摘要
滑坡的稳定性由内在因素和外在因素所决定,内在因素是边坡本身所固有的,外界因素主要包括地震、降雨、开挖等。进年来,由于降雨导致的边坡的失稳越来越频繁。因此对于降雨条件下坡面水运动的研究无论在理论上还是在工程应用上,都具有十分重要的意义。
阐述了非饱和土中水流动的基本规律和土水特征曲线。由于土水特征曲线具有滞后的特点,提出了根据初始含水量来确定数值模拟初始时步非饱和土的渗透系数。
编制了基于Richards控制方程的饱和-非饱和渗流有限元分析程序,一些算例证明了本程序的正确性。改进了传统流量的计算方法,使得计算精度明显提高。
分析了降雨条件下地表水入渗的过程,提出了降雨条件下非饱和渗流的二维数学模型及边界条件。一些计算算例说明降雨条件下非饱和渗流的基本规律。
编制了基于Saint-venant控制方程的坡面径流的有限元分析程序,利用解析解和试验数据证明了程序的正确性。
根据非饱和土上水的转化机理,编制了降雨条件下地表水入渗和产流耦合的计算程序,并根据土-水特征曲线,提出了判断地表饱和的条件,根据此条件,加速了收敛速度,节省了CPU的时间。给出了降雨条件下水的入渗的实际过程。
利用降雨条件下地表水入渗和产流耦合的计算程序,分析了降雨强度、初始含水量、饱和渗透系数、孔隙率以及饱和渗透系数比对非饱和土入渗和产流过程的影响,进一步证明了传统理论的正确性。
利用降雨条件下地表水入渗和产流耦合的计算程序,模拟了小降雨强度和大雨强度对地下水位变化的影响,并用数值计算给出了地表排水沟对地下水变化的影响不是很显著的结论。
The stability of the slope is determined by its internal and external factors. The internal factors of the slope are inherent, and the external factors mainly include earthquake, rainfall events, and human excavation. The slope failure occurred frequently because of rainfall events in recent years. As a result, a systemic study on shallow water flow over porous soil is of great importance both in theory and application to engineering.
The rule about water flow in the unsaturated soil and the soil-water characteristic curve are described in this thesis In the first time step during the numerical simulation, the permeability coefficient is calculated according to the initial water content of the unsaturated soil, because of as shown in the soil-water characteristic curve has the hysteresis phenomenon.
A saturated-unsaturated FEM seepage analysis program is developed based on the Richards equation. Some examples are given to show the validity of the program. A method to calculate the discharge is developed and more accurate than traditional method.
The infiltration process of the water on the surface is analysized under rainfall conditions, the two-dimensional mathematical model and its boundary conditions are presented. Some examples are given to explain the rules of unsaturated soil infiltration.
The slope runoff FEM analysis program is developed based on the Saint-venant equations. The numerical solutions are compared with the analytical solutions and the experiment data and the characteristic line method solutions, the result validate of the program.
The coupling analysis program of surface flow and subsurface flow over porous media is developed based on the conversion principles of water on the surface under rainfall conditions. A new method to judge the saturation of the surface is proposed in this thesis, the convergence is speeded up and the CPU time is saved by using this method.
Five parameters are studied .namely rainfall intensity, initial water content, vertical saturated hydraulic conductivities, porosity and the ratio of the vertical and the horizontal saturated hydraulic conductivities by using the coupling program, the
______________________________________________Abstract_____________________________________________
results show the validity of the traditional infiltration theory.
The alteration procedure of the underground water level is simulated under drizzle and storm rainfall conditions respectively adopting the coupling FEM analysis program of surface flow and subsurface flow . The numerical simulation of the underground water level shows that the drain ditch installed over the slope does not have an notable effect on the underground water level.
引文
1 刘洁,毛昶熙.堤坝饱和与非饱和渗流计算的有限单元法.水利水运科学研究.1997;(3):242~252
2 高骥,雷光耀,张锁春.堤坝饱和与非饱和渗流计算的数值分析.岩土工程学报.1988,10(6):28~37
3 李信,高骥,汪自力,李莉.饱和-非饱和土的渗流计算.水利学报.1992;(11):63~69
4 张家发,张伟,朱国胜,王满兴.三峡工程永久船闸高边坡降雨入渗实验研究.岩石力学与工程学报.1999,18(2):137~141
5 Lumb P. Effect of rainstorm on slope stability, sym. on HongKong soils.,Hong kong, 1962.73~87
6 Fredlund D G. Slope stability analysis incorporationing the effect of soil suction. In: Slope Stability. Anderson M. G. and Richards New Youk: Willey. 1987. 113~144
7 Sammori T and Tsuboyama Y. Parametric study on slope stability with numerical simulation in consideration of seepage process. In: Proc. 6th, Int. Symp. on Landslide. Bell (ed.) Balkema, Rotterdam. 1991. 539~544
8 Alonso E, Gens A, Lioret A, Delahaye C. Effect of rain infiltration on the stability of slopes. Unsaturated Soils. 1995. 1, 241~249
9 Shimada K, Fujii H & Nishimura S and Mcrii T. Stability of unsaturated slopes considering changes of matric suction. Unsaturated Soils 1995. 1,293~299
10 Sun Y, Nishigaki M & Kchno I. A study on stability analysis of shallow layer slope due to raining permeation. Unsaturated Soils, 1995. 1,315~320
11 Fredlund D G, Morgenstern N R and Widger A. Shear stength of unsaturated soils. Can. Geotech. J., 1978, 15, 313~321
12 雷志栋,杨诗秀,谢森传.土壤水动力学.北京:清华大学出版社,1988
13 雅·贝尔.地下水水力学.许涓铭等译.北京:地质出版社,1985.147~172
14 Heben F.Wang,Mary P.Anderso.n渗流数值模拟导论.大连理工大学出版社,1988.115~165
15 毛昶熙.渗流计算分析与控制.水利水电出版社.1988.1
16 L. Lam, D. G. Fredlund, S. L. Barbour. Transient seepage model for saturated-unsaturated soil systems: a geotechnical engineering approach. Geotechnique. 1987 24:565~580.
17 周维垣,肖洪天等.三峡船闸高边坡岩体渗流及稳定分析.岩石力学与工程学报.1998.11:818~822.
18 张家发.三维饱和非饱和稳定非稳定渗流场的有限元模拟.长江科学院院报.1997.9:35~38.
19 Charles W. W. Ng, Member, ASCE, Y. W. Pang. Influence of Stress state on soil-water characteristic and slope stability. Journal of Geotechnical and Geoenvironmental engineering. 2000. FEBRUARY.
20 T. T. Lim, H. Rahardjo, M. F. Chang, D. G. Fredlund. Effect of rainfall on matric suctions in a residual soil slope. Can. Geotech. J. 33: 618~628(1996).
21 Jose H. F. Pereira, delwyn G. Fredlund, Member, ASCE. Volume change behavior of collapsible compacted gneiss soil. Journal of getechnical and geoenvironmental engineering. 2000. October:907~916.
22 Vinod Kumar, C. S. Jaiswal, H. S. Chauhan. Numerical solution of 2D free surface flow to ditch drains in anisotropic soils. Journal of irrigation and drainage engineering. 2000 JULY/AUGUST:250~254.
23 Tai T. Wong, Delwyn G. Fredlund, John Krahn. A numerical study of coupled consolidation in unsaturated soils. Can. Geotech. J. 35:926~937(1998).
24 G. Gottardi, M. Venutelli. Computer program for the numerical simulation of one-dimensional infilration into unsaturated soil. Computer Geoscience. 1993,9:1239~1266.
25 邵龙潭,唐洪群,韩国城。有限元边坡稳定分析方法及其应用。计算力学学报,2001,1,81~87.
26 吴梦喜,高莲士。饱和-非饱和非稳定渗流数值分析。水利学报,1999,12:38~42.
27 Russell G. Mein, Curtis L. Larson. Modeling Infiltration during a Steady rain. Water Resouces Research. 1973 ,APRIL.
28 Ben Chie Yen, Ali Osman Akan. Effects of soil properties on overland flow and infiltration. Journal of Hydrolic Reseach 21 (2),1983.
29 沈冰.黄土沟壑区产流计算模型探讨.陕西机械学院学报.1983(2).:13~30.
30 刘贤赵,康绍忠.降雨入渗和产流问题研究的若干进展及评述.水土保持通报.1999,19(2):57~62.
31 高润德,彭良泉,王钊.雨水作用下非饱和土边坡的稳定性分析。人民长江。2001,32(11):25~27.
32 李兆平,张弥。降雨入渗对基坑工程安全性影响的研究。中国安全科学学报。2000,10(3):16~22.
33 黄兴法。坡面降雨径流的一种数值模拟方法。中国农业大学学报。1997,2(2):45~50.
34 陈力,刘清泉,李家春。坡面降雨入渗产流规律的数值模拟。2001,4:61~67。
35 陈善雄,陈守义。考虑降雨的非饱和土边坡稳定性分析方法。2001,22(4):447~450.
36 邓孺孺,黄慧萍。土壤下渗能力之定量分析。中山大学学报。1997,36(4):89~93.
37 罗振东,田向军,张桂芳,周礼。地下水及其通量的数值模拟。首都师范大学学报,2001,22(1):19~26.
38 林鹏,赵思健,李昂,李勉辉。坡积土渗水软化对边坡稳定性的影响。工程勘察,2001,1:26~28.
39 谢守益,徐卫亚。降雨诱发滑坡机制研究。武汉水力电力大学学报,1999,32(1):21~23.
40 胡明鉴,张平仓。斜坡稳定性及降雨条件下滑坡的试验研究。岩土工程学报。2001,23(4):454~457。
41 吴长文,陈法扬。坡面土壤侵蚀及其模型研究综述。南昌水专学报。1994,13(2):1~11.
42 沈冰,沈晋。坡地降雨漫流的有限元模拟。水利水电技术,1988年第4期:1~6.
43 戚隆溪,黄兴法。坡面降雨径流和土壤侵蚀的数值模拟。力学学报,1997,29(3):344~348.
44 邵龙潭,王助贫,关立军,许志强。非饱和土中水流入渗和气体排出过程的求解。2000,11(1):8~13.
45 李焯芬,陈虹。雨水渗透与香港滑坡灾害。水文地质工程地质。1997(4):34~38.
46 张书函,康绍忠,蔡焕杰。天然降雨条件下坡地水量转化的动力学模式及其应用。水利学报。1998(4):55~62.
47 A. Osman, A. M. ASCE. Similarity solution of overland flow on pervious surface. Journal of Hydraulic of Engineering. 1985,111 (7).
48 Fredlund D G等著。非饱和土土力学。陈仲颐等译。北京:中国建筑工业出版社。1997年5。
49 王百田,王斌瑞。黄土坡面地表处理与产流过程研究。水土保持学报。1994,8(2):18~24.
50 黄平,赵吉国,林少礼。山坡地分布型降雨下渗数学模型。中山大学学报。2000,39(6):107~111
51 吕喜玺,史学正,于东升。用人工模拟降雨研究南方低丘土壤的渗透。水土保持学报。1995,9(3):1~8
52 刘洪禄,杨培岭,刘玉桥,赵立新。不同田间工程措施条件下降水入渗规律的数值模拟。农业工程学报。1998,14(2):143~148.
53 王全九,王文焰,沈冰,邵明安。降雨-地表径流-土壤溶质相互作用深度。土壤侵蚀与水土保持学报。1998,4(2):41~46.
54 魏忠义,王治国,段喜明等。河沟流域水分入渗的数学模型。水土保持研究。2000,7(4):32~35.
55 李锡夔,武文华。非饱和土中溶混污染物运移模型及特征线有限元法。岩土工程学报, 1999,21 (4):427~437.
56 E.E.Alonso,A.Gens,A.Josa,杨代泉。非饱和土弹塑性应力应变特性模拟。岩土工程学报,1995,17(6):42~51.
57 李锡夔,范益群。非饱和土变形及渗流过程的有限元分析。岩土工程学报,1998,20(4):20~24.
58 杨庚玉。非饱和土弹塑性模型及其有限元法。中国矿业大学学报,1997,27(2)。
59 李宁,陈飞熊。饱和土体固-液两相介质动力耦合问题有限元解析。西安公路交通大学学报,1999,19(4):6~10.
60 李锡夔。饱和-非饱和土壤中污染物运移过程的数值模拟。力学学报,1998,30(3):321~331.
61 刘贤赵,康绍忠。连续与间歇积水入渗对比试验研究。水科学进展,1999,10(1):53~58.
62 夏禄清。露天矿区洪峰流量计算中入渗率μ值选取的探讨。四川冶金,1997年第3期:8~11.
63 陈士俊,张俊霞,李莉等。工程渗流有限元计算方法研究。人民黄河,2000,22(9):34~36.
64 朱伟,山村和野。雨水·洪水渗透时河堤的稳定性。岩土工程学报,1999,21(4):414~419.
65 靳长兴。坡度在坡面侵蚀中的作用。地理研究,1996,15(3):57~63.
66 王占礼,邵明安,刘文兆,梁一民。纸坊沟壑土壤侵蚀与产沙初步研究。天津师大学报,1999,19(1):45~50.
67 汪彗贞,李宪法。北京城区雨水入渗设施的计算方法。中国给水排水,2001,17:37~39.
68 范荣生,李占斌。坡地降雨溅蚀与输沙模型。水利学报,1993第6期:24~29.
69 王文焰,沈冰,张建丰。室内坡地降雨入渗及产流系统的研制。实验技术与管理,1991,8(5):12~16.
70 杜丽惠,江春波,曹丰生。三维渗流模型与防渗效果研究。人民黄河,2000,22(5):
40~41.
71 许秀元。河渠影响下土壤水-地下水联合运动的模拟研究。水利学报,1997年第12期:21~29.
72 江春波,杜丽惠。非均匀介质的三维渗流有限元模型。清华大学学报,1999,39(11):21~24.
73 张嘎,张建民,江春波。溪洛渡水电站上游围堰渗流分析及防渗型式比较。水力发电学报,2001年第1期:82~87.
74 H.A. Basha. Multidimensional steady infiltration with prescribed boundary conditions at the soil surface. Water resources research. 1994,30(7) : 2105~2116.
75 Michel C. Boufadel, T. Suidan. Steady Seepage in Trenches and dams: effect of capillary flow. Journal of Hydraulic Engineering, 1999,3: 286~294.
76 徐千军,张建红。确定稳定渗流自由面位置的一种简便方法。水动力学研究与进展,1999,14(4):418~423.
77 雷廷武,赵军,袁建平等。利用γ射线法测量径流含沙量及算法。农业工程学报,2002,18(1):18~21.
78 赵晓光,吴发启,刘秉正,康绍忠。再论土壤侵蚀的坡度界限。水土保持研究,1999,6(2):42~46.
79 赵慧丽,张弥。降雨入渗对基坑非饱和土瞬态含水率影响的数值计算。石家庄铁道学院学报,2000,13(4):44~46.
80 朱成立,邵孝候。地下排水和渗灌条件下麦田土壤水分变化模拟。河海大学学报,2000,28(2):23~26.
81 王少丽,李福祥,张友义。农田排水条件下降雨补给与地下水埋深关系的试验研究。灌溉排水,2000,19(3):54~57.
82 Peter S. Huyakom. A Three-Dimensional Finite-Element Model for Simulating water flow in Variably Saturated Porous Media. Water Resources Research. 1986,22(13).
83 罗先启,李海岭,葛修润,杨学堂。降雨条件下滑坡灾害及滑坡排水效果研究。岩土力学,2000,21(3):231~234.
84 刘艳华,龚壁卫,苏鸿。非饱和土的土水特征曲线研究。工程勘察,2002年第2期:8~11.
85 倪万魁,牛富俊,刘东燕。降雨入渗对饱和土强度的影响分析。工程勘察,2002年第2期:15~18.
86 徐捷,王钊,李未显。非饱和土的吸力量测技术。岩石力学与工程学报。2000,(19):905~909.
87 陈洪凯,唐红梅。散体滑坡室内启动模型试验。山地学报,2002,20(1):112~115.
88 林鲁生,蒋刚。考虑降雨入渗影响的边坡稳定分析方法探讨。武汉大学学报,2001,34(1):42~44.
89 蒋刚,王钊,邱金营。国产滤纸吸力-含水量关系率定曲线研究。岩土力学,2000,21(1):72~75.
90 黄平,赵吉国。森林坡地二维分布型水文数学模型的研究。水文,2000,20(4):1~4.
91 沈冰,王文焰,沈晋。短历时降雨强度对黄土坡地径流形成影响的实验研究。水利学报,1995年第3期:21~27.
92 朱伟,刘汉龙,高玉峰,山村和也。河堤内非稳定渗流的实测与分析。水利学报,2001年第3期:92~97.
93 陈守义。考虑入渗和蒸发影响的土坡稳定性分析方法。岩土力学,1997,18(2):8~22.
94 邵孝候,王靖波,刘才良,刘新仁。塑料暗管排降条件下麦田土壤水分变化规律模拟。南京农业大学学报,2000,23(2):47~52.
95 李小雁,龚家栋,高前兆。人工基水面临产流降雨量确定实验研究。水科学进展,2001,12(4):516~522.
96 汪金元,孙役,陈润发。降雨入渗下的三维正交裂隙网络饱和-非饱和渗流实验研究。岩石力学与工程学报。2001,10:1717~1720.
97 汪自力,朱明霞,高青伟,岳瑜素。饱和-非饱和渗流作用下边坡稳定分析混合法。郑州大学学报。2002,23(1):25~28.
98 陈正汉,王权民,李刚,孙树国。非饱和土的力学理论。重庆大学学报,2000(23):199~205.
99 拾兵,曹叔尤,刘兴年,黄尔。山地小流域及输沙过程的计算模型机器数值模拟。泥沙研究,2000第4期:77~80.
100 孙役,王恩志,黄远智。暴雨入渗下裂隙岩体边坡渗流及稳定分析。水利水电技术,1999年第5期:38~40.
101 卞传恂,黄永革,沈思跃,孟云侠。以土壤缺水量指标的干旱模型。水文,2000,20(2):5~9。
102 刘作新,李哲,孙中和,郑昭佩。灌溉排水,1998,17(3):5~9
103 杨兴国,彭素琴,柯晓新。甘肃河东地区降雨强度分析。甘肃气象,1994,12(1):2~4
104 刘贤赵,康绍忠。黄土区坡地降雨入渗产流过程中的滞后效应。水科学进展,2001,12(1):56~60
105 郝振纯。黄土地区降雨入渗模型初探。水科学进展,1994,5(3):186~192.
106 胡云进,速宝玉,仲济刚。有地表入渗的裂隙岩体渗流数值分析及工程应用。岩石力学与工程学报,2000,19:1019~1022.
107 袁建平,蒋定升,文秒霞。坡地土壤降雨入渗试验装置研究。水土保持通报,1999,19(1):24~28.
108 邵学军。一维坡面流动的基本理论及数值模拟研究。泥沙研究,1998年第3期:91~96.
109 张平,李日云。降雨入渗补给地下水的影响因素。辽宁大学学报,1999,26(2):119~122.
110 王新元,尹雁峰。苜蓿地人工降雨试验研究。海河水利,1997,6:4~6.
111 Engman E T. Roughness coefficient for routing surface runoff. J. Irrigation and Drainage Engineering, ASCE, 1976,112(1):39~54.
112 刘素嫒。SB-YZCP人工降雨模拟装置特性分析。中国水土保持,1999年第5期。
113 谢正辉,曾庆存,戴永久,王斌。有限元集中质量法在非饱和土壤水流中的应用。气候与环境研究,1998,3(1):73~81.
114 岳红光,曲艳杰。用人工降雨法研究产生径流时间。吉林水利,1998,11:12~14.
115 叶自桐,韩冰,杨金忠,周创兵。岩石裂隙毛管压力-饱和度关系曲线的试验研究。水科学进展,1998,9(2):112~117.
116 Y. Zarmi, J. Ben Asher, T. GreenGard. Constant Velocity Kinematic Analysis of an Infiltrating Microcatchment Hydrograph. Water Resources Research. 1983,19(1).
117 C.A.M. Franks. Characteristics of some rainfall-induced landslides on natural slopes,Lantau
Island, Hong Kong. Quarterly Journal of Engineering Geology, 1999,32,247-259.
118 Saleem Ahmad, Deepak Kashyap, B.S.Mathur. Numerical modeling of two-dimensional transient flow to diches. Journal of Irrigation and Drainage Engineering, 1991,117(6).
119 高贤能,黄润秋。有自由面渗流分析的高斯点法。水文地质工程地质,1997年第6期。
120 吴梦喜,张学勤。有自由面渗流分析的虚单元法。水利学报,1994年第8期:67~71.
121 S. Assouline. A model for soil relative hydraulic conductivity based on the water retention characteristic curve. Water Reources Research. 2001,37(2) : 265~271.
122 Richard L. Cooley. Some new procedures for numerical solution of variably saturated flow problems. Water Resouces Research, 1983, 19 (5): 1271~1285.
123 Mahmud Alam, A. Bhuiyan. Collocation finite-element simulation of dam-break flows. Journal of Hydraulic Engineering. 1995,121(2) : 118~127.
124 Gour-Tsyh Yeh. On the computation of darcian velocity and mass balance in the finite element modeling of groundwater flow. Water Resouces Research. 1981,17(5) : 1529~1533.
125 A. W. CRAIG W. L. WOOD. Cost-efficiency study of various methods for solving the seepage through dam problem using variational inequalities. International Journal For Numerical Methods In Engineering. 1981,17,1325~1333.
126 X. Du, T. Yao. Stability analysis of the unsaturated water flow equation. Water Resources Reserch.2001,37(7) : 1869~1881.
127 Fred L. Ogden, Brent A. Watts. Saturated area formation on nonconvergent hillslope topography with shallow soils. Water Resources Reseach..2000,36(7) : 1795~1804.
128 Joel E. VanderKwaak, Keith Loague. Hydrologic-response simulations for the R-5 catchment with a comprehensive physics-based model.2001,37(4) : 999~1013.
129 陈平,李祝贻。堤坝非稳定渗流计算程序的编制及其应用。水利水运科学研究,1990第4期:417~425.
130 徐永福。非饱和膨胀土结构性强度的研究。河海大学学报,1999,27(2):85~88.
131 王少丽,张友义,李福祥。涝渍兼明的明暗组合排水计算方法探讨。水利学报,2001年第12期。56~61.
132 S. Desai, C. Sherman. Unconfined Transient seepage in Sloping Banks. 1971, 2: 358~373.
133 Bathe, R. Khoshgoftaar. Finite Element free surface seepage analysis without mesh iteration. International Journal For numerical and analytical methods in geomechanics,1979,3: 13~22.
134 Peter W, J. Parekh, C. Peters. Numerical analysis of free surface seepage problems. Journal of the irrigation and drainage division. 1971,3: 165~179.
135 S. Desai. Seepage analysis of earth banks under drawdown. Journal of the soil mechanics and foundations division, 1972,11: 1143~1163.
136 黄领梅,沈冰,王志荣等。新疆和田地表径流模拟,西北农业大学学报,2000,28(3):46~50.
137 文康,金管生,李琪等。地表径流过程的数值模拟,北京,水力电力出版社,137~151。
138 Ali Osman Akan, Ben Chie Yen. Mathematical model of shallow water over porous media, Journal of the hydraulic division, 1981, April:479~494.
139 朱军。清华大学博士后论文,2001。
140 毛昶熙,段祥宝,李祖贻等。渗流数值计算与程序应用,河海大学出版社,1999,9。
141 Neuman, S. P. Galerkin approach to saturated-unsaturaed flow in porous media. Finite
elements in fluids. Vol. 1. viscous flow and hydrodynamical. London: Wiley, 1974:201~217.
142 Neuman, S. P. Saturated-unsaturated seepage by finite elements. Proc. ASCE, Hydraulics Div., 1973,99(12):2233~2250.
143 Brooks, R. H. and Corey, A. T. Hydraulic properties of porous media. Colorado State Univ., Hydrol. Paper, no.3,1964.
144 Christenen, H. R. Permeability-capillary potential curves for three prairie soils. Journal Paper No. J-1167 of Proj.504 of lowa Agricultural Experiment Station. 1943: 381~390.
145 Gardner, W. R. Calculation of capillary conductivity from pressure plate outflow data. Soil Sci. Soc.Am. Proc.20,1956:317~320.
146 Grader, W. R. Some steady state solutions of the unsaturated moisture flow equation with application to evaporation from a water table. Soil Sci.1958,85:228~232.
147 Davidson M R. A Green-Ampt model of infiltration in a cracked soil. Water Resour. Res., 1984.20(1): 1685~1690.
148 Davidson, J. M., Stone, L. R. Field measurement and use of soil-water properties. Water Resource Res.5,1969:1312~1321.
149 Davidson, M R. Numerical calculation of saturated-unsaturated infiltration in cracked soil. Water Resour. Res.,1985.21 (5):709~714.
150 Averjanov, S. F. About permeability of subsurface soils in case of incomplete saturation. In Eng. Collect., vol.7 1950: 19~21.
151 Van Genuchten, M. T. A closed form equation for prediction the hydraulic conductivity of unsaturated soils. Soil Sci. Soc.Am.,J.44,1980: 892~898.
152 Fredlund D G & Xing A. Equations for the soil-water characteristic curve. Canadian Geotechnical Journal, 1994, 31: 521~546.
153 Fredlund D G, Xing A and Huang S. Predicting the permeability function for unsaturated soils using the soil-water characteristic curve. Can. Geotech. J.,1994, 31: 533~546.
154 Rubin,J. Theoretical analysis of two-dimensional transient flow of water in unsaturated and partly unsaturated soils. Proc. Soil Sci. Soc. Amer.,1968, Vol.32: 607~615.
155 Freeze, R. A. Three-dimensional transient saturated-unsaturated flow in groundwater basin. Water Resources Res.,1971, 7. 929~941.
156 Remson, I., Hornberger, G. M. and Molz, F. J. Numerical methods in subsurface hydrology. Wiley-Interscience, 1971.
157 Richards, L. A. Capillary conduction of liquids through porous medium. J. Physics., vol. 1931:318~333.
158 赤井浩一,大西有三,西垣诚。有限要素法饱和-不饱和的浸透流解析。土木学会论文报告集,No.264 1977:87~96.
159 黄俊,苏向明,汪炜平。土坝饱和-非饱和渗流数值分析方法研究。岩土工程学报,1990,12(5):30~39。
160 陈虹,陈彤。堤坝饱和-非饱和渗流数值模拟。水动力学研究与进展,1997,12(3):356~364。
161 Freeze, R. A. and Cherry, J. A. Groundwater. England Cliffs, NJ: Prentice-Hall, 1979.
162 Forsyth, P. A. Comparison of the single-phase and two-phase numerical model formulation for saturated-unsaturated groundwater flow. Computer Methods Appl. Mech. Engrg. 1988.69.243~259.
163 Campbell, G. S. A simple method for determining unsaturated conductivity from moisture
retention data. Soil Sci. 117,1974:311~314.
164 Philip, J. R. Linearized unsteady multidimensional infiltration. Water Resources Res. 22,1986:1717~1727.
165 Horton, R. E. et al. Lamilar sheet flow, Trans. Am,. Geophys Union, 1943,15(2).
166 霍利[捷]M.侵蚀与环境。余新晓等译。中国环境出版社,1987.
167 赵鸿雁等。枯枝落叶层阻延径流速度的研究。西北水保所集刊(4)。陕西科技出版社,1991,12。
168 Smith, R. E. and Parlange, J. R. A parameter efficient hydrology infiltration model. Water Resouces Res ,1987,14(3): 533~538.
169 Kostiakov, A. N. On the dynamics of the coefficient of water percolation in soils and on the necessity of studying it from a dynamic point of view for the purpose of Amelioraiton. Trans. Com. Int. Soc. Soil Sci. 6th Moscow A, 1932.17~21.
170 Horton, R. E. An approach towards a physical interpretation of infiltration capacity. Soil Science Society of America Proceedings 5.1940.399~417.
171 Holtan, H. N. A concept for infiltration estimates in watershed engineering. USDA-ARS. 1961.41~51.
172 Boughton, W. C. A mathematical model for relating runoff to rainfall with daily data. Civil Engr. Trans. Inst. Engrs.(Aust). C.E. 1966, 8: 83~87.
173 SHU TUNG CHU, Infiltration during an unsteady rain ,Water Resour. Res. Vol. 14. No 3,461~466, June 1978.
174 Philip, J. R. The theory of infiltration: 4. Sorptivity and Algebraic infiltration equations. Soil Science,1957,84: 257~264.
175 Knight, J. H. Solutions of the nonlinear diffusion equation: existence, uniquences, and estimation. Ph.D. Thesis. Australian national University ,Canberra. 1973.
176 Brutsaert,W. Vertical infiltration in dry soil. Water Resources Research, 1977,13:363~368.
177 吴宏伟,陈守义,庞宇威。雨水入渗对非饱和土坡稳定性影响的参数研究。岩土力学,1999,20(1):1~14
178 刘德富,罗先启,滑坡地表排水布置及效果初探,葛洲坝水电工程学院学报,1994,16(2):24~31.
179 H. R. Thomos, Z. Zhou, Minimum time-step sige for diffusion problem in FEM analysis. International Journal for Numerical Methods In Engineering, Vol 40.3865~3880, (1997).
180 O.C.Zienkiewicz, The finite element method, the fourth edition, p438~p501.