半刚性基层沥青混凝土路面反射裂缝扩展和疲劳寿命研究
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摘要
半刚性基层沥青混凝土路面是我国高等级公路的主要结构形式,但该路面结构在运营早期容易因裂缝而出现各种病害,其中反射裂缝是半刚性基层沥青面层最主要的早期破坏形式之一。如何有效地控制其产生、发展和降低对路面结构疲劳寿命的影响至今仍是道路工程界面临的一大难题。采用传统的连续介质力学和疲劳强度理论难以真实描述裂缝问题的本质。本文利用改进的Williams级数、等参元和广义参数有限元法提出并建立了半刚性基层路面荷载型反射裂缝应力强度因子分析的广义参数Williams单元。将求解总体控制方程所得广义参数引入传统的疲劳断裂寿命预测中,计算路面结构反射裂缝扩展的疲劳寿命。因半刚性基层路面结构疲劳寿命与诸多因素有关,包括裂纹几何形状、扩展方向、扩展规律、材料自身特性、构件的几何形状、环境条件和载荷历程等,这些因素通常表现出一定的随机性,所以疲劳寿命也应是一随机量。基于此,本文开展了半刚性基层路面反射裂缝扩展的疲劳寿命随机分析,进而利用蒙特卡洛抽样计算路面结构的可靠度。主要研究工作如下：
第一部分：研究建立半刚性基层沥青混凝土路面结构弹性层状平面应变分析模型,并对该模型做了合理的假定和简化。根据反射裂缝的开裂模式引出线弹性断裂力学在路面结构中的一些基本理论和概念,并在线弹性断裂范围内利用Westergaard应力函数法给出了三种断裂模式下的应力场和位移场表达式,由此引出应力强度因子的概念。因反射裂缝多以Ⅰ-Ⅱ混合型裂缝形式出现,文中推导了更具灵活性的平面裂纹Williams级数特征展开。
第二部分：结合该模型,将其离散为裂尖奇异区和外围常规区,奇异区内部分别采用网格细分的普通有限单元和奇异单元处理。文中详细介绍了等参元和奇异元的一些基本概念以及构造原理等,并推导了二者的形函数,编制了相应的计算机程序。算例分析可知二者具有一个共同的缺陷：计算工作量大且不能直接确定裂尖应力强度因子,而需通过线性外推获得,此过程复杂,容易引入人为误差。
第三部分：针对当前大多数研究人员需借助有限元分析软件,或者利用普通有限元法获得反射裂缝裂尖处应力强度因子存在的这一些缺陷,本文提出并建立了广义参数Williams单元分析半刚性基层路面荷载型反射裂缝裂尖应力强度因子。其单元模型中含有与应力强度因子相关的参数,可以直接确定裂尖处应力强度因子,有效避免了普通有限元后处理计算应力强度因子的缺陷。对Williams单元构造原理研究发现：该单元位移场不再用单元结点参数表示,而转换为用总体场Williams级数中待定参数表示,因此奇异区内单元离散个数多少对总体自由度数并无影响,只取决于选取的Williams级数项数,由此细分奇异区离散网格并不增加总体自由度,从而提高了计算效率。并且只需已知奇异区与常规区分界线上结点坐标信息即可根据等比级数求和的方法形成奇异区内Williams单元刚度方程,格式简单,易于编程实现。
第四部分：将本文方法与传统的疲劳寿命预测理论和公式相结合,研究建立基于广义参数计算反射裂缝扩展的疲劳寿命的预测模型,避免了传统方法需根据结构响应量,先拟合确定应力强度因子再分析疲劳寿命的两步走思想。详细分析了面层模量和厚度与疲劳寿命之间的关系,据此给出了增大面层厚度或减小面层模量以提高路面疲劳寿命的工程措施。由于模量降低路面将会伴随产生一些新的早期破坏,因此选用降低模量提高路面疲劳寿命的方式尚需慎重对待。
第五部分：将传统的Paris疲劳寿命预测公式改进为形式更为灵活的级数表达形式,并引入广义参数计算路面结构的疲劳寿命,其形式简单易被工程人员接受。算例中考虑了单变量的随机性,利用蒙特卡洛抽样模拟技术计算了路面结构从起裂扩展至贯通整个面层的疲劳寿命,并根据疲劳寿命和设计寿命建立了半刚性基层路面可靠度分析模型,进一步计算了路面结构可靠指标。
The asphalt concrete pavement on semi-rigid base course is the main form of high-grade road in China, but various kinds of damages will happen to it for crack in their early service. Reflective cracking is one of major forms of early destruction in asphalt overlay on semi-rigid base. So how to effectively control its initiation, propagation and reduce its influence on fatigue life in pavement structures still remains a huge problem in road engineering. Traditional continuum mechanics and fatigue strength theory are difficulty to describe the essence of the cracking performance. On the basis of the improved Williams series, isoperimetric element and the method of finite element with generalized degrees of freedom (GDOFs), Williams element with GDOFs was proposed for analyzing stress intensity factor (SIF) of reflective cracking under surface loading. The generalized parameters which were from the solution of govern equation were introduced into the model of prediction the fatigue life, and determined the fatigue life for the reflective cracking propagation on pavement structure. As fatigue life is affected by many factors, such as crack geometry, extending direction, expanding law, materials, structure geometry, environment conditions and loading procession. These factors usually have some randomness, so fatigue life is also a random variable. For these reasons, the study will focus on predicting random fatigue life caused by reflective cracking propagation on semi-rigid base course, and using Monte Carlo Simulation Method (MCS) to value the reliability of the pavement structure. Main works are as follows:
Part I:the layered linear elastic plane strain fracture mechanics analysis model was constructed for semi-rigid pavement structure, and some reasonable assumptions and simplifications were made. By using the reflective cracking fracture modes, they led to some basic theory and concepts within the linear elastic fracture mechanics. Based on Westergaard stress function, study gave the stress and displacement field expression of three basic modes cracking, and then raised the conception of SIR Since reflective cracking usually acted as mixed mode I-II, this thesis deduced the more flexible Williams series characteristic expansion of plane crack.
Part II:the analysis model was discretized the singular region and regular region. And the singular region was disposed by employing the refined mesh of traditional finite element method and quarter-node singular element, respectively. Basic concepts and construction principles of isoperimetric element and quarter-node singular element were introduced in detail, and then their shape functions were derived. The two have a same defect from the examples:they cannot directly obtain SIF, but need use linear extrapolation method to acquire it. The process was very complex and large amount of calculation.
Part III:it was focused on the defect that researchers mostly use finite element method analysis software or the traditional finite element method to predict the SIF at crack tip, this study presented the Williams element with GDOFs for SIF of the pavement on semi-rigid base course. In this element model which has a parameter that is related to SIF, so that we can directly determine the SIF at crack tip, and effectively avoid the defects of the traditional finite element method. From the construction principles of Williams element, we found that this kind element no longer treated node parameters as unknown quantities but denoted as undetermined parameter in Williams series. So the number of elements of singular region had no effect on total degrees of freedom, it was only determined by how many number of terms the Williams series have. With these virtues, the Williams element greatly reduced the discrete degrees of freedom and increased the calculation efficiency. We just need know coordinate information of boundary nodes in singular region and region regular, then according to geometric series summation, we can form Williams element stiffness matrix in singular region easily.
Part IV:combining the Williams element with GDOFs and the traditional theory and formula for predicting fatigue life, the analysis model of fatigue life for reflective cracking propagation was constructed by the generalized parameters. It will avoid the two-step thinking that determined the SIF by the structural response, and soon the fatigue life was analyzed by the SIF. The relationship between surface modulus and layer thickness was analyzed in detail. The results show that when increasing surface layer thickness or decreasing surface modulus can improve the fatigue life, but modulus reduce will bring in some new pavement damage in their service. So the suggestion that was from decreasing surface modulus just for the aim of improving the fatigue life need deep consideration for choosing.
Part Ⅴ:Paris formula from traditional fatigue life prediction was turned into a revised flexible series form, and then introducing generalized parameter to predict the fatigue life of pavement structure, this format is simple and can easily be accepted by the engineering staff. In examples, we took into account the randomness of single variable, and the fatigue life was calculated by Monte Carlo simulation method from the crack extension through the entire surface. The reliability analysis model was established by the fatigue life and design life. Moreover, the reliability index was obtained for pavement structure.
第一部分：研究建立半刚性基层沥青混凝土路面结构弹性层状平面应变分析模型,并对该模型做了合理的假定和简化。根据反射裂缝的开裂模式引出线弹性断裂力学在路面结构中的一些基本理论和概念,并在线弹性断裂范围内利用Westergaard应力函数法给出了三种断裂模式下的应力场和位移场表达式,由此引出应力强度因子的概念。因反射裂缝多以Ⅰ-Ⅱ混合型裂缝形式出现,文中推导了更具灵活性的平面裂纹Williams级数特征展开。
第二部分：结合该模型,将其离散为裂尖奇异区和外围常规区,奇异区内部分别采用网格细分的普通有限单元和奇异单元处理。文中详细介绍了等参元和奇异元的一些基本概念以及构造原理等,并推导了二者的形函数,编制了相应的计算机程序。算例分析可知二者具有一个共同的缺陷：计算工作量大且不能直接确定裂尖应力强度因子,而需通过线性外推获得,此过程复杂,容易引入人为误差。
第三部分：针对当前大多数研究人员需借助有限元分析软件,或者利用普通有限元法获得反射裂缝裂尖处应力强度因子存在的这一些缺陷,本文提出并建立了广义参数Williams单元分析半刚性基层路面荷载型反射裂缝裂尖应力强度因子。其单元模型中含有与应力强度因子相关的参数,可以直接确定裂尖处应力强度因子,有效避免了普通有限元后处理计算应力强度因子的缺陷。对Williams单元构造原理研究发现：该单元位移场不再用单元结点参数表示,而转换为用总体场Williams级数中待定参数表示,因此奇异区内单元离散个数多少对总体自由度数并无影响,只取决于选取的Williams级数项数,由此细分奇异区离散网格并不增加总体自由度,从而提高了计算效率。并且只需已知奇异区与常规区分界线上结点坐标信息即可根据等比级数求和的方法形成奇异区内Williams单元刚度方程,格式简单,易于编程实现。
第四部分：将本文方法与传统的疲劳寿命预测理论和公式相结合,研究建立基于广义参数计算反射裂缝扩展的疲劳寿命的预测模型,避免了传统方法需根据结构响应量,先拟合确定应力强度因子再分析疲劳寿命的两步走思想。详细分析了面层模量和厚度与疲劳寿命之间的关系,据此给出了增大面层厚度或减小面层模量以提高路面疲劳寿命的工程措施。由于模量降低路面将会伴随产生一些新的早期破坏,因此选用降低模量提高路面疲劳寿命的方式尚需慎重对待。
第五部分：将传统的Paris疲劳寿命预测公式改进为形式更为灵活的级数表达形式,并引入广义参数计算路面结构的疲劳寿命,其形式简单易被工程人员接受。算例中考虑了单变量的随机性,利用蒙特卡洛抽样模拟技术计算了路面结构从起裂扩展至贯通整个面层的疲劳寿命,并根据疲劳寿命和设计寿命建立了半刚性基层路面可靠度分析模型,进一步计算了路面结构可靠指标。
The asphalt concrete pavement on semi-rigid base course is the main form of high-grade road in China, but various kinds of damages will happen to it for crack in their early service. Reflective cracking is one of major forms of early destruction in asphalt overlay on semi-rigid base. So how to effectively control its initiation, propagation and reduce its influence on fatigue life in pavement structures still remains a huge problem in road engineering. Traditional continuum mechanics and fatigue strength theory are difficulty to describe the essence of the cracking performance. On the basis of the improved Williams series, isoperimetric element and the method of finite element with generalized degrees of freedom (GDOFs), Williams element with GDOFs was proposed for analyzing stress intensity factor (SIF) of reflective cracking under surface loading. The generalized parameters which were from the solution of govern equation were introduced into the model of prediction the fatigue life, and determined the fatigue life for the reflective cracking propagation on pavement structure. As fatigue life is affected by many factors, such as crack geometry, extending direction, expanding law, materials, structure geometry, environment conditions and loading procession. These factors usually have some randomness, so fatigue life is also a random variable. For these reasons, the study will focus on predicting random fatigue life caused by reflective cracking propagation on semi-rigid base course, and using Monte Carlo Simulation Method (MCS) to value the reliability of the pavement structure. Main works are as follows:
Part I:the layered linear elastic plane strain fracture mechanics analysis model was constructed for semi-rigid pavement structure, and some reasonable assumptions and simplifications were made. By using the reflective cracking fracture modes, they led to some basic theory and concepts within the linear elastic fracture mechanics. Based on Westergaard stress function, study gave the stress and displacement field expression of three basic modes cracking, and then raised the conception of SIR Since reflective cracking usually acted as mixed mode I-II, this thesis deduced the more flexible Williams series characteristic expansion of plane crack.
Part II:the analysis model was discretized the singular region and regular region. And the singular region was disposed by employing the refined mesh of traditional finite element method and quarter-node singular element, respectively. Basic concepts and construction principles of isoperimetric element and quarter-node singular element were introduced in detail, and then their shape functions were derived. The two have a same defect from the examples:they cannot directly obtain SIF, but need use linear extrapolation method to acquire it. The process was very complex and large amount of calculation.
Part III:it was focused on the defect that researchers mostly use finite element method analysis software or the traditional finite element method to predict the SIF at crack tip, this study presented the Williams element with GDOFs for SIF of the pavement on semi-rigid base course. In this element model which has a parameter that is related to SIF, so that we can directly determine the SIF at crack tip, and effectively avoid the defects of the traditional finite element method. From the construction principles of Williams element, we found that this kind element no longer treated node parameters as unknown quantities but denoted as undetermined parameter in Williams series. So the number of elements of singular region had no effect on total degrees of freedom, it was only determined by how many number of terms the Williams series have. With these virtues, the Williams element greatly reduced the discrete degrees of freedom and increased the calculation efficiency. We just need know coordinate information of boundary nodes in singular region and region regular, then according to geometric series summation, we can form Williams element stiffness matrix in singular region easily.
Part IV:combining the Williams element with GDOFs and the traditional theory and formula for predicting fatigue life, the analysis model of fatigue life for reflective cracking propagation was constructed by the generalized parameters. It will avoid the two-step thinking that determined the SIF by the structural response, and soon the fatigue life was analyzed by the SIF. The relationship between surface modulus and layer thickness was analyzed in detail. The results show that when increasing surface layer thickness or decreasing surface modulus can improve the fatigue life, but modulus reduce will bring in some new pavement damage in their service. So the suggestion that was from decreasing surface modulus just for the aim of improving the fatigue life need deep consideration for choosing.
Part Ⅴ:Paris formula from traditional fatigue life prediction was turned into a revised flexible series form, and then introducing generalized parameter to predict the fatigue life of pavement structure, this format is simple and can easily be accepted by the engineering staff. In examples, we took into account the randomness of single variable, and the fatigue life was calculated by Monte Carlo simulation method from the crack extension through the entire surface. The reliability analysis model was established by the fatigue life and design life. Moreover, the reliability index was obtained for pavement structure.
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