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地下水涌水量的解析法

(2012-03-11 09:39:35)
标签:

肖友发

水文地质

矿坑涌水量

计算

杂谈

分类: 地勘行业

地下水涌水量的解析法

 

 

    解析法是目前矿坑涌水量计算中应用最普遍的一种方法。它是对矿区水文地质条件进告发要的简化后,用推导出来的地下水动力学公式来进行水文地质计算的方法。

    解析法分稳定流解析法和非稳定流解析法。

    采用解析法计算矿坑涌水量时,当矿坑的长度与宽度比小于10时,视为辐射流,把复杂的进水边界概化成一个“大井”进行计算,统称“大井”法;当矿坑长度与宽度比大于10,视为平行流,则概化为“水平廊道”进行计算,统称“廊道”法。

    用“大井”法计算矿坑涌水量时,其中的参数R、r应以矿坑 引用影响半径R0和引用半径r0代替。

    一、稳定流解析法

    (一)用“大井”法计算地下水为层流时的矿坑涌水量,其计算公式见表1所示。

表1  层流时稳定流解析法井筒涌水量计算公式

含水层类型

潜水

承压水

承压-潜水

计算公式中符号说明

计算公式

http://www.mining120.com/WebEditor/uploadfile/20100408133030615.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133030276.gif

 EQ http://www.mining120.com/WebEditor/uploadfile/20100408133031238.gif

图示

完整井

非完整井

http://www.mining120.com/WebEditor/uploadfile/20100408133031682.gif

(1)

http://www.mining120.com/WebEditor/uploadfile/20100408133031343.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133032980.gif

Q—竖井涌水量,m3/d;

K—渗透系数,m/d;

H—潜水含水层厚度或承压含水层由底板算起的水头值,m;

S—水位降低值,m;

r—井筒半径,m;

R—影响半径,m;

Rc—水流阻力系数;

b,b1,b2—井筒至供水或隔水边界的距离,m;

M—承压含水层的厚度,m;

h0—井筒中水柱高,m;

L—二供不、二隔水或一供一隔水边界之间的距离,m;

ξ0,ξ—取决于(http://www.mining120.com/WebEditor/uploadfile/20100408133032187.gif )的非完整井系数。i—映射井至抽水井的距离(其值取至1.5M为止),m

n= EQ http://www.mining120.com/WebEditor/uploadfile/20100408133032860.gif (n为整数)

σ—井、矿坑至边界距离,m;

x0—井或矿坑中心到两相交隔水边界交点的距离,m

http://www.mining120.com/WebEditor/uploadfile/20100408133033705.gif

(2)

http://www.mining120.com/WebEditor/uploadfile/20100408133033644.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133034662.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133034945.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133034376.gif

(3)

http://www.mining120.com/WebEditor/uploadfile/20100408133035448.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133035106.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133037691.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133037862.gif

(4)

http://www.mining120.com/WebEditor/uploadfile/20100408133037859.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133037181.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133038814.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133039715.gif

(5)

http://www.mining120.com/WebEditor/uploadfile/20100408133039998.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133039766.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133039819.gif

(6)

http://www.mining120.com/WebEditor/uploadfile/20100408133039202.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133040685.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133040626.gif

(7)

http://www.mining120.com/WebEditor/uploadfile/20100408133041970.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133042364.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133042701.gif

(8)

http://www.mining120.com/WebEditor/uploadfile/20100408133042922.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133043997.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133043658.gif

(9)

http://www.mining120.com/WebEditor/uploadfile/20100408133043879.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133043933.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133044163.gif

(10)

http://www.mining120.com/WebEditor/uploadfile/20100408133044385.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133044556.gif

    (二)用“大井”法计算地下水为紊流或混合流时的矿坑涌水量,其计算公式见表2-3所示。

表2  紊流或混合流态下竖井涌水量计算公式(一)

图形

含水层类型

紊流计算公式

http://www.mining120.com/WebEditor/uploadfile/20100408133044666.gif

(1)

潜 水

http://www.mining120.com/WebEditor/uploadfile/20100408133044831.gif

承压水

http://www.mining120.com/WebEditor/uploadfile/20100408133045230.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133045227.gif

(2)

潜 水

http://www.mining120.com/WebEditor/uploadfile/20100408133045169.gif

承压水

http://www.mining120.com/WebEditor/uploadfile/20100408133045842.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133046636.gif

(3)

潜 水

http://www.mining120.com/WebEditor/uploadfile/20100408133046179.gif

承压水

http://www.mining120.com/WebEditor/uploadfile/20100408133046345.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133047475.gif

(4)

潜 水

http://www.mining120.com/WebEditor/uploadfile/20100408133047590.gif

承压水

http://www.mining120.com/WebEditor/uploadfile/20100408133047526.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133047919.gif

(5)

潜 水

http://www.mining120.com/WebEditor/uploadfile/20100408133048656.gif

承压水

http://www.mining120.com/WebEditor/uploadfile/20100408133048822.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133048932.gif

(6)

潜 水

http://www.mining120.com/WebEditor/uploadfile/20100408133048197.gif

承压水

http://www.mining120.com/WebEditor/uploadfile/20100408133052359.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133052189.gif

(7)

潜 水

http://www.mining120.com/WebEditor/uploadfile/20100408133052974.gif

承压水

http://www.mining120.com/WebEditor/uploadfile/20100408133052691.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133053541.gif

(8)

潜 水

http://www.mining120.com/WebEditor/uploadfile/20100408133053984.gif

承压水

http://www.mining120.com/WebEditor/uploadfile/20100408133054832.gif

表3  紊流或混合流态下竖井涌水量计算公式(二)

混合流计算公式

适用条件

说明

http://www.mining120.com/WebEditor/uploadfile/20100408133054148.gif

远离地表

水体与隔

水边界

M—承压水含水层厚度m;

H—潜水含水层厚度或水头高度,m;

h0—井内水位高度,m;

m—水井影响区内的平均流态系数值,在1-2之间

b—水井到边界距离,m;如b值很大时,可舍去http://www.mining120.com/WebEditor/uploadfile/20100408133055674.gif 一项

http://www.mining120.com/WebEditor/uploadfile/20100408133055215.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133056794.gif

井位于

隔水边

界附近

http://www.mining120.com/WebEditor/uploadfile/20100408133056676.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133057860.gif

井位于

供水边

界附近

b1,b2值相对r值很大时,可舍去http://www.mining120.com/WebEditor/uploadfile/20100408133059884.gif 二项

Q—水井的出水量,m3/d;

r—水井半径,m;

K—渗透系数,m/d

http://www.mining120.com/WebEditor/uploadfile/20100408133059147.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133100216.gif

井位于二

直交隔水

边界附近

 

http://www.mining120.com/WebEditor/uploadfile/20100408133101956.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133101109.gif

井位于直

交的隔水

与供水边

界之间

 

http://www.mining120.com/WebEditor/uploadfile/20100408133102798.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133102852.gif

井位于二

直交的

供水边

界之间

 

http://www.mining120.com/WebEditor/uploadfile/20100408133103414.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133104263.gif

井位于二平行的隔水与供水边界之间

 

http://www.mining120.com/WebEditor/uploadfile/20100408133104875.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133104760.gif

井位于二平行的两条隔水边界之间

 

http://www.mining120.com/WebEditor/uploadfile/20100408133105552.gif

    二、非稳定流解析法

    用“大井”法计算矿坑涌水量时,其计算公式见表4-5所示。

表4  各种边界非稳定流井筒涌水量计算公式表(一)

含水层类型

潜水

承压水

承压-潜水

涌水量计算公式

http://www.mining120.com/WebEditor/uploadfile/20100408133105773.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133108239.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133109316.gif

计算示意图

井径

Rc计算公式

r2/4at≥0.05

r2/4at≤0.05

http://www.mining120.com/WebEditor/uploadfile/20100408133109426.gif

(1)

完整井

 

http://www.mining120.com/WebEditor/uploadfile/20100408133109703.gif

非完整井

 

http://www.mining120.com/WebEditor/uploadfile/20100408133109869.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133110268.gif

(2)

完整井

http://www.mining120.com/WebEditor/uploadfile/20100408133110551.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133110773.gif

非完整井

http://www.mining120.com/WebEditor/uploadfile/20100408133110714.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133110992.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133111898.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133111276.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133111391.gif

(3)

完整井

http://www.mining120.com/WebEditor/uploadfile/20100408133111612.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133111890.gif

非完整井

http://www.mining120.com/WebEditor/uploadfile/20100408133112964.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133112235.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133112401.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133112622.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133112564.gif

(4)

完整井

http://www.mining120.com/WebEditor/uploadfile/20100408133113750.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133113972.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133113187.gif

非完整井

http://www.mining120.com/WebEditor/uploadfile/20100408133113521.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133113799.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133114873.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133114256.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133114422.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133114475.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133114697.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133115825.gif

(5)

完整井

http://www.mining120.com/WebEditor/uploadfile/20100408133115991.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133115374.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133116445.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133116723.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133116833.gif

非完整井

http://www.mining120.com/WebEditor/uploadfile/20100408133116886.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133117344.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133117397.gif

(6)

完整井

http://www.mining120.com/WebEditor/uploadfile/20100408133117897.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133118859.gif

非完整井

http://www.mining120.com/WebEditor/uploadfile/20100408133118464.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133118573.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133118795.gif

(7)

完整井

http://www.mining120.com/WebEditor/uploadfile/20100408133119247.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133119413.gif

非完整井

http://www.mining120.com/WebEditor/uploadfile/20100408133120319.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133120260.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133120201.gif

(8)

完整井

http://www.mining120.com/WebEditor/uploadfile/20100408133120255.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133121888.gif

(9)

完整井

r2/4at≥0.05

r2/4at≤0.05

http://www.mining120.com/WebEditor/uploadfile/20100408133121938.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133121265.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133122508.gif

表5  各种边界非稳定流井筒涌水量计算公式表(二)

计算示意图

计算公式中符号说明及适用条件

http://www.mining120.com/WebEditor/uploadfile/20100408133109426.gif

(1)

 无越流无限含水层,抽水量固定不变。ξ0′取决于http://www.mining120.com/WebEditor/uploadfile/20100408133122618.gif

 r—井半径,m;u=http://www.mining120.com/WebEditor/uploadfile/20100408133122671.gif

http://www.mining120.com/WebEditor/uploadfile/20100408133110268.gif

(2)

 无越流固定流量抽水,井位于直线隔水边界了附近。如果2b≥1.5M时,ξ′(http://www.mining120.com/WebEditor/uploadfile/20100408133122949.gif )可忽略不计

http://www.mining120.com/WebEditor/uploadfile/20100408133111391.gif

(3)

 无越流固定流量抽水井位于直线供水边界附近

http://www.mining120.com/WebEditor/uploadfile/20100408133112564.gif

(4)

 无越流固定流量抽水,井位于平行的隔水与供水边界之间

http://www.mining120.com/WebEditor/uploadfile/20100408133115825.gif

(5)

 无越流固定流量抽水井位于平行二隔水边界之间

http://www.mining120.com/WebEditor/uploadfile/20100408133117397.gif

(6)

 无越流固定流量抽水井位于直交二隔水边界之间

http://www.mining120.com/WebEditor/uploadfile/20100408133118795.gif

(7)

 无越流固定流量抽水,井位于直交的隔水与供水边界之间

http://www.mining120.com/WebEditor/uploadfile/20100408133120201.gif

(8)

 无越流固定流量抽水,井位于三边隔水的半封闭含水层中

http://www.mining120.com/WebEditor/uploadfile/20100408133121888.gif

(9)

 固定流量抽水井,位于无越流封闭含水层的中心

 固定流量抽水井,位于无越流封闭含水层中任意一点

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