高速铁路红层泥岩路基动态响应及动力变形特性的综合研究
|
摘要
随着高速铁路的发展,铁路线路结构已经突破了传统的轨道-道床-土路基结构形式,既有有砟轨道,又有无砟轨道。对于有砟轨道,已经抛弃了将道砟层直接铺设在土质路基上的方法,而是采用多层结构系统。列车轴重和速度的提高,以及线路结构的变化,不仅使列车与线路系统的动力作用大幅加剧,而且也使二者之间的动力特性变得异常复杂,从而对线路系统提出了更高的要求。尤其是作为线路基础的路基结构,其动力特性更是决定了铁路整体系统的稳定和安全,路基的动态响应(动应力、动位移以及加速度等)自然应该成为研究的关键。
路基动态响应的分析因受列车类型、轴重、运行情况、线路结构和下部基础等诸多因素的影响而显得特别复杂,国内外许多学者就轨道、地基模型和振动响应特征等方面进行了大量的研究工作,并取得了一些重要的理论研究成果。但对路基的动力特性研究还不够深入,常常对其简化处理,导致计算模型不完善,理论计算和实测值有较大出入。
采用试验手段,尤其是现场测试,是分析路基动力学特性一种很直接也是最有效的方法,但事实表明试验测试也有自身的弊端,如模型试验对路基无限边界模拟困难以及存在尺寸效应,而现场试验造价又很高昂,并且受测试环境及测试仪器的影响等。目前采用数值仿真计算进行结构-路基系统的动力分析得到广泛应用,该方法能快速的进行不同条件下的动力计算,但仿真计算结果的好坏完全取决于模型所取参数,一旦参数选取不合理,则得到的结果与实际情况有很大的差异。如果能将试验测试和仿真计算有机的结合起来,比如通过试验手段为数值仿真计算提供关键的参数,尽量避免二者的缺陷,无疑是一种分析线路系统动力特性的新途径。
路基填料的动力特性关系到路基强度、疲劳特性、累积变形及其动力稳定性,并直接影响高速铁路路基设计、使用和维修。为了满足高速铁路的要求,现有路基都是采用高标准的路基填料,如级配碎石,A、B组填料等,工程造价不菲,为了节省工程投资和保护环境,有必要开发新的填料,以扩大路基填料的选用范围。
本文依托达成线红层泥岩路基循环加载试验和无砟轨道室内大比例模型试验,分别对有砟轨道、无砟轨道路基基床的动态特性进行分析；针对红层泥岩土在我国分布较广泛,研究其在循环荷载作用下的动力特性及路用性能,为红层泥岩路基设计提供参考,以试验所提供的参数为依据,开展两种轨道结构的动力仿真计算方法研究；在此基础上,引进正交试验设计方法和统计学理论,对影响线路动态响应的因素进行系统评价。主要研究内容和结论如下：
(1)有砟轨道现场循环加载试验
在达成线红层泥岩路基试验段,采用ZSS50循环加载设备模拟不同轴重列车的动力作用,进行有砟轨道路基基床现场循环加载试验。由试验可得出：
①路基面动应力在横断面上呈马鞍形分布,轨下位置处动应力值最大,靠近轨枕端部次之,路基中线下最小；动应力沿基床深度是逐渐减小的,在基床表层内衰减较快,在基床底层内衰减相对慢一些；动应力在路基基床底部已经衰减了80%,可见基床承担了绝大部分的动力作用；动位移、加速度的分布规律与动应力相似。
②轴重18T激振300万次后,路基面总变形为3.22cm,前100万次变形发展较快,占总变形的70%左右,后逐渐趋于稳定；红层泥岩基床底层变形为0.48cm,基床表层变形为0.12cm。轴重增加到25T,激振100万次后,路基面总沉降量发展到4.07cm,其中红层泥岩基床底层变形增加到1.0cm,基床表层变形增加到0.22cm。可见列车轴重对路基变形有较大影响。
(2)无砟轨道动态特性模型试验
开展无砟轨道路基基床室内大比例模型动态加载试验,模型以级配碎石为基床表层,以A、B组填料为基床底层。试验表明：
①路基表面动应力在横断面上呈马鞍形分布,钢轨下方动应力值较大,中间和两端其值较小；动应力沿基床深度逐渐减小,在路基基床底部已经衰减了70%,与有砟轨道一样,基床部分承担了大部分的动力作用。动位移、加速度的分布规律与动应力相似。
②随着加载频率的提高,动应力、动位移和加速度的值都是增大的；加速度受频率影响最大,其次为动位移,受加载频率影响最小的是动应力,其沿路基深度的衰减规律基本不变。
③在基床横断面方向,随着动荷载的增大,基床表面动态参数的马鞍形分布越来越明显；而外加动荷载对动参数沿基床深度的衰减规律影响甚小。
(3)红层泥岩路基土的动态特性研究
红层泥岩颗粒易破碎、强度低、遇水后易崩解与软化,目前工程界对红层泥岩能否用作高速铁路路基填料仍存在争议,但红层泥岩在我国西南、西北、中南及东南地区均有广泛分布,如果能使之用于高速铁路路基填筑,则可节省大量工程投资。
①对于侏罗系遂宁组红层泥岩土(达成线工点),在掌握其基本物理力学性质的基础上,采用英国GDS三轴试验系统,研究了红层泥岩填料在循环荷载作用下动态参数(模量、阻尼比)、临界动应力、动强度及累积变形的发展规律,为红层泥岩路基设计提供必要的参考依据。
②考虑土的应力状态、土的类型、物理性质以及循环荷载作用次数等主要因素,提出一个适合于红层泥岩路基土的累积变形计算方法,并用红层泥岩路基基床现场循环加载试验的结果对其检验和修正。
③考虑红层泥岩土的临界动应力以及遇水容易软化的特点,认为红层泥岩压实土不能作为路基基床表层,但可以满足作为达成线铁路路基基床底层填料的要求,在列车轴重不超过25T的情况下,其上的基床表层厚度要保证为0.6m。同时,现场循环加载试验表明红层泥岩路基的累积变形也能满足高速铁路路基的要求。
(4)轨道-路基系统动力仿真分析
通过有限元软件ABAQUS建模,并联合FLAC3D中的滞后阻尼反映土的非线性,采用合理的边界条件(粘弹性人工边界),对两种轨道结构形式进行仿真计算。
①以达成线现场激振试验段为原型,进行有砟轨道-路基系统的动力仿真计算,主要研究了车速、轴重、各结构层的刚度和厚度对土质路基受力和变形的影响特性,为有砟轨道路基的设计和力学参数的选择提供参考。
②以遂渝线无砟轨道铁路为原型,进行无砟轨道-路基系统的动力仿真计算,主要研究土质路基上板式轨道的受力特性,计算系统各层结构的动态响应以及车速、轴重和材料特性等对轨道-路基结构系统相互作用的影响特性,为板式轨道-路基的设计和力学参数的选择提供参考。
③由计算结果可知,路基表面动应力沿线路的纵向分布,有砟轨道的受力范围约为7根轨枕的间距(约3.6m),无砟轨道的受力范围为一个轨道单元(约5m)；在路基表面的横断面方向,有砟轨道的动应力为马鞍形分布,而无砟轨道路基表面的动应力分布较均匀,在底座边缘处产生最大动应力,底座范围以内的动应力变化不大；动应力沿路基深度的衰减,有砟轨道要快于无砟轨道。
(5)线路动力响应自身影响参数的综合评价
以上述试验结果为基础,引进正交试验设计方法和统计学理论,分别对有砟轨道和无砟轨道的动态响应结果进行分析,系统评价线路各组成部分的结构尺寸和力学性质对轨道、路基动力响应影响的敏感性。由分析可得：
①对于有砟轨道,道床刚度、基床表层刚度对道床动应力的影响很大；而道床厚度对路基面动应力有很大影响。
②对于无砟轨道,CA砂浆刚度、底座厚度对CA砂浆层动应力的影响很大；同时底座厚度对路基面动应力的影响也很大；扣件刚度是影响钢轨动位移的主要因素。
With the development of high-speed railway, the structure of railway has broken through the traditional forms composed of track-ballast-soil subgrade. In addition to the old ballast track, the new ballastless track has appeared in recent years. The ballast track has abandoned the old design method laying the ballast layer on the soil subgrade directly, instead of using the multi-layer structure system. The increasing train axle loads and speed, and changes in railway structure not only increase substantially the dynamic effect on the system of train and line, but also make the dynamic characteristics more complex, so a higher demand is put forward for the line system. As the base of railway, the dynamic characteristics of subgrade may determine the stability and security of the overall railway system, so its dynamic response (dynamic stress, dynamic deformation and acceleration, etc.) naturally becomes a critical research.
The analysis of dynamic response is particularly complex, which may be affected by such many factors as train type, axle load, operation, line structure and the lower part. Many scholars conducted a great deal of research work on the models of track and foundation, and the vibration response characteristics, and made some important results of theoretical studies. However, the subgrade models are often simplified due to its property is still not grasped, which resulting in the calculation model is imperfect, and there are greater access between theoretical results and measured datas.
Testing methods, especially the field tests, have always been a direct and most effective way in the analysis of subgrade dynamic property. But the fact that the pilot test also has its own drawbacks, for example, there are difficulties to simulate the infinite boundary of subgrade and size effect in model test, and field test cost is very high, and is subject to the testing environment and test equipment. Using numerical simulation to conduct the dynamic analysis of railway system has been widely applied, this method can quickly calculate for different conditions. However, the simulation results depend entirely on the model parameters, once the parameters are unreasonable, then the results are very different from the actual situation. The defects of test and simulation could be avoided if we combine the two ways organically, such as to provide key parameters for the numerical simulation by testing methods, this is undoubtedly a new way to analyze the dynamic behavior of railway.
The dynamic characteristics of subgrade filling are related to the strength, fatigue properties, accumulative deformation and dynamic stability of subgrade, and directly affect the design, use and maintenance of the high-speed railway. All existing subgrades use high standards filling to meet the requirements of high-speed railway, such as graded broken stone, and A, B group filling, etc, which led to the high project cost. In order to save the project investment and protect the environment, and expand the selection range, it is necessary to develop new filling.
This paper studied the dynamic characteristics of subgrade bed through ballastless track model tests and ballast track cyclic loading tests in Dazhou-Chendu railway. Because wider distribution of the red mudstone in our country, this paper studied the dynamic characteristics and pavement performance under cyclic loading, in order to provide a reference to the subgrade design of red mudstone. The methods of dynamic simulation for the two track structures were studied respectively relying on test parameters. On this base, the systematic evaluation of the factors which may affect the dynamic response was conducted, through the introduction of orthogonal experimental design and statistical theory. Main contents and conclusions are as follows.
(1) The field ballast track cyclic loading tests
In the test section of red mudstone subgrade, the field ballast track cyclic loading tests of subgrade bed were carrid out by the ZSS50equipment which can simulate the dynamic effect of different axle loads. The following conclusions can be drawn from the tests.
①The dynamic stress has a saddle-shaped distribution along the subgrade cross section, and the value under rail position is maximum. Along the depth direction of subgrade, dynamic stress gradually decreases. The dynamic stress in the surface layer of subgrade bed decays faster than that in the base layer. Dynamic stress at the bottom of subgrade bed has been decayed by80%, it indicates that subgrade bed bears most of the dynamic action. The distribution law of displacement and acceleration is similar with that of dynamic stress.
②After the18ton Axle load excited3million times, the total deformation of subgrade surface was3.22cm. The deformation in the first1million times developed faster, accounting for about70%of the total deformation, then the development gradually stabilized. The deformation of the base layer of subgrade bed was0.48cm, and that of the surface layer was0.12cm in the stage of18ton Axle load excitation. Axle load increased to25ton and excited3million times, the total deformation of subgrade surface was4.07cm. The deformation of the base layer of subgrade bed was1.0cm, and that of he surface layer was0.22cm. It can be seen that the train axle load has a greater impact on the subgrade deformation
(2) The ballastless track dynamic model tests
Large proportion of the ballasted track dynamic model test was carried out, the model was composed with the surface layer (graded broken stone) and the base layer(A, B group filling) of subgrade bed. The following conclusions can be drawn from the tests.
①The dynamic stress has a saddle-shaped distribution along the subgrade cross section, and the value under rail position is maximum. Along the depth direction of subgrade, dynamic stress gradually decreases. Dynamic stress at the bottom of subgrade bed has been decayed by70%, same as the ballast track, subgrade bed bears most of the dynamic action. The distribution law of displacement and acceleration is similar with that of dynamic stress.
②With the load frequency improves, both the dynamic stress, displacement and acceleration values are increasing. Acceleration is most affected by the frequency, followed by dynamic displacement, and dynamic stress is the minimum affected. The decay law of dynamic stress along the depth of subgrade is basically unchanged.
③With the increase of dynamic load, the saddle-shaped distribution of the dynamic parameters in subgrade surface is more and more obvious along the subgrade cross section. However, the effect of dynamic loads to the dynamic parameters along the depth direction is very small.
(3) Research on dynamic characteristics of red mudstone subgrade soil
Due to red mudstone particles are easily broken, low strength, easy disintegration and softening in water, there is a big controversy for the applicability of using red mudstone to fill railway subgrade in engineering field. But red mudstone are widely distributed in China's Southwest, Northwest, Central South and Southeast, if it can be used in the construction of high-speed railway, then a lot of engineering investment may be saved.
①For the Jurassic Suining group of red mudstone, after its basic physical and mechanical properties are grasped, this paper studied the dynamic parameters (modulus, damping ratio), critical dynamic stress, the dynamic strength and accumulative deformation by British GDS triaxial testing system, and hoped to provide the necessary reference for the design of red mudstone subgrade.
②Considering main factors such as soil type, soil stress state, soil physical state and the number of cyclic loads applications, this paper put forward a prediction model to calculate the accumulative strain of red-mudstone soils subjected to cyclic loads. The validity of this model was verified through the field excitation tests.
③From the point of the critical dynamic stress of red mudstone, meanwhile, the characteristics should be taken into consideration is that red mudstone is softened easily in water, it concludes that compacted red mudstone can be used to fill the base layer of subgrade bed, but can not meet the requirement of the surface layer of subgrade bed, the thickness of surface layer of subgrade must be ensured not less than0.6m. At the same time, the results of accumulative deformation in the field cyclic loading tests demonstrate that the red mudstone filling is applicable in high-speed railway.
(4) Dynamic simulation analysis of track-subgrade system
The model of track-subgrade system was built in the finite element software ABAQUS, associated with the hysteretic damping of FLAC3D which can simulate soil non-linearity, the two types of track structure were simulated using reasonable boundary conditions (visco-elastic artificial boundary).
①Based on the prototype of vibration test section in Dazhou-Chendu railway, the numerical simulation of ballast track-subgrade system was conducted. The force and deformation characteristics of the soil subgrade were mainly discussed in different conditions, including train speed, axle load, the stiffness and thickness of each layer of system structure. This could provide a reference for the design of ballast track subgrade and the choice of mechanical parameters.
②Based on the prototype of the subgrade in Suining-Chongqing railway, the numerical simulation of ballastless track-subgrade system was conducted. The force characteristics of slab track on soil subgrade, and the dynamic response of each layer of system structure were mainly discussed in different conditions, including train speed, axle load and material properties. This could provide a reference for the design of slab track-subgrade and the choice of mechanical parameters.
③The calculation results show the vertical distribution of dynamic stress in subgrade surface. For ballast track, the force range is about7sleepers spacing (about3.6m), for ballastless track, the force range is a track unit (about5m). In subgrade surface, for ballast track, dynamic stress has a saddle-shaped distribution along the subgrade cross section. For ballastless track, the distribution of dynamic stress is more uniform. The maximum value appears at the edge of the base, and there is a little change within the base. The dynamic stress of the ballast track decays faster than that of the ballastless track.
(5) Comprehensive evaluation of the impact parameter to dynamic response
Based on the results mentioned above, through the introduction of orthogonal experimental design and statistical theory, this paper analyzed the dynamic response of ballast track and ballastless track respectively, dynamic response the systematic evaluation of the factors which may affect the dynamic response was conducted. The sensitivity of the response of track and subgrade to the impact of the structural dimensions and mechanical properties was evaluated systematically.
①For ballast track, the main factors affecting the dynamic stress of ballast include the ballast stiffness and the stiffness of the surface layer of subgrade bed. The thickness of ballast has a significant impact on the dynamic stress in the subgrade surface.
②For ballastless track, the main factors affecting the dynamic stress of CA mortar layer include the CA mortar stiffness and base thickness. Meanwhile, base thickness has a significant impact on the dynamic stress in the subgrade surface, and fastener stiffness is a major factor in the influence of rail displacement.
路基动态响应的分析因受列车类型、轴重、运行情况、线路结构和下部基础等诸多因素的影响而显得特别复杂,国内外许多学者就轨道、地基模型和振动响应特征等方面进行了大量的研究工作,并取得了一些重要的理论研究成果。但对路基的动力特性研究还不够深入,常常对其简化处理,导致计算模型不完善,理论计算和实测值有较大出入。
采用试验手段,尤其是现场测试,是分析路基动力学特性一种很直接也是最有效的方法,但事实表明试验测试也有自身的弊端,如模型试验对路基无限边界模拟困难以及存在尺寸效应,而现场试验造价又很高昂,并且受测试环境及测试仪器的影响等。目前采用数值仿真计算进行结构-路基系统的动力分析得到广泛应用,该方法能快速的进行不同条件下的动力计算,但仿真计算结果的好坏完全取决于模型所取参数,一旦参数选取不合理,则得到的结果与实际情况有很大的差异。如果能将试验测试和仿真计算有机的结合起来,比如通过试验手段为数值仿真计算提供关键的参数,尽量避免二者的缺陷,无疑是一种分析线路系统动力特性的新途径。
路基填料的动力特性关系到路基强度、疲劳特性、累积变形及其动力稳定性,并直接影响高速铁路路基设计、使用和维修。为了满足高速铁路的要求,现有路基都是采用高标准的路基填料,如级配碎石,A、B组填料等,工程造价不菲,为了节省工程投资和保护环境,有必要开发新的填料,以扩大路基填料的选用范围。
本文依托达成线红层泥岩路基循环加载试验和无砟轨道室内大比例模型试验,分别对有砟轨道、无砟轨道路基基床的动态特性进行分析；针对红层泥岩土在我国分布较广泛,研究其在循环荷载作用下的动力特性及路用性能,为红层泥岩路基设计提供参考,以试验所提供的参数为依据,开展两种轨道结构的动力仿真计算方法研究；在此基础上,引进正交试验设计方法和统计学理论,对影响线路动态响应的因素进行系统评价。主要研究内容和结论如下：
(1)有砟轨道现场循环加载试验
在达成线红层泥岩路基试验段,采用ZSS50循环加载设备模拟不同轴重列车的动力作用,进行有砟轨道路基基床现场循环加载试验。由试验可得出：
①路基面动应力在横断面上呈马鞍形分布,轨下位置处动应力值最大,靠近轨枕端部次之,路基中线下最小；动应力沿基床深度是逐渐减小的,在基床表层内衰减较快,在基床底层内衰减相对慢一些；动应力在路基基床底部已经衰减了80%,可见基床承担了绝大部分的动力作用；动位移、加速度的分布规律与动应力相似。
②轴重18T激振300万次后,路基面总变形为3.22cm,前100万次变形发展较快,占总变形的70%左右,后逐渐趋于稳定；红层泥岩基床底层变形为0.48cm,基床表层变形为0.12cm。轴重增加到25T,激振100万次后,路基面总沉降量发展到4.07cm,其中红层泥岩基床底层变形增加到1.0cm,基床表层变形增加到0.22cm。可见列车轴重对路基变形有较大影响。
(2)无砟轨道动态特性模型试验
开展无砟轨道路基基床室内大比例模型动态加载试验,模型以级配碎石为基床表层,以A、B组填料为基床底层。试验表明：
①路基表面动应力在横断面上呈马鞍形分布,钢轨下方动应力值较大,中间和两端其值较小；动应力沿基床深度逐渐减小,在路基基床底部已经衰减了70%,与有砟轨道一样,基床部分承担了大部分的动力作用。动位移、加速度的分布规律与动应力相似。
②随着加载频率的提高,动应力、动位移和加速度的值都是增大的；加速度受频率影响最大,其次为动位移,受加载频率影响最小的是动应力,其沿路基深度的衰减规律基本不变。
③在基床横断面方向,随着动荷载的增大,基床表面动态参数的马鞍形分布越来越明显；而外加动荷载对动参数沿基床深度的衰减规律影响甚小。
(3)红层泥岩路基土的动态特性研究
红层泥岩颗粒易破碎、强度低、遇水后易崩解与软化,目前工程界对红层泥岩能否用作高速铁路路基填料仍存在争议,但红层泥岩在我国西南、西北、中南及东南地区均有广泛分布,如果能使之用于高速铁路路基填筑,则可节省大量工程投资。
①对于侏罗系遂宁组红层泥岩土(达成线工点),在掌握其基本物理力学性质的基础上,采用英国GDS三轴试验系统,研究了红层泥岩填料在循环荷载作用下动态参数(模量、阻尼比)、临界动应力、动强度及累积变形的发展规律,为红层泥岩路基设计提供必要的参考依据。
②考虑土的应力状态、土的类型、物理性质以及循环荷载作用次数等主要因素,提出一个适合于红层泥岩路基土的累积变形计算方法,并用红层泥岩路基基床现场循环加载试验的结果对其检验和修正。
③考虑红层泥岩土的临界动应力以及遇水容易软化的特点,认为红层泥岩压实土不能作为路基基床表层,但可以满足作为达成线铁路路基基床底层填料的要求,在列车轴重不超过25T的情况下,其上的基床表层厚度要保证为0.6m。同时,现场循环加载试验表明红层泥岩路基的累积变形也能满足高速铁路路基的要求。
(4)轨道-路基系统动力仿真分析
通过有限元软件ABAQUS建模,并联合FLAC3D中的滞后阻尼反映土的非线性,采用合理的边界条件(粘弹性人工边界),对两种轨道结构形式进行仿真计算。
①以达成线现场激振试验段为原型,进行有砟轨道-路基系统的动力仿真计算,主要研究了车速、轴重、各结构层的刚度和厚度对土质路基受力和变形的影响特性,为有砟轨道路基的设计和力学参数的选择提供参考。
②以遂渝线无砟轨道铁路为原型,进行无砟轨道-路基系统的动力仿真计算,主要研究土质路基上板式轨道的受力特性,计算系统各层结构的动态响应以及车速、轴重和材料特性等对轨道-路基结构系统相互作用的影响特性,为板式轨道-路基的设计和力学参数的选择提供参考。
③由计算结果可知,路基表面动应力沿线路的纵向分布,有砟轨道的受力范围约为7根轨枕的间距(约3.6m),无砟轨道的受力范围为一个轨道单元(约5m)；在路基表面的横断面方向,有砟轨道的动应力为马鞍形分布,而无砟轨道路基表面的动应力分布较均匀,在底座边缘处产生最大动应力,底座范围以内的动应力变化不大；动应力沿路基深度的衰减,有砟轨道要快于无砟轨道。
(5)线路动力响应自身影响参数的综合评价
以上述试验结果为基础,引进正交试验设计方法和统计学理论,分别对有砟轨道和无砟轨道的动态响应结果进行分析,系统评价线路各组成部分的结构尺寸和力学性质对轨道、路基动力响应影响的敏感性。由分析可得：
①对于有砟轨道,道床刚度、基床表层刚度对道床动应力的影响很大；而道床厚度对路基面动应力有很大影响。
②对于无砟轨道,CA砂浆刚度、底座厚度对CA砂浆层动应力的影响很大；同时底座厚度对路基面动应力的影响也很大；扣件刚度是影响钢轨动位移的主要因素。
With the development of high-speed railway, the structure of railway has broken through the traditional forms composed of track-ballast-soil subgrade. In addition to the old ballast track, the new ballastless track has appeared in recent years. The ballast track has abandoned the old design method laying the ballast layer on the soil subgrade directly, instead of using the multi-layer structure system. The increasing train axle loads and speed, and changes in railway structure not only increase substantially the dynamic effect on the system of train and line, but also make the dynamic characteristics more complex, so a higher demand is put forward for the line system. As the base of railway, the dynamic characteristics of subgrade may determine the stability and security of the overall railway system, so its dynamic response (dynamic stress, dynamic deformation and acceleration, etc.) naturally becomes a critical research.
The analysis of dynamic response is particularly complex, which may be affected by such many factors as train type, axle load, operation, line structure and the lower part. Many scholars conducted a great deal of research work on the models of track and foundation, and the vibration response characteristics, and made some important results of theoretical studies. However, the subgrade models are often simplified due to its property is still not grasped, which resulting in the calculation model is imperfect, and there are greater access between theoretical results and measured datas.
Testing methods, especially the field tests, have always been a direct and most effective way in the analysis of subgrade dynamic property. But the fact that the pilot test also has its own drawbacks, for example, there are difficulties to simulate the infinite boundary of subgrade and size effect in model test, and field test cost is very high, and is subject to the testing environment and test equipment. Using numerical simulation to conduct the dynamic analysis of railway system has been widely applied, this method can quickly calculate for different conditions. However, the simulation results depend entirely on the model parameters, once the parameters are unreasonable, then the results are very different from the actual situation. The defects of test and simulation could be avoided if we combine the two ways organically, such as to provide key parameters for the numerical simulation by testing methods, this is undoubtedly a new way to analyze the dynamic behavior of railway.
The dynamic characteristics of subgrade filling are related to the strength, fatigue properties, accumulative deformation and dynamic stability of subgrade, and directly affect the design, use and maintenance of the high-speed railway. All existing subgrades use high standards filling to meet the requirements of high-speed railway, such as graded broken stone, and A, B group filling, etc, which led to the high project cost. In order to save the project investment and protect the environment, and expand the selection range, it is necessary to develop new filling.
This paper studied the dynamic characteristics of subgrade bed through ballastless track model tests and ballast track cyclic loading tests in Dazhou-Chendu railway. Because wider distribution of the red mudstone in our country, this paper studied the dynamic characteristics and pavement performance under cyclic loading, in order to provide a reference to the subgrade design of red mudstone. The methods of dynamic simulation for the two track structures were studied respectively relying on test parameters. On this base, the systematic evaluation of the factors which may affect the dynamic response was conducted, through the introduction of orthogonal experimental design and statistical theory. Main contents and conclusions are as follows.
(1) The field ballast track cyclic loading tests
In the test section of red mudstone subgrade, the field ballast track cyclic loading tests of subgrade bed were carrid out by the ZSS50equipment which can simulate the dynamic effect of different axle loads. The following conclusions can be drawn from the tests.
①The dynamic stress has a saddle-shaped distribution along the subgrade cross section, and the value under rail position is maximum. Along the depth direction of subgrade, dynamic stress gradually decreases. The dynamic stress in the surface layer of subgrade bed decays faster than that in the base layer. Dynamic stress at the bottom of subgrade bed has been decayed by80%, it indicates that subgrade bed bears most of the dynamic action. The distribution law of displacement and acceleration is similar with that of dynamic stress.
②After the18ton Axle load excited3million times, the total deformation of subgrade surface was3.22cm. The deformation in the first1million times developed faster, accounting for about70%of the total deformation, then the development gradually stabilized. The deformation of the base layer of subgrade bed was0.48cm, and that of the surface layer was0.12cm in the stage of18ton Axle load excitation. Axle load increased to25ton and excited3million times, the total deformation of subgrade surface was4.07cm. The deformation of the base layer of subgrade bed was1.0cm, and that of he surface layer was0.22cm. It can be seen that the train axle load has a greater impact on the subgrade deformation
(2) The ballastless track dynamic model tests
Large proportion of the ballasted track dynamic model test was carried out, the model was composed with the surface layer (graded broken stone) and the base layer(A, B group filling) of subgrade bed. The following conclusions can be drawn from the tests.
①The dynamic stress has a saddle-shaped distribution along the subgrade cross section, and the value under rail position is maximum. Along the depth direction of subgrade, dynamic stress gradually decreases. Dynamic stress at the bottom of subgrade bed has been decayed by70%, same as the ballast track, subgrade bed bears most of the dynamic action. The distribution law of displacement and acceleration is similar with that of dynamic stress.
②With the load frequency improves, both the dynamic stress, displacement and acceleration values are increasing. Acceleration is most affected by the frequency, followed by dynamic displacement, and dynamic stress is the minimum affected. The decay law of dynamic stress along the depth of subgrade is basically unchanged.
③With the increase of dynamic load, the saddle-shaped distribution of the dynamic parameters in subgrade surface is more and more obvious along the subgrade cross section. However, the effect of dynamic loads to the dynamic parameters along the depth direction is very small.
(3) Research on dynamic characteristics of red mudstone subgrade soil
Due to red mudstone particles are easily broken, low strength, easy disintegration and softening in water, there is a big controversy for the applicability of using red mudstone to fill railway subgrade in engineering field. But red mudstone are widely distributed in China's Southwest, Northwest, Central South and Southeast, if it can be used in the construction of high-speed railway, then a lot of engineering investment may be saved.
①For the Jurassic Suining group of red mudstone, after its basic physical and mechanical properties are grasped, this paper studied the dynamic parameters (modulus, damping ratio), critical dynamic stress, the dynamic strength and accumulative deformation by British GDS triaxial testing system, and hoped to provide the necessary reference for the design of red mudstone subgrade.
②Considering main factors such as soil type, soil stress state, soil physical state and the number of cyclic loads applications, this paper put forward a prediction model to calculate the accumulative strain of red-mudstone soils subjected to cyclic loads. The validity of this model was verified through the field excitation tests.
③From the point of the critical dynamic stress of red mudstone, meanwhile, the characteristics should be taken into consideration is that red mudstone is softened easily in water, it concludes that compacted red mudstone can be used to fill the base layer of subgrade bed, but can not meet the requirement of the surface layer of subgrade bed, the thickness of surface layer of subgrade must be ensured not less than0.6m. At the same time, the results of accumulative deformation in the field cyclic loading tests demonstrate that the red mudstone filling is applicable in high-speed railway.
(4) Dynamic simulation analysis of track-subgrade system
The model of track-subgrade system was built in the finite element software ABAQUS, associated with the hysteretic damping of FLAC3D which can simulate soil non-linearity, the two types of track structure were simulated using reasonable boundary conditions (visco-elastic artificial boundary).
①Based on the prototype of vibration test section in Dazhou-Chendu railway, the numerical simulation of ballast track-subgrade system was conducted. The force and deformation characteristics of the soil subgrade were mainly discussed in different conditions, including train speed, axle load, the stiffness and thickness of each layer of system structure. This could provide a reference for the design of ballast track subgrade and the choice of mechanical parameters.
②Based on the prototype of the subgrade in Suining-Chongqing railway, the numerical simulation of ballastless track-subgrade system was conducted. The force characteristics of slab track on soil subgrade, and the dynamic response of each layer of system structure were mainly discussed in different conditions, including train speed, axle load and material properties. This could provide a reference for the design of slab track-subgrade and the choice of mechanical parameters.
③The calculation results show the vertical distribution of dynamic stress in subgrade surface. For ballast track, the force range is about7sleepers spacing (about3.6m), for ballastless track, the force range is a track unit (about5m). In subgrade surface, for ballast track, dynamic stress has a saddle-shaped distribution along the subgrade cross section. For ballastless track, the distribution of dynamic stress is more uniform. The maximum value appears at the edge of the base, and there is a little change within the base. The dynamic stress of the ballast track decays faster than that of the ballastless track.
(5) Comprehensive evaluation of the impact parameter to dynamic response
Based on the results mentioned above, through the introduction of orthogonal experimental design and statistical theory, this paper analyzed the dynamic response of ballast track and ballastless track respectively, dynamic response the systematic evaluation of the factors which may affect the dynamic response was conducted. The sensitivity of the response of track and subgrade to the impact of the structural dimensions and mechanical properties was evaluated systematically.
①For ballast track, the main factors affecting the dynamic stress of ballast include the ballast stiffness and the stiffness of the surface layer of subgrade bed. The thickness of ballast has a significant impact on the dynamic stress in the subgrade surface.
②For ballastless track, the main factors affecting the dynamic stress of CA mortar layer include the CA mortar stiffness and base thickness. Meanwhile, base thickness has a significant impact on the dynamic stress in the subgrade surface, and fastener stiffness is a major factor in the influence of rail displacement.
引文
[1]李成辉.轨道[M].成都：西南交通大学出版社,2005.
[2]江成,范佳,王继军.高速铁路无碴轨道设计关键技术[J].中国铁道科学.2004,25(2)：42-47.
[3]S.铁木辛柯.工程中的振动问题[M].北京：人民铁道出版社,1979.
[4]Grassie R W, Gregory D, Harrison and Johnson K L. The dynamic response of railway track to high frequency vertical excitation[J]. Mechanical Engineering Science,1982, 24 (2):77-90.
[5]孙璐,邓学钧.匀速运动的线源荷载激励下无限长梁动力分析[J].应用数学和力学.1998,19(4)：341-347.
[6]Kenney J T. Steady-state vibrations of beam on elastic foundation for moving load[J]. Journal of Appl. Mech.1954:359-364.
[7]Achenbach J D, Sun C T. Moving load on a flexibly supported Timoshenko beam [J]. Solids Structures.1965, Vol.1:355-370.
[8]Kerr A D. The continuously supported rail subjected to an axial force and a moving load[J]. Mech. Sci.1972:71-78.
[9]Fryba L. Vibration of Solids and Structures under Moving Loads[M]. Noordhoff International Publishing, Groningen, The Netherlands,1972.
[10]练松良.轨道结构刚度的理论计算[J].中国铁道科学.2004,25(1)：67-71.
[11]翟婉明,林建辉,王开云.铁路道床振动的理论模拟与试验研究[J].振动工程学报.2003,16(4)：404-408.
[12]蔡成标.无碴轨道动力学理论及应用[J].西南交通大学学报.2007,42(3)：255-261.
[13]张鸿儒,阎贵平,夏禾,等.弹性地基梁单元的等效结点荷载[J].北方交通大学学报.1996,20(5)：522-526.
[14]Eason G. The stresses produced in a semi-infinite solid by a moving Surface force[J]. Eng. Sci.1965, (2):581-609.
[15]Jones D V, Petyt M. Ground vibration in the vicinity of a rectangular load on a half-space[J]. Journal of Sound and Vibration.1993,166 (1):141-159.
[16]Jones D V, Petyt M. Ground vibration in the vicinity of a strip load A two-dimensional half-space model [J]. Journal of Sound and Vibration.1991,147 (1):155-166.
[17]Jones D V, Petyt M. Ground vibration in the vicinity of a strip Load:An elastic layer on a rigid foundation [J]. Journal of Sound and Vibration.1992,152 (3):501-515.
[18]Jones D V, Petyt M. Ground vibration in the vicinity of a strip load:an elastic layer on an elastic half-space [J]. Journal of Sound and Vibration.1993,161 (1):1-18.
[19]Jones D V, Petyt M. Ground vibration in the vicinity of a strip load:a two-dimensional half-space model[J]. Journal of Sound and Vibration.1991,147 (1):155-166.
[20]Grundmann H M, Lieb E. The response of a layered half-spaceto traffic loads moving along its surface [J]. Archive Appl. Mech.1999,69:55-67.
[21]杨英豪,王杰贤.列车运行时振波在土中的传递[J].西安建筑科技大学学报.1995,27(3)：329-334.
[22]蒋建群,周华飞,张土乔.弹性半空间体在移动集中荷载作用下的稳态响应[J].岩土工程学报.2004,26(4)：440-444.
[23]蒋建群,周华飞,张土乔.移动荷载下粘弹性地基上无限大板的稳态响应[J].中国公路学报.2006,19(1)：6-11.
[24]蒋建群,周华飞,张土乔.移动荷载下Kelvin地基上无限大板的稳态响应[J].浙江大学学报(工学版).2005,39(1)：27-32.
[25]张昀青.列车荷载作用下周围物体的动力响应解[J].铁道学报.2003,25 (4)：85-88.
[26]王常晶.列车移动荷载作用下地基的动应力及饱和软粘土特性研究[D].杭州：浙江大学,2006.
[27]苏谦.高速铁路路基空间时变耦合系统动力分析模型及其应用研究[D].成都：西南交通大学,2001.
[28]Lefeuve-Mesgouez G, Peplow A T, Le Houedec D. Surface vibration due to a sequence of high speed moving harmonic rectangular loads[J]. Soil Dynamics and Earthquake Engineering.2002,22 (6):459-473.
[29]谢卫平,王国波,于艳丽.移动荷载作用下基于薄层单元法的土动力分析[J].华中科技大学学报(城市科学版),2004,(2)：8-11.
[30]王文奇,刘保县,王永强.高速铁路路基动应力沿深度的衰减规律[J].西华大学学报(自然科学版),2008,27(5)：98-100.
[31]韩自力,张千里.既有线提速路基动应力分析[J].中国铁道科学,2005,26(5)：1-5.
[32]Hanazato, Toshikazu, Ugai, Keizo, ect. Three-dimensional analysis of traffic-induced ground vibrations [J]. Journal of Geotechnical Engineering.1991,117(8):1133-1151.
[33]李军世,李克钏.高速铁路路基动力反应的有限元分析[J].铁道学报,1995,17(1)：66-75.
[34]边学成.高速列车运动荷载作用下地基和隧道的动力响应分析[D].杭州：浙江大 学,2005.
[35]张远荣.高速铁路路基面竖向动应力的模拟计算[J].铁道建筑,2000(8)：21-23.
[36]梁波,蔡英.不平顺条件下高速铁路路基的动力分析[J].铁道学报.1999,21(1)：84-88.
[37]Hall Lars. Simulations and analyses of train-induced ground vibrations in finite element models[J]. Soil Dynamics and Earthquake Engineering.2003,23 (5): 403-413.
[38]宗军良,刘涛,等.既有线提速路基动力响应特性研究[J].中国铁道科学.2007,28(4)：7-11.
[39]邱延峻,张晓靖,魏永幸.列车速度对无砟轨道路基动力特性的影响[J].交通运输工程学报.2007,7(2)：1-5.
[40]聂志红,阮波,李亮.铁路道床路基动力响应的参数影响[J].交通运输工程学报.2004,4(1)：34-37.
[41]唐益群,栾长青,张曦,等.地铁振动荷载作用下隧道土体变形数值模拟[J].地下空间与工程学报.2008,4(1)：105-110.
[42]董亮,赵成刚,蔡德钩,等.高速铁路无砟轨道路基动力特性数值模拟和试验研究[J].土木工程学报.2008,41(10)：81-86.
[43]陈建国,肖军华,李前进,等.提速列车荷载作用下铁路路基动力特性的研究[J].岩土力学.2009,30(7)：1944-1950.
[44]聂志红.高速铁路轨道路基竖向动力响应研究[D].长沙：中南大学,2005.
[45]马学宁.车-路耦合条件下高速铁路路基及桥路过渡段结构系统动力分析[D].兰州：兰州交通大学,2009.
[46]陈震.高速铁路路基动力响应研究[D].武汉：中科院武汉岩土所,2006.
[47]Okumura Kuno K. Statistical analysis of field data of railway noise and vibration collected in an urban area[J]. Applied Acoustics.1991,33 (4):263-280.
[48]Fujikake T. A prediction method for the propagation of ground vibration from railway trains[J]. Journal of Sound and Vibration.1986,111 (2):357-360.
[49]Dawn T M., Stanworth C G. Ground vibrations from passing trains[J]. Journal of Sound and Vibration.1979, (8):355-362.
[50]Madshus C, Kaynia A M. High-speed railway lines on soft ground:dynamic behaviour at critical train speed[J]. Journal of Sound and Vibration.2000,231 (3):689-701、
[51]Norwegian Geotechnical Institute. NGI Report No515136-1 (October):Vibration criteria for road and rail traffic Vibbase-A database for measured vibrations from road and rail traffic.1995.
[52]杨灿文,龚亚丽.列车通过时路基的动应力和振动[J].土木工程学.1963,9(2)：49-57.
[53]蔡英,等.大秦重载铁路路基的动力响应及分析重载铁路线路结构与养护[M].北京：中国铁道出版社,1992.
[54]周神根.高速铁路路基基床设计[J].路基工程,1997,72(3)：1-5.
[55]王炳龙,余绍锋,周顺华,等.提速状态下路基动应力测试分析[J].铁道学报.2002,22(增)：79-81.
[56]赵洪雁.大秦线万吨列车对轨道的动态影响分析及对策建议[J].中国铁路.2004,9：44-47.
[57]王智猛,蒋关鲁,魏永幸,等.达成线红层泥岩路基循环加载试验研究[J].岩土工程学报.2008,30(12)：1888-1893.
[58]王智猛,蒋关鲁,等.遂渝线无砟轨道道岔区基床动力测试研究[J].铁道建筑.2008,(10)：84-87.
[59]宫全美,罗喆,袁建议.提速铁路基床长期累积沉降及等效循环荷载试验研究[J].铁道学报.2009,31(2)：88-93.
[60]冯立臣,蒋关鲁,王智猛.客运专线土质路基无砟轨道基床动态特性的模型试验研究[J].铁道建筑.2008,(8)：78-81.
[61]苏谦,蔡英.高速铁路级配碎石基床表层不同厚度动态大模型试验研究[J].铁道标准设计.2001,21(8)：2-4.
[62]曹新文,蔡英,苏谦.土工格室和土工网改善基床动态性能模型试验[J].西南交通大学学报.2001,36(4)：350-354.
[63]詹永祥,蒋关鲁.无砟轨道路基基床动力特性的研究[J].岩土力学.2010,31(2)：392-396.
[64]汤康民,蒋忠信.膨胀性红土铁路路基基床动力反应分析[J].西南交通大学学报.1994,29(1)：71-77.
[65]铁道建造物设计标准解说[土构造](案).平成3年(1991年)3月.
[66]平野雅之.按新轨道破坏理论估算轨道下沉量[J].铁道线路(日).1978,(8).
[67]蔡英,黄时寿.重载铁路的线路动力学测试及分析[J].西南交通大学学报.1993,91(3)：92-98.
[68]铁道部科学技术情报研究所译.德国铁路工程技术规范第五册,1995.
[69]汤康民.红粘土动力性质的研究[J].西南交通大学学报.1993,28(4)：12-16.
[70]梁波,孙遇祺.加筋粉煤灰的静动强度指标研究[J].实验力学.1998,19(1)56-59.
[71]关根悦夫著,孙明漳译.列车荷载引起的基床强度的变化[J].铁道线路.1983, 31 (2)：28-32.
[72]伊能忠敏,家田仁,等著,范培钟译.关于铁道道床的动强度问题-荷载频率对基床强度的影响[J].铁路线路.1982,30(8)：5-11.
[73]Heath D L. Design of conventional rail track foundation [J]. Proc. of the Institution of Civil Engineers,1972,51 (3):49-57.
[74]Lashine D L. The displacements in an elastic half-space due to a moving concentrated normal loads[R]. NASA, TRR-238,1996.
[75]孔祥辉,蒋关鲁,王智猛.循环荷载下红层泥岩土的动态特性[J].水文地质工程地质.2012,39(4)：75-79.
[76]蒋关鲁,房立凤,王智猛等.红层泥岩路基填料动强度和累积变形试验研究[J].岩土工程学报.2010,32(1)：124-129.
[77]蔡英,曹新文.重复加载下路基填土的临界动应力和永久变形初探[J].西南交通大学学报.1996,31(1)：1-5.
[78]刘晓红,杨果林,方薇.红黏土临界动应力与高铁无碴轨道路堑基床换填厚度[J].岩土工程学报.2011,33(3)：348-353.
[79]钟辉虹,汤康民,黄茂松.铁路粘土路基动力特性试验研究[J].西南交通大学学报.2002,37(5)：488-490.
[80]Seed H B, Chan C K, Monismith C L. Effect of repeated load on the strength and deformation of compacted clay [J]. Highway Research Record,1955,34:541-558.
[81]Barksdale R D. Laboratory evaluation of rutting in base course materials [C]. In Proceedings of the Third International Conference on Structural Design of Asphalt Pavements, London,1972:161-174.
[82]Hyodo M, Yasuhara K. Hirao K.Prediction of clay behavior in undrained and partially drained cyclic triaxial tests[J]. Soils and Foundations.1992,32(4):117-127.
[83]Monismith C L, Ogawa N, Freeme C R. Permanent deformation characteristics of subgrade soils due to repeated loading[J]. Transportation Research Record.1975, 537:1-17.
[84]Brown, Lashine A K F, Hyde A F L. Repeated load triaxial testing of silty clay [J]. Geotechnique,1975,2:95-114.
[85]Brown S F, Hyde A F L. Significance of cyclic confining stress in repeated load triaxial testing of granular materials [J]. Transportation Research Record,1985,537:49-58.
[86]曹新文.成都粘土基床动态特性的试验研究研究报告[R].成都铁路局基建处,1998,12.
[87]闫澎旺.往复荷载作用下重塑软粘土的变形特性[[J].岩土工程学报.1991,13(1)： 48-53.
[88]钟辉虹.粘土动力特性本构模型预测[D].成都：西南交通大学硕士学位论文,1996.
[89]蒋军,陈龙珠.长期循环荷载作用下粘土的一维沉降[J].岩土工程学报.2001,23(3)：366-369.
[90]李献民.高速铁路加筋过渡段静动力特性数值分析及试验研究[D].长沙：中南大学,2004.
[91]Li D Q, Selig E T. Cumulative plastic deformation for fine-grained subgrade soils[J]. Journal of Geotechnical Engineering,1996,122 (12):1006-1013.
[92]Chai J C, Miura N. Traffic-load-induced permanent deformation of road on soft subsoil[J]. Journal of Geotechnical and Geoenvironmental Engineering,2002,128 (11):907-916.
[93]Parr G B. Some aspects of the behaviour of London clay under repeated loading[D]. UK:University of Nottingham,1972.
[94]Li. Wheel-track dynamic interaction track substructure perspective [J]. Vehicle System Supplement,1995,24:183-196.
[95]Hargis, Louis L. A study of strain characteristics in a limestone gravel subjected to repetitive Ioad[J]. Texas ASM University, College station,1963.
[96]姚兆明,黄茂松,张宏博.长期循环荷载下粉细砂的累积变形特性[J].同济大学学报(自然科学版).2011,39(2)：204-208.
[97]黄茂松,李进军,李兴照.饱和软粘土的不排水循环累积变形特性[J].岩土工程学报.2006,28(7)：891-895.
[98]黄茂松,姚兆明.循环荷载下饱和软黏土的累积变形显式模型[J].岩土工程学报.2011,33(3)：325-331.
[99]李进军.交通荷载作用下饱和软粘土长期沉降分析[D].上海：同济大学,2005.
[100]边学成,蒋红光,申文明,等.基于模型试验的高铁路基动力累积变形研究[J].土木工程学报.2011,44(6)：112-119.
[101]陈颖平,黄博,陈云敏.循环荷载作用下软勃土不排水累积变形特性[J].岩土工程学报.2008,30(5)：764-768.
[102]白冰,周健.周期荷载作用下粘性土变形及强度特性述评[J].岩土力学.1999,20(3)：84-90.
[103]Mroz Z. On the description of anisotropic work hardening[J]. Journal of the Mechanics and Physics of Solids.1967,15 (3):163-175.
[104]Pro vest J H. Mathematical modeling of monotonic and cyclic undrained clay behaviour[J]. International Journal for Numerical and Analytical Methods in Geomechanics.1977 (1):195-216.
[105]Pro vest J H. Anisotropic undrained stress-strain behavior of clay [J]. Journal of the Geotechnical Engineering Division,, ASCE,1978,104 (8):1075-1090.
[106]Provest J H. A simple plastic theory for frictional cohesionless soils[J]. Soil Dynamics and Earthquake Engineering.1985,4 (1).
[107]Mroz Z., Norris V A, Zienkiewicz O C. An anisotropic critical state model for soils subjected to cyclic loading[J]. Geotechnique.1981,31 (4).
[108]Norris V A. Numerical modelling of response to cyclic loading using stress-reversal surface[C]. Int Symp on Numerical Models in Geomech, Zurich,1982.
[109]王建华,要明伦.软粘土不排水循环特性的弹塑性模拟[J].岩土工程学报.1996,18(3)：11-18.
[110]徐干成,谢定义,郑颖人.饱和砂土循环动应力应变特性的弹塑性模拟研究[J].岩土工程学报.1995,17(2)：1-12.
[111]Mroz Z, Norris V A, Zienkiewicz O C. Application of an anisotropic hardening model in the analysis of elasto-plastic deformation of soils. Geotechnique,1979, 29(1):1-34.
[112]Dafalias Y F, Popov E P. A model of nonlinearly hardening materials for complex loading [J]. Acta Mechanica,1975,21:173-192.
[113]Krieg R D. A practical two-surface plasticity theory[J]. Appl Mech, ASME,1975, 42:641-646.
[114]Dafalias Y F. Bounding surface plasticity (iv):mathematical formulation and hypoplasticity[J]. Engng Mech, ASCE,1986,112 (9):966-987.
[115]Dafalias Y F, Hernnann T. Bounding surface plasticity (v):application to isotropic cohesive soils[J]. Engng Mech, ASCE,1986,112 (12):1263-1291.
[116]Li X S, Dafalias Y F, Wang Z L. State dependent dilatancy in critical state constitutive modeling of sand[J]. Canadian Geotechnical Journal,1999,36(4):559-611.
[117]Li X S. A sand model with state-dependent dilatancy[J]. Geotechnique,2002,52 (3):173-186.
[118]Wang Z L, Dafalias Y F, Shen C K. Bounding surface hypoplasticy model for sand[J]. Engng Mech. ASCE,1990,116 (5):983-1001.
[119]钟辉虹,黄茂松,吴世明,等.循环荷载作用下软黏土变形特性研究[J].岩土工程学报.2002,24(5)：629-632.
[120]Sharp R W, Booker J R. Shakedown of pavements under moving surface loads[J]. Journal of Transportation Engineering,1984,110 (1):1-14.
[121]王飞,架茂田.海洋平台地基的极限分析与安定性分析[J].岩石力学与工程学报.2004,23(5)：797-803.
[122]Haldar A K, Reddy D V, Arockiasamy M. Foundation shakedown of offshore platforms[J]. Comput Geomech,1990, (10):231-245.
[123]Pycko S, Mroz Z. Alternative approach to shakedown as a solution of min-max problem[J]. Acta Mech.1992,93:205-222.
[124]Yu H S, Hossain M Z. Lower bound shakedown analysis of layered pavements discontinuous stress fields[J]. Computer Methods in Applied Mechanics and Engineering,1998, (167):209-222.
[125]Lekarp F, Richardson I R, Dawson R R. Influences on permanent deformation behavior of unbound granular materials[J]. Transportation Research Record,1996, (1547):68-75.
[126]Suiker A S J, Borst R. A numerical model for the cyclic deterioration of railway tracks[J]. International Journal for Numerical Methods In Engineering,2003,57: 441-470.
[127]Ge Y N. Cyclic constitutive modeling of granular materials[R]. The University of Colorado, Boulder,2003.
[128]George H M. Behavior of granular materials under cyclic and repeated loading[D]. The University of Alaska Fairbanks,2003.
[129]Werkmeister S, Dawson A R, Wellner F. Pavement design model for unbound granular materials[J]. Journal of Transportation Engineering,2004,130 (5):665-674.
[130]廖化荣,汤连生,刘增贤,等.循环荷载下路基红黏土临界应力水平分析[J].岩土力学.2009,30(3)：587-594.
[131]沈珠江.复杂荷载下砂土液化变形的结构性模型[J].土动力学理论与实践—第五届全国土动力学学术会议论文集,大连：大连理工大学出版社,1998：1-10.
[132]谢定义,张建民.周期荷载下饱和砂土瞬态孔隙水压力的变化机理与计算模型[J].土木工程学报.1990,23(2)：51-60.
[133]姚仰平,谢定义.土的动力本构关系的新探讨[J].西安建筑科技大学学报.1997,29(2)：159-163.
[134]邱长林,张敬.反复荷载作用下饱和砂土的一种普遍弹塑性模型[J].水利学报.1998,(12)：42-46.
[135]孔亮.复杂应力状态下土体弹塑性本构模型研究[D].重庆：后勤工程学院,2002.
[136]王其昌.高速铁路土木工程[M].成都：西南交通大学出版社,1999.
[137]刘学毅,王平.车辆-轨道-路基系统动力学[M].成都：西南交通大学出版社, 2010.
[138]铁道科学研究院.遂渝线无砟轨道试验段综合试验—路基基床动力特性测试[R].北京：中国铁道科学研究院,2007.
[139]Tatsuya Ishikawa, Etsuo Sekine, Seiichi Miura. Cyclic deformation of granular material subjected to moving-wheel loads[J]. Canadian Geotechnical Journal,2011 (48):691-703.
[140]Al Shaer A, et al. Experimental settlement and dynamic behavior of a portion of ballasted railway track under high speed trains[J]. Journal of Sound and Vibration, 2008,316 (5):211-233.
[141]蒋关鲁,孔祥辉,孟利吉,等.无砟轨道路基基床的动态特性[J].西南交通大学学报.2010,45(6)：855-862.
[142]陈云敏,边学成,蒋红光,等.一种高速铁路无砟轨道路基动力学模型试验系统：中国,ZL 201020666503.X[P].2011.
[143]王智猛.红层泥岩及其改良土填筑高速铁路路基适应性及工程技术研究[D].成都：西南交通大学,2008.
[144]冯立臣.土质路基无碴轨道基床动态特性的模型试验研究[D].成都：西南交通大学,2007.
[145]陶宏亮.高速铁路板式无碴轨道路基的动力响应及参数影响分析[D].长春：吉林大学,2009.
[146]Jiang G L, Tatsuoka F, Flora A, et al. Inherent and stress-state-induced anisotropy in very small strain stiffness of a sandy gravel[J]. Geotechnique,1997,47(3):509-521.
[147]何昌荣.动模量和阻尼的动三轴试验研究[J].岩土工程学报.1997,19(2)：39-48.
[148]蔡辉腾,李英民,欧秉松.福州地区典型土动剪切模量与阻尼比的试验研究[J].岩土力学.2010,31(2)：361-365.
[149]Larew H G, Lenards G A. A repeated load strength criterion[C]. Proceeding of Highway Research Board.1962,41:529-556.
[150]Mitchell R J, King R D. Cyclic loading of an Ottawa area Champian sea clay[J]. Canadian Geotechnical Journal.1976,14:52-63.
[151]Raymond G P, Gaskin P N, Addo-Abedi FY. Repeated compressive loading of Leda clay [J] Canadian Geotechnical Journal,1979,114 (1):1-10.
[152]Werkmeister S, Dawson A R, Wellner F. Permanent deformation behavior of granular materials and the shakedown concept[C]. Proceedings of 80th Annual Meeting, Transportation Research Board, Washington D C,2001.
[153]赵成刚.热动力学的稳态与非饱和土的临界状态[J].岩土工程学报.2012,34(4)：730-733.
[154]孔祥辉,蒋关鲁.循环荷载下红层泥岩土累积变形特性[J].长江科学院院报.2012,29(12)：68-72.
[155]堀井克己,舘山勝.砂質土の累稹变形特性に関する実驗式[C].土木学会第55回年次学衍講演会.平成12年.
[156]孟利吉.无砟轨道路基结构动力特性与影响因素的研究[D].成都：西南交通大学,2011.
[157]李永强,景立平,梁海安,等.汶川地震中土石坝地震灾变过程三维再现[J].水力发电学报.2011,30(6)：98-103.
[158]石亦平,周玉蓉.ABAQUS有限元分析实例详解[M].北京：机械工业出版社,2006.
[159]周镇勇.武广客运专线路基动力响应特性试验及数值模拟分析[D].长沙：中南大学,2010.
[160]肖军华.有砟轨道路基动力响应参数敏感性判别[J].铁道标准设计.2010,(7)：1-4.
[161]方开泰,马长兴.正交与均匀试验设计[M].北京：科学出版社,2001.
[2]江成,范佳,王继军.高速铁路无碴轨道设计关键技术[J].中国铁道科学.2004,25(2)：42-47.
[3]S.铁木辛柯.工程中的振动问题[M].北京：人民铁道出版社,1979.
[4]Grassie R W, Gregory D, Harrison and Johnson K L. The dynamic response of railway track to high frequency vertical excitation[J]. Mechanical Engineering Science,1982, 24 (2):77-90.
[5]孙璐,邓学钧.匀速运动的线源荷载激励下无限长梁动力分析[J].应用数学和力学.1998,19(4)：341-347.
[6]Kenney J T. Steady-state vibrations of beam on elastic foundation for moving load[J]. Journal of Appl. Mech.1954:359-364.
[7]Achenbach J D, Sun C T. Moving load on a flexibly supported Timoshenko beam [J]. Solids Structures.1965, Vol.1:355-370.
[8]Kerr A D. The continuously supported rail subjected to an axial force and a moving load[J]. Mech. Sci.1972:71-78.
[9]Fryba L. Vibration of Solids and Structures under Moving Loads[M]. Noordhoff International Publishing, Groningen, The Netherlands,1972.
[10]练松良.轨道结构刚度的理论计算[J].中国铁道科学.2004,25(1)：67-71.
[11]翟婉明,林建辉,王开云.铁路道床振动的理论模拟与试验研究[J].振动工程学报.2003,16(4)：404-408.
[12]蔡成标.无碴轨道动力学理论及应用[J].西南交通大学学报.2007,42(3)：255-261.
[13]张鸿儒,阎贵平,夏禾,等.弹性地基梁单元的等效结点荷载[J].北方交通大学学报.1996,20(5)：522-526.
[14]Eason G. The stresses produced in a semi-infinite solid by a moving Surface force[J]. Eng. Sci.1965, (2):581-609.
[15]Jones D V, Petyt M. Ground vibration in the vicinity of a rectangular load on a half-space[J]. Journal of Sound and Vibration.1993,166 (1):141-159.
[16]Jones D V, Petyt M. Ground vibration in the vicinity of a strip load A two-dimensional half-space model [J]. Journal of Sound and Vibration.1991,147 (1):155-166.
[17]Jones D V, Petyt M. Ground vibration in the vicinity of a strip Load:An elastic layer on a rigid foundation [J]. Journal of Sound and Vibration.1992,152 (3):501-515.
[18]Jones D V, Petyt M. Ground vibration in the vicinity of a strip load:an elastic layer on an elastic half-space [J]. Journal of Sound and Vibration.1993,161 (1):1-18.
[19]Jones D V, Petyt M. Ground vibration in the vicinity of a strip load:a two-dimensional half-space model[J]. Journal of Sound and Vibration.1991,147 (1):155-166.
[20]Grundmann H M, Lieb E. The response of a layered half-spaceto traffic loads moving along its surface [J]. Archive Appl. Mech.1999,69:55-67.
[21]杨英豪,王杰贤.列车运行时振波在土中的传递[J].西安建筑科技大学学报.1995,27(3)：329-334.
[22]蒋建群,周华飞,张土乔.弹性半空间体在移动集中荷载作用下的稳态响应[J].岩土工程学报.2004,26(4)：440-444.
[23]蒋建群,周华飞,张土乔.移动荷载下粘弹性地基上无限大板的稳态响应[J].中国公路学报.2006,19(1)：6-11.
[24]蒋建群,周华飞,张土乔.移动荷载下Kelvin地基上无限大板的稳态响应[J].浙江大学学报(工学版).2005,39(1)：27-32.
[25]张昀青.列车荷载作用下周围物体的动力响应解[J].铁道学报.2003,25 (4)：85-88.
[26]王常晶.列车移动荷载作用下地基的动应力及饱和软粘土特性研究[D].杭州：浙江大学,2006.
[27]苏谦.高速铁路路基空间时变耦合系统动力分析模型及其应用研究[D].成都：西南交通大学,2001.
[28]Lefeuve-Mesgouez G, Peplow A T, Le Houedec D. Surface vibration due to a sequence of high speed moving harmonic rectangular loads[J]. Soil Dynamics and Earthquake Engineering.2002,22 (6):459-473.
[29]谢卫平,王国波,于艳丽.移动荷载作用下基于薄层单元法的土动力分析[J].华中科技大学学报(城市科学版),2004,(2)：8-11.
[30]王文奇,刘保县,王永强.高速铁路路基动应力沿深度的衰减规律[J].西华大学学报(自然科学版),2008,27(5)：98-100.
[31]韩自力,张千里.既有线提速路基动应力分析[J].中国铁道科学,2005,26(5)：1-5.
[32]Hanazato, Toshikazu, Ugai, Keizo, ect. Three-dimensional analysis of traffic-induced ground vibrations [J]. Journal of Geotechnical Engineering.1991,117(8):1133-1151.
[33]李军世,李克钏.高速铁路路基动力反应的有限元分析[J].铁道学报,1995,17(1)：66-75.
[34]边学成.高速列车运动荷载作用下地基和隧道的动力响应分析[D].杭州：浙江大 学,2005.
[35]张远荣.高速铁路路基面竖向动应力的模拟计算[J].铁道建筑,2000(8)：21-23.
[36]梁波,蔡英.不平顺条件下高速铁路路基的动力分析[J].铁道学报.1999,21(1)：84-88.
[37]Hall Lars. Simulations and analyses of train-induced ground vibrations in finite element models[J]. Soil Dynamics and Earthquake Engineering.2003,23 (5): 403-413.
[38]宗军良,刘涛,等.既有线提速路基动力响应特性研究[J].中国铁道科学.2007,28(4)：7-11.
[39]邱延峻,张晓靖,魏永幸.列车速度对无砟轨道路基动力特性的影响[J].交通运输工程学报.2007,7(2)：1-5.
[40]聂志红,阮波,李亮.铁路道床路基动力响应的参数影响[J].交通运输工程学报.2004,4(1)：34-37.
[41]唐益群,栾长青,张曦,等.地铁振动荷载作用下隧道土体变形数值模拟[J].地下空间与工程学报.2008,4(1)：105-110.
[42]董亮,赵成刚,蔡德钩,等.高速铁路无砟轨道路基动力特性数值模拟和试验研究[J].土木工程学报.2008,41(10)：81-86.
[43]陈建国,肖军华,李前进,等.提速列车荷载作用下铁路路基动力特性的研究[J].岩土力学.2009,30(7)：1944-1950.
[44]聂志红.高速铁路轨道路基竖向动力响应研究[D].长沙：中南大学,2005.
[45]马学宁.车-路耦合条件下高速铁路路基及桥路过渡段结构系统动力分析[D].兰州：兰州交通大学,2009.
[46]陈震.高速铁路路基动力响应研究[D].武汉：中科院武汉岩土所,2006.
[47]Okumura Kuno K. Statistical analysis of field data of railway noise and vibration collected in an urban area[J]. Applied Acoustics.1991,33 (4):263-280.
[48]Fujikake T. A prediction method for the propagation of ground vibration from railway trains[J]. Journal of Sound and Vibration.1986,111 (2):357-360.
[49]Dawn T M., Stanworth C G. Ground vibrations from passing trains[J]. Journal of Sound and Vibration.1979, (8):355-362.
[50]Madshus C, Kaynia A M. High-speed railway lines on soft ground:dynamic behaviour at critical train speed[J]. Journal of Sound and Vibration.2000,231 (3):689-701、
[51]Norwegian Geotechnical Institute. NGI Report No515136-1 (October):Vibration criteria for road and rail traffic Vibbase-A database for measured vibrations from road and rail traffic.1995.
[52]杨灿文,龚亚丽.列车通过时路基的动应力和振动[J].土木工程学.1963,9(2)：49-57.
[53]蔡英,等.大秦重载铁路路基的动力响应及分析重载铁路线路结构与养护[M].北京：中国铁道出版社,1992.
[54]周神根.高速铁路路基基床设计[J].路基工程,1997,72(3)：1-5.
[55]王炳龙,余绍锋,周顺华,等.提速状态下路基动应力测试分析[J].铁道学报.2002,22(增)：79-81.
[56]赵洪雁.大秦线万吨列车对轨道的动态影响分析及对策建议[J].中国铁路.2004,9：44-47.
[57]王智猛,蒋关鲁,魏永幸,等.达成线红层泥岩路基循环加载试验研究[J].岩土工程学报.2008,30(12)：1888-1893.
[58]王智猛,蒋关鲁,等.遂渝线无砟轨道道岔区基床动力测试研究[J].铁道建筑.2008,(10)：84-87.
[59]宫全美,罗喆,袁建议.提速铁路基床长期累积沉降及等效循环荷载试验研究[J].铁道学报.2009,31(2)：88-93.
[60]冯立臣,蒋关鲁,王智猛.客运专线土质路基无砟轨道基床动态特性的模型试验研究[J].铁道建筑.2008,(8)：78-81.
[61]苏谦,蔡英.高速铁路级配碎石基床表层不同厚度动态大模型试验研究[J].铁道标准设计.2001,21(8)：2-4.
[62]曹新文,蔡英,苏谦.土工格室和土工网改善基床动态性能模型试验[J].西南交通大学学报.2001,36(4)：350-354.
[63]詹永祥,蒋关鲁.无砟轨道路基基床动力特性的研究[J].岩土力学.2010,31(2)：392-396.
[64]汤康民,蒋忠信.膨胀性红土铁路路基基床动力反应分析[J].西南交通大学学报.1994,29(1)：71-77.
[65]铁道建造物设计标准解说[土构造](案).平成3年(1991年)3月.
[66]平野雅之.按新轨道破坏理论估算轨道下沉量[J].铁道线路(日).1978,(8).
[67]蔡英,黄时寿.重载铁路的线路动力学测试及分析[J].西南交通大学学报.1993,91(3)：92-98.
[68]铁道部科学技术情报研究所译.德国铁路工程技术规范第五册,1995.
[69]汤康民.红粘土动力性质的研究[J].西南交通大学学报.1993,28(4)：12-16.
[70]梁波,孙遇祺.加筋粉煤灰的静动强度指标研究[J].实验力学.1998,19(1)56-59.
[71]关根悦夫著,孙明漳译.列车荷载引起的基床强度的变化[J].铁道线路.1983, 31 (2)：28-32.
[72]伊能忠敏,家田仁,等著,范培钟译.关于铁道道床的动强度问题-荷载频率对基床强度的影响[J].铁路线路.1982,30(8)：5-11.
[73]Heath D L. Design of conventional rail track foundation [J]. Proc. of the Institution of Civil Engineers,1972,51 (3):49-57.
[74]Lashine D L. The displacements in an elastic half-space due to a moving concentrated normal loads[R]. NASA, TRR-238,1996.
[75]孔祥辉,蒋关鲁,王智猛.循环荷载下红层泥岩土的动态特性[J].水文地质工程地质.2012,39(4)：75-79.
[76]蒋关鲁,房立凤,王智猛等.红层泥岩路基填料动强度和累积变形试验研究[J].岩土工程学报.2010,32(1)：124-129.
[77]蔡英,曹新文.重复加载下路基填土的临界动应力和永久变形初探[J].西南交通大学学报.1996,31(1)：1-5.
[78]刘晓红,杨果林,方薇.红黏土临界动应力与高铁无碴轨道路堑基床换填厚度[J].岩土工程学报.2011,33(3)：348-353.
[79]钟辉虹,汤康民,黄茂松.铁路粘土路基动力特性试验研究[J].西南交通大学学报.2002,37(5)：488-490.
[80]Seed H B, Chan C K, Monismith C L. Effect of repeated load on the strength and deformation of compacted clay [J]. Highway Research Record,1955,34:541-558.
[81]Barksdale R D. Laboratory evaluation of rutting in base course materials [C]. In Proceedings of the Third International Conference on Structural Design of Asphalt Pavements, London,1972:161-174.
[82]Hyodo M, Yasuhara K. Hirao K.Prediction of clay behavior in undrained and partially drained cyclic triaxial tests[J]. Soils and Foundations.1992,32(4):117-127.
[83]Monismith C L, Ogawa N, Freeme C R. Permanent deformation characteristics of subgrade soils due to repeated loading[J]. Transportation Research Record.1975, 537:1-17.
[84]Brown, Lashine A K F, Hyde A F L. Repeated load triaxial testing of silty clay [J]. Geotechnique,1975,2:95-114.
[85]Brown S F, Hyde A F L. Significance of cyclic confining stress in repeated load triaxial testing of granular materials [J]. Transportation Research Record,1985,537:49-58.
[86]曹新文.成都粘土基床动态特性的试验研究研究报告[R].成都铁路局基建处,1998,12.
[87]闫澎旺.往复荷载作用下重塑软粘土的变形特性[[J].岩土工程学报.1991,13(1)： 48-53.
[88]钟辉虹.粘土动力特性本构模型预测[D].成都：西南交通大学硕士学位论文,1996.
[89]蒋军,陈龙珠.长期循环荷载作用下粘土的一维沉降[J].岩土工程学报.2001,23(3)：366-369.
[90]李献民.高速铁路加筋过渡段静动力特性数值分析及试验研究[D].长沙：中南大学,2004.
[91]Li D Q, Selig E T. Cumulative plastic deformation for fine-grained subgrade soils[J]. Journal of Geotechnical Engineering,1996,122 (12):1006-1013.
[92]Chai J C, Miura N. Traffic-load-induced permanent deformation of road on soft subsoil[J]. Journal of Geotechnical and Geoenvironmental Engineering,2002,128 (11):907-916.
[93]Parr G B. Some aspects of the behaviour of London clay under repeated loading[D]. UK:University of Nottingham,1972.
[94]Li. Wheel-track dynamic interaction track substructure perspective [J]. Vehicle System Supplement,1995,24:183-196.
[95]Hargis, Louis L. A study of strain characteristics in a limestone gravel subjected to repetitive Ioad[J]. Texas ASM University, College station,1963.
[96]姚兆明,黄茂松,张宏博.长期循环荷载下粉细砂的累积变形特性[J].同济大学学报(自然科学版).2011,39(2)：204-208.
[97]黄茂松,李进军,李兴照.饱和软粘土的不排水循环累积变形特性[J].岩土工程学报.2006,28(7)：891-895.
[98]黄茂松,姚兆明.循环荷载下饱和软黏土的累积变形显式模型[J].岩土工程学报.2011,33(3)：325-331.
[99]李进军.交通荷载作用下饱和软粘土长期沉降分析[D].上海：同济大学,2005.
[100]边学成,蒋红光,申文明,等.基于模型试验的高铁路基动力累积变形研究[J].土木工程学报.2011,44(6)：112-119.
[101]陈颖平,黄博,陈云敏.循环荷载作用下软勃土不排水累积变形特性[J].岩土工程学报.2008,30(5)：764-768.
[102]白冰,周健.周期荷载作用下粘性土变形及强度特性述评[J].岩土力学.1999,20(3)：84-90.
[103]Mroz Z. On the description of anisotropic work hardening[J]. Journal of the Mechanics and Physics of Solids.1967,15 (3):163-175.
[104]Pro vest J H. Mathematical modeling of monotonic and cyclic undrained clay behaviour[J]. International Journal for Numerical and Analytical Methods in Geomechanics.1977 (1):195-216.
[105]Pro vest J H. Anisotropic undrained stress-strain behavior of clay [J]. Journal of the Geotechnical Engineering Division,, ASCE,1978,104 (8):1075-1090.
[106]Provest J H. A simple plastic theory for frictional cohesionless soils[J]. Soil Dynamics and Earthquake Engineering.1985,4 (1).
[107]Mroz Z., Norris V A, Zienkiewicz O C. An anisotropic critical state model for soils subjected to cyclic loading[J]. Geotechnique.1981,31 (4).
[108]Norris V A. Numerical modelling of response to cyclic loading using stress-reversal surface[C]. Int Symp on Numerical Models in Geomech, Zurich,1982.
[109]王建华,要明伦.软粘土不排水循环特性的弹塑性模拟[J].岩土工程学报.1996,18(3)：11-18.
[110]徐干成,谢定义,郑颖人.饱和砂土循环动应力应变特性的弹塑性模拟研究[J].岩土工程学报.1995,17(2)：1-12.
[111]Mroz Z, Norris V A, Zienkiewicz O C. Application of an anisotropic hardening model in the analysis of elasto-plastic deformation of soils. Geotechnique,1979, 29(1):1-34.
[112]Dafalias Y F, Popov E P. A model of nonlinearly hardening materials for complex loading [J]. Acta Mechanica,1975,21:173-192.
[113]Krieg R D. A practical two-surface plasticity theory[J]. Appl Mech, ASME,1975, 42:641-646.
[114]Dafalias Y F. Bounding surface plasticity (iv):mathematical formulation and hypoplasticity[J]. Engng Mech, ASCE,1986,112 (9):966-987.
[115]Dafalias Y F, Hernnann T. Bounding surface plasticity (v):application to isotropic cohesive soils[J]. Engng Mech, ASCE,1986,112 (12):1263-1291.
[116]Li X S, Dafalias Y F, Wang Z L. State dependent dilatancy in critical state constitutive modeling of sand[J]. Canadian Geotechnical Journal,1999,36(4):559-611.
[117]Li X S. A sand model with state-dependent dilatancy[J]. Geotechnique,2002,52 (3):173-186.
[118]Wang Z L, Dafalias Y F, Shen C K. Bounding surface hypoplasticy model for sand[J]. Engng Mech. ASCE,1990,116 (5):983-1001.
[119]钟辉虹,黄茂松,吴世明,等.循环荷载作用下软黏土变形特性研究[J].岩土工程学报.2002,24(5)：629-632.
[120]Sharp R W, Booker J R. Shakedown of pavements under moving surface loads[J]. Journal of Transportation Engineering,1984,110 (1):1-14.
[121]王飞,架茂田.海洋平台地基的极限分析与安定性分析[J].岩石力学与工程学报.2004,23(5)：797-803.
[122]Haldar A K, Reddy D V, Arockiasamy M. Foundation shakedown of offshore platforms[J]. Comput Geomech,1990, (10):231-245.
[123]Pycko S, Mroz Z. Alternative approach to shakedown as a solution of min-max problem[J]. Acta Mech.1992,93:205-222.
[124]Yu H S, Hossain M Z. Lower bound shakedown analysis of layered pavements discontinuous stress fields[J]. Computer Methods in Applied Mechanics and Engineering,1998, (167):209-222.
[125]Lekarp F, Richardson I R, Dawson R R. Influences on permanent deformation behavior of unbound granular materials[J]. Transportation Research Record,1996, (1547):68-75.
[126]Suiker A S J, Borst R. A numerical model for the cyclic deterioration of railway tracks[J]. International Journal for Numerical Methods In Engineering,2003,57: 441-470.
[127]Ge Y N. Cyclic constitutive modeling of granular materials[R]. The University of Colorado, Boulder,2003.
[128]George H M. Behavior of granular materials under cyclic and repeated loading[D]. The University of Alaska Fairbanks,2003.
[129]Werkmeister S, Dawson A R, Wellner F. Pavement design model for unbound granular materials[J]. Journal of Transportation Engineering,2004,130 (5):665-674.
[130]廖化荣,汤连生,刘增贤,等.循环荷载下路基红黏土临界应力水平分析[J].岩土力学.2009,30(3)：587-594.
[131]沈珠江.复杂荷载下砂土液化变形的结构性模型[J].土动力学理论与实践—第五届全国土动力学学术会议论文集,大连：大连理工大学出版社,1998：1-10.
[132]谢定义,张建民.周期荷载下饱和砂土瞬态孔隙水压力的变化机理与计算模型[J].土木工程学报.1990,23(2)：51-60.
[133]姚仰平,谢定义.土的动力本构关系的新探讨[J].西安建筑科技大学学报.1997,29(2)：159-163.
[134]邱长林,张敬.反复荷载作用下饱和砂土的一种普遍弹塑性模型[J].水利学报.1998,(12)：42-46.
[135]孔亮.复杂应力状态下土体弹塑性本构模型研究[D].重庆：后勤工程学院,2002.
[136]王其昌.高速铁路土木工程[M].成都：西南交通大学出版社,1999.
[137]刘学毅,王平.车辆-轨道-路基系统动力学[M].成都：西南交通大学出版社, 2010.
[138]铁道科学研究院.遂渝线无砟轨道试验段综合试验—路基基床动力特性测试[R].北京：中国铁道科学研究院,2007.
[139]Tatsuya Ishikawa, Etsuo Sekine, Seiichi Miura. Cyclic deformation of granular material subjected to moving-wheel loads[J]. Canadian Geotechnical Journal,2011 (48):691-703.
[140]Al Shaer A, et al. Experimental settlement and dynamic behavior of a portion of ballasted railway track under high speed trains[J]. Journal of Sound and Vibration, 2008,316 (5):211-233.
[141]蒋关鲁,孔祥辉,孟利吉,等.无砟轨道路基基床的动态特性[J].西南交通大学学报.2010,45(6)：855-862.
[142]陈云敏,边学成,蒋红光,等.一种高速铁路无砟轨道路基动力学模型试验系统：中国,ZL 201020666503.X[P].2011.
[143]王智猛.红层泥岩及其改良土填筑高速铁路路基适应性及工程技术研究[D].成都：西南交通大学,2008.
[144]冯立臣.土质路基无碴轨道基床动态特性的模型试验研究[D].成都：西南交通大学,2007.
[145]陶宏亮.高速铁路板式无碴轨道路基的动力响应及参数影响分析[D].长春：吉林大学,2009.
[146]Jiang G L, Tatsuoka F, Flora A, et al. Inherent and stress-state-induced anisotropy in very small strain stiffness of a sandy gravel[J]. Geotechnique,1997,47(3):509-521.
[147]何昌荣.动模量和阻尼的动三轴试验研究[J].岩土工程学报.1997,19(2)：39-48.
[148]蔡辉腾,李英民,欧秉松.福州地区典型土动剪切模量与阻尼比的试验研究[J].岩土力学.2010,31(2)：361-365.
[149]Larew H G, Lenards G A. A repeated load strength criterion[C]. Proceeding of Highway Research Board.1962,41:529-556.
[150]Mitchell R J, King R D. Cyclic loading of an Ottawa area Champian sea clay[J]. Canadian Geotechnical Journal.1976,14:52-63.
[151]Raymond G P, Gaskin P N, Addo-Abedi FY. Repeated compressive loading of Leda clay [J] Canadian Geotechnical Journal,1979,114 (1):1-10.
[152]Werkmeister S, Dawson A R, Wellner F. Permanent deformation behavior of granular materials and the shakedown concept[C]. Proceedings of 80th Annual Meeting, Transportation Research Board, Washington D C,2001.
[153]赵成刚.热动力学的稳态与非饱和土的临界状态[J].岩土工程学报.2012,34(4)：730-733.
[154]孔祥辉,蒋关鲁.循环荷载下红层泥岩土累积变形特性[J].长江科学院院报.2012,29(12)：68-72.
[155]堀井克己,舘山勝.砂質土の累稹变形特性に関する実驗式[C].土木学会第55回年次学衍講演会.平成12年.
[156]孟利吉.无砟轨道路基结构动力特性与影响因素的研究[D].成都：西南交通大学,2011.
[157]李永强,景立平,梁海安,等.汶川地震中土石坝地震灾变过程三维再现[J].水力发电学报.2011,30(6)：98-103.
[158]石亦平,周玉蓉.ABAQUS有限元分析实例详解[M].北京：机械工业出版社,2006.
[159]周镇勇.武广客运专线路基动力响应特性试验及数值模拟分析[D].长沙：中南大学,2010.
[160]肖军华.有砟轨道路基动力响应参数敏感性判别[J].铁道标准设计.2010,(7)：1-4.
[161]方开泰,马长兴.正交与均匀试验设计[M].北京：科学出版社,2001.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |