堤防渗流计算(有详细的计算过程和程序)

【转贴】堤防渗流计算（有详细的计算过程和程序）
可以当作计算书使用
本帖转载自【水利部落论坛】
/dispbbs.asp?boardID=44&ID=948&page=1
根据堤《防工程设计规范GB50286-98 》
附录E.2.1 不透水堤基 均质土堤 下游无排水设备或有贴坡式排水
项目 计算式 数值 单位 备注
上游坡度m1 = 3 = 3 / 1:m1
下游坡度m2 = 3 = 3 / 1:m2
堤顶宽度B = 6 = 6 m
堤顶高程▽顶 = 27 = 27 m
堤底高程▽底 = 17 = 17 m
上游水位▽1 = 24.8 = 24.8 m
下游水位▽2 = 18 = 18 m
渗透系数k = 1.00E-05 = 1.00E-05 m/s
堤身高度H = 27-17 = 10 m
上游水深H1 = 24.8-17 = 7.8 m
下游水深H2 = 18-17 = 1 m
L = (27-24.8)×3+6+10×3 = 42.6 m 上有水面至下游堤脚
ΔL = 3×7.8/(2×3+1) = 3.343 m m1H1/(2m1+1)
L1 = 42.6+3.343 = 45.943 m L+ΔL
试算法计算逸出高度h0，假设h0的试算范围h01～h02，计算的步长以及精度
h01 = 1 = 1 m
h02 = 10 = 10 m
步长 = 0.02 = 0.02 m
精度 = 0.01 = 0.01 m
试算得到h0 = 2.54 = 2.54 m 手动输入
q/k = (7.8^2-2.54^2)/(2×(45.943-3×2.54)) = 0.7096 m
q/k = 0.7047 = 0.7047 m
平均q/k = (0.7096+0.7047)/2 = 0.7072 m
平均渗流量q = 0.7072×0.00001 = 7.07E-06 m3/s/m
浸润线方程 y=SQRT(6.4516+1.4144x)
下游坝坡最大渗出坡降J = 1/3 = 0.333 / 1/m2


附录E.2.2 不透水堤基 均质土堤 下游设褥垫式排水


项目 计算式 数值 单位 备注
上游坡度m1 = 3 = 3 / 1:m1
下游坡度m2 = 5 = 5 / 1:m2
堤顶宽度B = 6 = 6 m
堤顶高程▽顶 = 27 = 27 m
堤底高程▽底 = 17 = 17 m
上游水位▽1 = 24.8 = 24.8 m
下游水位▽2 = 18 = 18 m
褥垫长度Lr = 5 = 5 m 到下游堤脚
渗透系数k = 1.00E-05 = 1.00E-05 m/s
堤身高度H = 27-17 = 10 m
上游水深H1 = 24.8-17 = 7.8 m
下游水深H2 = 18-17 = 1 m
L = (27-24.8)×3+6+10×5-5 = 57.6 m 上游水面至褥垫
ΔL = 3×7.8/(2×3+1) = 3.343 m m1H1/(2m1+1)
L1 = 57.6+3.343 = 60.943 m L+ΔL
逸出高度h0 = SQRT(60.943^2+7.8^2)-60.943 = 0.497 m
排水体工作长度a0 = 0.497/2 = 0.249 m h0/2
q/k = 0.497 = 0.497 m h0
渗流量q = 0.497×0.00001 = 4.97E-06 m3/s/m
浸润线方程 y=SQRT(0.247-0.994x)
下游坝坡最大渗出坡降J = 1/5 = 0.2 / 1/m2


附录E.2.3 不透水堤基 均质土堤 下游设棱体排水

项目 计算式 数值 单位 备注
上游坡度m1 = 3 = 3 / 1:m1
下游坡度m2 = 5 = 5 / 1:m2
堤顶宽度B = 6 = 6 m
堤顶高程▽顶 = 27 = 27 m
堤底高程▽底 = 17 = 17 m
上游水位▽1 = 24.8 = 24.8 m
下游水位▽2 = 18 = 18 m
棱体顶高程 = 19 = 19 m 到下游堤脚
棱体临水坡坡率m3 = 2 = 2 / 1:m3
渗透系数k = 1.00E-05 = 1.00E-05 m/s
堤身高度H = 27-17 = 10 m
棱体高度HL = 19-17 = 2 m
上游水深H1 = 24.8-17 = 7.8 m
下游水深H2 = 18-17 = 1 m
L = (27-24.8)×3+6+10×

5-2×5-2×2 = 48.6 m 上游水面至棱体
ΔL = 3×7.8/(2
×3+1) = 3.343 m m1H1/(2m1+1)
L1 = 48.6+3.343 = 51.943 m L+ΔL
系数c = 1.115 = 1.115 / 与m3有关
逸出高度h0 = 1+SQRT((1.115×51.943)^2+(7.8-1)^2)-1.115×51.943 = 1.398 m
q/k = (7.8^2+1.398^2)/(2×51.943) = 0.604 m
渗流量q = 0.604×0.00001 = 6.04E-06 m3/s/m
浸润线方程 y=SQRT(1.9544-1.208x)
下游坝坡最大渗出坡降J = 1/5 = 0.2 / 1/m2


附录E.3.1 透水堤基无排水


附录E.3.1 透水堤基 均质土堤 下游无排水设备或有贴坡式排水
项目 计算式 数值 单位 备注
1.计算参数
上游坡度m1 = 3 = 3 / 1:m1
下游坡度m2 = 5 = 5 / 1:m2
堤顶宽度B = 6 = 6 m
堤顶高程▽顶 = 27 = 27 m
堤底高程▽底 = 17 = 17 m
透水地基底高程▽底 = 7 = 7 m 不透水地基顶高程
上游水位▽1 = 24.8 = 24.8 m
下游水位▽2 = 18 = 18 m
渗透系数k = 1.00E-05 = 1.00E-05 m/s
堤基渗透系数k0 = 5.00E-05 = 5.00E-05 m/s
2.不透水堤基对应渗流量计算
堤身高度H = 27-17 = 10 m
上游水深H1 = 24.8-17 = 7.8 m
下游水深H2 = 18-17 = 1 m
L = (27-24.8)×3+6+10×5 = 62.6 m 上有水面至下游堤脚
ΔL = 3×7.8/(2×3+1) = 3.343 m m1H1/(2m1+1)
L1 = 62.6+3.343 = 65.943 m L+ΔL
试算法计算逸出高度h0，假设h0的试算范围h01～h02，计算的步长以及精度
h01 = 1 = 1 m
h02 = 10 = 10 m
步长 = 0.02 = 0.02 m
精度 = 0.01 = 0.01 m
试算得到h0 = 2.54 = 2.8 m 程序计算
q/k = (7.8^2-2.8^2)/(2×(65.943-5×2.8)) = 0.5102 m
q/k = 0.5011 = 0.5011 m
平均q/k = (0.5102+0.5011)/2 = 0.5057 m
平均渗流量qD = 0.5057×0.00001 = 5.06E-06 m3/s/m
浸润线方程 y=SQRT(7.84+1.0114x)
下游坝坡最大渗出坡降J = 1/5 = 0.2 / 1/m2
3.堤基渗流量计算
透水地基厚度T = 17-7 = 10 m
堤基渗流量q基 = 0.00005×(7.8-1)×10/(62.6+5×7.8+0.88×10) = 3.08E-05 m3/s/m
4.总渗流量 = 0.00000506+0.0000308 = 3.59E-05 m3/s/m
5.浸润线计算
h01 = 1 = 1 m
h02 = 10 = 10 m
步长 = 0.001 = 0.001 m
精度 = 0.001 = 0.001 m
试算得到h0 = 2.0361 = 1.894 m 程序计算
q’ = 3.55212E-05 = 3.55E-05 m3/s/m
浸润线方程 x=14.0766(y-1.894)+0.1408(y^2-3.5872)


附录E.3.2 透水堤基 均质土堤 下游设褥垫式排水


项目 计算式 数值 单位 备注
1.计算参数
上游坡度m1 = 3 = 3 / 1:m1
下游坡度m2 = 5 = 5 / 1:m2
堤顶宽度B = 6 = 6 m
堤顶高程▽顶 = 27 = 27 m
堤底高程▽底 = 17 = 17 m
透水地基底高程▽底 = 7 = 7 m 不透水地基顶高程
上游水位▽1 = 24.8 = 24.8 m
下游水位▽2 = 18 = 18 m
褥垫长度Lr = 5 = 5 m 到下游堤脚
渗透系数k = 1.00E-05 = 1.00E-05 m/s
堤基渗透系数k0 = 5.00E-05 = 5.00E-05 m/s
2.不透水堤基对应渗流量计算
堤身高度H = 27-17 = 10 m
上游水深H1 = 24.8-17 = 7.8 m
下游水深H2 = 18-1

7 = 1 m
L = (27-24.8)×3+6+10×5-5 = 57.6 m 上游水面至褥垫
ΔL = 3×7.8/(2×3+1) = 3.343 m m1H1/(2m1+1
)
L1 = 57.6+3.343 = 60.943 m L+ΔL
逸出高度h0 = SQRT(60.943^2+7.8^2)-60.943 = 0.497 m
排水体工作长度a0 = 0.497/2 = 0.249 m h0/2
q/k = 0.497 = 0.497 m h0
渗流量qD = 0.497×0.00001 = 4.97E-06 m3/s/m
浸润线方程 y=SQRT(0.247-0.994x)
下游坝坡最大渗出坡降J = 1/5 = 0.2 / 1/m2
2.堤基渗流量计算
透水地基厚度T = 17-7 = 10 m
堤基渗流量q基 = 0.00005×(7.8-1)×10/(57.6+5×7.8+0.88×10) = 3.23E-05 m3/s/m
3.总渗流量 = 0.00000497+0.00003226 = 3.72E-05 m3/s/m
4.浸润线计算
逸出高度h0 = 0.00003723/(0.00001+0.00005/0.44) = 0.301 m
q’ = 4.4223E-05 = 4.42E-05 m3/s/m
浸润线方程 x=11.3071(y-0.301)+0.1131(y^2-0.0906)


附录E.3.3 透水堤基 均质土堤 下游设棱体排水


项目 计算式 数值 单位 备注
1.计算参数
上游坡度m1 = 3 = 3 / 1:m1
下游坡度m2 = 5 = 5 / 1:m2
堤顶宽度B = 6 = 6 m
堤顶高程▽顶 = 27 = 27 m
堤底高程▽底 = 17 = 17 m
透水地基底高程▽底 = 7 = 7 m 不透水地基顶高程
上游水位▽1 = 24.8 = 24.8 m
下游水位▽2 = 18 = 18 m
棱体顶高程 = 19 = 19 m 到下游堤脚
棱体临水坡坡率m3 = 2 = 2 / 1:m3
渗透系数k = 1.00E-05 = 1.00E-05 m/s
堤基渗透系数k0 = 5.00E-05 = 5.00E-05 m/s
2.不透水堤基对应渗流量计算
堤身高度H = 27-17 = 10 m
棱体高度HL = 19-17 = 2 m
上游水深H1 = 24.8-17 = 7.8 m
下游水深H2 = 18-17 = 1 m
L = (27-24.8)×3+6+10×5-2×5-2×2 = 48.6 m 上游水面至棱体
ΔL = 3×7.8/(2×3+1) = 3.343 m m1H1/(2m1+1)
L1 = 48.6+3.343 = 51.943 m L+ΔL
系数c = 1.115 = 1.115 / 与m3有关
逸出高度h0 = 1+SQRT((1.115×51.943)^2+(7.8-1)^2)-1.115×51.943 = 1.398 m
q/k = (7.8^2+1.398^2)/(2×51.943) = 0.604 m
渗流量q = 0.604×0.00001 = 6.04E-06 m3/s/m
浸润线方程 y=SQRT(1.9544-1.208x)
下游坝坡最大渗出坡降J = 1/5 = 0.2 / 1/m2
2.堤基渗流量计算
透水地基厚度T = 17-7 = 10 m
堤基渗流量q基 = 0.00005×(7.8-1)×10/(48.6+5×7.8+0.88×10) = 3.53E-05 m3/s/m
3.总渗流量 = 0.00000604+0.00003527 = 4.13E-05 m3/s/m
4.浸润线计算
逸出高度h0 = 1.337570369 = 1.338 m
q’ = 4.4789E-05 = 4.48E-05 m3/s/m
浸润线方程 x=11.1632(y-1.338)+0.1116(y^2-1.7902)


附录E.4 不稳定渗流计算
项目 计算式 数值 单位 备注
上游坡度m1 = 3 = 3 / 1:m1
下游坡度m2 = 5 = 5 / 1:m2
堤顶宽度B = 6 = 6 m
堤顶高程▽顶 = 27 = 27 m
堤底高程▽底 = 17 = 17 m
上游水位▽1 = 24.8 = 24.8 m
下游水位▽2 = 18 = 18 m
土的孔隙率n = 88.00% = 88.00% / 到下游堤脚
土的饱和度SW％ = 50.00% = 50.00% / 到下游堤脚
渗透系数k = 1.00E-05 = 1.00E-05 m/s
洪水持续时间t = 11 = 11 天 950400妙
土的有效孔隙率n0 = 0.

88×(1-0.5) = 44.00% / 到下游堤脚
上游水位处堤宽b’ = 6+(27-24.8)×(3+5) = 23.6 m
上游水深H = 24.8-17 = 7.8 m
渗流在背坡出现所需时间T
= 0.44×7.8×(3+5+23.6/7.8)/(4×0.00001) = 946000 s 10.949天
洪水持续时间t = 11天 > 10.949天 不需计算浸润线锋面距迎水坡脚距离L
浸润线锋面距迎水坡脚距离L = 2×SQRT(0.00001×7.8×946000/0.44) = 25.9 m m1H1/(2m1+1)



h0.exe 程序计算输入文件"in.dat"(不透水堤基)

1
10
0.02
0.01
3
3
7.8
1
45.943

h0.exe数据文件示例见附件
程序文件也在里面


不透水堤基DOS程序计算结果RESULT.DAT


不透水堤基均质土堤 下游无排水设备或有贴坡式排水 试算法计算逸出高度h0的DOS程序计算结果如下：

***************************************************************************
*** 土堤渗流逸出高度计算程序 ***
*** DEVELOPED BY SANTALIN COPYRIGHT (C) 2007 CASDIC SG3 ***
***************************************************************************

******************** 您输入的数据 ********************

根据堤防规范附录E.2.1 不透水堤基 均质土堤 下游无排水设备或有贴坡式排水的情况
试算法计算逸出高度h0，假设h0的试算范围h01～h02，计算的步长以及精度

试算范围 h01=1.000000 m,h02=10.000000 m
试算步长mystep=0.020000 m
试算精度jd=0.01000 m
上下游坡度m1=3.000000,m2=3.000000
上下游水深h1=7.800000 m,h2=1.000000 m
上游水面边线到下游堤脚水平距离L1=45.943001 m


******************** 结果输出 ********************

试算得到 h0 ＝ 2.5400 m

q/k1 ＝ 0.7096 m

q/k2 ＝ 0.7047 m


************ Design By SantaLin (All Rights Reserved) ************


h0t.exe 程序计算输入文件"in.dat" (透水堤基)

1
10
0.00001
0.00001
5.25E-05
3
1
7.00E-05
3.00E-05
10

h0t.exe数据文件示例见附件
程序文件也在里面


透水堤基均质土堤DOS程序计算结果


透水堤基均质土堤 下游无排水设备或有贴坡式排水 试算法计算逸出高度h0的DOS程序计算结果如下：
***************************************************************************
*** 透水堤基土堤渗流逸出高度计算程序 ***
*** DEVELOPED BY SANTALIN COPYRIGHT (C) 2007 CASDIC SG3 ***
***************************************************************************

******************** 您输入的数据 ********************

根据堤防规范附录E.3.2 透水堤基 均质土堤 下游无排水设备或有贴坡式排水的情况
试算法计算逸出高度h0，假设h0的试算范围h01～h02，计算的步长以及精度

试算范围 h01=1.000000 m,h02=10.000000 m
试算步长mystep=0.00001 m
试算精度jd=0.00001 m
渗流量q=0.000052 m3/s/m
下游坡度m2=3.000000
下游水

深h2=1.000000 m
堤身渗透系数k=0.000070 m/s
堤基渗透系数k0=0.000030 m/s
透水地基厚度T=10.000000 m


******************** 结果输出 ********************

试算得到 h0 ＝ 1.7034 m

fLe
ft = h0 - h2 ＝ 0.7034 m

fRight ＝ 0.7034 m


************ Design By SantaLin (All Rights Reserved) ************



程序使用说明


建立程序输入文件与DOS程序放在同一个目录下
文件名必须为:
in.dat
数据的意义参看输出文件说明
运行程序会生成输出文件result.dat，如上

这两个程序下载地址：
/土堤渗流逸出高度计算程序.zip
或者从附件下载


附录E.5 背水坡渗流出口比降计算

项目 计算式 数值 单位 备注

1.计算参数
下游坡度m2 = 5 = 5 / 1:m2
堤底高程▽底 = 17 = 17 m
下游水位▽2 = 18 = 18 m
逸出高度h0 = 2.54 = 2.54 m
下游水深H2 = 18-17 = 1 m

2.不透水地基逸出坡降计算
下游无水时
渗出点A坡降Jo = 1/SQRT(1+5^2) = 0.196 /
堤坡与不透水面交点B坡降Jo = 1/5 = 0.2 / 1/m2
下游有水时
渗出段AB内的点
计算点高程 = 19 = 19 m AB段(18~19.54)内
y = 19-17 = 2 / AB段(2.54~1)内
渗出点A坡降Jo = 1/SQRT(1+5^2) = 0.196 /
n = 0.25×1/2.54 = 0.098 /
计算点坡降J = 0.196×((2.54-1)/(2-1))^0.098 = 0.204 / 在下游坡面渗出
浸没段BC内的点 适用于y/H2<0.95
计算点高程 = 17.7 = 17.7 m BC段(17~19.413)内
y = 17.7-17 = 0.7 / BC段(0~0.95)内
背坡与水平面夹角απ = atan(1/5) = 0.197 rad 11.287度
α = 0.197/π = 0.063 /
a0 = 1/(2×(0.063×(5+0.5)×SQRT(1+5^2))) = 0.283 /
b0 = 5/(2×(5+0.5)^2) = 0.083 /
1/2α-1 1/(2×0.063)-1 = 6.937 /
计算点坡降J = 0.283×(0.7/1)^6.937/(1+0.083×1/(2.54-1)) = 0.023 /

3.透水地基逸出坡降计算
下游无水时
渗出段AB内的点
计算点高程 = 19 = 19 m AB段(17~19.54)内
y = 19-17 = 2 / AB段(0~2.54)内
计算点坡降J = 1/SQRT(1+5^2)×(2.54/2)^0.25 = 0.208 /
地基段BC内的点
计算点与堤脚距离x = 3 = 3 m
计算点坡降J = 1/(2×SQRT(5))×SQRT(2.54/3) = 0.206 /
下游有水时
渗出段AB内的点
计算点高程 = 19 = 19 m AB段(18~19.54)内
y = 19-17 = 2 / AB段(1~2.54)内
计算点坡降J = 1/SQRT(1+5^2)×(2.54/2)^0.25 = 0.208 /
浸没坡段BC内的点
计算点高程 = 17.7 = 17.7 m BC段(0.283~2.823)内
y = 17.7-17 = 0.7 / BC段(0~2.54)内
背坡与水平面夹角απ = atan(1/5) = 0.197 rad 11.287度
α = 0.197/π = 0.063 /
α1 = 1/(1+0.063) = 0.941 / 1/(1+α)
l1 = 2.54×5 = 12.7 / h0×m2
l2 = 1×5 = 5 / H2×m2
r = 0.7×5 = 3.5 / y×m2
计算点坡降J = 0.234 = 0.234 / 在下游坡面渗出
浸没地基面段CD内的点
计算点距堤脚距离x = 2 = 2 m
计算点坡降J = 0.108 = 0.108 / 在下游坡面渗出



附

录E.6 水位降落时均质土堤的浸润线

项目 计算式 数值 单位 备注

1.计算参数
上游坡度m1 = 3 = 3 / ( 1:m1 )
堤底高程▽底 = 17 = 17 m
堤身土料渗透系数k = 1.00E-05 = 1.00E-05 m/s ＝ 0.001cm/s ＝ 0.864m/d
土体的孔
隙率n = 39.70% = 39.70% /
降前水位▽1 = 27 = 27 m ( 0.0003125m/s )
降后水位▽0 = 20 = 20 m ( 0.00023148m/s )
水位降落所需时间T = 22 = 22 h ( = 79200 秒 = 0.9167 天 )
计算上游浸润线时间t = 15 = 15 h ( = 54000 秒 = 0.625 天 )

2.h0(t)计算
降前水深H1 = 27-17 = 10 m ( ▽1-▽底 )
降后水深H0 = 20-17 = 3 m ( ▽0-▽底 )
降距H = 10-3 = 7 m ( H1-H0 )
水位降落的速度V = 7/(22/24) = 7.636 m/d ( = 0.00009m/s= 0.00212m/h )
百分数α = 113.7×(0.0001175)^(0.607^(6+log(0.001)))/100 = 15.03% / ( 公式一 )
给水度μ = 0.1503×0.397 = 0.0597 /
k/(μV) = 0.864/(0.0597×7.636) = 1.895 / ( 1/10<k/(μV)<60,需要计算浸润线 )
0.31H(1/T)(k/(μV))1/4 = 0.31×7×1/79200×(1.895)^(1/4) = 0.0000321 /
h0(t) = 7-0.0000321t
h0(t) = 7-0.0000321×54000 = 5.2666 m ( t = 15h = 54000s )

3.试算法计算t时刻渗流量q(t)和上游坡出渗点高度he(t)
he(t)1 = 3+0.01 = 3.01 m ( H0+Step )
he(t)2 = 3+5.2666 = 8.267 m ( H0+h0(t) )
步长Step = 0.01 = 0.01 m
精度 = 0.001 = 0.001 m
L = 10×3 = 30 m ( H1×m1 )
试算得到he(t) = 5.34 = 5.34 m ( 程序计算 )
q/k1 = ((3+5.2666)^2-5.34^2)/(2×(30-3×5.34)) = 1.424 m
q/k2 = (5.34-3)/3×(1+ln(5.34/(5.34-3))) = 1.424 m
平均q/k = (1.424+1.424)/2 = 1.424 m
平均渗流量q = 1.424×0.00001 = 1.42E-05 m3/s/m

4.计算 t = 15h 时刻上游段浸润线
[H0+h0(t)]2 = (3+5.2666)^2 = 68.3367 m2
2q/k = 2×1.424 = 2.848 m
浸润线方程 y=SQRT(68.3367-2.848x)




附录E.7 双层堤基渗流计算和覆盖的计算
附录E.7.1 背水侧无限长双层堤基渗流计算和覆盖的计算

项目 计算式 数值 单位 备注

1.计算参数
上游坡度m1 = 3 = 3 / ( 1:m1 )
下游坡度m2 = 5 = 5 / ( 1:m2 )
堤顶宽度B = 6 = 6 m
堤顶高程▽顶 = 27 = 27 m
堤底高程▽底 = 17 = 17 m
弱透水地基底高程▽弱 = 7 = 10 m
强透水地基底高程▽强 = 7 = 5 m
上游水位▽1 = 24.8 = 24.8 m
下游水位▽2 = 18 = 18 m
堤底高程▽底 = 17 = 17 m
迎水侧有限长度L = 100 = 100 m
堤身土料渗透系数k = 1.00E-05 = 1.00E-05 m/s ( ＝ 0.001cm/s ＝ 0.864m/d )
弱透水堤基渗透系数k1 = 5.00E-05 = 5.00E-05 m/s ( ＝ 0.005cm/s ＝ 4.32m/d
强透水堤基渗透系数k0 = 7.00E-03 = 7.00E-03 m/s ( ＝ 0.7cm/s ＝ 604.8m/d

2.越流系数A计算
k0/k1 = 0.007/0.00005 = 140 / ( 属于双层堤基 )
堤身高度Hd = 27-17 = 10 m ( ▽顶-▽底 )
上游水深H = 24.8-17 = 7.8 m ( ▽1-▽底 )
弱透水层厚度T1 = 17-10 = 7 m ( ▽底-▽弱 )
强透水层厚度T0 = 10-5 = 5 m (

▽弱-▽强 )
堤底宽度b = 6+10×(3+5) = 86 m ( B+Hd×(m1+m2) )
越流系数A = SQRT(0.00005/(0.007×7×5)) = 0.014 m-1

3.弱透水层CD段承压水头计算(x以下游堤脚为原点，向下游为正)
计算点坐标x = 10 = 10 m ( x>0 )
h = 7.8×e^(-0.014×10)/(1+0.014×86-th(0.014×100)) = 5.142 m

4.
弱透水层CD段承压水头计算(x’以下游堤脚为原点，向上游为正)
计算点坐标x’ = 10 = 10 m ( x’>0 )
h = 7.8×(1+0.014×10)/(1+0.014×86-th(0.014×100)) = 6.743 m


附录E.7 双层堤基渗流计算和覆盖的计算
附录E.7.2 透水地基上弱透水层等厚有限长，强透水层无限长双层堤基渗流计算

项目 计算式 数值 单位 备注

1.计算参数
上游坡度m1 = 3 = 3 / ( 1:m1 )
下游坡度m2 = 3 = 3 / ( 1:m2 )
堤顶宽度B = 6 = 6 m
堤顶高程▽顶 = 27 = 27 m
堤底高程▽底 = 17 = 17 m
弱透水地基底高程▽弱 = 7 = 10 m
强透水地基底高程▽强 = 7 = 5 m
上游水位▽1 = 24.8 = 24.8 m
下游水位▽2 = 18 = 18 m
迎水侧有限长度L1 = 30 = 30 m ( 弱透水地基 )
背水侧有限长度L2 = 100 = 100 m ( 弱透水地基 )
堤身土料渗透系数k = 1.00E-05 = 1.00E-05 m/s ( ＝ 0.001cm/s ＝ 0.864m/d )
弱透水堤基渗透系数k1 = 5.00E-05 = 5.00E-05 m/s ( ＝ 0.005cm/s ＝ 4.32m/d )
强透水堤基渗透系数k0 = 7.00E-03 = 7.00E-03 m/s ( ＝ 0.7cm/s ＝ 604.8m/d )

2.越流系数A计算
k0/k1 = 0.007/0.00005 = 140 / ( >100,属于双层堤基 )
弱透水层厚度T1 = 17-10 = 7 m ( ▽底-▽弱 )
强透水层厚度T0 = 10-5 = 5 m ( ▽弱-▽强 )
堤身高度Hd = 27-17 = 10 m ( ▽顶-▽底 )
上游水面距不透水地基H = 24.8-5 = 19.8 m ( ▽1-▽强 )
堤底距不透水地基H1 = 17-5 = 12 m ( ＝ ▽底-▽强 ＝ T1+T0 )
弱透水层底距不透水地基H0 = 10-5 = 5 m ( ▽弱-▽强 )
堤底宽度b = 6+10×(3+3) = 66 m ( B+Hd×(m1+m2) )
越流系数A = SQRT(0.00005/(0.007×7×5)) = 0.014 m-1
A(0.441T0) = 0.014×0.441×5 = 0.031 / ( <1,公式适用 )
d’ 1/0.014×arth(0.031) = 2.215 m ( = 1/Aarth(A(0.441T0)) )

3.试算法计算ζ以确定出逸段与非出逸段的分界点,假设ζ的试算范围ζ1～ζ2，计算的步长以及精度
ζ1 = 0.0001 = 0 m ( = precision )
ζ2 = 100 = 100 m ( = L2 )
步长STEP = 0.01 = 0.01 m
精度precision = 0.0001 = 0.0001 m
试算得到ζ = 64.46 = 64.46 m ( 手动输入 )
方程左边 = 0.105 = 0.105 m ( 手动输入 )
方程右边 = 0.105 = 0.105 m ( 手动输入 )

4.出逸段AB透水层水位计算(x以下游堤脚为原点，向下游为正)
计算点坐标x = 10 = 10 m ( 0 < x < 35.54 = L2-ζ )
h = 1.482 = 1.482 m

5.非出逸段BC透水层水位计算(x’以弱透水层最下游点为原点，向上游为正)
计算点坐标x’ = 10 = 10 m ( 0 < x’ < 64.46 = ζ )
x’/T0 = 10/5 = 2 m
Δ0 = (12-5)

×0.441×5/(64.46+0.441×5) = 0.232 m
Δx’/Δ0 = 0 = 0 m
Δx’ = 0.232×0 = 0 m
h = 5+(12-5)×(10+0.441×5)/(64.46+0.441×5)-0 = 6.282 m



5.非出逸段BC透水层水位计算(x’以弱透水层最下游点为原点，向上游为正)
计算点坐标x’ = 2.1 = 2.1 m ( 0 < x’ < 64.46 = ζ )
x’/T0 = 2.1/5 = 0.42 m
Δ0 = (12-5)×0.441×5
/(64.46+0.441×5) = 0.232 m
Δx’/Δ0 = 0.246 = 0.246 m ( 查表E.7.2 )
Δx’ = 0.232×0.246 = 0.057 m
h = 5+(12-5)×(2.1+0.441×5)/(64.46+0.441×5)-0.057 = 5.395 m



附录E.7 双层堤基渗流计算和覆盖的计算
附录E.7.2 透水地基上弱透水层不等厚或不均质，强透水层无限长双层堤基渗流计算

项目 计算式 数值 单位 备注

1.计算参数
上游坡度m1 = 3 = 3 / ( 1:m1 )
下游坡度m2 = 5 = 5 / ( 1:m2 )
堤顶宽度B = 6 = 6 m
堤顶高程▽顶 = 27 = 27 m
堤底高程▽底 = 17 = 17 m
弱透水地基底高程▽弱 = 10 = 10 m
强透水地基底高程▽强 = 7 = 7 m
上游水位▽1 = 24.8 = 24.8 m
下游水位▽2 = 18 = 18 m
弱透水层 无限长
强透水堤基渗透系数k0 = 7.00E-03 = 7.00E-03 m/s ( ＝ 0.7cm/s ＝ 604.8m/d )

2.递推计算下游等效长度S下
下游弱透水层分段数N = 3 = 3 段 ( 以不等厚或不均质分 )

2.1递推计算
段次 = 0 = 0
强透水层厚度T0 = 10-7 = 3 m ( ▽弱-▽强 )
等效长度S0 = 0 = 0 m ( 取0 )
D0 = (1/0.022+0)/(1/0.022-0) = 1 /
段次 = 1
第1段渗透系数k1 = 5.00E-05 = 5.00E-05 m/s ( ＝ 0.005cm/s ＝ 4.32m/d )
第1段厚度t1 = 5 = 5 m
第1段长度L1 = 6 = 6 m
越流系数A1 = SQRT(0.00005/(0.007×3×5)) = 0.022 m-1
β1 = 2×0.022×6 = 0.264 / ( 2AiLi )
等效长度S1 = 1/0.022×(1×e^0.264-1)/(1×e^0.264+1) = 5.965 m
D1 = (1/0.028+5.965)/(1/0.028-5.965) = 1.401 m
段次 = 2
第2段渗透系数k2 = 5.00E-05 = 5.00E-05 m/s ( ＝ 0.005cm/s ＝ 4.32m/d )
第2段厚度t2 = 3 = 3 m
第2段长度L2 = 10 = 10 m
越流系数A2 = SQRT(0.00005/(0.007×3×3)) = 0.028 m-1
β2 = 2×0.028×10 = 0.56 / ( 2AiLi )
等效长度S2 = 1/0.028×(1.401×e^0.56-1)/(1.401×e^0.56+1) = 15.026 m
D2 = (1/0.035+15.026)/(1/0.035-15.026) = 3.219 m ( ▽底-▽弱 )
段次 = 3
第3段渗透系数k3 = 5.00E-05 = 5.00E-05 m/s ( ＝ 0.005cm/s ＝ 4.32m/d )
第3段厚度t3 = 2 = 2 m
第3段长度L3 = 30 = 30 m
越流系数A3 = SQRT(0.00005/(0.007×3×2)) = 0.035 m-1
β3 = 2×0.035×30 = 2.1 / ( 2AiLi )
等效长度S3 = 1/0.035×(3.219×e^2.1-1)/(3.219×e^2.1+1) = 26.477 m

2.2下游等效长度S下 = 26.477 = 26.477 m ( 即等效长度S3 )

3.递推计算下游等效长度S上
上游弱透水层分段数N = 3 = 3 段 ( 以不等厚或不均质分 )

3.1 递推计算
段次 = 0 = 0
强透水层厚度T0 = 15.026-3.219 = 11.807 m ( ▽弱-▽强 )
等效长度S0 = 0

= 0 m ( 取0 )
D0 = (1/0.018+0)/(1/0.018-0) = 1 /
段次 = 1
第1段渗透系数k1 = 5.00E-05 = 5.00E-05 m/s ( ＝ 0.005cm/s ＝ 4.32m/d )
第1段厚度t1 = 7 = 7 m
第1段长度L1 = 10 = 10 m
越流系数A1 = SQRT(0.00005/(0.007×3×7)) = 0.018 m-1
β1 = 2×0.018×10 = 0.36 / ( 2AiLi )
等效长度S1 = 1/0.018×(1×e^0.36-1)/(1×e^0.36+1) = 9.893 m
D1 = (1/0.022+9.893)/(1/0.022-9.893) = 1.556 m

段次 = 2
第2段渗透系数k2 = 5.00E-05 = 5.00E-05 m/s ( ＝ 0.005cm/s ＝ 4.32m/d )
第2段厚度t2 = 5 = 5 m
第2段长度L2 = 6 = 6 m
越流系数A2 = SQRT(0.00005/(0.007×3×5)) = 0.022 m-1
β2 = 2×0.022×6 = 0.264 / ( 2AiLi )
等效长度S2 = 1/0.022×(1.556×e^0.264-1)/(1.556×e^0.264+1) = 15.413 m
D2 = (1/0.028+15.413)/(1/0.028-15.413) = 2.518 m ( ▽底-▽弱 )
段次 = 3
第3段渗透系数k3 = 5.00E-05 = 5.00E-05 m/s ( ＝ 0.005cm/s ＝ 4.32m/d )
第3段厚度t3 = 3 = 3 m
第3段长度L3 = 50 = 50 m
越流系数A3 = SQRT(0.00005/(0.007×3×3)) = 0.028 m-1
β3 = 2×0.028×50 = 2.8 / ( 2AiLi )
等效长度S3 = 1/0.028×(2.518×e^2.8-1)/(2.518×e^2.8+1) = 34.03 m

3.2 上游等效长度S上 = 34.03 = 34.03 m ( 即等效长度S3 )

4. 背水侧弱透水层下各点的承压水头计算(x以下游堤脚原点，向下游为正)
计算点坐标x = 10 = 10 m ( x > 0 )
上下游水头差H = 24.8-18 = 6.8 m
堤身高度Hd = 27-17 = 10 m ( ▽顶-▽底 )
堤底宽度b = 6+10×(3+5) = 86 m ( B+Hd×(m1+m2) )
计算点的承压水头h = (26.477-10)×6.8/(34.03+86+26.477) = 0.765 m ( x = 10m )



附录E.7 双层堤基渗流计算和覆盖的计算
附录E.7.4 递推公式计算盖重

项目 计算式 数值 单位 备注

1.计算参数
上游坡度m1 = 3 = 3 / ( 1:m1 )
下游坡度m2 = 5 = 5 / ( 1:m2 )
堤顶宽度B = 6 = 6 m
堤顶高程▽顶 = 27 = 27 m
堤底高程▽底 = 17 = 17 m
弱透水地基底高程▽弱 = 10 = 10 m
强透水地基底高程▽强 = 7 = 7 m
上游水位▽1 = 24.8 = 24.8 m
下游水位▽2 = 18 = 18 m
弱透水层 无限长
强透水堤基渗透系数k0 = 7.00E-03 = 7.00E-03 m/s ( ＝ 0.7cm/s ＝ 604.8m/d )

2.递推计算下游等效长度S下
下游弱透水层分段数N = 3 = 3 段 ( 以不等厚或不均质分 )

2.1递推计算
段次 = 0 = 0
强透水层厚度T0 = 10-7 = 3 m ( ▽弱-▽强 )
等效长度S0 = 0 = 0 m ( 取0 )
D0 = (1/0.022+0)/(1/0.022-0) = 1 /
段次 = 1
第1段渗透系数k1 = 5.00E-05 = 5.00E-05 m/s ( ＝ 0.005cm/s ＝ 4.32m/d )
第1段厚度t1 = 5 = 5 m
第1段长度L1 = 6 = 6 m
是否有盖重 无盖重
盖重厚度t’ = 1 = 0 m
盖重渗透系数k’ = 2.00E-06 = 2.00E-06 m/s ( ＝ 0.0002cm/s ＝ 0.1728m/d )
等效厚度t1’ = 0.00005×0/0.000002 = 0 m
等效总厚度tz’ = 5+0 = 5 m
越流系数A1 = SQRT(0.00005/(0.007×3×5

)) = 0.022 m-1
β1 = 2×0.022×6 = 0.264 / ( 2AiLi )
等效长度S1 = 1/0.022×(1×e^0.264-1)/(1×e^0.264+1) = 5.965 m
D1 = (1/0.028+5.965)/(1/0.028-5.965) = 1.401 m
段次 = 2
第2段渗透系数k2 = 5.00E-05 = 5.00E-05 m/s ( ＝ 0.005cm/s ＝ 4.32m/d )
第2段厚度t2 = 3 = 3 m
第2段长度L2 = 10 = 10 m
是否有盖重 无盖重
盖重厚度t’ = 1 = 0 m
盖重渗透系数k’ = 2.00E-06 = 2.00E-06 m/s ( ＝ 0.0002cm/s ＝ 0.1728m/
d )
等效厚度t1’ = 0.00005×0/0.000002 = 0 m
等效总厚度tz’ = 3+0 = 3 m
越流系数A2 = SQRT(0.00005/(0.007×3×3)) = 0.028 m-1
β2 = 2×0.028×10 = 0.56 / ( 2AiLi )
等效长度S2 = 1/0.028×(1.401×e^0.56-1)/(1.401×e^0.56+1) = 15.026 m
D2 = (1/0.016+15.026)/(1/0.016-15.026) = 1.633 m ( ▽底-▽弱 )
段次 = 3
第3段渗透系数k3 = 5.00E-05 = 5.00E-05 m/s ( ＝ 0.005cm/s ＝ 4.32m/d )
第3段厚度t3 = 2 = 2 m
第3段长度L3 = 30 = 30 m
是否有盖重 有盖重
盖重厚度t’ = 1 = 1 m
盖重渗透系数k’ = 7.00E-06 = 7.00E-06 m/s ( ＝ 0.0007cm/s ＝ 0.6048m/d )
等效厚度t1’ = 0.00005×1/0.000007 = 7.143 m
等效总厚度tz’ = 2+7.143 = 9.143 m
越流系数A3 = SQRT(0.00005/(0.007×3×9.143)) = 0.016 m-1
β3 = 2×0.016×30 = 0.96 / ( 2AiLi )
等效长度S3 = 1/0.016×(1.633×e^0.96-1)/(1.633×e^0.96+1) = 38.758 m

2.2下游等效长度S下 = 38.758 = 38.758 m ( 即等效长度S3 )



3.递推计算下游等效长度S上
上游弱透水层分段数N = 3 = 3 段 ( 以不等厚或不均质分 )

3.1 递推计算
段次 = 0 = 0
强透水层厚度T0 = 15.026-1.633 = 13.393 m ( ▽弱-▽强 )
等效长度S0 = 0 = 0 m ( 取0 )
D0 = (1/0.018+0)/(1/0.018-0) = 1 /
段次 = 1
第1段渗透系数k1 = 5.00E-05 = 5.00E-05 m/s ( ＝ 0.005cm/s ＝ 4.32m/d )
第1段厚度t1 = 7 = 7 m
第1段长度L1 = 10 = 10 m
是否有盖重 无盖重
盖重厚度t’ = 0.5 = 0 m
盖重渗透系数k’ = 7.00E-06 = 7.00E-06 m/s ( ＝ 0.0007cm/s ＝ 0.6048m/d )
等效厚度t1’ = 0.00005×0/0.000007 = 0 m
等效总厚度tz’ = 7+0 = 7 m
越流系数A1 = SQRT(0.00005/(0.007×3×7)) = 0.018 m-1
β1 = 2×0.018×10 = 0.36 / ( 2AiLi )
等效长度S1 = 1/0.018×(1×e^0.36-1)/(1×e^0.36+1) = 9.893 m
D1 = (1/0.015+9.893)/(1/0.015-9.893) = 1.349 m
段次 = 2
第2段渗透系数k2 = 5.00E-05 = 5.00E-05 m/s ( ＝ 0.005cm/s ＝ 4.32m/d )
第2段厚度t2 = 5 = 5 m
第2段长度L2 = 6 = 6 m
是否有盖重 有盖重
盖重厚度t’ = 1 = 1 m
盖重渗透系数k’ = 8.00E-06 = 8.00E-06 m/s ( ＝ 0.0008cm/s ＝ 0.6912m/d )
等效厚度t1’ = 0.00005×1/0.000008 = 6.25 m
等效总厚度tz’ = 5+6.25 = 11.25 m
越流系数A2 = SQRT(0.00005/(0.007×3×11.25)) = 0.015 m-1
β2 = 2×0.015×6 = 0.18 / ( 2AiLi )
等效长度S2 = 1/0.015×(1.349×e^0.18-1)/(1.349

×e^0.18+1) = 15.68 m
D2 = (1/0.016+15.68)/(1/0.016-15.68) = 1.67 m ( ▽底-▽弱 )
段次 = 3
第3段渗透系数k3 = 5.00E-05 = 5.00E-05 m/s ( ＝ 0.005cm/s ＝ 4.32m/d )
第3段厚度t3 = 3 = 3 m
第3段长度L3 = 50 = 50 m
是否有盖重 有盖重
盖重厚度t’ = 1 = 1 m
盖重渗透系数k’ = 8.00E-06 = 8.00E-06 m/s ( ＝ 0.0008cm/s ＝ 0.6912m/d )
等效厚度t1’ = 0.00005×1/0.000008 = 6.25 m
等效总厚度tz’ = 3+6.25 = 9.25 m
越流系数A3 = SQRT(0.00005/(0.007
×3×9.25)) = 0.016 m-1
β3 = 2×0.016×50 = 1.6 / ( 2AiLi )
等效长度S3 = 1/0.016×(1.67×e^1.6-1)/(1.67×e^1.6+1) = 49.018 m

3.2 上游等效长度S上 = 49.018 = 49.018 m ( 即等效长度S3 )

4. 背水侧弱透水层下各点的承压水头计算(x以下游堤脚原点，向下游为正)
计算点坐标x = 7 = 7 m ( x > 0 )
上下游水头差H = 24.8-18 = 6.8 m
堤身高度Hd = 27-17 = 10 m ( ▽顶-▽底 )
堤底宽度b = 6+10×(3+5) = 86 m ( B+Hd×(m1+m2) )
计算点的承压水头h = (38.758-7)×6.8/(49.018+86+38.758) = 1.243 m ( x = 7m )