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| Displacement function method on thermal stress and thermal deformation problems for layered pavement structure |
| WANG Lujun1,2,ZHU Bin1,2,WEN Kai1,2,YANG Songqing1,2 |
| (1. Institute of Geotechnical Engineering,Zhejiang University,Hangzhou,Zhejiang 310058,China;2. MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering,Zhejiang University,Hangzhou,Zhejiang 310058,China) |
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Abstract Based on the thermo-elasticity and McNamee-Gibson displacement function,a displacement function method,to study the development of thermal stress and thermal deformation in layered pavement structure,is presented. Starting with the governing equations of plane strain problem of thermo-elasticity,a relationship between the generalized strain and stress is established by using the displacement function and Laplace-Fourier transform. Combining with the contact and boundary conditions,strict solutions of the thermal-induced stress and deformation of the layered system are derived. The results show that the proposed method is capable of producing accurate solution to the thermal-induced deformation problems of layered pavement structures. Due to the time effect of heat conduction,the heat loading affects mainly the surface and base layers at the initial stage,and then the influenced region develops gradually towards the inner layers with the time going. The vertical thermal-induced expansion diminishes with the depth and the greatest expansion takes place at the surface layer,leading to the stress concentration and accordingly possible pavement cracking. It is therefore recommended that the bonding conditions between the surface and base layers should be strengthened to ensure the structural integrity of pavement structures.
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[1] 吴赣昌. 层状路面结构温度应力分析[J]. 中国公路学报,1993,6(4):1–8.(WU Ganchang. Thermal stress analysis of layered structure pavement[J]. China Journal of Highway and Transport,1993,6(4):1–8.(in Chinese))
[2] 任瑞波,钟 阳,殷建华. 路面结构在动荷载作用下路表弯沉的求解[J]. 岩土工程学报,2000,22(6):738–740.(REN Ruibo,ZHONG Yang,YIN Jianhua. The solution of road surface deflection in the dynamic case[J]. Chinese Journal of Geotechnical Engineering,2000,22(6):738–740.(in Chinese))
[3] 凌建明,王 伟,邬洪波. 行车荷载作用下湿软路基残余变形的研究[J]. 同济大学学报:自然科学版,2002,30(11):1 315–1 320. (LING Jianming,WANG Wei,WU Hongbo. On residual deformation of saturated clay subgrade under vehicle load[J]. Journal of Tongji University:Natural Science,2002,30(11):1 315–1 320.(in Chinese))
[4] 边学成,陈云敏. 列车移动荷载作用下分层地基响应特性[J]. 岩石力学与工程学报,2007,26(1):182–189.(BIAN Xuecheng,CHEN Yunming. Characteristics of layered ground responses under train moving loads[J]. Chinese Journal of Rock Mechanics and Engineering,2007,26(1):182–189.(in Chinese))
[5] 汤连生,林沛元,吴 科,等. 交通荷载下层状路基动附加应力的弹性计算模型[J]. 岩石力学与工程学报,2009,28(11):2 208–2 214. (TANG Liansheng,LIN Peiyuan,WU Ke,et al. Elastic calculation model for dynamic additional stresses in layered subgrade under traffic load[J]. Chinese Journal of Rock Mechanics and Engineering,2009,28(11):2 208–2 214.(in Chinese))
[6] 卢 正,王长柏,付建军,等. 交通荷载作用下公路路基工作区深度研究[J]. 岩土力学,2013,34(2):316–321.(LU Zheng,WANG Changbai,FU Jianjun,et al. Research on influence depth of road subgrade induced by vehicle loads[J]. Rock and Soil Mechanics,2013,34(2):316–321.(in Chinese))
[7] 蔡袁强,赵 莉,曹志刚,等. 不同频率循环荷载下公路路基粗粒填料长期动力特性试验研究[J]. 岩石力学与工程学报,2017,36(5):1 238–1 246.(CAI Yuanqiang,ZHAO Li,CAO Zhigang,et al. Experimental study of dynamic characteristics of unbound granular materialsunder cyclic loading with different frequencies[J]. Chinese Journal of Rock Mechanics and Engineering,2017,36(5):1 238– 1 246.(in Chinese))
[8] BIOT M A. Thermo elasticity and irreversible thermodynamics[J]. Journal of Applied Physics,1956,27(3):240–253.
[9] SMITH D W,BOOKER J R. Boundary integral analysis of transient thermoelasticity[J]. International Journal for Numerical and Analytical Methods in Geomechanics,1989,13(3):283–302.
[10] 孙立军,秦 健. 沥青路面温度场的预估模型[J]. 同济大学学报:自然科学版,2006,34(4):480–483.(SUN Lijun,QIN Jian. Prediction model on temperature field in asphalt pavement[J]. Journal of Tongji University:Natural Science,2006,34(4):480–483.(in Chinese))
[11] HOU P F,LEUNG A Y T,CHEN C P. Fundamental solution for transversely isotropic thermoelastic materials[J]. International Journal of Solids and Structures,2008,45(2):392–408.
[12] SMALL J C,BOOKER J R. The behavior of layered soil or rock containing a decaying heat source[J]. International Journal for Numerical and Analytical Methods in Geomechanics,1986,10(5):501–519.
[13] ZHONG Y,GENG L T. Thermal stresses of asphalt pavement under dependence of material characteristics on reference temperature[J]. Mechanics of Time-Dependent Materials,2009,13(1):81–91.
[14] 艾智勇,王路君,曾 凯. 稳定温度场下层状路面体系的解析层元解[J]. 同济大学学报:自然科学版,2014,42(11):1 665–1 669.(AI Zhiyong,WANG Lujun,ZENG Kai. Analytical layer-element solution for layered pavement in stable temperature field[J]. Journal of Tongji University:Natural Science,2014,42(11):1 665–1 669.(in Chinese))
[15] WANG L J,AI Z Y. Plane strain and three-dimensional analyses for thermo-mechanical behavior of multilayered transversely isotropic materials[J]. International Journal of Mechanical Sciences,2015,103:199–211.
[16] CARTER J P,BOOKER J R. Finite element analysis of coupled thermoelasticity[J]. Computers and Structures,1989,31(1):73–80.
[17] 钱国平,郭忠印,郑健龙,等. 环境条件下沥青路面热黏弹性温度应力计算[J]. 同济大学学报:自然科学版,2003,31(2):150–155. (QIAN Guoping,GUO Zhongyin,ZHENG Jianlong,et al. Calculation for thermal stresses of asphalt pavement under environmental conditions based on thermalviscoelasticity theory[J]. Journal of Tongji University:Natural Science,2003,31(2):150–155.(in Chinese))
[18] 艾长发,黄大强,高晓伟,等. 高寒地区沥青路面温度行为数值分析[J]. 重庆交通大学学报:自然科学版,2017,36(2):24–31.(AI Changfa,HUANG Daqiang,GAO Xiaowei,et al. Numerical analysis of asphalt pavement structure temperature behavior in cold regions[J]. Journal of Chongqing Jiaotong University:Natural Science,2017,36(2):24–31.(in Chinese))
[19] VERRUIJT A. Displacement functions in the theory of consolidation or in thermoelasticity[J]. Zeitschrift für angewandte Mathematik und Physik ZAMP,1971,22(5):891–898.
[20] SNEDDON IN. The use of integral transform[M]. New York:McGraw-Hill,1972:1–60.
[21] TALBOT A. The accurate numerical inversion of Laplace transforms[J]. Journal of Institute of Mathematics and Its Application,1979,23(1):97–120.
[22] 赵光恒,张子明. 有限深弹性层上基础梁的计算[J]. 河海大学学报:自然科学版,1984,(2):32–45.(ZHAO Guangheng,ZHANG Ziming. Computation of foundation beams on elastic layers of finite depth[J]. Journal of Hohai University:Natural Science,1984,(2):32–45.(in Chinese))
[23] 王复明. 有限深非均质地基的力学计算[C]// 第三届全国结构工程学术会议论文集. 北京:清华大学出版社,1994:1 199–1 203. (WANG Fuming. Mechanical calculation of finite inhomogeneous soil[C]// Proceedings of the Third National Conference of Structure Engineering. Beijing:Tsinghua University Press,1994:1 199–1 203. (in Chinese)) |
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