大体积桥塔既有裂纹在温度疲劳荷载下扩展概率研究
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摘要
混凝土导热性能极差,体积庞大的混凝土桥塔暴露于自然环境中时,会因外界环境因素变化的影响产生非线性温度分布,从而导致拉压循环的温度疲劳应力,同时由于桥塔的结构要求,常规的设置伸缩缝消散温度应力的方式难以奏效。而裂纹是混凝土不可避免的问题,在裂纹尖端存在的应力集中现象,使混凝土抗疲劳性能大为劣化,裂纹继续扩展的可能性非常大。目前因为结构设计中混凝土抗拉强度假设为零以及混凝土不受拉的通行结构设计理念,使得关于带裂纹的混凝土拉压循环疲劳性能研究还鲜有涉足。本文对带预裂纹的混凝土拉压循环疲劳特性进行了试验研究与分析处理,并结合某斜拉桥大体积桥塔的温度观测与温度应力计算,对桥塔即有裂纹在温度疲劳荷载下的扩展概率进行分析。在国家自然科学基金项目(50908184)资助下,全文作了如下研究工作：
(1)在对混凝土拉压疲劳试验方法深入了解的基础上,设计并进行了带有预制裂纹混凝土试件的拉压循环疲劳试验,对疲劳试验的结果进行了分析整理,作出了S-N、P-N、P-S-N疲劳曲线。并使用极大似然法测定疲劳性能曲线,对试验结果可靠性进行了验证。将指数形式S-N表达式变形整理为更为直观的疲劳应力S与疲劳寿命对数值lgN之间一次、二次、三次多项式形式,确立带预裂纹混凝土疲劳应力与疲劳寿命的对应关系。并采用Goodman直线与Gerber二次抛物曲线形式,给出了带预制裂纹C50混凝土的等寿命疲劳图。
(2)由试验过程中测得的试件变形量与疲劳荷载循环次数的a-N关系曲线,将带预制裂纹混凝土裂纹开展划分为四个阶段,对各个阶段的开裂机理进行分析,得出了骨料质量(强度与形状)对带裂纹混凝土疲劳寿命有着极为重要的意义。
(3)提出潜行裂纹面和等效潜行裂纹假说,解决了因混凝土材料自身的离散性,难以准确把握不同位置处裂纹开展真实情况的问题,同时得出可以忽略初始裂纹深、宽度的简化公式,使试验与分析结果更能适用于初始裂纹深度与宽度不确定的实际工程应用。
(4)使用割线法与最小二乘法得到疲劳裂纹扩展速率与应力强度因子变程之间的关系,给出了混凝土在不同存活率下,Pairs裂纹扩展模型中重要疲劳参数C、m值的取值范围。
(5)针对体积较大的混凝土桥塔温度应力分析,做了六条基本假定,对系统进行适当的简化,建立能反映温度场和温度应力的主要影响因素和内在规律、即满足实际需要又切实可行的分析模型。进行了第三类边界条件与第一类边界条件的分析比对,选用适当的边界条件对桥塔进行温度应力分析。
(6)使用ABAQUS有限元分析软件,按为期四个月的桥塔实测外界自然环境为基础,对所选桥塔节段进行了温度场与温度应力场分布的计算,并由有限元分析得到的温度场与温度应力分布结果,并依此作出温度疲劳荷载谱。
(7)使用MATLAB软件编辑了使用雨流法处理温度应力疲劳荷载谱的程序流,得到均值与幅值循环数分布,及均值幅值联合概率密度图。证明温度疲劳荷载循环中的均值与幅值均近似服从正态分布,荷载均、幅值循环服从高斯分布。
(8)利用Lin-Yang裂纹扩展模型,引入随机变量过程,导出裂纹扩展概率密度公式。使用无限寿命安全可靠性模型定性分析裂纹扩展到须处理标准的可能性并基于裂纹扩展随机性的安全可靠性模型,得到裂纹扩展到须处理标准随时间的累积概率。
With the poor heat conduction performance and the influence of external environment factors, the mass concrete bridge tower, exposing to the natural environment, is in nonlinear temperature distribution and leading to tension and compression cycle temperature fatigue stress. Furthermore, the conventional way by establishing expansion joints to dissipate temperature stress doesn't work because of the bridge tower structure requirement. At the same time, the crack is an inevitable problem of concrete, and the stress concentration phenomenon existing in the crack tip makes the concrete fatigue performance greatly degrade and the crack extension possibility is very large. At present, the research of pre-crack concrete fatigue performance is very few because the structure design concept is that the concrete tensile strength is zero. Based on the research and analysis of pre-crack concrete fatigue characteristic test in combination with observation and calculation of the temperature stress of the cable-stayed bridge tower, the reliability analysis of crack extension is done. With the national natural science fund project (50908184), the following researches are carried out:
(1) A tension and compression fatigue test of pre-crack concrete is designed and carried out based on the in-depth understanding of existing concrete fatigue test methods. The fatigue test results are analyzed earnestly and the S-N, P-N, P-S-N fatigue curves are plotted. Furthermore, the maximum likelihood method of fatigue performance curves is used to verify the reliability of test results. The pre-crack concrete fatigue stress (S) and fatigue life (N) corresponding formula is established by deforming the index form S-N expression to more intuitive linear, quadratic, cubic polynomials on the fatigue stress (S) and fatigue life logarithm form (lgN).
(2) By analyzing the a-Ncurve of the deformation and fatigue loading cycle times, the crack propagation process of pre-crack concrete is divided into four stages and it is concluded that the aggregate quality (strength and shape) plays a very important role in pre-crack concrete fatigue life.
(3) The equivalent hidden crack model is put forward to solve the problem that it is difficult to accurately grasp the true propagation process of the cracks at different locations because of the discreteness of concrete material itself. Meanwhile the simplified formula that can ignore the initial crack depth and width is obtained and the analysis results are more applicable in the actual engineering projects in which the initial crack depth and width is variable.
(4) By using the secant method and the least square method, the relationship between the fatigue crack propagation rate and the stress intensity factor variation is established and the important fatigue parameters in Pairs formula, C and m, at different survival rates are given. The constant life fatigue diagram of C50pre-crack concrete is drawn by the means of the Goodman linear and Gerber quadratic parabolic curve.
(5) To felicitously simplify the system and build a feasible model, the six fundamental assumptions, which can be used to report the influencing factors and inherent laws on the temperature field and stress of mass concrete bridge tower, are supposed. By comparing the third boundary condition and the first boundary condition, the appropriate boundary conditions on the bridge tower temperature stress analysis is chosen.
(6) According to the observation of the external natural environment for four months, the temperature and stress field distribution analysis of the selected bridge tower segment is calculated by using ABAQUS finite element analysis software. The temperature fatigue load spectrum is made based on the temperature and stress field distribution results.
(7) To get mean and amplitude cycle number distribution and mean-amplitude joint probability density diagram, the process flow of the temperature fatigue load spectrum, performed by the rain flow method, is edited by using MATLAB software. It can be proved that both the mean and amplitude cycle number distribution of temperature fatigue loading obey the normal distribution and the load cycle characteristics are in two-parameter lognormal distribution.
(8) The crack propagation probability density formula is derived by using Lin-Yang crack propagation model and introducing random variable process. The possibility of cracks extending to the damaging level is analyzed with infinite life safety reliability model and the cumulative probability of crack extension over time is founded on the safety reliability model of crack extension randomness.
(1)在对混凝土拉压疲劳试验方法深入了解的基础上,设计并进行了带有预制裂纹混凝土试件的拉压循环疲劳试验,对疲劳试验的结果进行了分析整理,作出了S-N、P-N、P-S-N疲劳曲线。并使用极大似然法测定疲劳性能曲线,对试验结果可靠性进行了验证。将指数形式S-N表达式变形整理为更为直观的疲劳应力S与疲劳寿命对数值lgN之间一次、二次、三次多项式形式,确立带预裂纹混凝土疲劳应力与疲劳寿命的对应关系。并采用Goodman直线与Gerber二次抛物曲线形式,给出了带预制裂纹C50混凝土的等寿命疲劳图。
(2)由试验过程中测得的试件变形量与疲劳荷载循环次数的a-N关系曲线,将带预制裂纹混凝土裂纹开展划分为四个阶段,对各个阶段的开裂机理进行分析,得出了骨料质量(强度与形状)对带裂纹混凝土疲劳寿命有着极为重要的意义。
(3)提出潜行裂纹面和等效潜行裂纹假说,解决了因混凝土材料自身的离散性,难以准确把握不同位置处裂纹开展真实情况的问题,同时得出可以忽略初始裂纹深、宽度的简化公式,使试验与分析结果更能适用于初始裂纹深度与宽度不确定的实际工程应用。
(4)使用割线法与最小二乘法得到疲劳裂纹扩展速率与应力强度因子变程之间的关系,给出了混凝土在不同存活率下,Pairs裂纹扩展模型中重要疲劳参数C、m值的取值范围。
(5)针对体积较大的混凝土桥塔温度应力分析,做了六条基本假定,对系统进行适当的简化,建立能反映温度场和温度应力的主要影响因素和内在规律、即满足实际需要又切实可行的分析模型。进行了第三类边界条件与第一类边界条件的分析比对,选用适当的边界条件对桥塔进行温度应力分析。
(6)使用ABAQUS有限元分析软件,按为期四个月的桥塔实测外界自然环境为基础,对所选桥塔节段进行了温度场与温度应力场分布的计算,并由有限元分析得到的温度场与温度应力分布结果,并依此作出温度疲劳荷载谱。
(7)使用MATLAB软件编辑了使用雨流法处理温度应力疲劳荷载谱的程序流,得到均值与幅值循环数分布,及均值幅值联合概率密度图。证明温度疲劳荷载循环中的均值与幅值均近似服从正态分布,荷载均、幅值循环服从高斯分布。
(8)利用Lin-Yang裂纹扩展模型,引入随机变量过程,导出裂纹扩展概率密度公式。使用无限寿命安全可靠性模型定性分析裂纹扩展到须处理标准的可能性并基于裂纹扩展随机性的安全可靠性模型,得到裂纹扩展到须处理标准随时间的累积概率。
With the poor heat conduction performance and the influence of external environment factors, the mass concrete bridge tower, exposing to the natural environment, is in nonlinear temperature distribution and leading to tension and compression cycle temperature fatigue stress. Furthermore, the conventional way by establishing expansion joints to dissipate temperature stress doesn't work because of the bridge tower structure requirement. At the same time, the crack is an inevitable problem of concrete, and the stress concentration phenomenon existing in the crack tip makes the concrete fatigue performance greatly degrade and the crack extension possibility is very large. At present, the research of pre-crack concrete fatigue performance is very few because the structure design concept is that the concrete tensile strength is zero. Based on the research and analysis of pre-crack concrete fatigue characteristic test in combination with observation and calculation of the temperature stress of the cable-stayed bridge tower, the reliability analysis of crack extension is done. With the national natural science fund project (50908184), the following researches are carried out:
(1) A tension and compression fatigue test of pre-crack concrete is designed and carried out based on the in-depth understanding of existing concrete fatigue test methods. The fatigue test results are analyzed earnestly and the S-N, P-N, P-S-N fatigue curves are plotted. Furthermore, the maximum likelihood method of fatigue performance curves is used to verify the reliability of test results. The pre-crack concrete fatigue stress (S) and fatigue life (N) corresponding formula is established by deforming the index form S-N expression to more intuitive linear, quadratic, cubic polynomials on the fatigue stress (S) and fatigue life logarithm form (lgN).
(2) By analyzing the a-Ncurve of the deformation and fatigue loading cycle times, the crack propagation process of pre-crack concrete is divided into four stages and it is concluded that the aggregate quality (strength and shape) plays a very important role in pre-crack concrete fatigue life.
(3) The equivalent hidden crack model is put forward to solve the problem that it is difficult to accurately grasp the true propagation process of the cracks at different locations because of the discreteness of concrete material itself. Meanwhile the simplified formula that can ignore the initial crack depth and width is obtained and the analysis results are more applicable in the actual engineering projects in which the initial crack depth and width is variable.
(4) By using the secant method and the least square method, the relationship between the fatigue crack propagation rate and the stress intensity factor variation is established and the important fatigue parameters in Pairs formula, C and m, at different survival rates are given. The constant life fatigue diagram of C50pre-crack concrete is drawn by the means of the Goodman linear and Gerber quadratic parabolic curve.
(5) To felicitously simplify the system and build a feasible model, the six fundamental assumptions, which can be used to report the influencing factors and inherent laws on the temperature field and stress of mass concrete bridge tower, are supposed. By comparing the third boundary condition and the first boundary condition, the appropriate boundary conditions on the bridge tower temperature stress analysis is chosen.
(6) According to the observation of the external natural environment for four months, the temperature and stress field distribution analysis of the selected bridge tower segment is calculated by using ABAQUS finite element analysis software. The temperature fatigue load spectrum is made based on the temperature and stress field distribution results.
(7) To get mean and amplitude cycle number distribution and mean-amplitude joint probability density diagram, the process flow of the temperature fatigue load spectrum, performed by the rain flow method, is edited by using MATLAB software. It can be proved that both the mean and amplitude cycle number distribution of temperature fatigue loading obey the normal distribution and the load cycle characteristics are in two-parameter lognormal distribution.
(8) The crack propagation probability density formula is derived by using Lin-Yang crack propagation model and introducing random variable process. The possibility of cracks extending to the damaging level is analyzed with infinite life safety reliability model and the cumulative probability of crack extension over time is founded on the safety reliability model of crack extension randomness.
引文
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