沥青路面温度应力及超孔隙水压力计算
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摘要
除了行车荷载之外,温度和湿度等环境因素对沥青路面的使用性能也有着重要的影响。其中,温度因素的影响尤为重要,原因在于它直接影响路面结构的承载力,引起的低温开裂不但会涉及到高额的维修费用,还会导致和加速路面结构的其它破坏形式,例如,水分通过裂缝渗入后,会造成沥青膜的剥离、基层和土基承载力的降低和丧失等。因此,根据沥青路面的实际情况,深入分析路面结构温度应力的变化规律,及其与各种影响因素之间的关系,以提高沥青路面的使用性能有着重要的实际工程意义。
在过去40多年中,关于沥青路面温度应力问题的研究取得了极大的进展,但仍然存在不足之处。目前沥青路面温度应力的理论研究主要基于层状弹性理论体系,在计算和求解过程中,通常忽略温度对沥青路面材料特性的影响,而将材料特性假定为固定常数。实际上,沥青混合料是一种感温性材料,温度变化时,混合料的弹性模量、温度收缩系数以及泊松比均会发生变化。将材料特性视为固定常数的假定虽然带来了计算上的简便,但也导致了计算结果与沥青路面的实际情况不符,因而限制了计算结果的实际应用。
论文将沥青混合料的材料特性作为随温度变化的函数,分别利用传递矩阵方法和刚度矩阵方法推导了沥青路面温度应力问题的解析解,并对沥青路面温度应力的影响因素、低温开裂预估以及光纤光栅传感技术在沥青路面实测工作中的应用等问题进行了研究。此外,还利用刚度矩阵方法,推导了沥青路面超孔隙水压力问题的解析解。主要工作内容如下:
(1)以热弹性理论为基础,并将沥青路面的材料特性作为温度的函数,利用传递矩阵法以及Laplace和Hankel积分变换的数学方法,推导了层状弹性体系温度应力问题的解析解。分析了温度变化条件下,沥青路面温度场和沥青层材料特性的变化规律,以及随温度变化的材料特性对温度应力的影响。由于在理论解的推导过程中考虑了温度变化对沥青混凝土材料特性的影响,温度应力的计算结果更为符合沥青路面的真实受力状态。
(2)利用刚度矩阵法推导了沥青路面温度应力问题的解析解,推导过程中考虑了温度变化对材料特性的影响,并将解析解分解为由外荷载引起和由温度荷载引起的两部分,使得状态向量表达式的意义更加明确。由于刚度矩阵的元素仅仅含有负指数项,所以计算时不会出现溢出或病态现象,进而可以克服传递矩阵法容易溢出的缺点。利用刚度矩阵法计算沥青路面温度应力问题时非常稳定。基于计算实例,深入分析了沥青层随温度变化的弹性模量、温度收缩系数和泊松比对温度应力计算结果的影响。
(3)拟合了沥青混凝土的各种材料特性同温度之间的函数关系,并分析了沥青路面的温度应力与路面结构厚度、基层材料特性之间的关系,通过计算实例进行了低温开裂预估,预估结果与沥青路面的真实开裂温度比较接近,验证了本文理论计算模型的合理性。
(4)应用大连理工大学抗震研究所自行设计的光纤光栅传感器,将其组成分布式监测系统,对静载试验条件下沥青路面的应变进行了实时监测,同时对气温变化引起的路面结构温度和应变进行了数月的监测工作,并与理论计算结果进行了对比分析。验证了该光纤光栅传感系统用于沥青路面实测工作的可行性以及本文理论解的正确性。
(5)把浸水沥青路面视为多层饱和弹性半空间轴对称体,基于Biot固结方程,利用刚度矩阵法及Laplace和Hankel积分变换的数学方法,推导了沥青路面超孔隙水压力问题的解析解。并对一个浸水沥青路面的实例进行了计算,分析了超孔隙水压力随时间和深度的变化规律。
Besides vehicle load, the environment factors such as temperature and moisture have great effect on flexible pavement. Thereinto, the effect of temperature on pavement performance is generally considered to be a very important factor since it directly affects the pavement structural capacity and thermal cracking is associated with high repair costs and the acceleration of other failure mechanism, such as weakening of subgrade and aggregate layers through water infiltration, stripping in asphalt layers, loss of subgrade support, and so on. Therefore, it has important realistic significance in pavement engineering to lead a further analysis of the interaction between thermal stresses of the pavement and the influencing factors, taking consideration into the real behavior of material characteristics in asphalt pavement, so as to improve asphalt concrete's thermal resistance.
Significant advancements have been achieved over the past 40 years in understanding the mechanisms of thermal fatigue cracking and researches on thermo-stresses of flexible pavement are mainly based on multilayered elastic theoretical system. However, during the calculation of thermo-stresses, the effect of temperature on flexible pavement is usually neglected and it is assumed that material characteristics of asphalt mixture are constant at present. In fact, asphalt concrete is a kind of material sensitive to temperature. The modulus of elasticity, Poisson's ratio and the coefficient of thermal expansion of asphalt concrete are not constant at different temperature. This assumption of temperature-independent material characteristics brings convenience in calculation, but leads to the significant difference between calculating results and the real state of flexible pavement, and limits the applicability of the solutions obtained to certain ranges of temperature.
This current research presents an analytical study of thermal stresses of asphalt pavement by transfer matrix method and stiffness matrix method, respectively, in which material characteristics are taken as parameters dependent on reference temperature. Then, numerical simulation and analysis of thermo-stresses, prediction of low temperature cracking, and the feasibility of fiber Bragg grating (FBG) sensors in flexible pavement are thoroughly investigated. In addition, analytical solutions of excess pore fluid stresses in flexible pavement is derived by stiffness matrix method. The main contents of the current research are as follows:
(1) Based on thermo-elastic theory and material characteristics being regarded as functions of temperature, analytical solutions of thermo-stresses in multilayered elastic system are derived by transfer matrix method and mathematical methods of Laplace and Hankel integral transformations. Distribution of temperature and material characteristics of asphalt layer, effect of temperature-dependent material characteristics on thermo-stresses in flexible pavement are analyzed under daily variation of temperature. Because of the consideration of the effect of temperature on material characteristics, calculating results of thermo-stresses are more close to the real status of flexible pavement.
(2) Taking the effect of temperature on material characteristics of flexible pavement into consideration, analytical solutions of thermo-stresses are derived by stiffness matrix method. The analytical solutions are clear in concept because the expression of state vectors is resolved into two parts: one caused by vehicle load and the other caused by temperature. Moreover, because the elements of matrix do not include positive exponential function, the calculation is not overflowed and the shortages of transfer matrix method can be overcome. Based on a calculation example, the effects of temperature-dependent modulus, coefficient of thermal expansion, and Poisson's ratio of asphalt layer on thermo-stresses are analyzed.
(3) With reference to relevant literatures, the functional relationship between modulus of elasticity, coefficient of thermal expansion, and Poisson's ratio and temperature are fitted. Hereby, influences of pavement structural thicknesses and material characteristics of base course on thermo-stresses are studied and critical cracking temperature is predicted for a practical flexible pavement, which accords well with the real situation of low temperature cracking.
(4) Some FBG sensors packaged and designed by Institute of Earthquake Engineering of Dalian University of Technology are used in a real flexible pavement, and a real-time optical FBG sensor system is built up with these sensors. Strain of pavement structure under static load, temperature and strain distribution of asphalt pavement caused by air temperature changes are monitored with this system for several months and compared with the analytical results. The agreement of experimental observations and calculation results shows the feasibility of FBG sensors in temperature and strain monitoring of flexible pavement structure and the correctness of analytical solutions in this paper.
(5) Permeated flexible pavement is regarded as an axial symmetric body of multilayered saturation elastic half space. Based on the fundamental thermal Boit consolidation equations, explicit solution of the excess pore fluid stresses for flexible pavement is obtained by stiffness matrix method and some mathematic methods such as Laplace and Hankel integral transformations. The stresses of the permeated flexible pavement are calculated and analyzed based on a practical flexible pavement.
在过去40多年中,关于沥青路面温度应力问题的研究取得了极大的进展,但仍然存在不足之处。目前沥青路面温度应力的理论研究主要基于层状弹性理论体系,在计算和求解过程中,通常忽略温度对沥青路面材料特性的影响,而将材料特性假定为固定常数。实际上,沥青混合料是一种感温性材料,温度变化时,混合料的弹性模量、温度收缩系数以及泊松比均会发生变化。将材料特性视为固定常数的假定虽然带来了计算上的简便,但也导致了计算结果与沥青路面的实际情况不符,因而限制了计算结果的实际应用。
论文将沥青混合料的材料特性作为随温度变化的函数,分别利用传递矩阵方法和刚度矩阵方法推导了沥青路面温度应力问题的解析解,并对沥青路面温度应力的影响因素、低温开裂预估以及光纤光栅传感技术在沥青路面实测工作中的应用等问题进行了研究。此外,还利用刚度矩阵方法,推导了沥青路面超孔隙水压力问题的解析解。主要工作内容如下:
(1)以热弹性理论为基础,并将沥青路面的材料特性作为温度的函数,利用传递矩阵法以及Laplace和Hankel积分变换的数学方法,推导了层状弹性体系温度应力问题的解析解。分析了温度变化条件下,沥青路面温度场和沥青层材料特性的变化规律,以及随温度变化的材料特性对温度应力的影响。由于在理论解的推导过程中考虑了温度变化对沥青混凝土材料特性的影响,温度应力的计算结果更为符合沥青路面的真实受力状态。
(2)利用刚度矩阵法推导了沥青路面温度应力问题的解析解,推导过程中考虑了温度变化对材料特性的影响,并将解析解分解为由外荷载引起和由温度荷载引起的两部分,使得状态向量表达式的意义更加明确。由于刚度矩阵的元素仅仅含有负指数项,所以计算时不会出现溢出或病态现象,进而可以克服传递矩阵法容易溢出的缺点。利用刚度矩阵法计算沥青路面温度应力问题时非常稳定。基于计算实例,深入分析了沥青层随温度变化的弹性模量、温度收缩系数和泊松比对温度应力计算结果的影响。
(3)拟合了沥青混凝土的各种材料特性同温度之间的函数关系,并分析了沥青路面的温度应力与路面结构厚度、基层材料特性之间的关系,通过计算实例进行了低温开裂预估,预估结果与沥青路面的真实开裂温度比较接近,验证了本文理论计算模型的合理性。
(4)应用大连理工大学抗震研究所自行设计的光纤光栅传感器,将其组成分布式监测系统,对静载试验条件下沥青路面的应变进行了实时监测,同时对气温变化引起的路面结构温度和应变进行了数月的监测工作,并与理论计算结果进行了对比分析。验证了该光纤光栅传感系统用于沥青路面实测工作的可行性以及本文理论解的正确性。
(5)把浸水沥青路面视为多层饱和弹性半空间轴对称体,基于Biot固结方程,利用刚度矩阵法及Laplace和Hankel积分变换的数学方法,推导了沥青路面超孔隙水压力问题的解析解。并对一个浸水沥青路面的实例进行了计算,分析了超孔隙水压力随时间和深度的变化规律。
Besides vehicle load, the environment factors such as temperature and moisture have great effect on flexible pavement. Thereinto, the effect of temperature on pavement performance is generally considered to be a very important factor since it directly affects the pavement structural capacity and thermal cracking is associated with high repair costs and the acceleration of other failure mechanism, such as weakening of subgrade and aggregate layers through water infiltration, stripping in asphalt layers, loss of subgrade support, and so on. Therefore, it has important realistic significance in pavement engineering to lead a further analysis of the interaction between thermal stresses of the pavement and the influencing factors, taking consideration into the real behavior of material characteristics in asphalt pavement, so as to improve asphalt concrete's thermal resistance.
Significant advancements have been achieved over the past 40 years in understanding the mechanisms of thermal fatigue cracking and researches on thermo-stresses of flexible pavement are mainly based on multilayered elastic theoretical system. However, during the calculation of thermo-stresses, the effect of temperature on flexible pavement is usually neglected and it is assumed that material characteristics of asphalt mixture are constant at present. In fact, asphalt concrete is a kind of material sensitive to temperature. The modulus of elasticity, Poisson's ratio and the coefficient of thermal expansion of asphalt concrete are not constant at different temperature. This assumption of temperature-independent material characteristics brings convenience in calculation, but leads to the significant difference between calculating results and the real state of flexible pavement, and limits the applicability of the solutions obtained to certain ranges of temperature.
This current research presents an analytical study of thermal stresses of asphalt pavement by transfer matrix method and stiffness matrix method, respectively, in which material characteristics are taken as parameters dependent on reference temperature. Then, numerical simulation and analysis of thermo-stresses, prediction of low temperature cracking, and the feasibility of fiber Bragg grating (FBG) sensors in flexible pavement are thoroughly investigated. In addition, analytical solutions of excess pore fluid stresses in flexible pavement is derived by stiffness matrix method. The main contents of the current research are as follows:
(1) Based on thermo-elastic theory and material characteristics being regarded as functions of temperature, analytical solutions of thermo-stresses in multilayered elastic system are derived by transfer matrix method and mathematical methods of Laplace and Hankel integral transformations. Distribution of temperature and material characteristics of asphalt layer, effect of temperature-dependent material characteristics on thermo-stresses in flexible pavement are analyzed under daily variation of temperature. Because of the consideration of the effect of temperature on material characteristics, calculating results of thermo-stresses are more close to the real status of flexible pavement.
(2) Taking the effect of temperature on material characteristics of flexible pavement into consideration, analytical solutions of thermo-stresses are derived by stiffness matrix method. The analytical solutions are clear in concept because the expression of state vectors is resolved into two parts: one caused by vehicle load and the other caused by temperature. Moreover, because the elements of matrix do not include positive exponential function, the calculation is not overflowed and the shortages of transfer matrix method can be overcome. Based on a calculation example, the effects of temperature-dependent modulus, coefficient of thermal expansion, and Poisson's ratio of asphalt layer on thermo-stresses are analyzed.
(3) With reference to relevant literatures, the functional relationship between modulus of elasticity, coefficient of thermal expansion, and Poisson's ratio and temperature are fitted. Hereby, influences of pavement structural thicknesses and material characteristics of base course on thermo-stresses are studied and critical cracking temperature is predicted for a practical flexible pavement, which accords well with the real situation of low temperature cracking.
(4) Some FBG sensors packaged and designed by Institute of Earthquake Engineering of Dalian University of Technology are used in a real flexible pavement, and a real-time optical FBG sensor system is built up with these sensors. Strain of pavement structure under static load, temperature and strain distribution of asphalt pavement caused by air temperature changes are monitored with this system for several months and compared with the analytical results. The agreement of experimental observations and calculation results shows the feasibility of FBG sensors in temperature and strain monitoring of flexible pavement structure and the correctness of analytical solutions in this paper.
(5) Permeated flexible pavement is regarded as an axial symmetric body of multilayered saturation elastic half space. Based on the fundamental thermal Boit consolidation equations, explicit solution of the excess pore fluid stresses for flexible pavement is obtained by stiffness matrix method and some mathematic methods such as Laplace and Hankel integral transformations. The stresses of the permeated flexible pavement are calculated and analyzed based on a practical flexible pavement.
引文
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