[1] PECK R B. Deep excavations and tunnelling in soft ground[A]// Proceedings of the 7th International Conference on Soil Mechanics and Foundation Engineering[C]. Mexico:Sociedad Mexicana de Mecanica de Suelos, 1969: 225-290.
[2] Attewell P B, Woodman J P. Predicting the dynamics of ground settlement and its derivatives caused by tunnelling in soil[J]. Ground Engineering, 1982, 15(8): 13-20.
[3] O'Reilly M, New B. Settlements Above Tunnels in The United Kingdom - Their Magnitude And Prediction[A]// Tunnels & Tunnelling International[C]. 2015: 56-66.
[4] Sagaseta C. Analysis of undrained soil deformation due to ground loss[J].Geotechnique, 1988, 38(3):301-320.
[5] Verruijt A, Booker J R. Surface settlements due to deformation of a tunnel in an elastic half plane[J].Geotechnique, 1996, 46(4): 753-756.
[6] 周小文, 濮家骝. 砂土中隧洞开挖引起的地面沉降试验研究[J]. 岩 土力学, 2002, 23(5):1074-1079. (Zhou Xiaowen, Pu Jialiu. Centrifuge model test on ground settlement induced by tunneling in sandy soil[J]. Rock and Soil Mechanics, 2002, 23(5):1074-1079. (in Chinese)).
[7] 朱合华, 徐前卫, 廖少明, 等. 土压平衡盾构法施工参数的模型试 验研究[J]. 岩土工程学报, 2006, 25(5):553-557. (Zhu Hehua, Xu Qianwei, Liao Shaoming, et al. Experimental study on working parameters of EPB shield machine[J]. Chinese Journal of Geotechnical Engineering, 2006, 25(5):553-557. (in Chinese))
[8] 丁春林, 朱世友, 周顺华. 地应力释放对盾构隧道围岩稳定性和地 表沉降变形的影响[J]. 岩石力学与工程学报, 2002, 21(11):1633-1638. (Ding Chunlin, Zhu Shiyou, Zhou Shunhua. Influence of in-situ stress release on the stability of surrounding rock masses and ground surface settlement for shield-driven tunnel[J]. Chinese Journal of Rock Mechanics and Engineering, 2002, 21(11):1633-1638. (in Chinese))
[9] Rowe R K, Lee K M. Subsidence owing to tunnelling. II. Evaluation of a prediction technique[J]. Canadian Geotechnical Journal, 1992, 29(6):941-954.
[10] Lumb P. The variability of natural soils[J]. Canadian Geotechnical Journal, 2011, 3(2):74-97.
[11] Vanmarcke E H. Probabilistic modeling of soil profiles[J]. Journal of the Geotechnical Engineering Division, 1977, 103:1227-1246.
[12] Vanmarcke E H. Randomfields:analysis and synthesis[M]. Cambridge:MIT Press, 1983.
[13] Fenton G A, Griffiths D V. Statistics of free surface flow through stochastic earth dam[J]. Journal of Grotechnical Engineering, 1996, 122(6): 427-436.
[14] Griffiths D V, Fenton G A. Three-dimensional seepage through spatially random soil[J]. Journal of Geotechnical and Geoenvironmental Engineering, 1997, 123(2): 153-160.
[15] 李典庆, 祁小辉, 周创兵, 等. 考虑参数空间变异性的无限长边坡可靠度分析[J]. 岩土工程学 报, 2013, 35(10): 1799-1806. (Li Dianqing, Qi Xiaohui, Zhou Chuangbing, et al. Reliability analysis of infinite slope considering parameter space variability[J]. Journal of Geotechnical Engineering, 2013, 35 (10): 1799-1806. (in Chinese))
[16] 蒋水华, 李典庆, 周创兵, 等. 考虑自相关函数影响的边坡可靠度分析[J]. 岩土工程学报, 2014, 36(3): 508-518. (Jiang Shuihua, Li Dianqing, Zhou Chuangbing, et al. Reliability analysis of slopes considering the influence of autocorrelation functions[J]. Journal of Geotechnical Engineering, 2014, 36 (3): 508-518. (in Chinese))
[17] 蒋水华, 李典庆, 周创兵, 等. 考虑参数空间变异性的非饱和土坡可靠度分析[J]. 岩土力学, 2014(9): 2569-2578. (Jiang Shuihua, Li Dianqing, Zhou Chuangbing, et al. Reliability analysis of unsaturated soil slopes considering parameter space variability[J]. Geotechnical Mechanics, 2014(9): 2569-2578. (in Chinese))
[18] 李健斌, 陈健, 罗红星, 等. 基于随机场理论的双线盾构隧道地层变形分析[J]. 岩石力学与工程学报, 2018, 37(7): 1748-1765. ( Li Jianbin, Chen Jian, Luo Hongxing, et al. Analysis of Formation Deformation in Double Line Shield Tunnels Based on Random Field Theory [J]. Journal of Rock Mechanics and Engineering, 2018, 37 (7): 1748-1765. (in Chinese))
[19] 包昊, 周旭辉, 薛亚东. 土体空间变异性对盾构隧道收敛的影响分析[J]. 现代隧道技术, 2020, 57(201): 411-417. (Bao Hao, Zhou Xuhui, Xue Yadong. Analysis of the Influence of Soil Spatial Variability on the Convergence of Shield Tunnels [J]. Modern Tunnel Technology, 2020, 57 (201): 411-417. (in Chinese))
[20] 李萍, 白健忠, Griffiths D V, 等. 黄土边坡可靠度的随机有限元分析[J]. 地球科学与环境学报, 2019, 41(1): 116-126. (Li Ping, Bai Jianzhong, Griffiths D V, et al. Random finite element analysis of reliability of loess slopes [J]. Journal of Earth Science and Environment, 2019, 41(1): 116-126. (in Chinese)).
[21] Chiles J P, Delfiner P.Geostatistics: modeling spatial uncertainty[M]. John Wiley & Sons, 1999.
[22] Davis M W. Production of conditional simulations via the LUtriangular decomposition of the covariance matrix. Mathematical Geology, 1987, 19(2) : 91-98.
[23] Cooley J W, Tukey J W. An algorithm for the machine calculation of complexfourier series[J]. Mathematics of Computation, 1965, 19(90) : 297-301.
[24] 程红战, 陈健, 李健斌, 等. 基于随机场理论的盾构隧道地表变形分析[J]. 岩石力学与工程学报, 2016, 35(202): 4256-4264. (Cheng Hongzhan, Chen Jian, Li Jianbin, et al. Surface deformation analysis of shield tunnels based on random field theory [J]. Journal of Rock Mechanics and Engineering, 2016, 35(202): 4256-4264. (in Chinese))
[25] 王干. 黄土地铁隧道盾构开挖面稳定性研究[D]. 西安:西安理工大学, 2017. (Wang Gan. Study on the Stability of Shield Tunnel Excavation Face in Loess Metro Tunnel [D]. Xi'an: Xi'an University of Technology, 2017. (in Chinese))
[26] Mollon G, Phoon K K, Dias D, et al. Validation of a New 2D Failure Mechanism for the Stability Analysis of a Pressurized Tunnel Face in a Spatially Varying Sand[J]. Journal of Engineering Mechanics, 2011, 137(1): 8-21.
[27] Cho S E. Probabilistic Stability Analysis of Rainfall-induced Landslides Considering Spatial Variability of Permeability[J]. Engineering Geology, 2014, 171: 11-20.
[28] 倪万魁, 牛富俊, 刘东燕. 黄土土性的空间自相关性研究[J]. 地球科学与环境学报, 2002(2): 4-8, 12. (Ni Wankui, Niu Fujun, Liu Dongyan. Spatial autocorrelation study of loess soil properties [J]. Journal of Earth Science and Environment, 2002(2): 4-8, 12. (in Chinese))
[29] 曾宇, 刘瑞全, 李云. 隧道开挖应力释放数值模拟研究[J]. 城市建设理论研究(电子版), 2013(33):1-3. (Zeng Yu, Liu Ruiquan, Li Yun. Numerical simulation study on stress release during tunnel excavation [J]. Urban Construction Theory Research (Electronic Edition), 2013(33):1-3. (in Chinese)).
[30] 侯晓坤, 李同录, 赵谦, 等. 黄土地区路堑高边坡可靠度设计标准研究[J].工程地质学报,2015(23): 142-149. (Hou Xiaokun, Li Tonglu, Zhao Qian, et al. Research on Reliability Design Standards for High Slope Cutting in Loess Regions[J]. Journal of Engineering Geology, 2015(23): 142-149. (in Chinese))
[31] Zhang J Z, Huang H W, Zhang D M, et al. Effect of ground surface surcharge on deformational performance of tunnel in spatially variable soil[J].Computers and Geotechnics, 2021, 136: 104229.
[32] 靳雪梅, 黄宏伟, 张东明. 关于土的空间变异性对盾构隧道施工影响的探讨[J]. 现代隧道技术, 2022, 59(2): 62-70. (Jin Xuemei, Huang Hongwei, Zhang Dongming. The Impact of Spatial Variability of Soils on Shield Tunnelling[J]. Modern Tunnel- ling Technology, 2022, 59(2): 62-70. (in Chinese))
[33] 田宁, 陈健, 田铠玮, 等. 基于三维随机场的地表堆载引发运营隧道变形分析[J]. 岩土工程学报, 2022, 44(202): 120-124. (Tian Ning, Chen Jian, Tian Kaiwei, et al. Deformation analysis of operating tunnels caused by surface loading based on three-dimensional random fields [J]. Journal of Geotechnical Engineering, 2022, 44(202): 120-124. (in Chinese))