en
×

分享给微信好友或者朋友圈

使用微信“扫一扫”功能。
参考文献 1
LIP, QIANH, WuJ. Accelerate research on land creation[J].Nature, 2014, 510(7503): 29–31.
参考文献 2
许增荣. 实际浸水环境下黄土湿陷性分析与浸水环境分级[J]. 铁道工程学报, 2013, 30(2): 11-16.
XUZeng-rong. Analysis of Collapsibility of Loess inReal Soaking Environment and Grading of Soaking Environment [J]. Journal of Railway EngineeringSociety, 2013, 30(2): 11-16.
参考文献 3
吴宏伟. 大气–植被–土体相互作用:理论与机理[J]. 岩土工程学报, 2017, 39(1): 1-47.
WUHong-wei. Atmosphere-plant-soil interactions: theories and mechanisms [J]. Chinese Journal ofEngineeringGeotechnical , 2017, 39(1): 1-47.
参考文献 4
吴奇凡, 樊军, 杨晓莉等. 晋陕蒙接壤区露天矿层状土壤水分入渗特征与模拟[J]. 土壤学报, 2015, 52(6): 1280-1290.
WUQi-fan, FANJun, YANGXiao-li, et al. Experiment and simulation of infiltration from layered soils in open pit mine in Jin-Shaan-Meng adjacent region [J]. Acta Pedologica Sinca, 2015, 52(6): 1280-1290.
参考文献 5
吴奇凡, 樊军, 王继军. 晋陕蒙接壤区露天矿不同质地土壤水分运动特征与模拟[J]. 煤炭学报, 2015, 40(5): 1134-1142.
WUQi-fan, FANJun, WANGJi-jun. Water movement and simulation of different soil textures at open pit mine in Jin-Shan-Meng adjacent region [J]. Journal of China Coal Society, 2015, 40(5): 1134-1142.
参考文献 6
李毅, 邵明安. 雨强对黄土坡面土壤水分入渗及再分布的影响[J]. 应用生态学报, 2006, 17 (12): 2271-2276.
LIYi, SHAOMing-an. Effects of rainfall intensity on rainfall infiltration in soil on loess slope land [J]. Chinese Journal of Applied Ecology, 2006, 17 (12): 2271-2276.
参考文献 7
包含, 侯立柱, 刘江涛等. 室内模拟降雨条件下土壤水分入渗及再分布试验[J]. 农业工程学报, 2011, 27(7): 70-75.
BAOHan, HOULi-zhu, LIUJiang-tao, et al. Experiment on process of soil water infiltration and redistribution under simulated rainfall [J]. Transactions of the CSAE, 2011, 27(7): 70-75.
参考文献 8
李萍, 李同录, 王阿丹. 黄土中水分迁移规律现场试验研究[J]. 岩土力学, 2013, 34(5): 1331-1339.
LIPing, LITong-lu, WANGA-dan. In-situ test research on regularities of water migration in loess [J]. Rock and Soil Mechanics, 2013, 34(5): 1331-1339.
参考文献 9
MAY, FENGS Y, SUD Y, et al. Modeling water infiltration in a large layered soil column with a modified Green–Ampt model and HYDRUS-1D [J]. Computers and Electronics in Agriculture, 2010, 71(S): S40–S47.
参考文献 10
王文焰, 汪志荣, 王全九, 等. 黄土中Green-Ampt入渗模型的改进与验证[J]. 水利学报, 2003, 34 (5): 30-34.
WANGWen-yan, WANGZhi-rong, WANGQuan-jiu, et al. Separation and convergence of residual flows in Yangshan Harbor area [J]. Journal of Hydraulic Engineering, 2003, 34 (5): 30-34.
参考文献 11
MEINR G, LARSONC L, Modeling the infiltration component of the rainfall–runoff process[R]. WRRC Bull, 1971,vol. 43. Water Resources Research Center, University of Minnesota, Minneapolis, Minnesota.
参考文献 12
LIX, ZHANGL M, FREDLUNDD C. Wetting front advancing column test for measuring unsaturated hydraulic conductivity[J]. Canadian Geotechnical Journal, 2009, 46(12): 1431-1445.
参考文献 13
胡海军, 李常花, 崔玉军等. 增湿情况重塑黄土非饱和渗透系数的测定方法研究[J]. 水利学报, 2018, 49(10): 1216-1226.
HUHai-jun, LIChang-hua, CUIYu-jun, et al. Research on the determination of permeability coefficient of unsaturated remolded loess under wetting condition [J]. Journal of Hydraulic Engineering, 2018, 49(10): 1216-1226.
参考文献 14
PHILIPJ R. The theory of infiltration 7[J]. Soil Sciences, 1958, 85(6): 333-337.
参考文献 15
BOUWERH. Unsaturated flow in ground water hydraulics[J]. Journal of Hydraulics Division, ASCE, 1964, 90(5): 121-144.
参考文献 16
BOUWERH. Rapid field measurement of air-entry value and hydraulic conductivity of soil as significant parameters in flow system analysis [J]. Water Resources Research, 1966, 2(4):729-738.
参考文献 17
MEINR G, FARRELLD A. Determination of wetting front suction in the Green-Ampt equation [J]. Soil Science Society of America Proceedings, 1974, 38(4): 872-876.
参考文献 18
NEUMANS P. Wetting front pressure head in the infiltration model of Green and Ampt [J]. Water Resources Research, 1976, 12(3): 564–566.
参考文献 19
BRAKENSIEK, D. L, Estimating the effective capillary pressure in the Green and Ampt infiltration equation [J]. Water Resources Research, 1977, 13(3): 680-682.
参考文献 20
BODMANG B, COLMANE A. Moisture and energy conditions during downward entry of water into soils[J]. Soil Science Society of America Proceedings, 1943, 8: 116-122.
参考文献 21
罗扬,王铁行,王娟娟.含节理黄土渗流数值模型研究[J].工程地质学报, 2014, 22(6):1115-1122.
LUOYang, WANGTie-hang, WangJuan-juan. Finite element seepage flow model for unsaturated loess with joints[J]. Journal of Engineering Geology, 2014, 22(6):1115-1122.
参考文献 22
阙云,林登辉,陈嘉.强降雨条件下含大孔隙土柱水分非平衡运移特性[J]. 同 济 大 学 学 报(自 然 科 学 版), 2017, 45(4):488-496.
QUEYun, LIN Deng-hui CHRN Jia. Water transport characteristics of no-equilibrium flow on soil column with macropore under heavy rainfall condition[J]. Journal of Tongji university (Natural Science), 2017, 45(4): 488-496.
参考文献 23
SIMUNEKJ, JARVISN J, GENUCHTEN MTVANet al. Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone[J]. Journal of Hydrology, 2003, 272(1): 14-35
参考文献 24
彭振阳,黄介生,伍靖伟,等. 基于分层假设的 Green-Ampt 模型改进[J]. 水科学进展, 2012, 23(1): 59-66.
PENGZhen-yang, HUANGJie-sheng, WU Jing-weiet al. Modification of Green-Ampt model based onthe stratification hypothesis[J]. Advances in WaterScience, 2012, 23(1): 59-66.
参考文献 25
张杰,韩同春,豆红强,等. 探讨考虑气阻作用下分层假定的雨水入渗计算分析模型[J]. 岩土工程学报, 2013, 35(12): 2219-2225.
ZHANGJie, HANTong-chun, DOUHong-qiang, et al. Analysis model for rainwater infiltration considering gas resistance under stratified assumption[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(12): 2219-2225.
参考文献 26
GENUCHTEN MTHVAN . A closed-form equation for predicting the hydraulic conductivity of unsaturated soils [J]. Soil Science Society of American Journal, 1980, 44(5): 892-898.
参考文献 27
钟佩文, 张慧莉, 田堪良, 等. 持续降雨入渗对黄土边坡稳定性的影响[J]. 人民黄河, 2018, 40(1): 76-81.
ZHONGPei-wen, ZHANGHui-li, TIANKan-liang, et al. Study on the Influence of Continuous Rainfall Infiltration on the Loess Slope Stability[J]. Yellow River, 2018, 40(1): 76-81.
参考文献 28
邵明安, 王全九, HortonR. 推求土壤水分运动参数的简单入渗法Ⅱ.实验验证[J].土壤学报, 2000, 37 (2): 217-224.
SHAOMing-an, WANGQuan-jiu. A simple infiltrationmethod for estimating soil hydraulic properties ofunsaturated soils, II: Experimental results[J]. ActaSinciaPedologica , 2000, 37(1): 217-224.
参考文献 29
贺春雄. 延安治沟造地工程水毁成因及对策[J]. 陕西水利, 2014, (1): 161-162.
HEChun-xiong. Causes and measures of water damage in Yan'an gully reclamation engineering [J]. Shaanxi Water Resources, 2014, (1): 161-162.
目录 contents

    摘要

    为合理预测积水和降雨情况下非饱和重塑黄土水分迁移过程,在Green-Ampt修正模型和王文焰等提出的模型基础上,提出了能合理考虑浸润锋处吸力作用和水分剖面形状的改进模型,并给出了该模型计算方法以及求解Richard方程的数值方法所需渗透参数的可靠确定方法。研究结果表明:与Green-Ampt修正模型和王文焰等提出的模型相比,改进模型能更准确地预测室内一维非饱和重塑黄土土柱积水入渗试验中浸润锋迁移过程和各测点水分变化过程;采用改进浸润锋前进法获得的饱和渗透系数或非饱和渗透系数函数,比采用根据室内饱和渗透试验和持水曲线间接获得的这些参数所得预测结果更为准确;降雨分析中,改进模型得到径流发生后的水分剖面基本接近于数值方法分析结果,特别是在试样干密度比较大的情况。

    Abstract

    In order to simulate the water transport process in the unsaturated remolded loess under ponding and rain fall condition, the improved infiltration model based on modified Green-Ampt model and model proposed by Wang Wenyan et al, which can consider the effect of suction at wetting front and the water content profile reasonably, was proposed. The reliable method for determining the parameters needed in the models based on modified Green-Ampt model and the numerical method for solving Richard's equations was also recommended. The research results show that the improved model can predict the process of wetting front movement and the water content change at measured points in the ponding test under one-dimensional ponding infiltration more accurately, compared with the modified Green-Ampt model and the model proposed by Wang Wenyan et al. When the saturated permeability or unsaturated conductivity function was determined directly by improved wetting front advancing method during ponding infiltration test, the results are more close to the measured values compared with those parameters indirectly determined by saturated permeability test and water retention curve. For rainfall infiltration, the water profile after runoff obtained by the improved model method is similar to that obtained by numerical method, especially for the soil with higher dry density.

    为满足经济的发展,西北地区如延安和兰州市开展了“削山造城”的工程建[1],这些工程涉及深厚重塑黄土填方。众所周知,黄土的力学性质具有显著的水敏性,即其强度和变形模量与含水率密切相关,所以研究长期环境作用下地层水分迁移规律对于深厚黄土地基沉降计算及相应的加固措施具有重要的指导意义。许增荣[2]根据浸水环境对黄土湿陷性影响程度将浸水环境分为了4个等级。黄土地层的浸水情况有降雨入渗,河流、渠道等地表水的入渗,灌溉用水入渗,管道漏水等局部浸水入渗,地下水位上升入渗等。在构筑物运营期间,降雨入渗是发生最为频繁的地层浸水情况。通常积水入渗试验是降雨入渗的极端情况而被室内试验所采[3,4,5]。实际降雨情况下的水分入渗,已有大量的试验研究如李毅[6]、包含[7]和李萍[8]通过室内或原位实验研究了不同降雨强度下黄土地层的水分迁移规律。针对积水和降雨入渗条件下土体水分迁移过程的计算,基于近似物理模型如Green-Ampt模型的解析方法和求解Richard方程的数值方法是常用的两类方法。

    基于近似物理模型的解析方法计算简便,特别是考虑浸润锋处吸力合理计算后的Green-Ampt修正模型能较好模拟积水情况下累积入渗量和时间的关[9],然而不能较好地计算水分剖面以及实际浸润锋迁移过程。为了模拟积水情况下水分剖面变化过程,王文焰[10] 在Green-Ampt模型基础上提出了考虑积水入渗过程中原状黄土水分剖面形状的入渗模型,本文应用该模型预测重塑黄土积水入渗情况水分迁移过程时,发现由于其不合理地考虑浸润区吸力作用而过快地预测了浸润锋迁移速率;结合Green-Ampt修正模型,本文提出了能合理考虑浸润锋处吸力作用和水分剖面形状的改进模型,并基于Mein和Larson[11]降雨分析理论,将该模型引入到降雨情况下的水分剖面计算。

    求解Richard方程的数值方法能严谨求解水分入渗过程,然而非饱和渗透参数的准确选取是影响该方法预测准确度的重要因[9],有时不能采用间接法如VG模型获得的非饱和渗透系数参数而需要反[4,5]。基于近似物理模型的解析方法同样存在该问题,鉴于浸润锋前进[12]或改进的浸润锋前进[13]能较精确测试非饱和土的渗透系数,本文应用改进的浸润锋前进法来获得非饱和渗透系数。

    为了检验本文改进模型和改进浸润锋前进法获取非饱和渗透系数的可靠性,应用Green-Ampt修正模型、王文焰[10]提出的模型和本文改进模型等解析方法以及求解Richard方程的数值方法模拟了室内重塑黄土一维积水入渗水分迁移过程并进行了对比。为了检验本文改进模型在降雨入渗分析中水分剖面计算的可靠性,应用本文改进模型、Green-Ampt修正模型和求解Richard方程的数值方法模拟了降雨情况下水分迁移过程并进行了对比。

  • 1 模拟方法

  • 1.1 基于Green-Ampt修正模型和王文焰等提出模型的改进模型

  • 1.1.1 积水入渗情况

    对于积水入渗情况,Green-Ampt模型采用的水分剖面如图1所示,其将实际入渗深度为Zf的浸润体简化为长度为Zs的饱和体,水力梯度i采用式(1)计算,根据达西定律得到入渗量增量,该值等于饱和体长度增量下土体水量的增量如式(2)所示,由式(1)和式(2)得到饱和体深度Zs和时间的关系如式(3)所示。

    i=H+Zs+SmZs
    (1)
    Ksidt=(θs-θi)dZs
    (2)
    t=θs-θiKsZs-(H+Sm)lnH+Zs+SmH+Sm
    (3)

    式中: H为积水水头,Zs为Green-Ampt模型的浸润锋深度(也即饱和体深度),Sm为Green-Ampt模型浸润锋Zs处的吸力水头(取为正值),Ks为饱和渗透系数,θi为土体初始体积含水率,θs为土体饱和体积含水率。

    图1
                            积水入渗下Green-Ampt模型、王文焰等提出的以及实际的水分剖面示意图

    图1 积水入渗下Green-Ampt模型、王文焰等提出的以及实际的水分剖面示意图

    Fig.1 The water content profiles adopted by Green-Ampt model, proposed by Wang W Y et al and the actual water content profile during ponding infiltration

    该模型浸润锋处吸力水头Sm并非土体初始含水率θi对应的吸力水头,Philip[14]认为Sm是一个数学量,没有实际的物理意义,该值远小于浸润锋下土体初始含水率对应的吸力水头Si。Bourwer[15]最早给出了Sm的计算公式如式(4)所示,并认为Sm可近似取为增湿过程中进水值即增湿过程中气不连续时对应的吸力值,然而该值不容易测定,其建议取为饱和样(对应于抽真空饱和样)脱湿过程中进气值的50%,该确定方法比较简单可[16]。在浸润锋以上为饱和的假设下,Mein和Larson[11]应用式(5)获得Sm,该值在初始含水率变化较大范围内相差很小,其对不同初始含水率和不同降雨强度下采用相同的值。Mein和Farrell[17]经过推导认为应用式(4)获得Sm是合理可靠的。Neuman[18]通过推导得到了浸润锋处吸力值表达式与式(4)相同。Brakensiek[19]通过比较,表明上述各种方法可得相近的结果,对于采用上述等效吸力的模型称为Green-Ampt修正模型。已有大量研究表明, Green-Ampt修正模型在模拟入渗量和时间的关系上具有较高的准确[9,24],说明了上述确定Sm的方法是有足够精度的。从公式(4)可见,Sm小于初始含水率对应的吸力水头Si

    Sm=0SiKKsdS
    (4)
    Sm=KiKsSdKKs-Ki
    (5)

    式中: SiKi分别为初始含水率对应的吸力水头和渗透系数,S K分别为吸力水头和渗透系数。

    Green-Ampt模型及修正模型仅能计算如图1所示等效饱和体深度,王文焰[10]根据大量黄土区实测水分剖面,假定入渗深度为Zf的区域近似由上部长度为Zf/2的饱和区(严格来讲是传导区,因为饱和区和过渡区的区间都很[20],其中传导区和过渡区为接近饱和的区域,所以这里仍用饱和区称之)和下部长度为Zf/2、水分剖面为椭圆的非饱和浸润区组成如图1所示,提出了能计算不同时刻水分剖面的模型,然而在计算浸润锋处等效吸力Sm上却没有采用上述确定方法,其采用下部Zf/2非饱和浸润区平均初始含水率对应的吸力Si施加于上部饱和区底部,得到上部Zf/2饱和区的水力梯度如式(6)所示,根据达西定律和水量平衡原理,得到式(7),将式(6)代入式(7)整理可得入渗深度Zf和时间t的关系如式(8)所示;如上文所述作用于长度Zs饱和体的等效吸力Sm小于Si,而将Si作用于长度为Zf/2的饱和区,可见过大估计了下部吸力的作用。该模[10]计算所得现场积水入渗试验中的水分剖面运移过程较为符合实测,可能在于原状黄土常存在节理和大孔隙,节[21]或大孔[22,23]存在导渗的作用,加快了浸润锋迁移速率,对此问题应采用相应模[21,22,23]进行分析,而不应单独在模型中增加吸力作用。

    i=H+0.5Zf+Si0.5Zf
    (6)
    Ksidt=0.5(θs-θi)dZf+0.125π(θs-θi)dZf
    (7)
    t=(4+π)(θs-θi)16Ks2Zf-4(H+Si)lnH+0.5Zf+SiH+Si
    (8)

    彭振阳[24]借助王文焰[10]提出的分层假定,采用求解Richard方程的数值方法获得了饱和区和非饱和区的比例变化;在计算浸润锋锋面吸力上,其建立了非饱和浸润区等效渗透系数K¯和整个入渗区等效渗透系数K¯w的计算公式,如式(9a)和式(9b)所示,采用式(10)计算浸润锋Zf处吸力S′m。张杰[25]沿用式(10)并给出了更严格的Zf-t的关系表达式,并在此基础上提出了考虑气阻效应下的改进模型。式(10)的理论基础在文献[24]中并没有明确给出,在不考虑气阻效应情况下,本文认为应该用式(11)计算S′m,因为Green-Ampt修正模型在模拟入渗率方面具有很高的精[9,24],式(11)能保证与Green-Ampt修正模型具有相同的入渗率。为了求解方便,本文并不用式(11)求解S′m,而是应用该式的右端项来计算入渗量的增量也即Green-Ampt修正模型来求出等效饱和体长度Zs,然后根据等效饱和体水量如图1所示阴影面积与饱和区及浸润区水量相等,来得到实际浸润锋深度Zf和饱和体深度Zs的关系如式(12a)所示。当应用王文焰[10]所采用饱和区和非饱和浸润区长度相等的假定,也即ε=0.5,此时ZfZs的关系如式(12b)所示。下文采用式(12b)来求解实际浸润锋位置并结合浸润区为椭圆形求解水分剖面并称之为本文改进模型。

    K¯Ks=1-Ki/Ksln(Ks/Ki)
    (9a)
    K¯w=K¯KsεK¯+(1-ε)Ks
    (9b)

    式中:ε为浸润区占入渗区的比例,其随Zf的增加而线性增加,可表示为ε=aZf+b

    H+SmH+S'm=K¯Ks
    (10)
    K¯wH+Zf+S'mZf=KsH+Zs+SmZs
    (11)

    式中:Zs为如图1所示的饱和体长度,按浸润区为椭圆过渡,经过换算Zs等于(1-ε+0.25πε)Zf

    Zf=(1-0.25π)b-1+(0.25πb-b+1)2+Zs(π-4)a(0.5π-2)a
    (12a)
    Zf=8π+4Zs
    (12b)
  • 1.1.2 降雨入渗情况

    对于不同降雨强度下的水分入渗模拟,Mein和Larson应用Green-Ampt修正模型进行了降雨入渗分 [11],得到与求解Richard方程的数值计算方法相近的入渗率和时间关系,但其并没有引入水分剖面形状来预测实际水分剖面。本文应用上述改进模型,获得实际水分剖面。当降雨强度小于饱和渗透系数时,不会发生径流,入渗率f(t)一直等于降雨强度P。当降雨强度大于饱和渗透系数时,在地表发生径流前,入渗率等于降雨强度;发生径流时,降雨强度P等于入渗强度Ksi,据此可得径流发生时等效饱和体长度Zs,进而根据式(12b)得到此时的实际入渗深度Zf;根据此时入渗量Fp等于等效饱和体范围内土体水量变化,可得Fp如式(13)所示,进一步可得径流发生的时刻tp如式(14)所示。径流发生后,假定水及时排走没有积水水头,即发生积水水头为0的积水入渗,入渗量F和时间的关系可按式(15)计算,入渗深度Zf由式(16)和式(12b)计算得到。

    Fp=SmKs(θs-θi)P-Ks
    (13)
    tp=FpP
    (14)
    t=tp+1KsF-Fp+Sm(θs-θi)lnSm(θs-θi)+FpSm(θs-θi)+F
    (15)
    Zs=Fθs-θi
    (16)
  • 1.2 基于求解Richard方程的数值方法

    Hydrus-1d软件应用迦辽金有限元法求解给定初始条件和边界条件下的一维Richard方程,获得非饱和土水分迁移过程。一维Richard方程如式(17)所示。对于本文积水和降雨入渗中初始含水率沿深度均相等情况,初始条件如式(18)所示,下边界条件为自由排水边界如式(19)所示。对于积水入渗情况,上边界条件如式(20a)所示;对于降雨入渗情况,径流发生前,上边界条件如式(20b)所示,当计算到上边界水头为0的时刻,即为径流时刻,从该时刻开始,将上边界条件定义为水头为0的边界,即应用式(20a)所示边界条件并将H设置为0;另外还分析了停雨后1小时的水分再分布,该过程将上边界设置为流量为0的边界即将式(20b)所示P设置为0。求解时需要hθ的关系,以及Khθ的关系;然而有时不能采用间接法如VG模型获得的非饱和渗透系数参数而需要反[4,5],本文采用改进的浸润锋前进[13]进行求取,具体参数确定过程见下节。

    θt=zKhz+K
    (17)
    θ(z,0)=θi(z)
    (18)
    hz=0
    (19)
    h(0,t)=H
    (20a)
    -Khz(0,t)-K=-P
    (20b)

    式中:z坐标取向上为正,地表处z=0;此处h为吸力水头,当孔隙水压力为负时取为负值,H代表积水水头,P为降雨强度。

  • 2 两类模拟方法的验证与分析

  • 2.1 积水入渗情况水分运移计算的验证与结果分析

  • 2.1.1 试验情况及参数确定

    为检验上述两类模拟方法在模拟重塑黄土积水情况下水分迁移的可靠性,以延安治沟造地工程建设中开挖边坡土料制取的两种干密度重塑黄土土柱积水入渗试[27]为对象进行模拟,两种干密度分别为1.35g/cm3和1.53g/cm3,土柱初始质量含水率均约为12.5%,初始体积含水率分别为0.174和0.194,积水水头为2cm,土柱高220cm,在不同高度处布置水分仪获得了积水过程中的含水率变化,土柱底部为透气板,且入渗速率相对松散土壤或砂土较慢,浸润锋下的气压阻渗作用可以不考虑。

    为了能用上述两类方法模拟试验中水分运移过程,本文测试了饱和渗透系数和持水曲线,获得了各分析方法所需参数如表1所示,其中间接法1采用室内制取相同初始状态的土样进行增湿或脱湿测试的持水曲线如图2,应用VG模型如式(21a)拟合;对制成相同初始状态的试样进行浸水饱和,应用变水头法测得的饱和渗透系数Ks,应用VG-Mualem模型即式(21b)间接获得非饱和渗透系数函数,进而获得Sm。间接法2除饱和渗透系数应用改进的浸润锋前进法根据积水入渗土柱试验获得的饱和渗透系数外,其他参数与间接法1相同。直接法则采用改进的浸润锋前进[13]根据积水入渗土柱试验获得的非饱和渗透系数函数。

    表1 各模拟分析中所需参数

    Table 1 Parameters needed in simulation methods

    土柱

    参数

    确定方法

    两类方法公用参数基于Green-Ampt修正模型的方法基于求解Richard方程的方法

    王文焰等

    提出的模型

    Green-Ampt修正模型及改进模型

    干密度

    1.35 g/cm³

    间接法1Ks=5.16×10-5cm/s注1θs=0.409注2θi=0.174Si=409cmSm=63.1cm注3θr=0.054, a=15.5kPa, n=2.05
    间接法2Ks=6.1×10-5cm/s,θs=0.409,θi=0.174Si=409cmSm=63.1cmθr=0.054, a=15.5kPa, n=2.05
    直接法Ks=6.1×10-5cm/s,θs=0.409,θi=0.174-Sm=72.7cmθr=0.114, a=16.5kPa, n=3.10

    干密度

    1.53 g/cm³

    间接法1Ks=0.65×10-5cm/s,θs=0.364,θi=0.194Si=450cmSm=77.1cm注3θr=0.051, a=21.3kPa, n=1.91
    间接法2Ks=1.8×10-5cm/s,θs=0.364,θi=0.194Si=450cmSm=77.1cmθr=0.051, a=21.3kPa, n=1.91
    直接法Ks=1.8×10-5cm/s,θs=0.364,θi=0.194-Sm=86.1cmθr=0.138, a=16.5kPa, n=2.60

    注:注1:抽真空样饱和渗透系数两种干密度样分别为6.50×10-5cm/s和3.32×10-5cm/s,由于浸水饱和试样与一维土柱试验入渗后饱和度接近,渗透系数均采用浸水饱和试样的渗透系数。注2:根据浸水饱和样及一维土柱试验入渗后土柱含水率确定θs,该含水率对应土柱入渗试验中传导区含水[20]与并不是完全饱和的含水率。注3:根据式(5)计算得到两种干密度试样Sm分别为65.6cm和80.1cm,鉴于式(4)更为严格,这里仅采用式(4)计算得到的值。

    图2
                            持水曲线

    图2 持水曲线

    Fig.2 Soil water retention curve

    (21a)

    K=KsΘ0.5[1-(1-Θ1/m)m]2
    (21b)

    式中: θw为体积含水率,ψ为基质吸力,单位为kPa;a、n、θr、θs为拟合参数; a单位为kPa;n为曲线斜率有关的参数,m=1-1/nθs选取为土柱积水入渗后试样的饱和含水率;Θ=θw-θrθs-θr=1+(ψa)n-m

    其中根据改进的浸润锋前进法获得非饱和渗透参数的过程如下,根据土柱上各测点含水率开始变化的时间即浸润锋达到该处的时间,按幂函数关系拟合得到浸润锋迁移距离和时间的关系,对于两种干密度样,所得结果分别如式(22a)和(22b)所示,相关系数均在0.997以上。应用该关系很容易得到不同时刻浸润锋迁移速率vZf,以其中一个测点A为例,按式(23a)计算得到t1~t2时间段通过A断面的水流速度v,浸润锋前进[12]采用式(23b)计算相应水力梯度i,依据改进的浸润锋前进[13]相应采用式(23c)计算t1~t2时间段A断面的水力坡降i,根据达西定律便可得到该时间段平均吸力下的渗透系数,选取不同的时间段便可得到不同吸力下的渗透系数。图3给出了应用改进的浸润锋前进法所得不同吸力下的渗透系数结果,这里选取了水分变化过程比较合理的测点。从结果上来看虽然有一定的离散,但每个土柱所用的两个测点获得的不同吸力下的渗透系数都比较接近。应用VG模型即式(20b),对所得非饱和渗透系数和基质吸力的关系进行拟合,拟合得到的饱和渗透系数在抽真空饱和样和浸水饱和样所测渗透系数之间,可见虽然浸水饱和样和土柱入渗试验后的饱和度接近,在渗透系数上仍存在试样不对等性,文[28]则建议采用入渗试验后的土柱进行渗透试验获得饱和渗透系数。由于应用式(20b)拟合非饱和渗透系数时,所得an与原持水曲线拟合参数不同,因此需要在新的an下,重新对持水曲线拟合,得到残余含水率θr分别为0.114和0.138,虽然该参数有较大改变,但前后两次所得持水曲线在大于初始含水率时都很接近测试点,而入渗过程是增湿过程,所得持水曲线和非饱和渗透系数函数在含水率大于初始含水率时具有足够的精度。

    Zf=1.053t0.622
    (22a)
    Zf=0.692t0.592
    (22b)
    v(zA,t1+t22)=14θzA,t2+θzA,t1-2θi                       ×vZf(t1)+vZf(t2)
    (23a)
    i (zA,t2)=ψzA,t1-ψzA,t20.5γw[vZf(t1)+vZf(t2)]t2-t1+1
    (23b)
    i (zA,t1+t22)=14i (zA,t1)+2i (zA,t2)+i (zA,t3)
    (23c)

    式中:θzA,t2代表t2时刻,深度zA处测点A的体积含水率;ψ表示基质吸力(kPa),由前面所测持水曲线拟合函数根据含水率反算得到;θi表示初始体积含水率;vZf表示t1~t2时间段浸润锋迁移速度。

    html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F005.jpg

    (a) 干密度1.35g/cm3土柱

    html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F006.jpg

    (b) 干密度1.53g/cm3土柱

    图3 改进的浸润锋前进法所得非饱和渗透系数

    Fig.3 Unsaturated hydraulic conductivity obtained by improved wetting front advancing method

  • 2.1.2 模拟结果分析

    图4给出了各方法所得浸润锋入渗深度和时间的关系以及与实测结果的对比。总体上,王文焰等提出的模[10]过快地预测了入渗过程,Green-Ampt修正模型较慢地预测了入渗过程,而采用相同参数情况下改进模型较Green-Ampt修正模型提高了浸润锋迁移速率,相比前两种方法均更加接近实测值。针对采用不同方法确定的参数,采用间接法1所得参数误差较大,而采用间接法2或直接法所得参数预测结果均较为接近实测值,说明饱和渗透系数的准确性在很大程度决定了预测的准确度。另外整体上,对干密度1.53 g/cm3土柱预测较为准确,这可能与1.35g/cm3土柱具有导渗的大孔隙有关。综合以上分析,下文仅给出改进模型以及Hydrus采用直接法所得参数的分析结果。

    html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F008.jpg

    (a) 干密度1.35g/cm3土柱

    html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F009.jpg

    (b) 干密度1.53g/cm3土柱

    图4 积水入渗过程中浸润锋入渗深度与时间的关系

    Fig.4 The relationship between the depth of wetting front and time during ponding infiltration

    图5给出了离土柱顶面不同深度测点处体积含水率随时间的变化,其中由于深200cm处测点水分

    html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F011.jpg

    (a) 干密度1.35g/cm3土柱

    html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F012.jpg

    (b) 干密度1.53g/cm3土柱

    图5 积水入渗过程中各测点含水率随时间变化预测与

    Fig.5 Comparison of predicted and measured water content change at measuring points during ponding infiltration

    注:实测值的对比

    变化过程中,浸润锋到达了底部,因此这里便没给出该情况的模拟结果。从结果上看,改进模型和Hydrus软件都能模拟出浅部测点体积含水率变化快,深部测点体积含水率变化稍慢的特点。总体上,对于干密度1.53g/cm3土柱预测较好,而对干密度1.35g/cm3土柱预测稍差。

    图6给出了浸润锋到达各测点时的水分分布预测值和实测结果的对比。从结果上来看,改进模型和Hydrus软件所得结果很接近,只是在浸润锋位置处稍有差异。有限的实测点结果接近于两种方法所得的水分分布线,说明两种方法的可靠性。另外根据Hydrus软件所得结果,分析水分剖面从饱和到非饱和的过渡点,得到饱和区(严格来讲为传导区)所占比例随着入渗深度的增加由0.3变化到0.6。

    html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F014.jpg

    (a) 干密度1.35g/cm3土柱

    html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F015.jpg

    (b) 干密度1.53g/cm3土柱

    图6 积水入渗过程浸润锋到达各测点时的水分分布预测值和实测结果对比

    Fig.6 Comparison of the predicted and measured water content profile when wetting front arrived at measurement points during ponding infiltration

  • 2.2 降雨入渗情况的验证与分析

    为了获得积水入渗和降雨入渗的差别以及改进模型相对于Green-Ampt修正模型在降雨入渗过程分析的适宜性,对比了Green-Ampt修正模型、本文改进模型和Hydrus降雨情况下浸润锋入渗规律和水分剖面并与积水情况进行了对比。

    根据近年来陕北地区7月份经常遭受暴雨,24小时降雨量可达200mm以上,结合取土地区的降雨量资[29],这里给出特大暴雨强度1.17cm/h,大雨强度0.208cm/h和中雨强度0.104cm/h下降雨1天和停雨1天的分析结果。对于Green-Ampt修正模型和本文改进模型,按式(14)计算得到干密度1.35g/cm3和干密度1.53g/cm3黄土地层仅特大暴雨情况下分别在3.4h和0.73h发生径流,其他两种雨强在1天内均未发生径流;Hydrus分析结果表明1天内也仅特大暴雨下发生了径流,径流时间分别为4.5h和0.8h,这与Green-Ampt修正模型和本文改进模型所得结果相近。

    图7给出了积水和三种雨强条件下浸润锋入渗深度和时间的关系。对于Green-Ampt修正模型和本文改进模型,径流之前,由于地表处于非饱和状态不能应用改进模型预测,图中仅给出了径流发生后的入渗深度和时间的关系,从结果上可见本文改进模型比Green-Ampt修正模型更加接近Hydrus所得结果。对比三种雨强和积水入渗结果,特大暴雨情况比较接近于积水入渗情况,特别是干密度为1.53g/cm3地层;这也说明了积水入渗可以作为降雨入渗的极端条件予以研究。

    html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F017.jpg

    (a) 干密度1.35g/cm3地层

    html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F018.jpg

    (b) 干密度1.53g/cm3地层

    图7 降雨24h过程中入渗深度和时间的关系及与积水入渗的对比

    Fig.7 The relationship between the infiltration depth and time during 24h rainfall compared with that under ponding condition

    图8给出了特大暴雨情况下,在降雨24小时和停雨24小时时间段,两种干密度地层水分入渗及水分再分布过程水分剖面图。Hydrus分析结果表明初始入渗时地表由非饱和状态逐渐过渡到饱和状态,Green-Ampt修正模型和本文改进模型不能预测径流发生前的水分分布变化;发生径流时及降雨24h时,本文改进模型所得水分分布与Hydrus所得水分分布接近,特别是干密度1.53g/cm3地层,而Green-Ampt修正模型预测水分剖面精度较差。相对于降雨24h,发生径流时Green-Ampt修正模型和本

    html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F020.jpg

    (a) 干密度1.35g/cm3地层

    html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F021.jpg

    (b) 干密度1.53 g/cm3地层

    图8 降雨一天及停雨一天过程中的水分剖面变化

    Fig.8 The change of water content profile during one day of rain and following one day without rain

    文改进模型所得结果与Hydrus分析结果差异较大,

    这主要是径流发生的时间不同导致两者入渗量不同,另外如前面分析表明入渗深度浅时,饱和区所占比例小,改进模型在此阶段采用了相对较大的饱和区比例。降雨结束后,改进模型不能预测水分重分布,Hydrus得到地表含水率减少并且更深处水分增加,这与已有实测结[6,7]相符;需要说明的是,该分析过程宜用增湿后脱湿的持水曲线函数,另外停雨后一般涉及到蒸发,需要测试或计算蒸发强度E,应用将式(20b)中P替换为-E的上边界条件进行计算。

  • 3 结论

    在Green-Ampt修正模型和王文焰等提出的模[10]基础上,提出了可较为合理预测入渗过程中水分剖面及迁移过程的改进模型,应用各模型和求解Richard方程的数值方法模拟了室内重塑黄土积水入渗试验,并对比了特定雨强下改进模型和数值方法所得的水分剖面。主要结论如下:

    (1)改进模型合理考虑了浸润锋处吸力作用和水分剖面形状,相比Green-Ampt修正模型和王文焰等提出的模型,能更好地模拟室内非饱和重塑黄土积水入渗试验中水分迁移过程。

    (2)根据土柱入渗试验各测点水分变化,采用改进的浸润锋前进[13]获得的饱和渗透系数或非饱和渗透系数函数时,能较好地预测水分迁移过程,而采用室内制样获得的饱和渗透系数和间接法获得的非饱和渗透系数函数时预测误差较大。

    (3)根据Mein和Larson提出的降雨入渗理论,将改进模型推广到降雨情况下径流发生后的水分剖面预测,所得结果与求解Richard方程的数值方法分析结果接近,特别是在试样干密度比较大的情况,改进模型相对数值方法计算简便、易于应用。另外应用Hydrus软件可以分析得到径流发生前和停雨后的水分迁移变化过程,结果与已有试验规律相符,显示出较强的模拟能力。

  • 参考文献

    • 1

      LI P, QIAN H, Wu J. Accelerate research on land creation[J].Nature, 2014, 510(7503): 29–31.

    • 2

      许增荣. 实际浸水环境下黄土湿陷性分析与浸水环境分级[J]. 铁道工程学报, 2013, 30(2): 11-16.

      XU Zeng-rong. Analysis of Collapsibility of Loess inReal Soaking Environment and Grading of Soaking Environment [J]. Journal of Railway Engineering

      Society, 2013, 30(2): 11-16.

    • 3

      吴宏伟. 大气–植被–土体相互作用:理论与机理[J]. 岩土工程学报, 2017, 39(1): 1-47.

      WU Hong-wei. Atmosphere-plant-soil interactions: theories and mechanisms [J]. Chinese Journal of

      Geotechnical Engineering , 2017, 39(1): 1-47.

    • 4

      吴奇凡, 樊军, 杨晓莉等. 晋陕蒙接壤区露天矿层状土壤水分入渗特征与模拟[J]. 土壤学报, 2015, 52(6): 1280-1290.

      WU Qi-fan, FAN Jun, YANG Xiao-li, et al. Experiment and simulation of infiltration from layered soils in open pit mine in Jin-Shaan-Meng adjacent region [J]. Acta Pedologica Sinca, 2015, 52(6): 1280-1290.

    • 5

      吴奇凡, 樊军, 王继军. 晋陕蒙接壤区露天矿不同质地土壤水分运动特征与模拟[J]. 煤炭学报, 2015, 40(5): 1134-1142.

      WU Qi-fan, FAN Jun, WANG Ji-jun. Water movement and simulation of different soil textures at open pit mine in Jin-Shan-Meng adjacent region [J]. Journal of China Coal Society, 2015, 40(5): 1134-1142.

    • 6

      李毅, 邵明安. 雨强对黄土坡面土壤水分入渗及再分布的影响[J]. 应用生态学报, 2006, 17 (12): 2271-2276.

      LI Yi, SHAO Ming-an. Effects of rainfall intensity on rainfall infiltration in soil on loess slope land [J]. Chinese Journal of Applied Ecology, 2006, 17 (12): 2271-2276.

    • 7

      包含, 侯立柱, 刘江涛等. 室内模拟降雨条件下土壤水分入渗及再分布试验[J]. 农业工程学报, 2011, 27(7): 70-75.

      BAO Han, HOU Li-zhu, LIU Jiang-tao, et al. Experiment on process of soil water infiltration and redistribution under simulated rainfall [J]. Transactions of the CSAE, 2011, 27(7): 70-75.

    • 8

      李萍, 李同录, 王阿丹. 黄土中水分迁移规律现场试验研究[J]. 岩土力学, 2013, 34(5): 1331-1339.

      LI Ping, LI Tong-lu, WANG A-dan. In-situ test research on regularities of water migration in loess [J]. Rock and Soil Mechanics, 2013, 34(5): 1331-1339.

    • 9

      MA Y, FENG S Y, SU D Y, et al. Modeling water infiltration in a large layered soil column with a modified Green–Ampt model and HYDRUS-1D [J]. Computers and Electronics in Agriculture, 2010, 71(S): S40–S47.

    • 10

      王文焰, 汪志荣, 王全九, 等. 黄土中Green-Ampt入渗模型的改进与验证[J]. 水利学报, 2003, 34 (5): 30-34.

      WANG Wen-yan, WANG Zhi-rong, WANG Quan-jiu, et al. Separation and convergence of residual flows in Yangshan Harbor area [J]. Journal of Hydraulic Engineering, 2003, 34 (5): 30-34.

    • 11

      MEIN R G, LARSON C L, Modeling the infiltration component of the rainfall–runoff process[R]. WRRC Bull, 1971,

      vol. 43. Water Resources Research Center, University of Minnesota, Minneapolis, Minnesota.

    • 12

      LI X, ZHANG L M, FREDLUND D C. Wetting front advancing column test for measuring unsaturated hydraulic conductivity[J]. Canadian Geotechnical Journal, 2009, 46(12): 1431-1445.

    • 13

      胡海军, 李常花, 崔玉军等. 增湿情况重塑黄土非饱和渗透系数的测定方法研究[J]. 水利学报, 2018, 49(10): 1216-1226.

      HU Hai-jun, LI Chang-hua, CUI Yu-jun, et al. Research on the determination of permeability coefficient of unsaturated remolded loess under wetting condition [J]. Journal of Hydraulic Engineering, 2018, 49(10): 1216-1226.

    • 14

      PHILIP J R. The theory of infiltration 7[J]. Soil Sciences, 1958, 85(6): 333-337.

    • 15

      BOUWER H. Unsaturated flow in ground water hydraulics[J]. Journal of Hydraulics Division, ASCE, 1964, 90(5): 121-144.

    • 16

      BOUWER H. Rapid field measurement of air-entry value and hydraulic conductivity of soil as significant parameters in flow system analysis [J]. Water Resources Research, 1966, 2(4):729-738.

    • 17

      MEIN R G, FARRELL D A. Determination of wetting front suction in the Green-Ampt equation [J]. Soil Science Society of America Proceedings, 1974, 38(4): 872-876.

    • 18

      NEUMAN S P. Wetting front pressure head in the infiltration model of Green and Ampt [J]. Water Resources Research, 1976, 12(3): 564–566.

    • 19

      BRAKENSIEK, D. L, Estimating the effective capillary pressure in the Green and Ampt infiltration equation [J]. Water Resources Research, 1977, 13(3): 680-682.

    • 20

      BODMAN G B, COLMAN E A. Moisture and energy conditions during downward entry of water into soils[J]. Soil Science Society of America Proceedings, 1943, 8: 116-122.

    • 21

      罗扬,王铁行,王娟娟.含节理黄土渗流数值模型研究[J].工程地质学报, 2014, 22(6):1115-1122.

      LUO Yang, WANG Tie-hang, Wang Juan-juan. Finite element seepage flow model for unsaturated loess with joints[J]. Journal of Engineering Geology, 2014, 22(6):1115-1122.

    • 22

      阙云,林登辉,陈嘉.强降雨条件下含大孔隙土柱水分非平衡运移特性[J]. 同 济 大 学 学 报(自 然 科 学 版), 2017, 45(4):488-496.

      QUE Yun, LIN Deng-hui CHRN Jia. Water transport characteristics of no-equilibrium flow on soil column with macropore under heavy rainfall condition[J]. Journal of Tongji university (Natural Science), 2017, 45(4): 488-496.

    • 23

      SIMUNEK J, JARVIS N J, VAN GENUCHTEN MTet al. Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone[J]. Journal of Hydrology, 2003, 272(1): 14-35

    • 24

      彭振阳,黄介生,伍靖伟,等. 基于分层假设的 Green-Ampt 模型改进[J]. 水科学进展, 2012, 23(1): 59-66.

      PENG Zhen-yang, HUANG Jie-sheng, WU Jing-weiet al. Modification of Green-Ampt model based on

      the stratification hypothesis[J]. Advances in Water

      Science, 2012, 23(1): 59-66.

    • 25

      张杰,韩同春,豆红强,等. 探讨考虑气阻作用下分层假定的雨水入渗计算分析模型[J]. 岩土工程学报, 2013, 35(12): 2219-2225.

      ZHANG Jie, HAN Tong-chun, DOU Hong-qiang, et al. Analysis model for rainwater infiltration considering gas resistance under stratified assumption[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(12): 2219-2225.

    • 26

      VAN GENUCHTEN MTH . A closed-form equation for predicting the hydraulic conductivity of unsaturated soils [J]. Soil Science Society of American Journal, 1980, 44(5): 892-898.

    • 27

      钟佩文, 张慧莉, 田堪良, 等. 持续降雨入渗对黄土边坡稳定性的影响[J]. 人民黄河, 2018, 40(1): 76-81.

      ZHONG Pei-wen, ZHANG Hui-li, TIAN Kan-liang, et al. Study on the Influence of Continuous Rainfall Infiltration on the Loess Slope Stability[J]. Yellow River, 2018, 40(1): 76-81.

    • 28

      邵明安, 王全九, Horton R. 推求土壤水分运动参数的简单入渗法Ⅱ.实验验证[J].土壤学报, 2000, 37 (2): 217-224.

      SHAO Ming-an, WANG Quan-jiu. A simple infiltration

      method for estimating soil hydraulic properties of

      unsaturated soils, II: Experimental results[J]. Acta

      Pedologica Sincia , 2000, 37(1): 217-224.

    • 29

      贺春雄. 延安治沟造地工程水毁成因及对策[J]. 陕西水利, 2014, (1): 161-162.

      HE Chun-xiong. Causes and measures of water damage in Yan'an gully reclamation engineering [J]. Shaanxi Water Resources, 2014, (1): 161-162.

胡海军

机 构:西北农林科技大学 水利与建筑工程学院,陕西 杨凌 712100

Affiliation:College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling, Shaanxi 712100, China

角 色:第一作者

Role:First author

作者简介:胡海军,男,博士,讲师,硕士生导师,主要从事结构性黄土的宏微观特性、离散元数值模拟方面的研究;E-mail:

李博鹏

机 构:西北农林科技大学 水利与建筑工程学院,陕西 杨凌 712100

Affiliation:College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling, Shaanxi 712100, China

田堪良

机 构:西北农林科技大学 水土保持研究所,陕西 杨凌 712100

Affiliation:Institute of Soil and Water Conservation, Northwest A&F University, Yangling 712100, China

巴亚东

机 构:西北农林科技大学 水利与建筑工程学院,陕西 杨凌 712100

Affiliation:College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling, Shaanxi 712100, China

崔玉军

机 构:Ecole des Ponts Paris Tech, Laboratoire Navier/CERMES, Paris 77455 France

Affiliation:Ecole des Ponts Paris Tech, Laboratoire Navier/CERMES, Paris 77455 France

html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F001.jpg
土柱

参数

确定方法

两类方法公用参数基于Green-Ampt修正模型的方法基于求解Richard方程的方法

王文焰等

提出的模型

Green-Ampt修正模型及改进模型

干密度

1.35 g/cm³

间接法1Ks=5.16×10-5cm/s注1θs=0.409注2θi=0.174Si=409cmSm=63.1cm注3θr=0.054, a=15.5kPa, n=2.05
间接法2Ks=6.1×10-5cm/s,θs=0.409,θi=0.174Si=409cmSm=63.1cmθr=0.054, a=15.5kPa, n=2.05
直接法Ks=6.1×10-5cm/s,θs=0.409,θi=0.174-Sm=72.7cmθr=0.114, a=16.5kPa, n=3.10

干密度

1.53 g/cm³

间接法1Ks=0.65×10-5cm/s,θs=0.364,θi=0.194Si=450cmSm=77.1cm注3θr=0.051, a=21.3kPa, n=1.91
间接法2Ks=1.8×10-5cm/s,θs=0.364,θi=0.194Si=450cmSm=77.1cmθr=0.051, a=21.3kPa, n=1.91
直接法Ks=1.8×10-5cm/s,θs=0.364,θi=0.194-Sm=86.1cmθr=0.138, a=16.5kPa, n=2.60
html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F003.jpg
html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F002.jpg
html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F005.jpg
html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F006.jpg
html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F008.jpg
html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F009.jpg
html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F011.jpg
html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F012.jpg
html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F014.jpg
html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F015.jpg
html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F017.jpg
html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F018.jpg
html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F020.jpg
html/jtuns/19018/alternativeImage/58f8e88b-9c59-4b66-b227-cd705758d7f6-F021.jpg

图1 积水入渗下Green-Ampt模型、王文焰等提出的以及实际的水分剖面示意图

Fig.1 The water content profiles adopted by Green-Ampt model, proposed by Wang W Y et al and the actual water content profile during ponding infiltration

表1 各模拟分析中所需参数

Table 1 Parameters needed in simulation methods

图2 持水曲线

Fig.2 Soil water retention curve

图3 改进的浸润锋前进法所得非饱和渗透系数 -- (a) 干密度1.35g/cm3土柱

Fig.3 Unsaturated hydraulic conductivity obtained by improved wetting front advancing method

图3 改进的浸润锋前进法所得非饱和渗透系数 -- (b) 干密度1.53g/cm3土柱

Fig.3 Unsaturated hydraulic conductivity obtained by improved wetting front advancing method

图4 积水入渗过程中浸润锋入渗深度与时间的关系 -- (a) 干密度1.35g/cm3土柱

Fig.4 The relationship between the depth of wetting front and time during ponding infiltration

图4 积水入渗过程中浸润锋入渗深度与时间的关系 -- (b) 干密度1.53g/cm3土柱

Fig.4 The relationship between the depth of wetting front and time during ponding infiltration

图5 积水入渗过程中各测点含水率随时间变化预测与 -- (a) 干密度1.35g/cm3土柱

Fig.5 Comparison of predicted and measured water content change at measuring points during ponding infiltration

图5 积水入渗过程中各测点含水率随时间变化预测与 -- (b) 干密度1.53g/cm3土柱

Fig.5 Comparison of predicted and measured water content change at measuring points during ponding infiltration

图6 积水入渗过程浸润锋到达各测点时的水分分布预测值和实测结果对比 -- (a) 干密度1.35g/cm3土柱

Fig.6 Comparison of the predicted and measured water content profile when wetting front arrived at measurement points during ponding infiltration

图6 积水入渗过程浸润锋到达各测点时的水分分布预测值和实测结果对比 -- (b) 干密度1.53g/cm3土柱

Fig.6 Comparison of the predicted and measured water content profile when wetting front arrived at measurement points during ponding infiltration

图7 降雨24h过程中入渗深度和时间的关系及与积水入渗的对比 -- (a) 干密度1.35g/cm3地层

Fig.7 The relationship between the infiltration depth and time during 24h rainfall compared with that under ponding condition

图7 降雨24h过程中入渗深度和时间的关系及与积水入渗的对比 -- (b) 干密度1.53g/cm3地层

Fig.7 The relationship between the infiltration depth and time during 24h rainfall compared with that under ponding condition

图8 降雨一天及停雨一天过程中的水分剖面变化 -- (a) 干密度1.35g/cm3地层

Fig.8 The change of water content profile during one day of rain and following one day without rain

图8 降雨一天及停雨一天过程中的水分剖面变化 -- (b) 干密度1.53 g/cm3地层

Fig.8 The change of water content profile during one day of rain and following one day without rain

image /

无注解

注1:抽真空样饱和渗透系数两种干密度样分别为6.50×10-5cm/s和3.32×10-5cm/s,由于浸水饱和试样与一维土柱试验入渗后饱和度接近,渗透系数均采用浸水饱和试样的渗透系数。注2:根据浸水饱和样及一维土柱试验入渗后土柱含水率确定θs,该含水率对应土柱入渗试验中传导区含水[20]与并不是完全饱和的含水率。注3:根据式(5)计算得到两种干密度试样Sm分别为65.6cm和80.1cm,鉴于式(4)更为严格,这里仅采用式(4)计算得到的值。

无注解

无注解

无注解

无注解

无注解

无注解

实测值的对比

实测值的对比

无注解

无注解

无注解

无注解

无注解

无注解

  • 参考文献

    • 1

      LI P, QIAN H, Wu J. Accelerate research on land creation[J].Nature, 2014, 510(7503): 29–31.

    • 2

      许增荣. 实际浸水环境下黄土湿陷性分析与浸水环境分级[J]. 铁道工程学报, 2013, 30(2): 11-16.

      XU Zeng-rong. Analysis of Collapsibility of Loess inReal Soaking Environment and Grading of Soaking Environment [J]. Journal of Railway Engineering

      Society, 2013, 30(2): 11-16.

    • 3

      吴宏伟. 大气–植被–土体相互作用:理论与机理[J]. 岩土工程学报, 2017, 39(1): 1-47.

      WU Hong-wei. Atmosphere-plant-soil interactions: theories and mechanisms [J]. Chinese Journal of

      Geotechnical Engineering , 2017, 39(1): 1-47.

    • 4

      吴奇凡, 樊军, 杨晓莉等. 晋陕蒙接壤区露天矿层状土壤水分入渗特征与模拟[J]. 土壤学报, 2015, 52(6): 1280-1290.

      WU Qi-fan, FAN Jun, YANG Xiao-li, et al. Experiment and simulation of infiltration from layered soils in open pit mine in Jin-Shaan-Meng adjacent region [J]. Acta Pedologica Sinca, 2015, 52(6): 1280-1290.

    • 5

      吴奇凡, 樊军, 王继军. 晋陕蒙接壤区露天矿不同质地土壤水分运动特征与模拟[J]. 煤炭学报, 2015, 40(5): 1134-1142.

      WU Qi-fan, FAN Jun, WANG Ji-jun. Water movement and simulation of different soil textures at open pit mine in Jin-Shan-Meng adjacent region [J]. Journal of China Coal Society, 2015, 40(5): 1134-1142.

    • 6

      李毅, 邵明安. 雨强对黄土坡面土壤水分入渗及再分布的影响[J]. 应用生态学报, 2006, 17 (12): 2271-2276.

      LI Yi, SHAO Ming-an. Effects of rainfall intensity on rainfall infiltration in soil on loess slope land [J]. Chinese Journal of Applied Ecology, 2006, 17 (12): 2271-2276.

    • 7

      包含, 侯立柱, 刘江涛等. 室内模拟降雨条件下土壤水分入渗及再分布试验[J]. 农业工程学报, 2011, 27(7): 70-75.

      BAO Han, HOU Li-zhu, LIU Jiang-tao, et al. Experiment on process of soil water infiltration and redistribution under simulated rainfall [J]. Transactions of the CSAE, 2011, 27(7): 70-75.

    • 8

      李萍, 李同录, 王阿丹. 黄土中水分迁移规律现场试验研究[J]. 岩土力学, 2013, 34(5): 1331-1339.

      LI Ping, LI Tong-lu, WANG A-dan. In-situ test research on regularities of water migration in loess [J]. Rock and Soil Mechanics, 2013, 34(5): 1331-1339.

    • 9

      MA Y, FENG S Y, SU D Y, et al. Modeling water infiltration in a large layered soil column with a modified Green–Ampt model and HYDRUS-1D [J]. Computers and Electronics in Agriculture, 2010, 71(S): S40–S47.

    • 10

      王文焰, 汪志荣, 王全九, 等. 黄土中Green-Ampt入渗模型的改进与验证[J]. 水利学报, 2003, 34 (5): 30-34.

      WANG Wen-yan, WANG Zhi-rong, WANG Quan-jiu, et al. Separation and convergence of residual flows in Yangshan Harbor area [J]. Journal of Hydraulic Engineering, 2003, 34 (5): 30-34.

    • 11

      MEIN R G, LARSON C L, Modeling the infiltration component of the rainfall–runoff process[R]. WRRC Bull, 1971,

      vol. 43. Water Resources Research Center, University of Minnesota, Minneapolis, Minnesota.

    • 12

      LI X, ZHANG L M, FREDLUND D C. Wetting front advancing column test for measuring unsaturated hydraulic conductivity[J]. Canadian Geotechnical Journal, 2009, 46(12): 1431-1445.

    • 13

      胡海军, 李常花, 崔玉军等. 增湿情况重塑黄土非饱和渗透系数的测定方法研究[J]. 水利学报, 2018, 49(10): 1216-1226.

      HU Hai-jun, LI Chang-hua, CUI Yu-jun, et al. Research on the determination of permeability coefficient of unsaturated remolded loess under wetting condition [J]. Journal of Hydraulic Engineering, 2018, 49(10): 1216-1226.

    • 14

      PHILIP J R. The theory of infiltration 7[J]. Soil Sciences, 1958, 85(6): 333-337.

    • 15

      BOUWER H. Unsaturated flow in ground water hydraulics[J]. Journal of Hydraulics Division, ASCE, 1964, 90(5): 121-144.

    • 16

      BOUWER H. Rapid field measurement of air-entry value and hydraulic conductivity of soil as significant parameters in flow system analysis [J]. Water Resources Research, 1966, 2(4):729-738.

    • 17

      MEIN R G, FARRELL D A. Determination of wetting front suction in the Green-Ampt equation [J]. Soil Science Society of America Proceedings, 1974, 38(4): 872-876.

    • 18

      NEUMAN S P. Wetting front pressure head in the infiltration model of Green and Ampt [J]. Water Resources Research, 1976, 12(3): 564–566.

    • 19

      BRAKENSIEK, D. L, Estimating the effective capillary pressure in the Green and Ampt infiltration equation [J]. Water Resources Research, 1977, 13(3): 680-682.

    • 20

      BODMAN G B, COLMAN E A. Moisture and energy conditions during downward entry of water into soils[J]. Soil Science Society of America Proceedings, 1943, 8: 116-122.

    • 21

      罗扬,王铁行,王娟娟.含节理黄土渗流数值模型研究[J].工程地质学报, 2014, 22(6):1115-1122.

      LUO Yang, WANG Tie-hang, Wang Juan-juan. Finite element seepage flow model for unsaturated loess with joints[J]. Journal of Engineering Geology, 2014, 22(6):1115-1122.

    • 22

      阙云,林登辉,陈嘉.强降雨条件下含大孔隙土柱水分非平衡运移特性[J]. 同 济 大 学 学 报(自 然 科 学 版), 2017, 45(4):488-496.

      QUE Yun, LIN Deng-hui CHRN Jia. Water transport characteristics of no-equilibrium flow on soil column with macropore under heavy rainfall condition[J]. Journal of Tongji university (Natural Science), 2017, 45(4): 488-496.

    • 23

      SIMUNEK J, JARVIS N J, VAN GENUCHTEN MTet al. Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone[J]. Journal of Hydrology, 2003, 272(1): 14-35

    • 24

      彭振阳,黄介生,伍靖伟,等. 基于分层假设的 Green-Ampt 模型改进[J]. 水科学进展, 2012, 23(1): 59-66.

      PENG Zhen-yang, HUANG Jie-sheng, WU Jing-weiet al. Modification of Green-Ampt model based on

      the stratification hypothesis[J]. Advances in Water

      Science, 2012, 23(1): 59-66.

    • 25

      张杰,韩同春,豆红强,等. 探讨考虑气阻作用下分层假定的雨水入渗计算分析模型[J]. 岩土工程学报, 2013, 35(12): 2219-2225.

      ZHANG Jie, HAN Tong-chun, DOU Hong-qiang, et al. Analysis model for rainwater infiltration considering gas resistance under stratified assumption[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(12): 2219-2225.

    • 26

      VAN GENUCHTEN MTH . A closed-form equation for predicting the hydraulic conductivity of unsaturated soils [J]. Soil Science Society of American Journal, 1980, 44(5): 892-898.

    • 27

      钟佩文, 张慧莉, 田堪良, 等. 持续降雨入渗对黄土边坡稳定性的影响[J]. 人民黄河, 2018, 40(1): 76-81.

      ZHONG Pei-wen, ZHANG Hui-li, TIAN Kan-liang, et al. Study on the Influence of Continuous Rainfall Infiltration on the Loess Slope Stability[J]. Yellow River, 2018, 40(1): 76-81.

    • 28

      邵明安, 王全九, Horton R. 推求土壤水分运动参数的简单入渗法Ⅱ.实验验证[J].土壤学报, 2000, 37 (2): 217-224.

      SHAO Ming-an, WANG Quan-jiu. A simple infiltration

      method for estimating soil hydraulic properties of

      unsaturated soils, II: Experimental results[J]. Acta

      Pedologica Sincia , 2000, 37(1): 217-224.

    • 29

      贺春雄. 延安治沟造地工程水毁成因及对策[J]. 陕西水利, 2014, (1): 161-162.

      HE Chun-xiong. Causes and measures of water damage in Yan'an gully reclamation engineering [J]. Shaanxi Water Resources, 2014, (1): 161-162.