【作者】 张瑞；

【导师】 王东升；

【作者基本信息】 哈尔滨工业大学 ， 交通运输工程， 2019， 硕士

【摘要】 客观准确地反映材料的力学行为和车辆荷载的作用特征,不断改进沥青路面的力学理论解法与计算,是完善其结构设计方法的理论需求,始终是道路工程领域的研究重点。当前国际各种沥青路面设计方法,均采用垂直荷载下的层状弹性体系力学理论,难以计算多次重复荷载下路面材料的蠕变、松弛等行为,也无法分析车辆荷载水平力作用的影响。为突破这一局限,需要完成水平和垂直荷载作用下层状黏弹性体系的理论求解、数值计算及应用分析等系列研究。首先,完成旋转高次抛物面水平和垂直荷载下层状黏弹性体系的解析求解。基于非轴对称水平荷载下的一般解,利用定解条件,分别求得弹性半空间体和多层体系的解析解,并完成双圆水平和垂直荷载的叠加分析。采用三维广义Maxwell模型,描述路面各层材料的黏弹性本构方程,基于拉普拉斯积分变换求解其置换参数;采用长期固定荷载和间歇式半正弦波荷载模拟车辆轴载谱,获得其拉普拉斯积分变换的象函数;进而,根据对应原理,得到黏弹性层状体系解析解表达式。其次,应用C++语言,开发黏弹性的半空间体和多层体系的数值计算程序。针对含贝塞尔函数无穷积分的解析解,采用复化Gauss积分法,解决其数值计算精度问题;针对象空间解的拉普拉斯逆变换,采用F.Durbin法,解决其数值计算效率和精度问题。分析黏弹性半空间体解析解表达式特点,提出两类计算逻辑及程序,并对比其计算效率与精度,论证了程序的适用条件。开发多层黏弹性体系计算程序,基于半空间体解验证其精度,并论证荷载长期重复作用下程序计算的稳定性。从而为综合荷载重复作用下的路基路面结构黏弹性力学响应计算和分析,提供了精度、效率和稳定性满足要求的程序。再次,应用该计算程序,分析沥青路面黏弹性力学响应的交通、环境和结构组合等影响因素及其规律。选用半空间体和三层体系,分析荷载动态参数对其黏弹性力学行为的影响规律:不同水平荷载作用系数下各点位黏弹性力学响应的计算表明,水平力的影响深度各异;确定不同车速轴载谱的加载周期,计算各车速下路面表面点位的黏弹性位移,结果表明随车速减小,路面表面的黏弹性变形显著增加,分析了表面黏弹性变形的形态。选择不同温度,取用相应温度下沥青层的广义Maxwell方程中黏弹性参数,计算半正弦波荷载作用下半空间体和三层体系的黏弹性响应,分析了随温度变化主应力与最大剪应力峰值沿深度的分布规律。为指导路面结构组合设计,选用含半刚性基层和柔性基层的两类三层体系,即基层分别为弹性和黏弹性材料,分析连续2次加载和卸载过程中不同点位的应力和位移动态变化规律。结果表明,半刚性基层路面,其表面水平位移、最大主应力和最大剪应力,以及面层层底的最大主应力和最大剪应力,都显著高于柔性基层的;加载时,其表面的垂向位移和基层层底的最大拉应力更大,但卸载时,这两个指标则较柔性基层的小。选用黏性和弹性比例差异显著的两种材料,上述指标计算结果表明,程序合理地反映了材料黏弹性对永久变形和应力的影响。最后,针对RIOHTrack典型路面结构,分析重复荷载动态作用下的黏弹性力学响应。基于实测沥青混合料的动态模量数据,给出获取广义Maxwell模型材料参数的方法。基于路面温度场动态变化的实测数据,针对三种典型结构在高温和低温时段,计算半正弦波荷载作用下最大主应力和最大剪应力的峰值随深度的变化,表明结构组合影响显著;计算80km/h行车速度的荷载连续作用24h后路面表面垂向和水平向的永久变形量,表明柔性基层的变形值最大。选取修正三维广义Maxwell模型和Kelvin模型,分别完成相应黏弹性力学计算,结果表明重复荷载长期作用下,二者路面的垂向和水平永久变形差异显著,其规律符合线性固体模型的特征。针对典型路面结构,采用层状弹性力学和层状黏弹性体系力学,分别计算半刚性基层疲劳寿命和面层永久变形,结果表明黏弹性力学可更客观描述轴载动态加载的影响,有益于环道路面加速加载的计算和验证。上述解析求解、数值计算、程序开发和路面结构黏弹性力学响应分析的系列成果,实现了路面力学从弹性理论到黏弹性理论的跨越,突破了垂直荷载下理论体系的局限,为计算动态重复车辆荷载动作用下的路面黏弹性力学响应提供了工具。可为沥青路面结构的加速加载试验的验证提供理论支撑,对更深刻认识沥青路面在动态荷载作用下的力学响应演化规律及破坏机制,对完善沥青路面结构设计方法,有较为重要的理论意义和工程实际价值。更多还原

【Abstract】 Reflecting objectively and accurately the mechanical behavior of materials and the action characteristics of vehicle loads,and constantly improving the theoretical solution and calculation of asphalt pavement mechanics are the theoretical requirements of improving its structural design method,and are always the research focus in the field of road engineering.At present,the mechanics theory of layered elastic system under vertical loads is adopted in various international asphalt pavement design methods.It is difficult to calculate the creep and relaxation behavior of pavement materials under repeated loads,and to analyze the influence of horizontal force of vehicle loads.In order to overcome this limitation,a series of studies on theoretical solution,numerical calculation and application analysis of layered viscoelastic systems under horizontal and vertical loads need to be completed.Firstly,the analytical solution of layered viscoelastic system under horizontal and vertical loads of rotating high order paraboloid was completed.Based on the general solutions under non-axisymmetric horizontal loads,the analytical solutions of elastic half-space and multi-layer systems were obtained by using the definite conditions,and the overlapping analysis of horizontal and vertical loads of double circles was completed.The three-dimensional generalized Maxwell model was used to describe the viscoelastic constitutive equation of pavement materials,and the displacement parameters were solved based on Laplace integral transformation.The axle load spectrum was simulated by long-term fixed load and intermittent half-sinusoidal wave load,and the image function of Laplace integral transformation was obtained.Then,according to the corresponding principle,the analytical solution expression of viscoelastic layered system was obtained.Secondly,a numerical program for viscoelastic half-space and multi-layer systems was developed by using C++ language.Aiming at the analytic solution of infinite integral with Bessel function,the complex Gauss integral method was used to solve the problem of numerical calculation accuracy,and the inverse Laplace transform of image space solution was used to solve the problem of numerical calculation efficiency and accuracy by F.Durbin method.The characteristics of analytical solutions for viscoelastic half-space bodies were analyzed.Two kinds of computational logic and programs were proposed.The computational efficiency and accuracy were compared,and the applicable conditions of the program were demonstrated.A multi-layer viscoelastic system calculation program was developed to verify the accuracy of the program based on the half-space system,and to demonstrate the stability of the program calculation under long-term repeated loads.Thus,a program for calculating and analyzing the viscoelastic mechanical response of subgrade and pavement structures under repeated loads was provided,which satisfies the requirements of accuracy,efficiency and stability.Thirdly,the program was applied to analyze the traffic,environment and structure combination of viscoelastic response of asphalt pavement.Half-space and three-layer system were selected to analyze the influence of dynamic load parameters on viscoelastic mechanical behavior.The calculation of viscoelastic mechanical response at different points under different horizontal load coefficients showed that the influence depth of horizontal force varies.The loading period of axle load spectrum at different speeds was determined,and the viscoelastic displacement of pavement surface points under different speeds was calculated.The results showed that the viscoelastic displacement of pavement surface points decreases with vehicle speed.The viscoelastic deformation of pavement surface increased significantly,and the shape of viscoelastic deformation of pavement surface was analyzed.The viscoelastic response of half-space and three-layer systems under half-sinusoidal loading was calculated by using the viscoelastic parameters in the generalized Maxwell equation of asphalt layer at different temperatures.The distribution of principal stress and maximum shear stress peak along depth with temperature was analyzed.In order to guide the combination design of pavement structure,two kinds of three-layer systems including semi-rigid base and flexible base were selected,namely,elastic and viscoelastic materials,respectively.The dynamic changes of stress and displacement at different points during two successive loading and unloading were analyzed.The results showed that the horizontal displacement,maximum principal stress and maximum shear stress on the surface of semi-rigid base pavement,as well as the maximum principal stress and maximum shear stress at the bottom of the surface layer are significantly higher than those of the flexible base pavement;the vertical displacement of the surface and the maximum tensile stress at the bottom of the base were larger when loading,but the two indexes were smaller when unloading.Two kinds of materials with significant difference in viscoelastic and elastic proportions were selected.The calculation results of the above indexes showed that the program reasonably reflects the effect of viscoelastic material on permanent deformation and stress.Finally,the viscoelastic response of typical RIOHTrack pavement structure under repeated loading was analyzed.Based on the measured dynamic modulus data of asphalt mixture,a method for obtaining material parameters of generalized Maxwell model was presented.Based on the measured data of dynamic change of pavement temperature field,the peak values of maximum principal stress and maximum shear stress under half sinusoidal wave load were calculated for three typical structures at high and low temperatures,which indicated that the combination of structures has a significant effect on pavement surface.The permanent deformation of pavement surface in vertical and horizontal directions was calculated after 24 hours of continuous loading at 80 km/h speed,which indicated that the flexible foundation is formed.The deformation value of the layer was the largest.The modified three-dimensional generalized Maxwell model and Kelvin model were selected to complete the corresponding viscoelastic mechanics calculation.The results showed that the vertical and horizontal permanent deformations of the two pavements are significantly different under long-term repeated loads,and their regularities conform to the characteristics of the linear solid model.For typical pavement structures,layered elasticity and layered viscoelastic system mechanics were used to calculate the fatigue life of semi-rigid base course and the permanent deformation of surface layer respectively.The results showed that viscoelastic mechanics can describe the effect of dynamic loading of axle load more objectively,which was beneficial to the calculation and verification of accelerated loading of annular road surface.The above series of results of analytical solution,numerical calculation,program development and viscoelastic response analysis of pavement structure have realized the leap from elastic theory to viscoelastic theory of pavement mechanics,broken through the limitations of theoretical system under vertical loads,and provided a tool for calculating viscoelastic response of pavement under dynamic repeated vehicle loads.It can provide theoretical support for the verification of accelerated loading test of asphalt pavement structure,and has important theoretical significance and practical engineering value for a deeper understanding of the evolution law of mechanical response and failure mechanism of asphalt pavement under dynamic loading,and for improving the design method of asphalt pavement structure.更多还原