基于横观各向同性的路面设计

理论及方法的研究

Rsesarch of theory and  methodology of pavement design based on cross-anisotropy

研究生：栗振锋

指导教师：郭忠印教授

二〇〇五年八月

摘要

自1999年起，分别在长安大学胡长顺教授和同济大学郭忠印教授的指导下进行考虑材料横观各向同性特性路面设计理论与方法的研究。对轴对称荷载作用下，层间完全连续的半空间体、多层弹性体系、工程应用等方面进行了探讨。

硕士阶段主要完成了：(1)导出完整的状态转移矩阵的显式表达式；(2)给出了半无限体表面位移Hankel积分变换表达式；(3)分析了材料横观各向同性5个独立的弹性参数对(2)中位移Hankel积分变换表达式的影响(双因素分析)。

在博士论文阶段完成的工作主要有：

(一)理论建立方面

(1)半空间体：完善并提高了硕士阶段的工作内容。又分别导出半空间体一般解的Hankel变换式；半空间体一般解的积分式(类似于布辛尼斯克公式)；得到了垂直集中力和圆形轴对称荷载作用下的表面位移显示表达式。

(2)多层弹性体系：首次给出多层体系的初始值解，解决了多层体系计算中的关键技术问题，建立了基于横观各向同性的多层体系计算理论。

(二)工程应用方面

(1)问题的提出

国内外已有较多的试验验证了路面材料具有明显的横观各向同性特性。美国等研究人员试验结果表明：粘性土的水平模量与垂直模量的比值约为0.9～4，沥青混合料的水平模量与垂直模量比值为0.2～0.5，碎石材料的水平与垂直的模量比值为0.03～0.21。但基于横观各向同性的路面响应模型还未建立起来(Tutumluer，2002)。

运用现行的路面设计理论预测碎石基层底部的拉应力，往往得到较大的数值，而拉应力是不能够靠碎石颗粒问来传递的。因此，需寻求一种新的路面计算理论来比较准确地描述路面的实际受力状况。

(2)路面结构分析程序

现有国际上的基于横观各向同性的路面结构分析程序主要有：澳大利亚的路面设计程序和美国伊利诺伊大学的分析程序等，但大都基于有限元数值法。本文基于(一)中所建立的多层弹性体系理论首次编制了基于解析解的路面结构分析程序ANISOLAYER。

(3)土基表面弯沉盆分析

较多的土基表面弯沉实测数值要比现行理论计算值小，因此有研究人员分析时在土基一定深度内人为地放置一刚性层等，采用上述所建立的理论，结合粘性土试验数据，当土基材料的水平与垂直模量比大于1.0时，土基表面的理论计算弯沉值将变小。

(4)半刚性基层路面结构分析

无论从弯沉的角度，还是基层底部拉应力，路基项部压应变等设计指标来看，随着土基水平模量的变化，对他们的影响都不大。土基横观各向同性的变化与路表弯沉有较好的线性相关性。

(5)含有碎石层的路面结构分析

a：AC+碎石层：考虑碎石材料的横观各向同性特性，可较好地解决现行路面设计理论在预测碎石层底部过大拉应力的问题。总的来讲，从路表弯沉、沥青层底部拉应变、路基顶部压应变来看，碎石材料的这一特性都将使路面的使用寿命降低。建议设计规范考虑碎石基层横观各向同性特性所带来的不安全性。从给出的一个“AC+碎石层"的例子分析来看，主要控制此类路面寿命的设计指标为路基顶部的压应变；

b：AC+碎石层+半刚性层：对于此类路面的结构分析认为，较厚的沥青面层，受碎石的横观各向同性特性影响较少。对于“AC+碎石层+半刚性层"的例子分析来看，主要控制其使用寿命的指标为沥青层底部的拉应变。

c：AC+半刚性层+碎石层：碎石的横观各向同性特性都将使路面的使用寿命下降，其中对于半刚性基层底部拉应力影响较大。AC+半刚性层+碎石层"的例子分析认为，控制路面寿命的指标主要为半刚性基层底部的拉应力。

关键词：轴对称，横观各向同性，多层体系，响应模型，半刚性基层，设计方法，碎石基层，路面设计理论，力学模型

ABSTRACT

Since 1999，The research of pavement’s  design theory and methodology considering the material anisotropy has been  done with the tutor of Prof. HU ChangShun of Chang’an Univ．and Prof. GUO ZhongYin of Tongji  Univ．Discussing the  problem of half-space body，multilayer elastic body and the engineering application．

In my stage  for Master degree：(1)The whole explicit expressions of state-transition matrix were  derived；(2)The  integral transformation expressions of surface displacement for half-space  body were given；(3)Analyzing  the effect of 5 independent anisotropic elastic parameters to the integral  expressions of surface displacement for half-space body．

In my stage  for Doctor degree：

(一)Theory establishing

(1) Half-space  body：The research  work of Master stage is been developed．Also the The integral transformation expressions of general  solutions for half-space body were given，the explicit expressions of surface displacement are given under  the vertically forced force and uniformed round axisymmetrical load．

(2)Multilayer  elastic system：The  initial value solutions of multilayer elastic system are first given，the key technical problem of  calculating the multilayer elastic system is solved．The theory of computation for  multilayer elastic system is established based on the cross-anisotropy．

(二)The engineering application

(1) Statement  of problem

Many  experiment has proved the material cross-anisotropy at home and abroad．The test result of American  researchers showed that：the ratio of horizontal modulus with the vertical modulus is about  0.9-4 for clay soil，that of HMA is about 0.2-0.5，hat of crushed stone is 0.03-0.21．But the response model of pavement design based  on the cross-anisotropy is not established(Tutumluer,2002)．

Using the  current pavement theory to predict the tension stress at the bottom of  granular base，the  solutions are often bigger，but the granular base is not destroyed．So，the new pavement design  theory is needed to express accurately the real stress state of pavement  structure．

(2) The  pavement structural analysis programs

The current  international pavement structural analysis programs based on the cross-anisotropy  mostly have：The  Australian pavement analysis program and the program of Illinois Univ．，but most of them are based  on the FEM．The  paper first give the pavement analysis program ANISOLAYER of analytic  solution based on the cross-anisotropy．

(3) Analyzing  of subgrade surface displacement basin

The most  measured values of subgrade surface displacement are smaller than that of  theory，so some  researchers analyzed the displacement by putting the stiff layer within the  subgrade．Because  of the soil cross-anisotropy，when the ratio of horizontal modulus with the vertical modulus is  greater than 1.0，the  calculating theoretical values is smaller，maybe close to the measured values．

(4) Analyzing  of semi-rigid base pavement structure

From the point  of the displacement，the tension stress at the bottom of the semi-rigid base，or the compressive strain at  the top of subgrade，the cross-anisotropy of soil has less effect on them．

The cross—anisotropy of subgrade has  the better linear relation with the surface displacement of the subgrade．

(5) Analyzing  of pavement structure including the granular base

a：AC+granular base：Considering the  CROSS-anisotropy of granular base，the tension stress at the bottom of the base would be decreased  effectively，from  the point of displacement，the tension strain at the bottom of AC layer and the compressive strain  at the top of subgrade，the cross-anisotropy of crushed stone would decrease the life of  pavement．It is  suggested that the unsafety on account of the crushed stone cross-anisotropy  should be considered in the design specifications．From the given example，the compressive strain at the  top of subgrade would control the life of this type of pavement．

b：AC+crushed stone layer+semi-rigid  layer：The cross-anisotropy  of crushed stone has less effect on the thicker AC layer from the given  example，the  tension strain at the bottom of the AC would control the life of the type  pavement．

c：AC+semi·rigid layer+crushed stone  layer：The cross．anisotropy of crushed stone  would decrease the life of the pavement，it has greater effect on the tension stress at the bottom of the  semi-rigid base．From  the given example，the tension stress at the bottom of the semi—rigid base would control the  life of the type pavement．

Keyword：axisymmetry，cross—anisotropy，layered system，response model，semi-rigid base，design method，gravel base，theory of pavement design，mechanical model