水工混凝土受压疲劳性能及累积损伤研究
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摘要
受高应力循环荷载作用的水工建筑物,例如遭受高烈度地震的混凝土坝、大功率泄洪的泄洪建筑物、受迫于机组振动的混凝土机墩、受高速水流冲击的水垫塘等,其混凝土结构内部应力场会发生剧烈变化,极易引发疲劳损伤或破坏。水工混凝土是重要建筑物,一旦失事后果不堪设想。因此,研究水工混凝土疲劳特性,确保水工建筑物长周期安全稳定运行,是一个非常具有工程意义的课题。尤其是汶川地震后,也激起了众多学者对经受地震后的水工建筑物进行震损分析的浓厚兴趣。由于使用工况、使用环境以及配合比等的不同,水工混凝土的力学特性和疲劳性能,与普通混凝土相比有着自身独特的特点。国内外,有关水工混凝土疲劳损伤的研究报道很少。为此,本文在国家自然科学基金(编号：51009074)的资助下,针对水工混凝土开展了受压疲劳性能及累积损伤研究。本文的主要试验与理论研究工作包括以下几方面：
(1)对120个水工混凝土试件开展了抗压试验、疲劳试验及低周疲劳试验。通过对试验数据的定性分析发现,水工混凝土抗压应力应变曲线较为平缓,韧性较好,有利于抗疲劳损伤；疲劳破坏与抗压破坏的损伤机理基本相同,只是在产生裂纹的数量、分布、走向等有所差异；在给定应力水平下的疲劳寿命非常离散,需借助可靠性原理进行分析处理；疲劳最大应变、疲劳变形模量、疲劳残余应变在疲劳过程中均呈三阶段发展规律。
(2)应用概率统计方法对疲劳寿命数据进行分析处理发现,水工混凝土疲劳寿命既接受对数正态分布,也接受三参数Weibull分布,但无论是P-N图的拟合程度和柯尔莫哥洛夫检验的效果来看,均以三参数Weibull分布为佳,且随着应力水平降低,水工混凝土疲劳寿命离散性随之加大。
(3)通过对疲劳寿命进行可靠性分析,得到了水工混凝土的S-N曲线和P-S-N曲线方程,及其相对应的疲劳极限强度；三参数Weibull分布和对数正态分布下的S-N曲线相差不大,而在高可靠度上却差别明显,对数正态分布相对保守,从材料自身特性和损伤机理分析,宜选用三参数Weibull分布下的S-N曲线和P-S-N曲线；通过对不同混凝土的疲劳特性进行归纳分析得出,水工混凝土的疲劳性能优于普通混凝土。
(4)利用求解三参数Weibull分布置信限的方法,得到了水工混凝土疲劳寿命在不同应力水平下的三参数Weibull分布的置信限,进一步得到水工混凝土的γ-S-N曲线和γ-P-S-N曲线及其高置信度、高可靠度的疲劳极限强度和安全寿命,对水工结构疲劳可靠性设计有参考价值。
(5)基于原始Miner准则,建立起疲劳累积损伤极限状态方程,并用蒙特卡罗法求解动态可靠度。通过算例发现,求解得到的动态可靠度,能合理评价水工建筑物疲劳累积损伤程度。
(6)在三个假设的基础上,定义了描述混凝土在疲劳荷载作用下损伤与应变概率关系的P-D-ε曲线,证明了该曲线的一个重要性质,即其上任意一点疲劳应变的失效概率与相应损伤量的可靠度相等：通过对疲劳应变实测数据的分析处理,给定损伤量下的疲劳应变较好的服从三参数Weibull分布,得到了水工混凝土的P-D-ε曲线,可求得不同可靠度下的损伤阈值应变、极限应变以及给定疲劳应变的损伤量,可为疲劳损伤的定量评定提供理论基础。
(7)基于抗压强度分布,通过原始S-N曲线方程,推导出一种新的疲劳寿命概率分布模型,并给出了求解该分布参数的方法；采用本文提出的新概率分布模型进行统计分析得出,低周疲劳寿命数据服从新的概率分布模型,并进一步得到水工混凝土低周疲劳S-N曲线方程。该方法充分利用了抗压强度的有关数据信息,所用试件少,精度较高,有一定的推广价值。
(8)通过对疲劳过程中强度衰减变化的分析,提出了一个低周疲劳强度衰减模型和寿命预测方法,与实测的疲劳应变发展过程及Miner准则对比分析得出,本文提出的模型及方法适用于混凝土低周疲劳,能较好地反映出混凝土的低周疲劳损伤机理。
(9)应用损伤力学理论,对疲劳变形模量试验数据进行分析处理,得到了低周疲劳变形模量发展规律公式,以及基于变形模量的累积损伤计算公式及其损伤破坏判据；综合以上研究成果,提出了一个水工结构受压低周疲劳累积损伤计算方法和流程,并对FLAC-3D软件进行二次开发,编制了基于有限元的水工结构低周疲劳累积损伤计算程序。通过算例表明,计算方法、流程及程序能够合理反映水工结构低周疲劳累积损伤过程和破坏形态。
(10)应用未达到抗压强度前的应力应变曲线,提出了一个推求混凝土抗压强度和峰值应变的方法。经过试验验证,该方法适用于高应力循环荷载作用下的低周疲劳,并具有足够的精度,可进一步得到混凝土低周疲劳荷载下的真实应力水平,并在此基础上,得到了疲劳残余应变的发展规律公式,以及基于残余应变的疲劳失稳判据。通过对疲劳寿命的估算比较,残余应变发展规律公式及判据是较为合理的。
Many hydraulic structures may be subjected to the cyclic load of high stress, such as concrete dam under the high intensity earthquake, flood discharge structure with large-power discharge, machine foundation concrete in forced vibration, water cushion pool by the impact of high-speed flow, and so on. Because the inner stress field of these structures acutely changes, it is very possible to result in fatigue damage or failure. Hydraulic structures are very important structures. If these structures wreck, the consequences are unimaginable. Therefore, studying the fatigue property of hydraulic concrete is very meaningful in engineering in order to ensure hydraulic structures working safely and stably for long. Especially, earthquake disaster in Wenchuan excited many researchers to initiate seismic damage analysis of hydraulic structures. Because of the difference of use profile, use condition and mixing proportion, the hydraulic concrete has particular mechanics character and fatigue property by comparing with common concrete. As this research is seldom reported at home and abroad, research on fatigue damage of hydraulic concrete was specially carried out in this dissertation at the support of the National Natural Science Fundation (No.51009074). The experimental and theoretic research involves several aspects as follows:
(1) The compressive experiment, fatigue experiment and low-cycle fatigue experiment on 120 specimens of hydraulic concrete were performed. The qualitative analysis of experimental data shows that the flexibility of hydraulic concrete is better because the compressive stress-strain curve is relatively flat, and it is beneficial to the resistance of fatigue damage; damage mechanism of compression failure and fatigue failure is basically same, but the quantity, direction and distribution of fracture is different; fatigue life at the given stress level is very discrete, so the reliability theory will be adopted to analyze this data; maximum strain, deformation modulus, and residual strain possess three separate development phases of all the fatigue life.
(2) According to the statistical analysis of fatigue life, the results show it follows both lognormal distribution and three-parameter Weibull distribution, but the latter is more suitable by the P-N figure fitting and kolmogorov test. With the decrease of stress level, the scatter of fatigue life increases.
(3) By the reliability analysis of fatigue life, the S-N curve, P-S-N curve and fatigue limit strength are obtained. The S-N curve under lognormal distribution and three-parameter Weibull distribution are approximate, but at the interval of high reliability the two are different, and the former make the result pessimism. In the light of self character and damage mechanism, this paper suggests making use of the S-N curve and P-S-N curve under three-parameter Weibull distribution. By summarization and comparison, the fatigue property of hydraulic concrete has advantage over other concrete.
(4) By making use of the calculative method of confidence limits of three-parameter Weibull distribution, the confidence limits of fatigue life of hydraulic concrete at the different stress level are calculated. Furthermore, theγ-S-N curve,γ-P-S-N curve, fatigue limit strength and safety life of high reliability and confidence are obtained. These results have reference value for the fatigue reliability design of hydraulic structure.
(5) Based on original Miner rule, the limit state equation of fatigue cumulative damage is established, and the dynamic reliability by using Monte Carlo method can be computed. The computational example shows the calculative dynamic reliability can reasonably evaluate fatigue cumulative damage of hydraulic structure.
(6) On the basis of three hypotheses, the P-D-εcurve which describes probabilistic relationship between damage and strain of concrete under fatigue load is defined. The important property of this curve that the failure probability of strain equals reliability of damage at every point has been proved. The analysis and treatment of test data indicates that fatigue strain in case of specified damage follows three-parameter Weibull distribution. The P-D-εcurve of hydraulic concrete was obtained. Furthermore, it is easy to calculate threshold strain, limit strain and fatigue damage at the given reliability. This research lays theoretical foundation for the quantitative evaluation of fatigue damage.
(7) Based on the distribution of the static compressive strength, a new distribution which fatigue life follows is deduced by the equation model of the original S-N curve, and the solution approach of the new distribution parameters is given. By statistical analysis, low-cycle fatigue life follows this new distribution. Moreover, the S-N curve equation of low-cycle fatigue of hydraulic concrete can be put forward. Because of fully using the relevant data of compressive strength, this method spends fewer specimens, has the higher accuracy, and is of widespread usage.
(8) By the process analysis of strength degradation, the new model of strength degradation and predictor method of life period for concrete under low-cycle fatigue load can be proposed. By comparison with the development process of actual strain and Miner criterion, the model and method are suitable to low-cycle fatigue of concrete, and can correctly reflect the damage mechanics of low-cycle fatigue of concrete.
(9) With the aid of the theory of damage mechanics, by studying test data of fatigue deformation modulus, development model of fatigue deformation modulus, calculation formula of fatigue damage, and the instability criterion of fatigue damage are obtained for hydraulic concrete. By synthesizing the above research results, the calculative method and process of cumulative damage under low-cycle fatigue load are put forward for hydraulic structures. By means of the Further Development of FLAC-3D Software, based on the finite element method the computational program of cumulative damage under low-cycle fatigue load is given for hydraulic structures. According to computational example, the above method, process and program can rationally reflect the process of fatigue damage and failure mode of hydraulic structures.
(10) The method is proposed, which could get compression strength and peak strain of concrete by using stress-strain curve before failure. It is verified by the tests that this method can apply to low-cycle fatigue, has sufficient accuracy, and can achieve actual stress level of fatigue test. On this basis, the development formula of fatigue residual strain and criterion of fatigue failure are obtained. By comparison with estimation of fatigue life, the above formula and criterion are reasonable.
(1)对120个水工混凝土试件开展了抗压试验、疲劳试验及低周疲劳试验。通过对试验数据的定性分析发现,水工混凝土抗压应力应变曲线较为平缓,韧性较好,有利于抗疲劳损伤；疲劳破坏与抗压破坏的损伤机理基本相同,只是在产生裂纹的数量、分布、走向等有所差异；在给定应力水平下的疲劳寿命非常离散,需借助可靠性原理进行分析处理；疲劳最大应变、疲劳变形模量、疲劳残余应变在疲劳过程中均呈三阶段发展规律。
(2)应用概率统计方法对疲劳寿命数据进行分析处理发现,水工混凝土疲劳寿命既接受对数正态分布,也接受三参数Weibull分布,但无论是P-N图的拟合程度和柯尔莫哥洛夫检验的效果来看,均以三参数Weibull分布为佳,且随着应力水平降低,水工混凝土疲劳寿命离散性随之加大。
(3)通过对疲劳寿命进行可靠性分析,得到了水工混凝土的S-N曲线和P-S-N曲线方程,及其相对应的疲劳极限强度；三参数Weibull分布和对数正态分布下的S-N曲线相差不大,而在高可靠度上却差别明显,对数正态分布相对保守,从材料自身特性和损伤机理分析,宜选用三参数Weibull分布下的S-N曲线和P-S-N曲线；通过对不同混凝土的疲劳特性进行归纳分析得出,水工混凝土的疲劳性能优于普通混凝土。
(4)利用求解三参数Weibull分布置信限的方法,得到了水工混凝土疲劳寿命在不同应力水平下的三参数Weibull分布的置信限,进一步得到水工混凝土的γ-S-N曲线和γ-P-S-N曲线及其高置信度、高可靠度的疲劳极限强度和安全寿命,对水工结构疲劳可靠性设计有参考价值。
(5)基于原始Miner准则,建立起疲劳累积损伤极限状态方程,并用蒙特卡罗法求解动态可靠度。通过算例发现,求解得到的动态可靠度,能合理评价水工建筑物疲劳累积损伤程度。
(6)在三个假设的基础上,定义了描述混凝土在疲劳荷载作用下损伤与应变概率关系的P-D-ε曲线,证明了该曲线的一个重要性质,即其上任意一点疲劳应变的失效概率与相应损伤量的可靠度相等：通过对疲劳应变实测数据的分析处理,给定损伤量下的疲劳应变较好的服从三参数Weibull分布,得到了水工混凝土的P-D-ε曲线,可求得不同可靠度下的损伤阈值应变、极限应变以及给定疲劳应变的损伤量,可为疲劳损伤的定量评定提供理论基础。
(7)基于抗压强度分布,通过原始S-N曲线方程,推导出一种新的疲劳寿命概率分布模型,并给出了求解该分布参数的方法；采用本文提出的新概率分布模型进行统计分析得出,低周疲劳寿命数据服从新的概率分布模型,并进一步得到水工混凝土低周疲劳S-N曲线方程。该方法充分利用了抗压强度的有关数据信息,所用试件少,精度较高,有一定的推广价值。
(8)通过对疲劳过程中强度衰减变化的分析,提出了一个低周疲劳强度衰减模型和寿命预测方法,与实测的疲劳应变发展过程及Miner准则对比分析得出,本文提出的模型及方法适用于混凝土低周疲劳,能较好地反映出混凝土的低周疲劳损伤机理。
(9)应用损伤力学理论,对疲劳变形模量试验数据进行分析处理,得到了低周疲劳变形模量发展规律公式,以及基于变形模量的累积损伤计算公式及其损伤破坏判据；综合以上研究成果,提出了一个水工结构受压低周疲劳累积损伤计算方法和流程,并对FLAC-3D软件进行二次开发,编制了基于有限元的水工结构低周疲劳累积损伤计算程序。通过算例表明,计算方法、流程及程序能够合理反映水工结构低周疲劳累积损伤过程和破坏形态。
(10)应用未达到抗压强度前的应力应变曲线,提出了一个推求混凝土抗压强度和峰值应变的方法。经过试验验证,该方法适用于高应力循环荷载作用下的低周疲劳,并具有足够的精度,可进一步得到混凝土低周疲劳荷载下的真实应力水平,并在此基础上,得到了疲劳残余应变的发展规律公式,以及基于残余应变的疲劳失稳判据。通过对疲劳寿命的估算比较,残余应变发展规律公式及判据是较为合理的。
Many hydraulic structures may be subjected to the cyclic load of high stress, such as concrete dam under the high intensity earthquake, flood discharge structure with large-power discharge, machine foundation concrete in forced vibration, water cushion pool by the impact of high-speed flow, and so on. Because the inner stress field of these structures acutely changes, it is very possible to result in fatigue damage or failure. Hydraulic structures are very important structures. If these structures wreck, the consequences are unimaginable. Therefore, studying the fatigue property of hydraulic concrete is very meaningful in engineering in order to ensure hydraulic structures working safely and stably for long. Especially, earthquake disaster in Wenchuan excited many researchers to initiate seismic damage analysis of hydraulic structures. Because of the difference of use profile, use condition and mixing proportion, the hydraulic concrete has particular mechanics character and fatigue property by comparing with common concrete. As this research is seldom reported at home and abroad, research on fatigue damage of hydraulic concrete was specially carried out in this dissertation at the support of the National Natural Science Fundation (No.51009074). The experimental and theoretic research involves several aspects as follows:
(1) The compressive experiment, fatigue experiment and low-cycle fatigue experiment on 120 specimens of hydraulic concrete were performed. The qualitative analysis of experimental data shows that the flexibility of hydraulic concrete is better because the compressive stress-strain curve is relatively flat, and it is beneficial to the resistance of fatigue damage; damage mechanism of compression failure and fatigue failure is basically same, but the quantity, direction and distribution of fracture is different; fatigue life at the given stress level is very discrete, so the reliability theory will be adopted to analyze this data; maximum strain, deformation modulus, and residual strain possess three separate development phases of all the fatigue life.
(2) According to the statistical analysis of fatigue life, the results show it follows both lognormal distribution and three-parameter Weibull distribution, but the latter is more suitable by the P-N figure fitting and kolmogorov test. With the decrease of stress level, the scatter of fatigue life increases.
(3) By the reliability analysis of fatigue life, the S-N curve, P-S-N curve and fatigue limit strength are obtained. The S-N curve under lognormal distribution and three-parameter Weibull distribution are approximate, but at the interval of high reliability the two are different, and the former make the result pessimism. In the light of self character and damage mechanism, this paper suggests making use of the S-N curve and P-S-N curve under three-parameter Weibull distribution. By summarization and comparison, the fatigue property of hydraulic concrete has advantage over other concrete.
(4) By making use of the calculative method of confidence limits of three-parameter Weibull distribution, the confidence limits of fatigue life of hydraulic concrete at the different stress level are calculated. Furthermore, theγ-S-N curve,γ-P-S-N curve, fatigue limit strength and safety life of high reliability and confidence are obtained. These results have reference value for the fatigue reliability design of hydraulic structure.
(5) Based on original Miner rule, the limit state equation of fatigue cumulative damage is established, and the dynamic reliability by using Monte Carlo method can be computed. The computational example shows the calculative dynamic reliability can reasonably evaluate fatigue cumulative damage of hydraulic structure.
(6) On the basis of three hypotheses, the P-D-εcurve which describes probabilistic relationship between damage and strain of concrete under fatigue load is defined. The important property of this curve that the failure probability of strain equals reliability of damage at every point has been proved. The analysis and treatment of test data indicates that fatigue strain in case of specified damage follows three-parameter Weibull distribution. The P-D-εcurve of hydraulic concrete was obtained. Furthermore, it is easy to calculate threshold strain, limit strain and fatigue damage at the given reliability. This research lays theoretical foundation for the quantitative evaluation of fatigue damage.
(7) Based on the distribution of the static compressive strength, a new distribution which fatigue life follows is deduced by the equation model of the original S-N curve, and the solution approach of the new distribution parameters is given. By statistical analysis, low-cycle fatigue life follows this new distribution. Moreover, the S-N curve equation of low-cycle fatigue of hydraulic concrete can be put forward. Because of fully using the relevant data of compressive strength, this method spends fewer specimens, has the higher accuracy, and is of widespread usage.
(8) By the process analysis of strength degradation, the new model of strength degradation and predictor method of life period for concrete under low-cycle fatigue load can be proposed. By comparison with the development process of actual strain and Miner criterion, the model and method are suitable to low-cycle fatigue of concrete, and can correctly reflect the damage mechanics of low-cycle fatigue of concrete.
(9) With the aid of the theory of damage mechanics, by studying test data of fatigue deformation modulus, development model of fatigue deformation modulus, calculation formula of fatigue damage, and the instability criterion of fatigue damage are obtained for hydraulic concrete. By synthesizing the above research results, the calculative method and process of cumulative damage under low-cycle fatigue load are put forward for hydraulic structures. By means of the Further Development of FLAC-3D Software, based on the finite element method the computational program of cumulative damage under low-cycle fatigue load is given for hydraulic structures. According to computational example, the above method, process and program can rationally reflect the process of fatigue damage and failure mode of hydraulic structures.
(10) The method is proposed, which could get compression strength and peak strain of concrete by using stress-strain curve before failure. It is verified by the tests that this method can apply to low-cycle fatigue, has sufficient accuracy, and can achieve actual stress level of fatigue test. On this basis, the development formula of fatigue residual strain and criterion of fatigue failure are obtained. By comparison with estimation of fatigue life, the above formula and criterion are reasonable.
引文
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