作者中心
专家审稿
编委审稿
主编审稿
AN IMPROVED GREEN-AMPT MODEL AND ITS EXPERIMENTAL VERIFICATION
-
摘要: 鉴于Green-Ampt模型过于简化、难以反映实际入渗特征，且其假设与实际入渗规律不符，本文为了弥补Green-Ampt模型的不足，提出了一种改进的Green-Ampt模型。提出的模型考虑了含水率与土体深度的关系，将土壤剖面划分为饱和区、过渡区以及天然区，土柱试验验证了所提出模型的准确性，也证实了入渗过程中过渡区的存在。试验结果表明：Green-Ampt模型计算值明显偏离实际累计入渗量，提出的模型总体上更接近实际累计入渗量。将该模型用于非饱和斜坡稳定性分析，计算结果揭示了Green-Ampt模型低估了斜坡的稳定性系数。提出的改进Green-Ampt模型为分析降雨滑坡风险提供参考。
-
关键词:
- 非饱和土 /
- Green-Ampt模型 /
- 土柱试验 /
- 斜坡稳定性 /
- 稳定性系数
Abstract: Because Green-Ampt model is too simplified to accurately calculate the total infiltration volume, we propose an improved Green-Ampt model which conforms to the actual infiltration law in this paper. The proposed model divides the soil profile into saturated, transitional saturated and natural saturated zones. A soil column test is performed to verify the accuracy of the proposed model and the existence of transitional zone. Three indexes are used to evaluate the accuracy of the model. They are the mean absolute error(MAE), the mean absolute relative error(MARE) and the root mean square error(RMSE). The MAE, MARE and RMSE are smaller than those of the classical Green-Ampt model. As a result, the accuracy of the proposed model is higher than that of Green-Ampt model. The proposed model is also used to analyze the stability of an unsaturated soil slope. The calculated results show that the slope angle and precipitation rainfall intensity are inversely proportional to the slope safety factor, and the former has a greater influence impact on the slope safety factor. Compared with the proposed model, the Green-Ampt model underestimates the slope safety. The improved Green-Ampt model provides references for analyzing the risk of rainfall and landslides.-
Key words:
- Unsaturated soil /
- Green-Ampt model /
- Soil column test /
- Slope stability /
- Safety factor
-
图 2 土壤剖面体积含水率与深度关系
a. 提出的模型；b. Green-Ampt模型
Figure 2. Relationship between volume moisture content and depth of soil profile
图 3 土壤剖面渗透系数与深度的关系
a. 提出的模型；b. Green-Ampt模型
Figure 3. Relationship between permeability coefficient and depth of soil profile
图 5 试验装置设计
1. 水管；2. 控制阀；3. 水箱；4. 水；5. 排水管；6. 传感器；7. 土壤；8. 砂石；9. 数据采集装置；10. 计算机；11. 模型箱
Figure 5. Test device design
图 10 提出的模型得到的稳定性系数
a. 坡度为10°；b. 坡度为20°；c. 坡度为30°
Figure 10. The stability coefficient obtained by the presented model
图 11 提出的模型得到的稳定性系数
a. 降雨强度为0.0035 cm·min-1；b. 降雨强度为0.0065 cm·min-1；c. 降雨强度为0.0095 cm·min-1
Figure 11. The stability coefficient obtained by the presented model
图 12 提出的模型与Green-Ampt模型结果的比较
Figure 12. Comparison of results between the proposed model and the Green-Ampt model
图 13 降雨过程中最小稳定性系数的变化
a. 坡度的影响；b. 降水强度的影响
Figure 13. Variation of minimum stability coefficient during rainfall
表 1 基本物理指标
Table 1. Basic physical indicators
基本物理指标 干密度ρd/g·cm-3 比重Gs 孔隙比e 天然含水率w/% 残余含水wr/% 饱和含水ws/% 次生黄土 1.35 2.76 1.04 8.68 2.3 43 
下载: 导出CSV
表 2 计算参数
Table 2. Parameters for DEM simulations
参数 提出的模型 Green-Ampt模型 α/(°) 0 0 q/cm·min-1 0.0035 0.0035 sf/cm 63.08 63.08 θs/% 44 44 θi/% 11 11 ks/cm·min-1 6.00×10-4 6.00×10-4 ki/cm·min-1 7.80×10-5 —
下载: 导出CSV
表 3 提出的模型与经典的Green-Ampt模型的精度
Table 3. The accuracy of the proposed model and the Green-Ampt model
MAE/cm3 MARE/% RMSE/cm3 提出的模型 10.97 5.63 13.985 Green-Ampt模型 42.73 8.06 46.07
下载: 导出CSV
表 4 计算参数
Table 4. Parameters for analysis
参数 提出的模型 Green-Ampt模型 α/(°) 10，20，30 q/cm·min-1 0.0035，0.0065，0.0095 sf/cm 63.057 θs/% 44 44 θi/% 11 11 θr/% 2.3 2.3 ks/cm·min-1 6.00×10-4 6.00×10-4 ki/cm·min-1 7.80×10-5 — c/kPa 10 10 φ/(°) 35 35 γ/kN·m-3 20.2 20.2
下载: 导出CSV
-
Bishop A W, Alpan I, Blight G E, et al. 1961. Factors controlling the strength of partly saturated cohesive soils[C]//Research Conference on Shear Strength of Cohesive Soils. ASCE. Brakensiek D L, Onstad C A. 1977. Parameter estimation of the Green and Ampt Infiltration Equation[J]. Water Resources Research, 13 (6): 1009-1012. doi: 10.1029/WR013i006p01009 Brooks R H, Corey A T. 1964. Properties of porous media affecting fluid flow[J]. Journal of the Irrigation & Drainage Division Proceedings of the American Society of Civil Engineers, 92 (2): 61-88. Chen L, Young M H. 2006. Green-Ampt infiltration model for sloping surfaces[J]. Water Resources Research, 42 (7): 887-896. Cheng Y K, Liu C Y, Yan S, et al. 2018. Modeling of transient flow in unsaturated geomaterials for rainfall-induced landslides Using a Novel Spacetime Collocation Method[J]. Geofluids: 1-16. Collins B D, Znidarcic D. 2004. Stability analyses of rainfall induced landslides[J]. Journal of Geotechnical and Geoenvironmental Engineering, 130 (4): 362-372. doi: 10.1061/(ASCE)1090-0241(2004)130:4(362) Colman E A, Bodman G B. 1945. Moisture and energy conditions during downward entry of water into moist and layered soils[J]. Soil Science Society of America Journal, 9 (C): 3-11. doi: 10.2136/sssaj1945.036159950009000C0001x Dormand J R, Prince P J. 1980. A family of embedded Runge-Kutta Formulae[J]. Journal of Computational and Applied Mathematics, 6 (1): 19-26. doi: 10.1016/0771-050X(80)90013-3 Fredlund D G, Morgenstern N R, Widger R A. 1978. The shear strength of unsaturated soils[J]. Canadian Geotechnical Journal, 15 : 313-321. doi: 10.1139/t78-029 Green W H, Ampt G A. 1911. Studies on Soil Phyics[J]. The Journal of Agricultural Science, 4 (1): 1-24. doi: 10.1017/S0021859600001441 Hillel D, Gardner W R. 1970. Steady infiltration into crust-topped profiles[J]. Soil Science, 108 (2): 69-76. Li S H, Wu L Z, Luo X H. 2020. A novel method for locating the critical slip surface of a soil slope[J]. Engineering Applications of Artificial Intelligence, 94: 103733. doi: 10.1016/j.engappai.2020.103733 Liu C Z, Chen C L. 2020. Achievements and countermeasures in risk reduction of geological disasters in China[J]. Journal of Engineering Geology, 28 (2): 375-383. Mein R G, Larson C L. 1973. Modeling infiltration during a steady rain[J]. Water Resources Research, 9 (2): 384-394. doi: 10.1029/WR009i002p00384 Mishra S K, Kumar S R, Singh V P. 1999. Calibration and validation of a general infiltration model[J]. Hydrological Processes, 13 (11): 1691-1718. doi: 10.1002/(SICI)1099-1085(19990815)13:11<1691::AID-HYP818>3.0.CO;2-W Muntohar A S, Liao H J. 2010. Rainfall infiltration: infinite slope model for landslides triggering by rainstorm[J]. Natural Hazards, 54 : 967-984. doi: 10.1007/s11069-010-9518-5 Neuman S P. 1976. Wetting front pressure head in the infiltration model of Green and Ampt[J]. Water Resources Research, 12 (3): 564-566. doi: 10.1029/WR012i003p00564 Pan Y L, Jian W X. 2020. A study on the rainfall infiltration of granite residual soil slope with an improved Green-Amptmodel[J]. Rock and Soil Mechanics, 41 (8): 2685-2692. Peng Z Y, Huang J S, Wu J W, et al. 2012. Modification of Green-Ampt model based on the stratification hypothesis[J]. Advances in Water Science, 23 (1): 59-66. Silvestri V. 2006. A three-dimensional slope stability problem in clay[J]. Canadian Geotechnical Journal, 43 (2): 224-228. doi: 10.1139/t06-001 Song Y F, Fan W, Li J, et al. 2020. Risk assessment of property loss caused by unstable slopes under different rainfall conditions—A case study of Xinglong Town of Zhenba County[J]. Journal of Engineering Geology, 28 (2): 401-411. van Genuchten M Th. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J]. Soil Science Society of America Journal, 44 (5): 892-898. doi: 10.2136/sssaj1980.03615995004400050002x Vanapalli S K, Fredlund D G, Pufahl D E, et al. 1996. Model for the prediction of shear strength with respect to soil suction[J]. Canadian Geotechnical Journal, 33 : 379-392. doi: 10.1139/t96-060 Wang W Y, Wang Z Y, Wang Q J, et al. 2003. Improvement and evaluation of the Green-Ampt model in loess soil[J]. Journal of Hydraulic Engineering, 34 (5): 30-34. doi: 10.3321/j.issn:0559-9350.2003.05.005 Wu L Z, Liu G G, Wang L C, et al. 2016. Numerical analysis of 1 D coupled infiltration and deformation in layered unsaturated porous medium[J]. Environmental Earth Sciences, 75(9): 761. doi: 10.1007/s12665-016-5579-4 Wu L Z, Selvadurai A P S, Zhang L M, et al. 2016. Poromechanical coupling influences on potential for rainfall-induced shallow landslides in unsaturated soils[J]. Advances in Water Resources, 98 : 114-121. doi: 10.1016/j.advwatres.2016.10.020 Wu L Z, Zhang L M, Zhou Y, et al. 2018. Theoretical analysis and model test for rainfall-induced shallow landslides in the red-bed arearegion of Sichuan[J]. Bulletin of Engineering Geology and the Environment, 77 (4): 1343-1353. doi: 10.1007/s10064-017-1126-0 Wu L Z, Zhu S R, Peng P J. 2020. Application of the Chebyshev spectral method to the simulation of groundwater flow and rainfall-induced landslides[J]. Applied Mathematical Modelling, 80 : 408-425. doi: 10.1016/j.apm.2019.11.043 Xu Q. 2020. Understanding the landslide monitoring and early warning: Consideration to practical issues[J]. Journal of Engineering Geology, 28 (2): 360-374. Yao W M, Li C D, Zhan H B, et al. 2019. Time-dependent slope stability during intense rainfall with stratified soil water content[J]. Bulletin of Engineering Geology and the Environment, 78 : 4805-4819. doi: 10.1007/s10064-018-01437-3 Ye S H, Shi Y L. 2018. Stability analysis of multi-stage high slope with loess under rainfall infiltration[J]. Journal of Engineering Geology, 26 (6): 1648-1656. Zhang J, Han T C, Dou H Q, et al. 2014. Analysis slope safety based on infiltration model based on stratified assumption[J]. Journal of Central South University(Science and Technology), (9): 3211-3218. Zhang S, Xu Q, Zhang Q. 2017. Failure characteristics of gently inclined shallow landslides in Nanjiang, southwest of China[J]. Engineering Geology, 217 : 1-11. doi: 10.1016/j.enggeo.2016.11.025 Zhu J D, Yan H, Li S H, et al. 2019. Laboratory model experiment of landslides along loess mudstone interface induced by rainfall patterns[J]. Journal of Engineering Geology, 27 (3): 623-631. Zhu S R, Wu L Z, Peng J B. 2020. An improved Chebyshev semi-iterative method for simulating rainfall infiltration in unsaturated soils and its application to shallow landslides[J]. Journal of Hydrology: 125157. 刘传正, 陈春利. 2020. 中国地质灾害防治成效与问题对策[J]. 工程地质学报, 28 (2): 375-383. doi: 10.13544/j.cnki.jeg.2019-232 潘永亮, 简文星. 2020. 李林均等. 基于改进Green-Ampt模型的花岗岩残积土边坡降雨入渗规律研究[J]. 岩土力学, 41 (8): 2685-2692. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX202008020.htm 彭振阳, 黄介生, 伍靖伟, 等. 2012. 基于分层假设的Green-Ampt模型改进[J]. 水科学进展, 23 (1): 59-66. https://www.cnki.com.cn/Article/CJFDTOTAL-SKXJ201201008.htm 宋宇飞, 范文, 李军, 等. 2020. 不同降雨条件下不稳定斜坡财产损失风险评价——以镇巴县兴隆镇为例[J]. 工程地质学报, 28 (2): 401-411. doi: 10.13544/j.cnki.jeg.2019-255 王文焰, 汪志荣, 王全九, 等. 2003. 黄土中Green-Ampt入渗模型的改进与验证[J]. 水力学报, 34 (5): 30-34. https://www.cnki.com.cn/Article/CJFDTOTAL-SLXB200305005.htm 许强. 2020. 对滑坡监测预警相关问题的认识与思考[J]. 工程地质学报, 28 (2): 360-374. doi: 10.13544/j.cnki.jeg.2020-025 叶帅华, 时轶磊. 2018. 降雨入渗条件下多级黄土高边坡稳定性分析[J]. 工程地质学报, 26 (6): 1648-1656. doi: 10.13544/j.cnki.jeg.2017-552 张杰, 韩同春, 豆红强, 等. 2014. 基于分层假定入渗模型的边坡安全性分析[J]. 中南大学学报(自然科学版), (9): 3211-3218. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201409037.htm 朱建东, 鄢好, 李绍红, 等. 2019. 黄土-泥岩接触面滑坡的两种雨型模型试验[J]. 工程地质学报, 27 (3): 623-631. doi: 10.13544/j.cnki.jeg.2018-139 -
点击查看大图
计量
- 文章访问数: 75
- HTML全文浏览量: 11
- PDF下载量: 15
- 被引次数: 0
