福建省暴雨徑流查算圖表推理公式法

福建省推理公式計算設(shè)計洪水手冊一、基本公式:推理公式是無資料地區(qū)由暴雨推求洪水比較常用的方法，我省中小型水利工程設(shè)計洪水的計算也通常采用這種方法（一般在流域面積200km2以下采用！,它是假定匯流時間內(nèi)降雨強度是均勻，并將匯形面積曲線概化為矩形，導(dǎo)出如下計算公式:當tc辛?xí)r，即全面匯流情況下，Qm=0.278RFm T當tc<T時，即部分匯流情況下，Q=0.278^cF=0.278幺尸(2)m tC代 t式中：。刀為地表凈峰流量（m3/s），F(xiàn)為流域面積（km2）,七°為成峰的產(chǎn)流面積（即與tc相應(yīng)的部份面積中最大的一塊，km2）;t為流域匯流歷時（小時）；tc為地表產(chǎn)流歷時（小時）；R為匯流歷時內(nèi)的最大地表凈雨量（毫米）；昵為產(chǎn)流歷時內(nèi)的地表凈雨量（毫米）；0.278為換算系數(shù)。二、設(shè)計暴雨的計算1、查圖法計算設(shè)計暴雨（1）查算設(shè)計流域各種歷時的暴雨參數(shù)：根據(jù)設(shè)計流域所在地點，應(yīng)用年最大各種歷時的降雨量均值等值線圖和變差系數(shù)等值線圖，按地理內(nèi)插法賣取流域中心點的暴雨參數(shù)值，如果流域內(nèi)有兩條以上等值線通過，可按面積加權(quán)法計算。（2）計算設(shè)計頻率的各種歷時降雨量：根據(jù)上步查算的各種歷時降雨量的變差系iCv值，從皮爾遜皿型曲線的模比系數(shù)Kp值表中（Cs/Cv=3.5）分別賣取設(shè)計頻率P的Kp值，乘以相應(yīng)的歷時降雨量均值即得。（3）計算各種歷時的面雨量：根據(jù)設(shè)計流域的面積和降雨歷時，查讀暴雨點面關(guān)系表（附表1，得暴雨點面折算系數(shù)a，乘以相應(yīng)的點雨量即得（流域面積在10km2以下直接采用點雨量，不打折扣％（4）推求設(shè)計雨量的時程分配：把上面所求的設(shè)計降雨量代入24小時（或三天）的設(shè)計雨型表（附表3），即得設(shè)計雨量的時程分配。（5）設(shè)計凈雨的計算：24小時的設(shè)計雨量不扣損，直接用設(shè)計雨量過程作為設(shè)計凈雨過程。2、參證站法計算設(shè)計暴雨（1） 選擇在設(shè)計流域內(nèi)或附近有實測短歷時暴雨的雨量站為參證站，根據(jù)參證站實測各短歷時（1小時、3小時、6小時、24小時）的暴雨資料，用經(jīng)驗公式計算其頻率，皮爾遜皿型曲線適線，計算各短歷時暴雨設(shè)計參數(shù)，得到各頻率的設(shè)計暴雨量。（2） 設(shè)計流域的點、面雨量換算：根據(jù)設(shè)計流域的面積和設(shè)計暴雨歷時，查讀暴雨點面關(guān)系表（附表1），得暴雨點面折算系數(shù)a。用折算系數(shù)a乘以參證站相應(yīng)的點雨量，即得設(shè)計流域的面雨量（流域面積在10km2以下直接采用點雨量，不打折扣。（3）推求設(shè)計雨量的時程分配：把上面所求的設(shè)計降雨量代入24小時（或三天）的設(shè)計雨型表（附表3），即得設(shè)計雨量的時程分配。（4）設(shè)計凈雨的計算：24小時的設(shè)計雨量不扣損，直接用設(shè)計雨量過程作為設(shè)計凈雨過程。三、地理參數(shù)計算1、河長L河長L為流域的分水嶺至出口斷面的總長度（單位：km）,有多條支流時，應(yīng)選擇做為河源的支流■測其河長。2、河道平均坡降J河道平均坡降J為自分水嶺至出口斷面的河道平均比降（單位：％。）計算方法：用相應(yīng)比例的地圖（1:1萬或1：5萬）分別做出各等高線與河流的正交點位置，從出口斷面開始，分別列出各正交點的高程h、h、h......，以及各正交點之間的距離/、/、I......，然后0 1 2 1 2 3用下列公式計算流域平均坡降J。T(h+h)l+(h+h)l+……+(h+h)l-2hL「J=—0 1_1 1 2_2 n-1 n~n 0—X1000/OOL四、 雨力Sp及暴雨遞減系數(shù)n的計算雨力Sp即為t=1小時的雨強，Sp=R24.p*24n-1。暴雨遞減系數(shù)分為n、n,其中n為1小時以內(nèi)暴雨遞減系數(shù)，n為1~24小時暴雨

1 2 1 2遞減系數(shù)。推理公式計算設(shè)計洪水時所采用的n為n2，即為1~24小時的暴雨遞減系數(shù)。n2可用下式計算，也可查n2等值線圖。n=】g氣7%,

2lg24RR式中：a24p為參證點設(shè)計頻率的最大24小時降雨的雨強，即以24,=寸，a1,=十。五、 設(shè)計洪峰流量及洪水過程線計算：1、試算法計算地表洪峰流量s計算公式Q=0.278中衛(wèi)Fs式中：①為徑流系數(shù)；p為雨力；Tn為匯流時間。計算步驟：(1)匯流歷時t的計算：0.278LT= 1 1mJ3Q4(2)計算匯流參數(shù)m值：先確定流域所在的匯流分區(qū)，由設(shè)計流域的特征參數(shù)F(km2XL(km)sJ(%。)計算。=~^，而后根據(jù)°值及設(shè)計流域所在分區(qū)，用下式計算匯流1 1J3F4參數(shù)m值：沿?！?gt;1.5時，m=0.053°0.809；°<1.5時，m=0.063°0.384

內(nèi)陸0>1.5時，m=0.03900.712；9<1.5時，m=0.04500.335另外漳州地區(qū)匯流參數(shù)m值計算公式：m=0.05600.67(3)確定穩(wěn)定入滲率fc值：根據(jù)24小時設(shè)計凈雨過程，計算次凈雨平均強度，?次=，其中T是凈雨總量的有效歷時，即降雨過程的首末各時段雨強不及0.5(毫米/小時)者不參加歷時統(tǒng)計。然后以\值讀i?fc相關(guān)表求得fc(毫米/小時)值。次(4)雨力Sp計算：S=R4x24,-1(5)產(chǎn)流歷時tB計算：s1t=[(E)于]nBfc(6)試錯法計算Qm:當tB*時(一般情況時);①；T0.278①；T0.278乙iimJ3Q4°m②；Q=0.278中衛(wèi)尸③

m Tn計算方法是假定一個T，代入式①和式③，求出。，再用式②求出T',當TQT'時，得出的Q、T'即為所求值，否則重復(fù)上述步驟，直至符合要求。m式中：1為自分水嶺至出口斷面的河道長度(km)J為自分水嶺至出口斷面的河道比降(％。)n為24小時暴雨遞減系數(shù)。2、計算設(shè)計地表洪水過程線(1)把上述計算的24小時設(shè)計凈雨過程，用fc值將各時段的凈雨r分割成地表凈雨Ri 表i和地下凈雨R兩個部分，可列表計算。下i其中R=&xfxMi若計算結(jié)果R下>R時，則取R下=R,R表i=R「七式中：R〔為時段凈雨；尸?為總凈雨；fc為穩(wěn)定下滲率；△t為凈雨時段數(shù)（2）計算地表和地下設(shè)計洪量：分別由地表和地下凈雨求得。地表洪量W表=1000xR表xF (m3)地下洪量W下=1000xR下xF (m3)，式中（3）計算地表洪水過程線：先計算地表洪水過程線的形狀系數(shù)y=——匕 ，式中QxTx3600秫表T是地表洪水過程線的底寬，24小時設(shè)計雨量固定為50小時，3天設(shè)計雨量固定為80小時。然后根據(jù)y值查y~t~Q%關(guān)系表（附表6）的漲水部份和退水部份各個時刻t所對應(yīng)Qm的Q%值，乘以地表洪峰流量Qm表即得。Qm3、計算地下洪水過程線將地下洪量W下按等腰三角形分配，其底寬是地表洪水過程線底寬的兩倍。地下洪峰流量計算公式：Q=W下，式中T為50小時。地下洪峰流量出現(xiàn)在地表洪水過程m下3600xT線的50小時處，地下洪水過程線底寬是地表洪水過程線底寬的兩倍即為100小時。所以按等腰三角形進行各時刻地下洪水流量分配，即可求得地下洪水過程線。4、計算設(shè)計總洪水過程線根據(jù)前面求得地表和地下洪水過程線，將地下洪水過程線的Q置于地表洪水過程線m下的終止點，其起漲點和地表洪水過程線的起漲點重合，中間過程按直線內(nèi)插，然后把同時刻的流量疊加即得。福建省暴雨點面關(guān)系表

設(shè)計暴雨的a~F?t關(guān)系表*02040608010012014016018020022024011.0000.9450.9110.8840.8640.8470.8340.8230.8150.8070.8000.7950.79031.0000.9600.9310.9100.8930.8790.8670.8580.8510.8450.8400.8350.83061.0000.9770.9570.9420.9280.9170.9070.8990.8920.8860.8810.8750.871121.000.0.9860.9720.9610.9510.9430.9350.9280.9210.9150.9100.9050.901241.0000.9910.9830.9750.9690.9640.9590.9530.9490.9440.9400.9360.9333天1.0000.9950.9900.9850.9810.9770.9730.9700.9670.9650.9630.9600.958

福建省最大24小時降雨概化過程線時間12345678%3%R24-R63%R24-R63%R24-R63%R24-R64%R24-R64%R24-R67%R24-R67%R24-R6時間1314151617181920%50%R3-R150%R3-R1100%R133%R6-R333%R6-R334%R6-R37%R24-R67%R24-R6福建省最大三天（包括最大24小時）設(shè)計雨型表日程第--天第二天（最大24小時）時段歷時（小時）6666662136占H1%100占（H3-H1）%100占（H6-H3）%100占（H24-H6）%204238占（H3天-H24）%0101520福建省次凈雨強度/與穩(wěn)定入滲率六相關(guān)表附表4單位：毫米/小時0.00.10.20.30.40.50.60.70.80.900.00.00.10.10.20.20.30.30.40.410.50.50.60.60.70.70.80.80.90.920.91.01.01.11.11.21.21.21.31.331.41.41.41.51.51.61.61.61.71.741.81.81.81.91.92.02.02.02.12.152.12.22.22.22.32.32.42.42.42.562.52.52.62.62.62.72.72.72.82.872.82.92.92.93.03.03.03.13.13.183.23.23.23.33.33.33.43.43.43.493.53.53.53.63.63.63.73.73.73.8103.83.83.83.93.93.93.94.04.04.0114.14.14.14.14.24.24.24.24.34.3124.34.44.44.44.44.54.54.54.54.6134.64.64.64.74.74.74.74.84.84.8144.94.94.94.95.05.05.05.05.15.1155.15.15.25.25.25.25.35.35.35.3165.45.45.45.45.55.55.55.55.65.6175.65.65.65.75.75.75.75.85.85.8185.85.95.95.95.96.06.06.06.06.1196.16.16.16.26.26.26.26.26.36.3206.36.36.46.46.46.46.56.56.56.5216.66.66.66.66.66.76.76.76.76.8226.86.86.86.86.96.96.96.97.07.0237.07.07.17.17.17.17.17.27.27.2247.27.37.37.37.37.37.47.47.47.4

0.00.10.20.30.40.50.60.70.80.9257.57.57.57.57.57.67.67.67.67.6267.77.77.77.77.87.87.87.87.87.9277.97.97.97.98.08.08.08.08.08.1288.18.18.18.28.28.28.28.28.38.3298.38.38.38.48.48.48.48.48.58.5308.58.58.58.68.68.68.68.68.78.7318.78.78.78.88.88.88.88.88.98.9328.98.98.99.09.09.09.09.09.19.1339.19.19.19.19.29.29.29.29.29.3349.39.39.39.39.49.49.49.49.49.4359.59.59.59.59.59.69.69.69.69.6369.69.79.79.79.79.79.79.89.89.8379.89.89.99.99.99.99.99.910.010.03810.010.010.010.010.110.110.110.110.110.13910.210.210.210.210.210.210.310.310.310.34010.310.310.410.410.410.410.410.410.410.54110.510.510.510.510.510.610.610.610.610.64210.610.710.710.710.710.710.710.710.810.84310.810.810.810.810.910.910.910.910.910.94410.911.011.011.011.011.011.011.011.111.14511.111.111.111.111.111.211.211.211.211.24611.211.211.211.311.311.311.311.311.311.34711.411.411.411.411.411.411.411.511.511.54811.511.511.511.511.511.611.611.611.611.64911.611.611.611.711.711.711.711.711.711.75011.7

0.050.060.070.080.090.100.110.120.130.140.150.16漲水部分000000000000030.50.70.91.11.41.72.02.32.73.03.33.661.52.02.53.23.94.55.25.86.57.38.18.871.92.63.34.14.85.66.47.28.08.99.710.582.43.34.15.05.96.87.78.69.510.511.412.493.04.05.06.06.98.09.010.111.112.213.314.4103.74.85.97.18.29.410.511.813.014.215.416.7114.55.87.18.49.611.012.413.715.116.618.019.5125.57.08.510.011.513.114.716.317.919.621.222.9136.98.810.612.314.116.017.819.621.423.225.026.91411.113.616.118.520.923.425.828.230.432.534.536.41520.624.528.432.235.939.543.146.449.752.855.959.015.538.544.049.655.160.465.269.372.875.577.980.382.5洪峰16100.0100.0100.0100.0100.0100.0100.0100.0100.0100.0100.0100.0退水部分16.559.663.467.370.974.677.279.881.883.584.886.187.41737.042.347.452.257.160.964.367.269.771.873.975.61819.022.826.530.233.937.541.144.648.051.254.357.01910.614.117.520.924.327.731.034.137.139.742.344.7206.89.812.915.818.821.824.727.430.132.534.837.2215.07.610.212.815.418.020.522.825.127.229.331.4223.96.28.510.712.915.217.519.621.723.725.727.7233.15.17.29.111.113.015.117.119.121.022.824.6242.54.25.97.69.411.112.914.716.418.219.921.6252.03.55.06.58.09.511.112.814.516.017.419.0261.73.04.25.46.78.19.611.012.413.815.216.6附表524小時暴雨洪水概化過程線系數(shù)表24小時暴雨洪水概化過程線系數(shù)表300.81.21.62.02.42.93.44.25.16.27.38.4350.40.50.60.70.81.01.21.62.12.73.44.1400.20.20.30.40.50.60.80.91.11.31.61.9450.10.10.10.20.20.20.20.30.30.40.50.7500000000000002424小時暴雨洪水概化過程線系數(shù)表*3\0.170.180.190.200.210.220.230.240.250.26.0.270.28000000000000034.04.44.85.15.55.96.26.67.07.47.78.169.410.110.711.412.112.713.414.014.715.416.116.8漲711.312.112.913.714.415.216.016.717.518.319.119.9813.314.215.116.016.817.718.719.620.421.422.323.3水915.416.517.518.619.620.721.722.823.824.925.926.91017.919.220.421.622.724.025.226.427.628.930.131.3部1120.922.323.625.026.327.729.130.531.833.234.536.01224.526.127.629.130.632.233.835.336.838.439.941.4分1328.630.332.033.835.637.439.241.042.744.546.348.01438.139.941.643.345.046.748.450.151.753.555.256.91562.165.168.070.873.576.078.580.782.884.686.488.015.584.586.488.189.791.292.493.594.595.596.196.797.3洪峰16100.0100.0100.0100.0100.0100.0100.0100.0100.0100.0100.0100.0退16.588.589.690.591.392.293.093.994.795.596.296.997.51777.378.980.482.083.584.886.187.388.689.891.092.2水1859.762.064.366.368.270.171.973.875.777.579.381.11947.149.451.753.956.158.460.662.865.067.369.571.6部2039.541.743.946.048.150.352.554.656.658.760.863.02133.535.637.639.641.643.645.647.649.551.553.655.8附表5

分2229.731.633.535.437.339.241.143.145.046.948.950.82326.428.230.031.833.535.337.138.840.542.444.346.22423.425.126.728.330.031.633.334.936.638.340.041.82520.622.223.825.326.828.329.931.433.034.636.237.72618.019.420.922.423.925.326.828.229.731.132.634.03019.510.611.712.814.015.116.317.618.820.021.122.3354.95.76.57.48.39.210.010.911.912.813.714.7402.32.83.44.04.65.25.96.67.27.98.79.4450.91.11.41.72.02.42.73.03.43.74.14.450000000000000福建省三天暴雨洪水概化過程y?t?Q%關(guān)系表附表6Qm\%0.040.050.060.070.080.090.100.110.120.130000000000050.10.20.30.40.50.60.80.91.11.2100.30.50.70.91.21.51.82.12.42.7漲120.50.81.01.31.61.92.22.63.03.5140.71.01.31.72.02.42.73.23.74.3160.91.31.72.22.63.13.54.04.55.2水181.21.72.22.83.33.94.55.15.76.4201.62.32.93.64.24.95.66.47.28.0222.12.93.74.55.36.27.08.09.09.9部242.73.84.85.97.08.09.110.211.212.3253.14.45.66.88.09.210.311.412.513.7263.65.16.57.79.010.211.512.814.015.3份274.25.87.38.810.211.713.114.616.017.4284.96.68.310.011.613.314.916.518.119.7295.87.79.511.313.215.117.018.820.622.5307.19.311.413.515.617.619.721.723.825.8

319.211.914.516.919.321.724.126.428.730.93213.016.219.422.625.829.032.135.338.541.63323.027.932.937.742.547.151.756.060.364.533.542.548.253.959.364.569.073.076.479.582.1洪峰34100.0100.0100.0100.0100.0100.0100.0100.0100.0100.0退水部份34.555.661.566.971.274.977.880.382.484.586.33533.240.547.553.959.363.567.370.473.576.33618.222.827.431.736.140.344.648.953.257.13711.415.519.623.627.631.435.339.142.746.1388.712.215.719.122.525.829.232.435.638.6397.010.113.216.219.222.125.127.930.833.5406.08.711.313.916.619.221.924.627.129.6415.27.59.812.114.416.919.421.824.126.4424.66.58.510.512.614.817.119.221.423.5434.15.77.49.211.113.015.016.918.920.9443.75.26.78.39.911.613.415.217.018.8453.34.76.07.48.910.512.113.715.417.1463.04.25.46.78.09.410.912.413.815.4482.53.64.65.76.87.99.110.311.512.8502.13.03.94.85.86.87.88.99.911.0551.52.02.63.34.04.75.46.16.97.8601.01.41.82.22.73.23.84.45.05.6700.40.50.70.91.11.41.61.92.22.5800000000000福建省三天暴雨洪水概化過程y?t?Q%關(guān)系表附表6Q0.140.150.160.140.150.160.17漲0000051.51.71.92.10.180.190.200.210.220.230000002.42.62.93.23.53.8水部份103.13.54.04.44.95.56.06.57.17.7123.94.55.05.56.16.77.38.08.69.3144.85.46.16.77.48.18.99.610.311.1165.96.67.38.18.99.810.611.412.313.1187.28.08.99.810.611.612.513.414.315.2208.99.810.711.712.613.614.615.516.517.62210.911.913.014.115.116.217.318.419.520.62413.314.515.616.818.019.320.521.723.024.22514.816.117.318.519.721.122.323.725.026.32616.617.819.020.421.723.124.525.827.228.62718.820.221.623.024.425.827.228.529.931.12821.422.924.526.027.529.030.431.733.034.22924.426.127.929.531.132.734.235.737.138.33027.829.831.733.635.337.038.740.241.943.43133.135.537.840.142.444.746.949.151.153.23244.847.951.154.357.560.763.866.869.772.73368.572.375.778.781.684.186.688.790.692.233.584.586.688.690.391.993.394.695.796.597.3洪峰34100.0100.0100.0100.0100.0100.0100.0100.0100.0100.0退水部份34.587.989.390.892.093.294.395.396.497.498.43578.980.982.984.586.287.789.290.591.893.23660.764.167.169.772.174.576.778.981.183.03749.352.455.458.360.963.465.968.370.772.83841.544.246.849.552.154.757.359.962.364.63936.138.641.143.646.148.651.053.556.058.54032.134.536.939.341.744.046.348.750.953.14128.730.933.235.437.539.741.844.046.248.24225.727.729.931.934.036.038.140.242.344.34322.924.926.828.830.832.834.836.939.141.04420.622.524.326.128.029.931.933.835.938.14518.820.522.224.025.827.629.331.133.135.2

4616.918.520.121.823.525.227.028.830.732.84814.115.617.118.620.221.823.525.126.728.45012.113.214.515.917.318.720.221.723.224.7558.79.610.411.412.413.314.315.316.417.5606.37.07.78.49.19.810.511.211.912.6702.73.03.33.63.94.24.54.95.25.6800000000000六、算例：在漳州市龍文區(qū)境內(nèi)的九十九灣要修建排澇工程，控制流域面積F=100.5平方公里，主河道長度L=21.0公里，主河道平均坡降J=0.8%。，通過設(shè)計暴雨推求設(shè)計洪水（推理公式法），計算該流域二十年一遇24小時暴雨的設(shè)計洪水過程線（一）設(shè)計暴雨的計算：（雨量單位：mm）1、設(shè)計點雨量計算：因該流域無實測暴雨資料，選用流域附近的中山橋雨量站為參證站，計算設(shè)計流域的設(shè)計點雨量。經(jīng)計算，中山橋雨量站廠24=120.9mm，Cv=0.38,C/Cv=4.0。二十年一遇各歷時設(shè)計暴雨量見下表：時段H24H6H3H1雨量210142116882、設(shè)計面雨量計算：根據(jù)二十年一遇的各種歷時點雨量，查讀流域面積為100.5平方公里時各歷時的暴雨點面折算系數(shù)aF，計算相應(yīng)面雨量:計算表3（小時）13624aF0.8470.8790.9170.964點雨量88116142210面雨量74.5102.0130.2202.43、計算24小時設(shè)計雨量的時程分配:計算表4時程123456789101112雨量2.22.22.22.22.92.95.15.15.15.15.15.1時程131415161718192021222324

雨量13.813.874.59.39.39.65.15.14.34.34.34.34、計算二十年一遇的暴雨遞減指數(shù)n:2p=^^plga24p =〔log74.5-log(202.4/24)〕/log2421g24=0.69(二)、設(shè)計凈雨的計算：本次以24小時雨量計算設(shè)計洪水，所以不扣損，上面所求的設(shè)計雨量過程就作為24小時設(shè)計凈雨過程。三、用推理公式計算設(shè)計洪水：由上述推求的設(shè)計暴雨過程，列表進行計算，其中雨量單位為mm，流量單位為m3/s。1、 計算次凈雨平均強度，=^~=*24=8.4毫米〃小時，查表得fc=3.3毫米/小時T242、 用fc值把Ri分割成R下.和R表.兩個部份，計算表5時段序數(shù)時段凈雨Ri穩(wěn)定下滲率fc時段地下凈雨R下i時段地表凈雨R#(1)(2)(3)(4)(5)12.23.32.20.022.23.32.20.032.23.32.20.042.23.32.20.052.93.32.90.062.93.32.90.075.13.33.31.885.13.33.31.895.13.33.31.8105.13.33.31.8115.13.33.31.8125.13.33.31.81313.83.33.310.5

時段序數(shù)時段凈雨Ri穩(wěn)定下滲率fc時段地下凈雨R下i時段地表凈雨R#(1)(2)(3)(4)(5)1413.83.33.310.51574.53.33.371.2169.63.33.36.3179.33.33.36.0189.33.33.36.0195.13.33.31.82053.33.31.7214.23.33.30.9224.23.33.30.9234.23.33.30.9244.23.33.30.9E202.479.274128.4見計算表5第（3）?（5）欄。3、該設(shè)計流域匯流分區(qū)屬于沿海地區(qū)，根據(jù)流域特征F=100.5平方公里，L=21.0公里，J=0.8%。m=0.05390.809