑞忠.硅结构裂纹尖端应力场奇异性的分形力学意义.大连理工大学学报. 1997,(su pp):67~71
156倪玉山.混凝土细观结构断裂的分形分析.大连理工大学学报. 1997,(supp):72~76
157王铁成,杨建江,方芫.混凝土结构状态及其扩展的分形几何解析.大连理工大学学报. 1997,(supp):77~81
158李国强,邓学钧.级配骨料的分形效应.混凝土. 1995,(1):3~7
159徐定华,徐敏.混凝土材料学概论.中国标准出版社. 2002
160王谦源,张清.混凝土用砂的粒级分形评估.混凝土. 1994,(2):61~68
161王谦源,胡京爽.混凝土集料级配与分形.混凝土. 1997,(3):93~99
162 S. Diamond. Aspects of concrete porosity revisited. Cement and Concrete Research. 1999,(1):1181~118
163诸培南,翁臻培,王天顺.无机非金属材料显微结构图册.武汉工业大学出版社. 1994:208-219
164南策文.分相玻璃的分形几何.武汉工业大学学报. 1988,(1):141~144
165陆平.水泥材料科学导论[M].上海:同济大学出版社,1991:1~50.
166阿部忠行.小川进铺装ユンヶリートのフラクタル解析.日本土木学会论文集. 1992,(16):119~126
167潘国耀,毛若卿,袁坚.分形几何渗流理论在胶凝材料若干领域中的应用.硅酸盐建筑制品. 1996,(1):1~8
168金伟良,赵羽习.混凝土结构耐久性.科学出版社. 2002
169《普通混凝土长期性能和耐久性能试验方法》GBJ 82-8[S].中国标准出版社. 1986
170 ZinminWu, Shutong Yang. A analytical model to predict the effective fracture toughness of concrete for three-point bending notched beams. EngineeringFracture Mechanics. 2006,(73):2166~2191
171 H. W. Reinhardt, H. A. W. Cornelissen, D. A. Hordijk. Tensile tests and failure analysis of concrete. J Struct Engng. 1986,112(11):2462~2477
172 H. Tada, P. C. Paris, G. R. Irwin. The stress analysis of cracks handbook. St.Louis, MO:Paris Productions Incorporated. 1985
173《水工混凝土断裂试验规程》DL/T 5332-2005.中国电力出版社. 2006
174 A. Hillerborg, M. Modeer, P. E. Petersson. Analysis of crack formation and crack growth in concrete by means of fracturemechanics and finite elements. Cement and Concrete Research. 1976,6(6):773~782
175覃丽坤.冻融循环对混凝土力学性能的影响.岩石力学与工程学报. 2005,24(1):5048~5053
176商怀帅.不同水灰比混凝土冻融循环后双轴压缩试验研究.大连理工大学学报. 2007,47(6):862~865
177慕儒.冻融循环与外部弯曲应力、盐溶液复合作用下混凝土的耐久性与寿命预测.东南大学博士论文. PHD 2000
178朱卫中,王剑,钮长仁.应用弹性模量法研究负温混凝土冻融损伤的思考.低温建筑技术. 2001,(5):9~11
179 D. S. Zhang, X. Z. Cheng. Freeze-Thaw Durabiltity of Air-Entrained PEA Concrete. Sjostrom C. Durability of Building Materials and Components. E & FN SPON. 1996:482~490
180 D. S. Zhang. Air-Entrainment and Freeze-Thaw durability of OPC, PEA, GGBS Concrete. UK: University of Dundee. 1991
181潘钢华,秦鸿根,孙伟.粉煤灰混凝土冻融破坏机理研究.建筑材料学报. 2002,5(1):37~41
182 B. B. Sabir. Mechanical Properties and Frost Resistance of Silica Fume Concrete. Cement and Concrete Research. 1997,19:285~294
183 Jan Deja. Freezing and Deicing Salt Resistance of Blast Furnace Slag Concretes. Cement & Concrete Composites. 2003,25:357~361
184 Vedat A. Yerlici, Turan Ozturan. Factor Affecting Anchorage Bond Strength in High Performance Concrete. ACI Structural Journal. 2000,(21):5~6
185周万良,周士琼,李益进.水胶比、超细粉煤灰掺量对高性能混凝土钢筋握裹力的影响.混凝土与水泥制品. 2003,(2):16~18
186高向玲,李杰.钢筋混凝土粘结锚固的研究进展.结构工程师. 2001(2):29~34
187 K. G. Badu, G. S. N.Rao.Efficiency of Fly Ash in Concrete. Cement & Concrete Composites. 1993,15(3):223~229
188沈旦申.粉煤灰混凝土.中国铁道工业出版社. 1989
189 E. J. Sellevold. Silica fume-cement paste: hydration and pore Structure. Report BML 82.610. Norway. 1982:19~50
190何真,梁文泉.大体积混凝土中微膨胀剂的抗裂作用.武汉大学学报. 2001, 34(2):73~76
191李裕双,周汉舜.微膨胀剂聚丙烯纤维混凝土在桥面铺装中的应用.交通公路科技. 2006,(12):25~27
192朱锦章,罗昕,赵霄龙.超声回弹法评定冻融混凝土的抗压强度.低温建筑技术. 2005,(3):3-5
193赵霄龙.混凝土冻融损伤演化规律研究.华中科技大学. 2003
194 Z. P. Bazant. Mathematical model for freeze-thaw durability of concrete. Journal of the American Ceramic Society. 1998,71(9):776~783
195 W. K. Yip, F.K.Kong, K. S. Chan, M.K.Lim. A statistical model of microcracking of concrete under uniaxial compression. Theo and Appl. Frac Mech. 1995,(22):17~27
196 W. K. Yip. New damage variable in failure. Analysis of concrete. Jour of Mat in Civ Engrg, Nov. 1996,8(4):184~188
197刘远.基于损伤理论的混凝土抗冻耐久性随机预测方法研究.浙江大学硕士论文. 2006
198余寿文,冯西桥.损伤力学.清华大学出版社. 1997
199 S. D. Brown, R. B. Biddulph, P. D. Wilcox. A strength-poroity relation involving different pore geometry and oritn-ration. J Am Ceram Soc. 1964,47(07):0~322
200彭瑞东,谢和平,鞠杨.二维数字图像分形维数的计算方法.中国矿业大学学报. 2004,33(1):19-24.
201 B. E. Boser, I. M. Guyon , V. N. Vapnik. A training algorithm for optimal margin classifiers Proceedings of the fifth annual workshop on Computational learning theory. 1992:144~152
202 B. Scholkopf, C. J. C. Burges, A. J. Smola. Advances in Kernal Methods: Support Vector Learn-ing. MITPress. 1999
203邓乃杨,田英杰.数据挖掘中的新方法-支持向量机.科技出版社. 2004
204 JohnWiley, Sons. Statistical Learning Theory. VladimirN. Vapnik. 1998
205 N. Vladimir, Vapnik. The Nature of Statistical Learning Theory. Springer-Verlag. 1999
206 B. E. Boser, I. M. Guyon, V. N. Vapink. A training algorithm for optimal margin classifiers.In Proceedings of the 5th Annual ACM Workshop on computational Learning Theory. 1992:144~152.
207 Nello Cristianini, John Shawe-Taylor. An Introduction to Support Vector Machines and Other Kernel-based Learning Methods. The Syndicate of the Press of the University of Cambridge,England. 2000
208施鸿均,杨弋涛,孙保良.铝合金连铸工艺参数的辅助优化.塑性工程学报. 2003,10(4):344~346
209吴德会.基于最小二乘支持向量机的表面粗糙度预测模型铣削加工.中国机械工程. 2007,18(7):838~840
210关宇刚,孙伟,缪昌文.基于可靠度与损伤理论的混凝土寿命预测模型Ⅱ:模型验证与应用.硅酸盐学报. 2001,29(6):529~536.
2 Kaplan. M. F. Crack propagation and the fracture of concreteACI Journal. 1961, 3(11):591~610
3于骁中,谯常忻.岩石和混凝土断裂力学.中南工业大学出版社. 1998:67~69
4潘家铮.岩石混凝土损伤力学.中国矿业大学出版社. 1990:124~129
5杨延毅,周维垣.岩石与混凝土类材料断裂过程研究.水利学报. 1992, 5(11):69~74
6 RSM(Ouchterlong, F. Coordinator). Suggested methods for determining the fracture toughness of rock. International Journal of Rock Mechanics and Mining Science and Geomechanical Abstract. 1988,25:71~96
7王水林,葛修润.流形元方法在模拟裂纹扩展中的应用.岩石力学与工程学报. 1997,3(5):405~410
8周维垣,寇晓东.无单元法及其在岩土工程中的应用.岩土工程学报. 1998,6(1):18~20
9 Kesler, C. Naus, D. J. Lott, et al.Behavior of materials. In Proceedings of the International Conference on Mechanical Behavior of Materials Kyoto. 1971,7(4):231~255
10 Z. bazant, E. P. Chen. Scaling of structural failure. Applied Mechanical Review. 1997,11(10):593~627
11 J.Glucklich. The Structure of Concrete. Cement and Concrete Association. 1968, 7(4):176~189
12于骁中,居襄.断裂力学在水工结构设计中的应用.水利学报. 1980,8(5):86~87
13 F. H. Wuttmann. Structure of concrete with respect to crack formation. Fracture Mechanics of Concrete. Eds.Elsevier Science Publishers. 1989:257~262
14于骁中,居襄,曹建国.试件厚度对砂浆、混凝土断裂韧度的影响和缝端微裂纹区的形状和大小.水利学报. 1983,10(9):20~28
15 A. M. Neville. Properties of Concrete. London: Pitman Publishing limited.1981:193~196
16杨庆生,杨卫.断裂过程的有限元模拟.计算力学学报. 1997,5(4):407~412
17宋玉普.钢筋混凝土构件非线性有限单元法分析.大连理工大学学报. 1984,8(4):32~36
18 Z. P. Bazant,F.B.Liu. Nonlocal smeared cracking model for concrete fracture. Journal of Engineering Mechanics, ASCE. 1988,20(11):2493~2689
19 A. Hillerborg,M. Modeer, P. E. Peterson. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research. 1976,7(6):773~782
20用带切口的三点弯曲梁确定砂浆和混凝土的断裂能.RILEM试验标准.岩石、混凝土断裂与强度,1985
21 A. Hillerborg. Numerical method to simulate softening and fracture of concrete.Structural Application and Numerical Calculation.ed.George, C.sih and Ditommaso, A. Martinus Nijhoff Publishers.1985
22 Carmeliet, J. And Borst, R. D. Nonlocal damage and random fields.Computer Modelling of concrete Structures,Proceedings of EURO-C International Conference held in Innsbruck. Austria. 1994:63-72
23 A.Vervuurt, E.Schlangen, J. G.M.Van Mier,Tensile cracking in concrete and sandstone; part 1-basic instruments.Materials and structures. 1996,(29):9-18.
24 Z. P. bazantm, B. H. oh. Crack band model for concrete. Materials and Structures(RILEM). 1983,(16):155-177
25张东,吴科如.模拟混凝土断裂过程的影响因子矩阵法.同济大学学报. 1999,9(4):427~431
26 C. A. Brebbia, J. J. Connor. Crack growth in concrete using boundary elements. Computational,Mechanics Publications, Southampton UK and Boston USA
27谢和平.岩石、混凝土损伤力学.中国矿业大学出版社. 1990:243~248
28蔡四维,蔡敏.混凝土的损伤断裂.人民交通出版社. 1999:148-155
29 J. W. Dougil, et al. Journal of Engineering Mechanics, ASCE. 1976,(1):102-333
30 K. E. Loland. Continuous damage models for load-response estimation of concrete. Cement and Concrete Resrarch. 1980,5(10):392~492
31 J. Mazars. Application de le mecanique de lendonnagement an comportement non lineaire de structure. These de doctorat detat, Univ. Pris 6, Enset, Mai.1980 :122~134
32余天庆.混凝土的分段线性损伤模型.岩石、混凝土断裂与强度. 1985,11(2) :4~16
33钱济成,周建方.混凝土的两种损伤模型及其应用.河海大学学报. 1989,1(3):40~47
34 F. Supartono, F. Sidoroff. Anisotropic damage modeling for brittle elastic materials. Symposium of France-Poland. 1984:369~377
35 D. Krajcinovic, G. U. Fonseka. Continuous damage theory of brittle materials. Journal of applied Mechanics. 1981,21(48):809~824
36余天庆.损伤理论及其应用.国防工业出版社.1993:354~366
37 J. Kaufmann. Experimental Identification of Damage Mechanisms in Cementitious Porous Materials on Phase Transition of Pore Solution under Frost Deicing Salt Attack. thesis EPF Lausanne No 2037(1999)
38 M. A. Oritiz. constitutive theory for the inelastic behavior of concrete. Mechanics of Materials. 1985,5(4):67~93
39 M. Oritiz. An analysis study the localized failure models of concrete. Mechanics of Materials. 1987,7(6):159~174
40 H. Mihashi, M.A.Izumi. stochastic theory of concrete fracture. Cement and Concrete Research. 1977,9(7):411~422
41 N. J. Burt, J. W. Diygukk. Progressive failure in a heterogeneous medium. Journal of Engineering Mechanics, ASCE. 1977,24(13):365~376
42徐世烺.混凝土断裂韧度的概率统计分析.水利学报. 1984,9(10):23~27
43徐世琅,赵国藩.混凝土断裂韧度的概率模型研究.土木工程学报. 1988,11(11):9~23
44李平先,赵国藩,张雷顺.受冻融损伤混凝土与新混凝土的粘结剪切性能试验研究.建筑结构学报. 2004,25(5):111~117
45 T. C. Powers. Freezing Effect in Concrete. Durability of Concrete. 1975,9(2):47~10
46施士升.冻融循环对混凝土力学性能的影响.土木工程学报. 1997,30(4):35~42
47 Zou Chaoying, Zhao Juan, Liang Feng. Experimental Study on Stress-Strain Relationship of Frost-Resistant Concrete.Proceeding of The Eighth International Symposium on Structural Engineering for Young Exports. Xi’an, Science Press. 2004:1038~1042.
48 Chao-Ying Zou, Juan Zhao, Jian-Lin Luo, et al. Experimental Studies on Mechanical Properties of Concrete under Freeze-ThawAction.Proceeding of the Ninth International Symposium on Structural Engineering for Young Exports. Fuzhou, Science Press.2006:1759~1764
49 Chao-Ying Zou, Jian-Lin Luo, Juan Zhao, et al. Experimental Study on the Mechanical Behavior of Frost-Resistant Concrete under the Repetitive Load Action.Proceeding of the Ninth International Symposium on Structural Engineering for Young Exports. Fuzhou, Science Press. 2006:1955-1961
50覃丽坤,宋玉普,陈浩然.冻融循环对混凝土力学性能的影响.岩石力学与工程学报. 2005,8(1):5049~5053
51宋玉普,于长江,覃丽坤.冻融环境下混凝土双向受压强度与变形特性试验研究.大连理工大学学报. 2004,44(4):545~549
52于长江,宋玉普.冻融环境下混凝土双向拉压强度与变形特性的试验研究.混凝土. 2004,175(5):12~16
53商怀帅,宋玉普,覃丽坤.冻融循环后在三向受压荷载下混凝土性能的试验研究.水利学报. 2006,37(7):874~880
54覃丽坤,宋玉普,王玉杰.冻融环境对海水中混凝土抗压性能的影响.混凝土. 2004,171(1):16~18
55 W. Sun, Y. M. Zhang, H. D. Yan. Damage and Damage Resistance of High Strength Concrete under the Action of Load and Freeze-Thaw Cycles. Cement and Concrete Research. 1999,1(29):1519~1523
56 W. Sun, Y. M. Zhang, H. D. Yan,et al.Damage and its Restraint of Concrete with Different Strength Grades under Double Damage Factors. Cement & Concrete Composites. 1999,21:439~442
57邹超英,徐天水,胡琼.应力状态对抗冻混凝土力学性能的影响.低温建筑技术. 2005,108(6):6~8
58周圣斌,侯建国,杨小兵.钢筋混凝土结构冻融破坏的随机模糊可靠度分析.武汉大学学报. 2004,37(3):70~73
59 Zongjin Li, C. K. Chau, Xiangming Zhou. Accelerated Assessment and Fuzzy Evaluation of Concrete Durability. Journal of Materials in Civil Engineering. 2005,24(5-6):257~263
60刘远.基于损伤理论的混凝土抗冻耐久性随机预测方法研究.浙江大学硕士论文. 2006
61巩妮娜,刘西拉.从结构工程的角度看混凝土在冻融循环中的破坏标准.四川建筑科学研究. 2005,31(6):144~148
62 ACI 201.2R-92. Guide to Durable Concrete. Committee201, ACI. 1992
63 CEB/FIP Mode Code 1990.CEB/FIP Design Guide to Durable Concrete Structures.1990
64 BS 8110-1985. British Standards Institution. 1985
65 SL/T 5057-96水工混凝土结构设计规范. 1996
66 JTJ267-98港口工程混凝土结构设计规范. 1998
67中国工程院土木水利与建筑学部工程结构安全性与耐久性研究咨询项目组.混凝土结构耐久性设计及施工指南.中国建筑工业出版社. 2004
68 M. J. Setzer, R.Auberg . Frost Resistance of Concrete.Proceeding of the International RILEM Workshop on Resistance of Concrete to Freezing and Thawing with or without De-Icing Chemicals. New York. 1997
69黄士元.混凝土结构抗冻融(包括盐冻)侵蚀耐久性设计的建议.混凝土结构耐久性及耐久性设计会议.北京, 2002
70 M. Pigeon, J. Marchand , R. Pleau. Frost Resistance Concrete. Construction and Building Materials. 1996,10(5):339~348
71 J. Stefan, M. Jacques, H. Hugues. SEM Observations of the Microstructure of Frost Deteriorated and Self-Healed Concretes. Cement and Concrete Research. 1995,25(8):1781~1790
72 T. C. Powers. A Working Hypothesis for Further Studies of Frost Resistance of Concrete. Journal of ACI. 1945, 16(4):245~272
73 T. C. Powers. Freezing Effects in Concete. Durability of Concrete. 1975,1(2):332~338
74 A. M. Neville. Properties of Concrete. Pitman Publishing Ltd. 1995
75 P. K. Mihta, P.Schiessl,M.Raupach. Performance and Durability of Concrete systems.Proceedings of 9th International Congress on the Chemistry of Cement. 1992, 1(2):571~659
76 J. S. Ma. Mechanical Stability Criterion,Triple-Phase Condition,and Pressure Differences of Matter Condensed in a Porous Matrix. Journal of Colloid and Interface Science. 2001,(235):170~182
77 J. S. Max. Micro-Ice-Lens Formation in Porous Solid. Journal of Colloid andInterface Science. 2001,243:193~201
78 J. S. Max. Mechanisms of Frost Action.Proceedings of an International Workshop on Durability of Reinforced Concrete under Combined Mechanical and Climatic Loads. QingDao, 2005:263~274
79李金玉,曹建国,徐文雨.混凝土冻融破坏机理的研究.水利学报. 1999,5(1):41~49
80 G?ran Fagerlund. Mechanical Damage and Fatigue Effects Associated with Freeze-Thaw of Materials.Proceedings of the International RELEM Workshop. Essen,Germany. The Publishing Company of RELEM. 2002:117~132
81 P. Josef Kaufmann. Experimental Identification of Ice Formation in Small Concrete Pores. Cement and Concrete Research. 2004,34:1421~1427
82 Stefan Jacobsen. Calculating Liquid Transport into High-Performance Concrete during Wet Freeze-Thaw. Cement and Concrete Research. 2005,(35):213~219
83 D. Bager, S. Jacobsen. A Model for the Destructive Mechanism in Concrete Caused by Freeze-Thaw. Proceedings of the International RELEM Workshop(PRO25). Cachan,France. 2002:17~40
84李守巨,刘迎曦,陈昌林.混凝土大坝冻融破坏问题的数值计算分析.岩土力学. 2004,25(2):189~190
85 S. Kasparek, M.J.Setzer.Analysis of Heat Flux and Moisture Transport in Concrete during Freezing and Thawing.Proceedings of the International RELEM Workshop. Essen, Germany. The Publishing Company of RELEM. 2002:187~196
86 R. E. Beddoe. Low-Temperature Phase Transitions of Pore Water in Hardened Cement Paste.Proceedings of the International RELEM Workshop. Essen, Germany. The Publishing Company of RELEM. 2002:161~168
87 A. O. Mohamed, L. R. Kevin, J. J. stalnaker. Factors Affecting Resistance of Concrete to Freezing and Thawing Damage. Journal of materials in civil engineering. 2000,(2):26~32
88 P. E. Grattan-Bellew. Microstructural Investigation of Deteriorated Porland Cement Concretes. Construction and Building Materials. 1996,10(1):3~16
89 P. K. Mehta, P. J. M. Monterio. Concrete Structure,Propertied and Materials. New Jersey: Prentice Hall. 1993,(2):548~560
90 G. Nerbeck. Pore Structure-Significance of Tests and Properties of Concrete andConcrete and Concrete Making Materials. ASTM Special Technical Publication. 1982:211~219
91赵霄龙,卫军,黄玉盈.混凝土冻融耐久性劣化与孔结构变化的关系.武汉理工大学学报. 2002,6(12):14~17
92罗晓辉,卫军,罗昕.混凝土劣化与有害孔洞的物理关系.华中科技大学学报. 2006,34(3):94~96
93 A. O. Mohamed. Factors Affecting Resistance of Concrete to Freezing and Thawing Damage. Journal of Materials in Civil Engineering. 2000,(2):26~32
94 M. J. Setzer, R. Auberg. Frost Resistance of Concrete: Proceedings of the International RELEM Workshop on Resistance of Concrete to Freezing and Thawing with or without De-icing Chemicals[J].Journal of Cold Regions Engineering. 1999,(3):56~58
95谭克锋.水灰比和掺合料对混凝土抗冻性的影响.武汉理工大学学报. 2006,28(3):58~60
96 T. C. Powers. The Air-Requirement of Frost-Resistant Concrete. Proceedings of Highway Research Board 29. 1949:184~211
97 M. Pigeon, R. Pleau.Durability of Concrete in Cold Climates. London: Chapman & Hall, 1995
98 G. Pardini, G. Vigna Guidi, R. Pini. Structure and Porosity of Smectitic Mudrocks as Affected by Experimental Wetting-Drying Cycles and Freezing-Thawing Cycles. Catena. 1996,(27):149~165
99 S. Perron, J. J. Beaudoin. Freezing of Water in Portland Cement Paste- An Ac impedance Spectroscopy Study. Cement & Concrete Composites. 2002,(24):467~475
100 L. Basheer, P. A. M. Basheer, A.E. Long.Influence of Coarse Aggregate on the Permeation Durability and the Microstructure Characteristics of Ordinary Proland Cement Concrete. Construction and Building Materials. 2005,(19):682~690
101 Gao Peiwei, Deng Min, Feng Naiqian. The Influence of Superplasticizer and Superfine Mineral Powder on the Flexibility. Strength and Durability of HPC. Cement and Concrete Research. 2001,31:703~706
102 S. Chatterji. Freezing of Air-Entrained Cement-Based Materials and Specific Actions of Air-Entraning Agents[J].Cement & Concrete Composites. 2003,25:759~765
103 Lianxiang Du, J. F. Kevin. Mechanisms of Air Entraiment in Concrete. Cement and Concrete Research. 2005,(35):1463~1471
104 ASTM-C666,混凝土快速冻融试验方法.美国材料与试验协会,1986.
105 JIS-85,混凝土冻融试验方法.日本工业标准, 1985
106 GB J82-1985,混凝土长期性能和耐久性试验方法. 1985
107 RILEM TC 176 IDC: CIF-Test Test Method of Frost Resistance of Concrete. 2001
108孙振平,蒋正武,金慧忠. RILEM混凝土抗冻融性推荐测试方法CIF及评述.混凝土. 2006,197(3):15~21
109赵霄龙,卫军,黄玉盈.混凝土冻融耐久性劣化的评价指标对比.华中科技大学学报. 2003,31(2):103~105
110罗昕,卫军.冻融条件下混凝土劣化陡劣点的探讨.混凝土. 2005,193(11):14~17
111刘卫东,张东芹,刘胜利.超声波检测混凝土结构抗冻性的方法研究.无损检测. 2002,24(5):196~199
112税国双,汪越胜,曲建民.材料力学性能退化的超声波无损检测与评价.力学进展. 2005,35(1):52~68
113 Stefan Jacobsen, Jacques Marchand,Hugues Hornain. SEM Observations of the Microstructure of Frost Deteriorated and Self-Healed Concretes. Cement and Concrete Research. 1995,25(8):1781~1790
114韩继红,张雄.冻融破坏混凝土红外热象特征及损伤程度评定.无损检测. 1998,20(12):346~347
115 P. J. Prado, B. J. Balcom, S. D. Beyea. Concrete Freeze/Thaw as Studied by Magnetic Resonance Imaging. Cement and Concrete Research. 1998,28(2):261~270
116 Tetsuya Suzuki, Masayasu Ohtsu. Quantitative Damage Evaluation of Structural Concrete by a Compression Test Based on AE Rate Process Analysis. Construction and Building Materials. 2004,18:197~202
117 L. B. Wang, J. D. Frost, G. Z. Voyiadjis. Quantification of Damage Parameters Using X-ray Tomography Images. Mechanics and Materials. 2003,35:777~790
118 Z. P. Bazant. Mathematical Model for Freeze-Thaw Durability of Concrete. Journal of the American Ceramic Society. 1988.71(9):776~783
119 B. Zuber. Modeling the Mechanisms of Frost Degradation of Hydrated CementSystem. UniversitéLaval/Ecole Normale Supérieure de Cachan, 2000
120 B. Zuber, J. Marchand. Modeling the Deterioration of Hydrated Cement System Exposed to Frost action.Part 1: Description of the Mathematical Model. Cement and Concrete Research. 2000,(3):1929~1939
121 Mamoru Matsumoto, Shuichi Hokoi, Masanori Hatano. Model for Simulation of Freezing and Thawing Processes in Building Materials[J].Building and Environment. 2001,36:733~742
122 P. H?upl, J. Grunewald, H. fechner. Coupled Heat Air and Moisture Transfer in Building Structure. International Journal of Heat and Mass transfer. 1997,40(7):1633~1642
123 T. Lucas, J. M. Chourot, P. h. Bohuon. Freezing of a Porous Medium in Contact with a Concentrated Aqueous Freezant: Numerical Modeling of Coupled Heat and Mass Transport. International Journal of Heat and Mass transfer. 2001,(44):2093~2106
124 Muneo Hori. Micromechanical Analysis on Deterioration due to Freezing and Thawing in Porous Brittle Materials. International Journal of Engineering Science. 1998,36(4):511~522
125 M. J. Setzer. Development of the Micro-Ice-Lens Model. Proceedings of the International RILEM Workshop: Frost Resistance of Concrete. Essen, Germany. The Publishing Company of RELEM. 2002:133~145
126 M. J. Setzer. Modeling of Frost-Attack on HPC with CIF Test. Proceedings of International Conference on Durability of High-Performance Concrete and final workshop of CONlife. AEDIFICATIO Publishers. Freiburg. 2004:179~196
127蔡昊.混凝土抗冻耐久性预测模型.清华大学博士论文. 1998
128许丽萍,吴学礼,黄士元.抗冻耐久性设计.上海建材学院学报. 1993,6(2):112~123
129李金玉,邓正刚,曹建国.混凝土抗冻性的定量化设计.重点工程混凝土耐久性研究与工程应用.中国建材工业出版社. 2001
130陈宁,朱伟勇. M-J混沌分形图谱.东北大学出版社. 1998:1~14
131吴彤.自组织方法论研究.清华大学出版社. 2001:3~14
132王东生,曹磊.混沌、分形及其应用.中国科学技术大学出版社. 1995:93~103
133 B. B. Mandelbrot. How Long is the Coast of Britain, Statistical Self Similarityand Fractional Dimension. Science. 1967,(155):636-638
134 B. B. Mandelbrot. Fractals: Form Chance and Dimension. Freeman, SanFrancisco. 1977:7~20
135 B. B. Mandelbrot. The Fractal Geometry of Nature. New York, W. H. Freeman. 1982:1~25
136张济忠.分形.清华大学出版社. 1995:1~18
137敖力布,林鸿溢.分形学导论.内蒙古人民出版社. 1996:1~32
138 B. B. Mandelbrot. Fractal character of fracture surfaces of metals of metals. Nature, 1984, (308):72-723
139谢和平.分形一岩石力学导论.科学出版社. 1997:168-257
140 V. C. Saouma. Fractal characterization of concrete crack surfaces. Engng, Fracture Mech. 1990,35(1):25~28
141 A. B. Molosov, F.M.Borodich.Fractal fracture of brittle bodies undercompression(in Rassian). Doklady Akademii Nauk. 1992,324(3):546~549
142 F. M. Borodich. Fracture energy of fractal crack, propagation in concrete and rock(in Rassian). Doklady Akademii Nauk. 1992,325(6):1138~1141
143 D. A. Lange. Relationship between fracture surface roughness and fracture behavior of cement paste and mortar. J. of Am. Ceramic Soc. 1993,76(3):589~597
144 V. C. Saouma, C. C. Barton. Fractals, fracture and size efect in concrete. J. of Engng Mechanics ASCE. 1994,120(4):835~854
145 Keru Wu. Efect of metallica ggregate on strength and fracture properties of HPC. Cement and Concrete Reseach. 2001,(31):113~118
146 AnYan, Keru Wu. Effect of fracture path on the fracture energy of high-strength concrete. Cement and Concrete Research. 2001,(31):1601~1606
147董毓利.混凝土非线性力学基础.中国建筑工业出版社. 1997:173~-181
148 M. B. Feodor. Fractals and fractal scaling in fracture mechanics. International Journal of Fracture. 1999,(95):239-259
149 A. Carpinteri. Fractal nature of material microstructure and size efects on apparent mechanical properties. Mechanics of M aterials. 1994,(18):89~101
150 A. Carpinteri, B. Chiaia. Crack-resistance behavior as a consequence of self-similar fracture topologies. I ntenational Journal of Fracture. 1996,(76):327~340
151 M. B. Bruneto. Scaling phenomena due to fractal contact in concrete and rock fractures. Intenational Journal of Fracture. 1999,(95):221~238
152康光宗,湛君毅.混凝土结构裂缝宽度尺寸效应的分形行为.湖南城建高等专科学校学报. 1999,(2):1~3
153周克荣,肖小松,吴晓涵.混凝土立方体抗压强度尺寸效应中的分形行为.福州大学学报. 1996,(supp):63~68
154周克荣,肖小松,吴晓涵.混凝土轴心抗压强度尺寸效应中的分形行为.福州大学学报. 1996,(supp):58~62
155周瑞忠.硅结构裂纹尖端应力场奇异性的分形力学意义.大连理工大学学报. 1997,(su pp):67~71
156倪玉山.混凝土细观结构断裂的分形分析.大连理工大学学报. 1997,(supp):72~76
157王铁成,杨建江,方芫.混凝土结构状态及其扩展的分形几何解析.大连理工大学学报. 1997,(supp):77~81
158李国强,邓学钧.级配骨料的分形效应.混凝土. 1995,(1):3~7
159徐定华,徐敏.混凝土材料学概论.中国标准出版社. 2002
160王谦源,张清.混凝土用砂的粒级分形评估.混凝土. 1994,(2):61~68
161王谦源,胡京爽.混凝土集料级配与分形.混凝土. 1997,(3):93~99
162 S. Diamond. Aspects of concrete porosity revisited. Cement and Concrete Research. 1999,(1):1181~118
163诸培南,翁臻培,王天顺.无机非金属材料显微结构图册.武汉工业大学出版社. 1994:208-219
164南策文.分相玻璃的分形几何.武汉工业大学学报. 1988,(1):141~144
165陆平.水泥材料科学导论[M].上海:同济大学出版社,1991:1~50.
166阿部忠行.小川进铺装ユンヶリートのフラクタル解析.日本土木学会论文集. 1992,(16):119~126
167潘国耀,毛若卿,袁坚.分形几何渗流理论在胶凝材料若干领域中的应用.硅酸盐建筑制品. 1996,(1):1~8
168金伟良,赵羽习.混凝土结构耐久性.科学出版社. 2002
169《普通混凝土长期性能和耐久性能试验方法》GBJ 82-8[S].中国标准出版社. 1986
170 ZinminWu, Shutong Yang. A analytical model to predict the effective fracture toughness of concrete for three-point bending notched beams. EngineeringFracture Mechanics. 2006,(73):2166~2191
171 H. W. Reinhardt, H. A. W. Cornelissen, D. A. Hordijk. Tensile tests and failure analysis of concrete. J Struct Engng. 1986,112(11):2462~2477
172 H. Tada, P. C. Paris, G. R. Irwin. The stress analysis of cracks handbook. St.Louis, MO:Paris Productions Incorporated. 1985
173《水工混凝土断裂试验规程》DL/T 5332-2005.中国电力出版社. 2006
174 A. Hillerborg, M. Modeer, P. E. Petersson. Analysis of crack formation and crack growth in concrete by means of fracturemechanics and finite elements. Cement and Concrete Research. 1976,6(6):773~782
175覃丽坤.冻融循环对混凝土力学性能的影响.岩石力学与工程学报. 2005,24(1):5048~5053
176商怀帅.不同水灰比混凝土冻融循环后双轴压缩试验研究.大连理工大学学报. 2007,47(6):862~865
177慕儒.冻融循环与外部弯曲应力、盐溶液复合作用下混凝土的耐久性与寿命预测.东南大学博士论文. PHD 2000
178朱卫中,王剑,钮长仁.应用弹性模量法研究负温混凝土冻融损伤的思考.低温建筑技术. 2001,(5):9~11
179 D. S. Zhang, X. Z. Cheng. Freeze-Thaw Durabiltity of Air-Entrained PEA Concrete. Sjostrom C. Durability of Building Materials and Components. E & FN SPON. 1996:482~490
180 D. S. Zhang. Air-Entrainment and Freeze-Thaw durability of OPC, PEA, GGBS Concrete. UK: University of Dundee. 1991
181潘钢华,秦鸿根,孙伟.粉煤灰混凝土冻融破坏机理研究.建筑材料学报. 2002,5(1):37~41
182 B. B. Sabir. Mechanical Properties and Frost Resistance of Silica Fume Concrete. Cement and Concrete Research. 1997,19:285~294
183 Jan Deja. Freezing and Deicing Salt Resistance of Blast Furnace Slag Concretes. Cement & Concrete Composites. 2003,25:357~361
184 Vedat A. Yerlici, Turan Ozturan. Factor Affecting Anchorage Bond Strength in High Performance Concrete. ACI Structural Journal. 2000,(21):5~6
185周万良,周士琼,李益进.水胶比、超细粉煤灰掺量对高性能混凝土钢筋握裹力的影响.混凝土与水泥制品. 2003,(2):16~18
186高向玲,李杰.钢筋混凝土粘结锚固的研究进展.结构工程师. 2001(2):29~34
187 K. G. Badu, G. S. N.Rao.Efficiency of Fly Ash in Concrete. Cement & Concrete Composites. 1993,15(3):223~229
188沈旦申.粉煤灰混凝土.中国铁道工业出版社. 1989
189 E. J. Sellevold. Silica fume-cement paste: hydration and pore Structure. Report BML 82.610. Norway. 1982:19~50
190何真,梁文泉.大体积混凝土中微膨胀剂的抗裂作用.武汉大学学报. 2001, 34(2):73~76
191李裕双,周汉舜.微膨胀剂聚丙烯纤维混凝土在桥面铺装中的应用.交通公路科技. 2006,(12):25~27
192朱锦章,罗昕,赵霄龙.超声回弹法评定冻融混凝土的抗压强度.低温建筑技术. 2005,(3):3-5
193赵霄龙.混凝土冻融损伤演化规律研究.华中科技大学. 2003
194 Z. P. Bazant. Mathematical model for freeze-thaw durability of concrete. Journal of the American Ceramic Society. 1998,71(9):776~783
195 W. K. Yip, F.K.Kong, K. S. Chan, M.K.Lim. A statistical model of microcracking of concrete under uniaxial compression. Theo and Appl. Frac Mech. 1995,(22):17~27
196 W. K. Yip. New damage variable in failure. Analysis of concrete. Jour of Mat in Civ Engrg, Nov. 1996,8(4):184~188
197刘远.基于损伤理论的混凝土抗冻耐久性随机预测方法研究.浙江大学硕士论文. 2006
198余寿文,冯西桥.损伤力学.清华大学出版社. 1997
199 S. D. Brown, R. B. Biddulph, P. D. Wilcox. A strength-poroity relation involving different pore geometry and oritn-ration. J Am Ceram Soc. 1964,47(07):0~322
200彭瑞东,谢和平,鞠杨.二维数字图像分形维数的计算方法.中国矿业大学学报. 2004,33(1):19-24.
201 B. E. Boser, I. M. Guyon , V. N. Vapnik. A training algorithm for optimal margin classifiers Proceedings of the fifth annual workshop on Computational learning theory. 1992:144~152
202 B. Scholkopf, C. J. C. Burges, A. J. Smola. Advances in Kernal Methods: Support Vector Learn-ing. MITPress. 1999
203邓乃杨,田英杰.数据挖掘中的新方法-支持向量机.科技出版社. 2004
204 JohnWiley, Sons. Statistical Learning Theory. VladimirN. Vapnik. 1998
205 N. Vladimir, Vapnik. The Nature of Statistical Learning Theory. Springer-Verlag. 1999
206 B. E. Boser, I. M. Guyon, V. N. Vapink. A training algorithm for optimal margin classifiers.In Proceedings of the 5th Annual ACM Workshop on computational Learning Theory. 1992:144~152.
207 Nello Cristianini, John Shawe-Taylor. An Introduction to Support Vector Machines and Other Kernel-based Learning Methods. The Syndicate of the Press of the University of Cambridge,England. 2000
208施鸿均,杨弋涛,孙保良.铝合金连铸工艺参数的辅助优化.塑性工程学报. 2003,10(4):344~346
209吴德会.基于最小二乘支持向量机的表面粗糙度预测模型铣削加工.中国机械工程. 2007,18(7):838~840
210关宇刚,孙伟,缪昌文.基于可靠度与损伤理论的混凝土寿命预测模型Ⅱ:模型验证与应用.硅酸盐学报. 2001,29(6):529~536.