堤防渗流计算.docx
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堤防渗流计算.docx
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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 = 18-17 = 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.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)
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
2.1 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
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+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
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+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 /
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+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 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.7.1 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 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 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 (
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