[1] 中华人民共和国水利部. 渠系工程抗冻胀设计规范:SL 23-2006[S]. 北京:中国水利水电出版社, 2006. Ministry of Water Resources of the People's Republic of China. Design code for anti-frost-heave of canal and its structure:SL 23-2006[S]. Beijing:China Water & Power Press, 2006. (in Chinese)
[2] SWAMEE P K. Optimal irrigation canal sections[J]. Journal of Irrigation and Drainage Engineering, 1995, 121(6):467-469.
[3] SWAMEE P, MISHRA G, CHAHAR B. Comprehensive design of minimum cost irrigation canal sections[J]. Journal of Irrigation and Drainage Engineering, 2000, 126(5):322-327.
[4] 余长洪, 周明耀, 姜健俊, 等. 灌区节水改造中防渗渠道断面的优化设计[J]. 农业工程学报, 2004, 20(1):91-94. YU C H, ZHOU M Y, JIANG J J, et al. Optimal design of anti-seepage channel section for water-saving transformation in irrigation district[J]. Transactions of the Chinese Society of Agricultural Engineering, 2004, 20(1):91-94. (in Chinese)
[5] 脱云飞, 王克勤, 宋维峰, 等. 灌溉渠道优化设计方法研究[J]. 中国农村水利水电, 2012(4):58-60. TUO Y F, WANG K Q, SONG W F, et al. Research on optimal design and method of irrigation channel[J]. China Rural Water and Hydropower, 2012(4):58-60. (in Chinese)
[6] 辛英华, 王正中. U形衬砌渠道结构及水力最佳断面的分析[J]. 节水灌溉, 2008(2):36-38, 45. XIN Y H, WANG Z Z. The structural and hydraulic analysis on frost-heaving concrete lining of the U-shape canal[J]. Water Saving Irrigation, 2008(2):36-38, 45. (in Chinese)
[7] 王正中, 李甲林, 陈涛, 等. 弧底梯形渠道砼衬砌冻胀破坏的力学模型研究[J]. 农业工程学报, 2008, 24(1):18-23. WANG Z Z, LI J L, CHEN T, et al. Mechanics models of frost-heaving damage of concrete lining trapezoidal canal with arc-bottom[J]. Transactions of the Chinese Society of Agricultural Engineering, 2008, 24(1):18-23. (in Chinese)
[8] 王正中. 梯形渠道砼衬砌冻胀破坏的力学模型研究[J]. 农业工程学报, 2004, 20(3):24-29. WANG Z Z. Establishment and application of mechanics models of frost heaving damage of concrete lining trapezoidal open canal[J]. Transactions of the Chinese Society of Agricultural Engineering, 2004, 20(3):24-29. (in Chinese)
[9] 刘东, 胡宇祥, 付强, 等. 北方灌区混凝土衬砌渠道断面优化及参数分析[J]. 农业工程学报, 2015, 31(20):107-114. LIU D, HU Y X, FU Q, et al. Optimization and parameter analysis for channel cross section with concrete lining in northern irrigation district[J]. Transactions of the Chinese Society of Agricultural Engineering, 2015, 31(20):107-114. (in Chinese)
[10] 王正中, 沙际德, 蒋允静, 等. 正交各向异性冻土与建筑物相互作用的非线性有限元分析[J]. 土木工程学报, 1999, 32(3):55-60. WANG Z Z, SHA J D, JIANG Y J, et al. Nonlinear finite element analysis of interaction of orthotropic frozen ground and construction[J]. China Civil Engineering Journal, 1999, 32(3):55-60. (in Chinese)
[11] 刘旭东, 王正中, 闫长城, 等. 基于数值模拟的双层薄膜防渗衬砌渠道抗冻胀机理探讨[J]. 农业工程学报, 2011, 27(1):29-35. LIU X D, WANG Z Z, YAN C C, et al. Exploration on anti-frost heave mechanism of lining canal with double films based on computer simulation[J]. Transactions of the Chinese Society of Agricultural Engineering, 2011, 27(1):29-35. (in Chinese)
[12] 李爽, 王正中, 高兰兰, 等. 考虑混凝土衬砌板与冻土接触非线性的渠道冻胀数值模拟[J]. 水利学报, 2014, 45(4):497-503. LI S, WANG Z Z, GAO L L, et al. Numerical simulation of canal frost heaving considering nonlinear contact between concrete lining board and soil[J]. Journal of Hydraulic Engineering, 2014, 45(4):497-503. (in Chinese)
[13] 郝晋彩, 娄宗科, 高凤. 梯形渠道冻胀数值模拟与边坡系数优化[J]. 灌溉排水学报, 2017, 36(12):81-86. HAO J C, LOU Z K, GAO F. Numerical simulation and slope coefficient optimization of frost heave of trapezoidal channel[J]. Journal of Irrigation and Drainage, 2017, 36(12):81-86. (in Chinese)
[14] 安鹏, 邢义川, 张爱军, 等. 弧底梯形渠道抗冻胀结构优化与数值模拟[J]. 灌溉排水学报, 2017, 36(11):56-62. AN P, XING Y C, ZHANG A J, et al. Optimal analysis of anti-frost heaping canal with cross section of trapezoidal slopes and curved bed[J]. Journal of Irrigation and Drainage, 2017, 36(11):56-62. (in Chinese)
[15] LIU Z, YU X. Coupled thermo-hydro-mechanical model for porous materials under frost action:Theory and implementation[J]. Acta Geotechnica, 2011, 6(2):51-65.
[16] KURYLYK B L, WATANABE K. The mathematical representation of freezing and thawing processes in variably-saturated, non-deformable soils[J]. Advances in Water Resources, 2013, 60:160-177.
[17] 刘月, 王正中, 王羿, 等. 考虑水分迁移及相变对温度场影响的渠道冻胀模型[J]. 农业工程学报, 2016, 32(17):83-88. LIU Y, WANG Z Z, WANG Y, et al. Frost heave model of canal considering influence of moisture migration and phase transformation on temperature field[J]. Transactions of the Chinese Society of Agricultural Engineering, 2016, 32(17):83-88. (in Chinese)
[18] 代鸿, 曹波. 多目标模糊优化在船舶结构设计中的应用[J]. 舰船科学技术, 2017, 39(7A):4-6. DAI H, CAO B. Application of multi objective fuzzy optimization method in ship structure design[J]. Ship Science and Technology, 2017, 39(7A):4-6. (in Chinese)
[19] 张秀利, 梁迎春, 董申. 多目标结构模糊优化的分层序列法[J]. 机械设计与制造, 1999(5):44-45. ZHANG X L, LIANG Y C, DONG S. Lexicograhic method for fuzzy multiobjective optimization of structures[J]. Machinery Design & Manufacture, 1999(5):44-45. (in Chinese)
[20] 李炜. 水力计算手册[M]. 2版. 北京:中国水利水电出版社, 2006. LI W. Hydraulic calculation manual[M]. 2nd ed. Beijing:China Water & Power Press, 2006. (in Chinese)
[21] 刘晓燕, 赵军, 石成, 等. 土壤恒温层温度及深度研究[J]. 太阳能学报, 2007, 28(5):494-498. LIU X Y, ZHAO J, SHI C, et al. Study on soil layer of constant temperature[J]. Acta Energiae Solaris Sinica, 2007, 28(5):494-498. (in Chinese)
[22] 张建荣, 刘照球. 混凝土对流换热系数的风洞实验研究[J]. 土木工程学报, 2006, 39(9):39-42, 61. ZHANG J R, LIU Z Q. A study on the convective heat transfer coefficient of concrete in wind tunnel experiment[J]. China Civil Engineering Journal, 2006, 39(9):39-42, 61. (in Chinese)
[23] LI S Y, ZHANG M Y, PEI W S, et al. Experimental and numerical simulations on heat-water-mechanics interaction mechanism in a freezing soil[J]. Applied Thermal Engineering, 2018, 132:209-220.
