堤防渗流计算

堤防渗流计算（有详细的计算过程和程序）
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ml = 3 = 3 / 1:m1
下游坡度m2 = 3 = 3 / 1:m2
堤顶宽度B = 6 = 6 m
堤顶咼程▽顶=27 = 27 m
堤底咼程▽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 X3 = 42.6 m上有水面至下游堤脚
AL = 3 X8/(2 3+1) = 3.343 m m1H1/(2m1 + 1)
L1 = 42.6+3.343 = 45.943 m L+ AL
试算法计算逸出高度hO,假设hO的试算范围hO1〜h02，计算的步长以及精度hO1 = 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 = (7.8A2-2.54A2)/(2 (45.94X-3 2X4)) = 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 X.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
堤底咼程▽底=17 = 17 m
上游水位=24.8 = 24.8 m
堤顶宽度B = 6 = 6 m
堤顶高程▽顶=27 = 27 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) X 3+6+10X5 -5 = 57.6 m 上游水面至褥垫△L = 3X 7.8/(2 X 3+1) = 3.343 m m1H1/(2m1 + 1)
L1 = 57.6+3.343 = 60.943 m L+ △ L
逸出高度h0 = SQRT(60.943A2+7.8A2)-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 X 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
堤底咼程▽底=17 = 17 m
上游水位=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) X 3+6+10X5 -2X 5 -2X2 = 48.6 m 上游水面至棱体
△L = 3X 7.8/(2 X 3+1) = 3.343 m m1H1/(2m1 + 1)
L1 = 48.6+3.343 = 51.943 m L+ △ L
系数 c = 1.115 = 1.115 / 与m3有关
=1.398 m 逸出高度h0 = 1+SQRT((1.115X 51.943)A2+(7.8 -1)A2)- 1.115 X 51.943
q/k = (7.8人2+1.398人2)/(2 X 51.943) = 0.604 m
渗流量q = 0.604 X 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ml = 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
堤底咼程▽底=17 = 17 m
透水地基底咼程▽底=7 = 7 m 不透水地基顶咼程
上游水位▽】=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_kO = 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) X 3+6+10X5 = 62.6 m 上有水面至下游堤脚
△L = 3X 7.8/(2 X 3+1) = 3.343 m m1H1/(2m1 + 1)
L1 = 62.6+3.343 = 65.943 m L+ △ L
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
A A
平均q/k = (0.5102+0.5011)/2 = 0.5057 m
平均渗流量qD = 0.5057 X 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
=3.08E-05 m3/s/m 堤基渗流量q 基=0.00005 X (7.8 -1) X 10/(62.6+5 X 7.8+0.88 X 10)
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 A2-3.5872)
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
堤底咼程▽底=17 = 17 m
透水地基底咼程▽底=7 = 7 m 不透水地基顶咼程
上游水位▽】=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_kO = 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) X 3+6+10X5 -5 = 57.6 m 上游水面至褥垫
△L = 3X 7.8/(2 X 3+1) = 3.343 m m1H1/(2m1 + 1)
L1 = 57.6+3.343 = 60.943 m L+ △ L
逸出高度h0 = SQRT(60.943A2+7.8A2)-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 X 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
=3.23E-05 m3/s/m 堤基渗流量q 基=0.00 005X (7.8 -1) X 10/(57.6+5 X 7.8+0.88 X 10)
3. 总渗流量=0.00000497+0.00003226 = 3.72E-05 m3/s/m
4. 浸润线计算
q “ = 4.4223E-05 = 4.42E-05 m3/s/m
浸润线方程x=11.3071(y-0.301)+0.1131(y A2-0.0906)
附录E.4不稳定渗流计算
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ml = 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
堤底咼程▽底=17 = 17 m
上游水位▽】=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SV^ = 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 X (1 -0.5) = 44.00% / 到下游堤脚
上游水位处堤宽 b “ = 6+(27- 24.8) X (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 X 7.8 X (3+5+23.6/7.8)/(4 X 0.00001) =946000 s 10.949
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 = 2X SQRT(O.OOOO1X 7.8 X 946000心44) = 25.9 m m1H1/(2m1+1) 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
堤底咼程▽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
2.1下游无水时
渗出点A坡降Jo = 1/SQRT(1+5A2) = 0.196 /
堤坡与不透水面交点B坡降Jo = 1/5 = 0.2 / 1/m2
2.2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+5A2) = 0.196 /
n = 0.25 X 1/2.54 = 0.098 /
计算点坡降J = 0.196 X ((2.54 -1)/(2-1))A0.098 = 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an = ata n(1/5) = 0.197 rad 11.287 度
a = 0.197/ n = 0.063 /
a0 = 1/(2 X (0.063 X (5+0.5) X SQRT(1+5A2))) = 0.283 /
b0 = 5/(2 X (5+0.5)A2) = 0.083 /
1/2 a -1 1/(2 X 0.063) -1 = 6.937 /
计算点坡降J = 0.283X (0.7/1)A6.937/(1+0.083 X 1/(2.54 -1)) = 0.023 / 3. 透水地基逸出坡降计算
3.1 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+5A2)X (2.54/2)A0.25 = 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 X SQRT(5))X SQRT(2.54/3) = 0.206 / 3.2 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+5A2)X (2.54/2)A0.25 = 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an = ata n(1/5) = 0.197 rad 11.287 度
a = 0.197/ n = 0.063 /
a 1 = 1/(1+0.063) = 0.941 / 1/(1+ a )
l1 = 2.54 X5 = 12.7 / h0X m2
l2 = 1X5 = 5 / H2X m2
r = 0.7 X5 = 3.5 / y X m2
在下游坡面渗出
计算点坡降J = 0.234 = 0.234 /
浸没地基面段CD内的点
计算点距堤脚距离x = 2 = 2 m
在下游坡面渗出
计算点坡降J = 0.108 = 0.108 /
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
堤底咼程▽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▽】=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 ▽I - ▽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a = 113.7 X (0.0001175)A(0.607A(6+log(0.001)))/100 = 15.03% / 给水度卩=0.1503 X 0.397 = 0.0597 /
k/(卩V) = 0.864/(0.0597 X 7.636) = 1.895 / 1/10<k/( 卩V)<60 ,需要计算
0.31H(1/T)(k/( 卩V))1/4 = 0.31 X 7X 1/79200 X (1.895)人(1/4) = 0.0000321 h0(t) = 7-0.0000321t
h0(t) = 7- 0.0000321 X 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 = 10X3 = 30 m H1X m1
试算得到he(t) = 5.34 = 5.34 m 程序计算
q/k1 = ((3+5.2666)A2-5.34A2)/( 2X (30-3X 5.34)) = 1.424 m
q/k2 = (5.34- 3)/3 X (1+ln(5.34/(5.34 -3))) = 1.424 m
平均q/k = (1.424+1.424)/2 = 1.424 m 公式一
浸润线/
平均渗流量q = 1.424 X 0.00001 = 1.42E-05 m3/s/m
4. 计算t时刻上游段浸润线
[H0+h0(t)]2 = (3+5.2666)人2 = 68.3367 m2
2q/k = 2X 1.424 = 2.848 m
浸润线方程y=SQRT(68.3367-2.848x)
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
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
堤底咼程▽底=17 = 17 m
弱透水地基底咼程▽弱=7 = 10 m
强透水地基底高程▽强=7=5m
上游水位▽】=24.8 = 24.8 m
下游水位^2 = 18 = 18 m
堤底咼程▽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 ( 弱透水堤基渗透系数_k1 = 5.00E-05 = 5.00E-05 m/s ( =0.001cm/s =
=0.005cm/s
0.864m/d )
=4.32m/d )
强透水堤基渗透系数_kO = 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 / (
堤身高度Hd = 27-17 = 10 m ( ▽
属于双层堤基)
顶- ▽底)
上游水深H = 24.8-17 = 7.8 m ( ▽l- ▽底)弱透水层厚度T1 = 17-10 = 7 m ( ▽底- ▽弱)
强透水层厚度TO = 10-5 = 5 m ( ▽弱-▽强)
堤底宽度 b = 6+10X (3+5) = 86 m ( B+Hc K (m1+m2))
越流系数 A = SQRT(0.00005/(0.007 X 7X 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 X e A( -0.014 X 10)/(1+0.014 X 86 -th(0.014 X 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 = 7.8X(1+0.014X10)/(1+0.014 X86 -th(0.014 X100)) = 6.743 m
计算简图参看规范图 E.7.1
附录 E.7.2 透水地基上弱透水层等厚有限长
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
弱透水层底距不透水地基
H0 = 10-5 = 5 m （ ▽弱-▽强）
1. 计算参数
上游坡度 ml = 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 堤底咼程▽底=17 = 17 m
弱透水地基底咼程▽弱 =7 = 10 m 强透水地基底高程▽强 =7=5m 上游水位▽】=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 （ 弱透水堤基 渗透系数_k1 = 5.00E-05 = 5.00E-05 m/s （ 强透水堤基 渗透系数_kO = 7.00E-03 = 7.00E-03 m/s （
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） 堤身咼度Hd = 27-17 = 10 m （ ▽顶-▽底）
上游水面距不透水地基 H = 24.8-5 = 19.8 m （ ▽l - ▽强） 堤底距不透水地基 H1 = 17-5 = 12 m （ = ▽底-▽强 =T1+T0 ）
=0.001cm/s
= 0.864m/d )
=0.005cm/s = 4.32m/d ) =0.7cm/s
= 604.8m/d )
堤底宽度 b = 6+10X (3+3) = 66 m ( B+Hc K (m1+m2))
弱透水层底距不透水地基H0 = 10-5 = 5 m （▽弱-▽强）
A(0.441T0) = 0.014 X 0.441 X5 = 0.031 / ( <1 ，公式适用) d' 1/0.014 X arth(0.031) = 2.215 m ( = 1/Aarth(A(0.441T0)) )
3. 试算法计算Z以确定出逸段与非出逸段的分界点，假设Z的试算范围Z 1 的步长以及精度
Z 1 = 0.0001 = 0 m ( = precisi on )
Z 2 = 100 = 100 m ( = L2 )
步长STEP = 0.01 = 0.01 m
精度precision = 0.0001 = 0.0001 m
试算得到Z = 64.46 = 64.46 m ( 程序计算)
方程左边= 0.105 = 0.105 m ( 程序计算)
方程右边= 0.105 = 0.105 m ( 程序计算)
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- Z )
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 = Z )
x' /T0 = 10/5 = 2 m
△0 = (12- 5) X 0.441 X 5/(64.46+0.441 X 5) = 0.232 m
△x'/ △ 0 = 0 = 0 m
△x' = 0.232 X0= 0 m Z 2，计算
h = 5+(12- 5)X (10+0.441 X 5)/(64.46+0.441 X 5) -0 = 6.282 m
5. 非出逸段BC透水层水位计算
h = 5+(12- 5)X (10+0.441 X 5)/(64.46+0.441 X 5) -0 = 6.282 m
(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 = Z )
x' /T0 = 2.1/5 = 0.42 m
△0 = (12- 5) X 0.441 X 5/(64.46+0.441 X 5) = 0.232 m
△x'/ △ 0 = 0.246 = 0.246 m ( 查表E.7.2 )
△x' = 0.232 X 0.246 = 0.057 m
h = 5+(12- 5)X(2.1+0.441 X5)/(64.46+0.441 X5) -0.057 = 5.395 m
附录 E.7.2 透水地基上弱透水层不等厚或不均质
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
堤底咼程▽底=17 = 17 m
弱透水地基底咼程▽弱=10 = 10 m
上游水位▽】=24.8 = 24.8 m
(x '以弱透水层最下游点为原点，向上游为正)强透水地基底高程▽强=7=7m
上游水位▽】=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_kO = 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TO = 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
4.32m/d ) 第 1 段渗透系数—k1 =
5.00E-05 = 5.00E-05 m/s ( = 0.005cm/s =
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 X 3X 5)) = 0.022 m-1
3 1 = 2X 0.022 X6 = 0.26
4 / ( 2AiLi )
等效长度S1 = 1/0.022 X (1 X e A0.264 -1)/(1 X e9264+1) = 5.965 m
D1 = (1/0.028+5.965)/(1/0.028-5.965) = 1.401 m
段次=2
4.32m/d ) 第 2 段渗透系数—k2 =
5.00E-05 = 5.00E-05 m/s ( = 0.005cm/s =
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 X 3X 3)) = 0.028 m-1
3 2 = 2X 0.028 X 10 = 0.56 / ( 2AiLi )
越流系数A2 = SQRT(0.00005/(0.007 X 3X 3)) = 0.028 m-1
等效长度S2 = 1/0.028 X (1.401 X e A0.56 - 1)/(1.401 X eP.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/(0.007X3X2)) = 0.035 m-1
3 3 = 2X 0.035 X 30 = 2.1 / ( 2AiLi )
等效长度S3 = 1/0.035 X(3.219 X eA2.1 -1)/(3.219 X eA2.1+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/(0.007X3X7)) = 0.018 m-1
31 = 2X0.018X10 = 0.36 / ( 2AiLi )
等效长度S1 = 1/0.018 X (1 x e A0.36 -1)/(1 x eP.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/(0.007x3x5)) = 0.022 m-1
3 2 = 2X 0.022 X6 = 0.26
4 / ( 2AiLi )
等效长度S2 = 1/ 0.022x(1.556 x eA0.264 -1)/(1.556 x eA0.264+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/(0.007x3x 3)) = 0.028 m-1
33 = 2x0.028x50 = 2.8 / ( 2AiLi )
等效长度S3 = 1/0.028 x(2.518 x eA2.8 -1)/(2.518 x eA2.8+1) = 34.03 m
3.2上游等效长度S上=3
4.03 = 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+10x(3+5) = 86 m ( B+Hd x(m1+m2) )
计算点的承压水头h = (26.477- 10) x 6.8/(34.03+86+26.477) = 0.765 m ( x = 10m )
附录E.7.4递推公式计算盖重
最后一个了，本堤防渗流计算到此结束，谢谢支持!
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ml = 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
堤底咼程▽底=17 = 17 m
弱透水地基底咼程▽弱=10 = 10 m
强透水地基底高程▽强=7=7m
上游水位▽】=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_kO = 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
等效厚度 t1 ' = 0.00005 X 0/0.000002 = 0 m
等效总厚度tz ' = 3+0 = 3 m
强透水层厚度 TO = 10-7 = 3 m ( ▽弱-▽强) 等效长度SO = 0 = 0 m ( 取0 ) DO = (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
= 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
= 等效厚度 t1 ' = 0.00005 X 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 X 3X 5))
= 0.022 m-1
3 1 = 2X 0.022 X6 = 0.26
4 / ( 2AiLi )
等效长度 S1 = 1/0.02 2X (1 X e A 0.264 -1)/(1 X e A 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
= 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
= 4.32m/d )
0.1728m/d )
4.32m/d )
0.1728m/d )
越流系数 A2 = SQRT(0.00005/(0.007 X 3X 3))
= 0.028 m-1
等效长度 S0 = 0 = 0 m ( 取 0 )
3 2 = 2X 0.028 X 10 = 0.56 / ( 2AiLi ) 等效长度 S2 = 1/0.028 X (1.401 X e A 0.56 - 1)/(1.401 X e A 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 第 3 段厚度 t3 = 2 = 2 m ( =0.005cm/s = 4.32m/d ) 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 ( 等效厚度 t1 ' = 0.00005X 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 X 3X 9.143)) =0.0007cm/s = 0.6048m/d )
= 0.016 m-1
33 = 2X 0.016X 30 = 0.96 / ( 2AiLi ) 等效长度 S3 = 1/0.016 X (1.633X eA0.96 -1)/(1.633 X eA0.96+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 )
越流系数 A2 = SQRT(0.00005/(0.007 X 3X 11.25))
= 0.015 m-1
3 2 = 2X 0.015 X6= 0.18 / ( 2AiLi )
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 ' = 0.00005X 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 X 3X 7))
= 0.018 m-1
3 1 = 2X 0.018 X 10 = 0.36 / ( 2AiLi )
等效长度 S1 = 1/0.018 X (1 X e A 0.36 -1)/(1 X eP.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 ( 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 (
等效总厚度 tz ' = 5+6.25 = 11.25 m
=0.005cm/s = 4.32m/d )
=0.0008cm/s = 0.6912m/d )
等效厚度 t1 ' = 0.00005X 1/0.000008
= 6.25 m
等效长度 S2 = 1/0.015 X (1.349 x e A 0. 18-1”(1.349 x eP.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 ( 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 (
越流系数 A3 = SQRT(0.00005/(0.007x 3x 9.25))
= 0.016 m-1
3 3 = 2X 0.016 X 50 = 1.6 / ( 2AiLi )
等效长度 S3 = 1/0.016 x (1.67 x eA1.6 -1)/(1.67 x eA1.6+1)
= 49.018 m
3.2 上游等效长度 S 上=49.018 = 49.018 m (
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+10x (3+5) = 86 m ( B+Hd x (m1+m2) ) 计算点的承压水头 h = (38.758-
7) x 6.8/(49.018+86+38.758
) = 1.243 m ( x = 7m )
等效厚度 t1 ' = 0.00005x 1/0.000008 = 6.25 m
等效总厚度 tz ' = 3+6.25 = 9.25 m =0.005cm/s = 4.32m/d )
= 0.0008cm/s
= 0.6912m/d )
即等效长度 S3 )。