| [1] | 
																	 
														     			GAZETAS G,DOBRY R,TASSOULAS J L. Vertical response of arbitrarily shaped embedded foundations[J]. Journal of Geotechnical Engineering,1985,111(6):750-771.
														     																	     
																	 | 
																
 
																															
																	| [2] | 
																	 
														     			GAZETAS G,TASSOULAS J L. Horizontal stiffness of arbitrarily shaped embedded foundations[J]. Journal of Geotechnical Engineering,1987,113(5):440-457.
														     																	     
																	 | 
																
 
																															
																	| [3] | 
																	 
														     			GUHA I,RANDOLPH M F,WHITE D J. Evaluation of elastic stiffness parameters for pipeline-soil interaction[J]. Journal of Geotechnical and Geoenvironmental Engineering,2016,142(6):04016009.
														     																	     
																	 | 
																
 
																															
																	| [4] | 
																	 
														     			SHARMA J R. Development of a model for estimation of buried large diameter thin-walled steel pipe deflection due to external loads[Ph. D. Thesis][D]. Arlington:University of Texas at Arlington,2013.
														     																	     
																	 | 
																
 
																															
																	| [5] | 
																	 
														     			WHIDDEN W R. Buried flexible steel pipe:design and structural analysis[M]. Virginia,USA:ASCE,2009:73-86.
														     																	     
																	 | 
																
 
																															
																	| [6] | 
																	 
														     			BIOT M A. Bending of an infinite beam on an elastic foundation[J]. Journal of Applied Mechanics,ASME,1937,59:A1-A7.
														     																	     
																	 | 
																
 
																															
																	| [7] | 
																	 
														     			VESIC A B. Bending of beams resting on isotropic elastic solid[J]. Journal of the Engineering Mechanics Division,ASCE,1961,87(2):35-53.
														     																	     
																	 | 
																
 
																															
																	| [8] | 
																	 
														     			TERZAGHI K. Evaluation of coefficients of subgrade reaction[J]. Geotechnique,1955,5(4):297-326.
														     																	     
																	 | 
																
 
																															
																	| [9] | 
																	 
														     			DALOGLU A T,VALLABHAN C V G. Values of k for slab on Winkler foundation[J]. Journal of Geotechnical and Geoenvironmental Engineering,2000,126(5):463-471.
														     																	     
																	 | 
																
 
																															
																	| [10] | 
																	 
														     			俞 剑,张陈蓉,黄茂松. 被动状态下地埋管线的地基模量[J]. 岩石力学与工程学报,2012,31(1):123-132.(YU Jian,ZHANG Chenrong,HUANG Maosong. Subgrade modulus of underground pipelines subjected to soil movements[J]. Chinese Journal of Rock Mechanics and Engineering,2012,31(1):123-132.(in Chinese))
														     																	     
																	 | 
																
 
																															
																	| [11] | 
																	 
														     			YU J,ZHANG C R,HUANG M S. Soil-pipe interaction due to tunnelling:Assessment of Winkler modulus for underground pipelines[J]. Computers and Geotechnics,2013,50(5):17-28.
														     																	     
																	 | 
																
 
																															
																	| [12] | 
																	 
														     			王 雨,陈文化. 地层成层性对基床系数的影响分析[J]. 岩石力学与工程学报,2017,36(增2):4 304-4 312.(WANG Yu,CHEN Wenhua. Influence of soil stratification on coefficient of subgrade reaction[J]. Chinese Journal of Rock Mechanics and Engineering,2017,36(Supp.2):4 304-4 312.(in Chinese))
														     																	     
																	 | 
																
 
																															
																	| [13] | 
																	 
														     			王 雨,陈文化. 地埋梁与横观各向同性层状地基相互作用的广义VESIC解答[J]. 岩土工程学报,2018,40(12):2 241-2 248.(WANG Yu,CHEN Wenhua. Generalized VESIC solution for interaction of buried beam and transversely isotropic layered soil[J]. Chinese Journal of Geotechnical Engineering,2018,40(12):2 241-2 248.(in Chinese))
														     																	     
																	 | 
																
 
																															
																	| [14] | 
																	 
														     			SHELDON T,SEZEN H,MOORE I D. Beam-on-springs modeling of jointed pipe culverts[J]. Journal of Performance of Constructed Facilities,2016,30(2):1-9.
														     																	     
																	 | 
																
 
																															
																	| [15] | 
																	 
														     			TIAN Y H,CASSIDY M J,GAUDIN C. Advancing pipe-soil interaction models in calcareous sand[J]. Applied Ocean Research,2010,32(3):284-297.
														     																	     
																	 | 
																
 
																															
																	| [16] | 
																	 
														     			HOLDER M S,CASSIDY M J. A plasticity model for predicting the vertical and lateral behaviour of pipelines in clay soils[J]. Geotechnique,2010,60(4):247-263.
														     																	     
																	 | 
																
 
																															
																	| [17] | 
																	 
														     			HMADI K E,O?ROURKE M. Soil springs for buried pipeline axial motion[J]. Journal of Geotechnical Engineering,1988,114(11): 1 335-1 339.
														     																	     
																	 | 
																
 
																															
																	| [18] | 
																	 
														     			MATSUBARA K,HOSHIYA M. Soil spring constants of buried pipelines for seismic design[J]. Journal of Engineering Mechanics,2000,126(1):76-83.
														     																	     
																	 | 
																
 
																															
																	| [19] | 
																	 
														     			钟 阳,殷建华. 弹性层状体的求解方法[M]. 北京:科学出版社,2007:142-150.(ZHONG Yang,YIN Jianhua. Solving method of elastic layered body[M]. Beijing:Science Press,2007:142-150.(in Chinese))
														     																	     
																	 | 
																
 
																															
																	| [20] | 
																	 
														     			吴为义. 盾构隧道周围地下管线的性状研究[博士学位论文][D]. 杭州:浙江大学,2008.(WU Weiyi. Study on mechanical behaviors of buried pipelines induced by shield tunnelling construction[Ph. D. Thesis][D]. Hangzhou:Zhejiang University,2008.(in Chinese))
														     																	     
																	 | 
																
 
																															
																	| [21] | 
																	 
														     			邵 羽. 盾构双隧道施工对临近地埋管线的影响研究[博士学位论文][D]. 南宁:广西大学,2017.(SHAO Yu. Mechanism behaviors of existing buried pipelines due to twin shield tunnelling[Ph. D. Thesis][D]. Nanning:Guangxi University,2017.(in Chinese))
														     																	     
																	 | 
																
 
																															
																	| [22] | 
																	 
														     			WHITE D J,RANDOLPH M F. Seabed characterisation and models for pipeline-soil interaction[J]. International Journal of Offshore and Polar Engineering,2007,17(3):193-204.
														     																	     
																	 | 
																
 
																															
																	| [23] | 
																	 
														     			MYLONAKIS G,GAZETAS G. Settlement and additional internal forces of grouped piles in layered soil[J]. Geotechnique,1998,48(1):55-72.
														     																	     
																	 | 
																
 
																															
																	| [24] | 
																	 
														     			RANDOLPH M F,WROTH C P. Analysis of deformation of vertically loaded piles[J]. Journal of the Geotechnical Engineering Division,1978,104(12):1 465-1 488.
														     																	     
																	 | 
																
 
																															
																	| [25] | 
																	 
														     			方钱宝,马建林,喻 渝,等. 大断面黄土隧道围岩弹性抗力系数、变形模量与压缩模量试验研究[J]. 岩石力学与工程学报,2009,28(增2):3 932-3 937.(FANG Qianbao,MA Jianlin,YU Yu,et al. Experimental research on elastic resistant coefficient,deformation and compressive moduli of surrounding rock in large-section loess tunnel[J]. Chinese Journal of Rock Mechanics and Engineering,2009,28(Supp.2):3 932-3 937.(in Chinese))
														     																	     
																	 | 
																
 
																															
																	| [26] | 
																	 
														     			HALDAR S,BASU D. Analysis of beams on heterogeneous and nonlinear soil[J]. International Journal of Geomechanics,2016,16(4):04016004.
														     																	     
																	 |