拱壩基本參數(shù)應(yīng)力分析畢業(yè)論文

拱壩基本參數(shù)應(yīng)力分析畢業(yè)論文目錄第一章拱壩基本參數(shù)計算 21.1壩頂高程的確定 21.1.1壩頂超高計算 21.1.2壩頂高程計算 31.2壩型方案及結(jié)構(gòu)布置 3第二章應(yīng)力分析 62.1荷載計算 62.1.1自重 62.1.3泥沙壓力 92.1.4揚壓力 102.1.5溫度荷載 112.2地基位移計算 122.3拱冠應(yīng)力分析（拱冠梁法） 152.2.3拱冠徑向變位系數(shù)的確定 382.2.4拱冠梁變位的計算 412.2.5拱冠梁應(yīng)力計算 442.2.6拱圈應(yīng)力計算 52第三章壩肩穩(wěn)定分析 563.1穩(wěn)定分析 563.1.1計算式 563.1.2分析過程 57第四章溢流設(shè)計及消能防沖設(shè)計 604.1溢流面計算 604.2下游消能防沖復(fù)核 60第一章拱壩基本參數(shù)計算1.1壩頂高程的確定1.1.1壩頂超高計算根據(jù)《水利水電工程等級劃分及洪水標(biāo)準(zhǔn)》（SL252—2000）規(guī)定：龍源口水庫設(shè)計洪水標(biāo)準(zhǔn)采用50年一遇，校核洪水標(biāo)準(zhǔn)采用500年一遇，按照《漿砌石壩設(shè)計規(guī)》SL25—91，《砼拱壩設(shè)計規(guī)》SL282—2003中規(guī)定計算大壩需要的壩頂超高。壩頂超高按下式計算：△h=Zhi+h0+hC式中：Zhi—波浪高（m）h0—波浪中心線至水庫靜水位的高度（m）hC—安全超高（m）（正常運行情況hC=0.4m，非常運行情況hC=0.3m）g(Zhi)/V△2=0.0076V0-1/12(gD/V02)1/3gLm/V02=0.331V0-7/15(gD/V02)4/15h0=[π（Zhi）2/Lm]Cth（2πH1/Lm）式中：Lm—波長（m）D—吹程（D=3000m）V0—多年平均最大風(fēng)速，V0=17.5m/s，正常運用條件下采用V0′=1.5V0H1—水域平均水深（m）壩頂超高計算成果列如表1-4。表1-4壩頂超高計算成果表項目P（%）波浪高2hi（m）風(fēng)壅高h0（m）安全超高hC（m）合計（m）0.21.070.390.31.762.01.780.720.42.901.1.2壩頂高程計算壩頂高程計算結(jié)果列表于1-5。表1-5壩頂高程計算成果表項目P（%）水位（m）壩頂超高（m）計算壩頂高程（m）0.2321.001.76322.762.0319.982.90322.88取大值322.88m，本工程取323.00m。1.2壩型方案及結(jié)構(gòu)布置本工程按砌石拱壩進行設(shè)計，初擬壩底厚為10m。該壩址受地形、地質(zhì)條件的限制，右?guī)r山體下有一沖溝從坎肩后面通過，左岸山體稍欠單薄，拱端的位置由于受這些因素的制約，僅能在有限的圍進行選擇，拱壩的具體位置布置如圖所示。拱圈參數(shù)的擬定：1、中心角2φA：砌石拱壩頂拱中心角可選用80°～110°，下層可采用40°～80°。2、拱圈半徑：初步擬定可按下式計算，拱圈半徑R=L/(2sinφA)，式中L為弦長。3、拱冠梁的形式和尺寸壩頂高程處開挖后的河床寬度L經(jīng)多次布置，L最終選定為138.47m。根據(jù)經(jīng)驗公式，可求得壩頂?shù)缀穸?。式中：為壩頂厚?為壩底厚度;為開挖后壩頂高程河岸寬度;H為壩高。經(jīng)計算Tc=3.5mTb=15m已知Tc,Tb后，可查《砌石壩設(shè)計》拱冠梁經(jīng)驗斷面表格得出拱冠梁1-6斷面尺寸如下表h/H拱厚Tx/H上游偏距x下游偏距T-x0.00Tc=3.50.000.003.50.10Tc+0.123△T=4.910.031.623.290.20Tc+0.226△T=6.010.063.083.020.30Tc+0.340△T=7.410.084.373.040.40Tc+0.443△T=8.590.105.513.080.50Tc+0.528△T=9.570.126.213.360.60Tc+0.623△T=10.660.126.644.020.70Tc+0.698△T=11.530.136.804.730.80Tc+0.792△T=12.610.126.645.970.90Tc+0.897△T=13.820.116.167.661.00Tb=150.105.299.71拱圈幾何尺寸擬定見下表1-7：表1-7大壩幾何尺寸表高程（m）厚度（m）園心角（°）半徑（m）各層高差（m）φ左φ右RR外233.5555581.3584.8510.8312.26.01484875.7581.8510.8301.48.59464460.6969.285.42969.57454449.6659.235.4290.610.66434342.3152.975.4285.211.53424234.2945.825.4279.812.61404021.3033.912691528299.0824.0810.8第二章應(yīng)力分析2.1荷載計算拱壩受的荷載包括：自重、靜水壓力、動水壓力、揚壓力、泥沙壓力、冰壓力、浪壓力、溫度作用以及地震作用等，基本上與重力壩相同。但由于拱壩本身的特點，有些荷載的計算及其對壩體應(yīng)力的影響與重力壩不盡相同。2.1.1自重由于永久性設(shè)備的自重相對于壩體自重可以忽略不計，所以自重計算只包括壩體自重計算。由于拱壩各壩塊的水平截面都呈扇形，如圖2-1所示，截面A1與A2間的壩塊自重G可按辛普森公式計算，即：G=（2.1）式中，γm—砌體容重，21.70kN/m3；ΔZ—計算壩塊高度，m；A1、A2、Am—上、下兩端和中間截面的面積，㎡；圖2-1壩體自重計算圖為了計算方便，教材還介紹下式計算：G=（2.2）取單位長度的壩塊，2.1.2靜水壓力靜水壓力是壩體承受的最主要荷載，由拱梁系統(tǒng)共同承擔(dān)，可通過拱梁分載法來確定拱系和梁系的荷載分配。但在拱梁分載法計算中，一般近似假定由梁承擔(dān)，通過梁的變位考慮其對拱的影響。上游靜水壓力應(yīng)根據(jù)水庫功能和荷載組合所規(guī)定的水庫水位確定，下游靜水壓力應(yīng)根據(jù)相應(yīng)的不利下游水位根據(jù)SL282—2003《混凝土拱壩設(shè)計規(guī)》附錄B.1計算確定。水的容重宜采用9.8KN/m3。水平靜水壓力根據(jù)SL282—2003《混凝土拱壩設(shè)計規(guī)》附錄B.1，水平靜水壓力計算公式為：p=γwH（2.3）式中，p—計算點處靜水壓力強度，kPa；H—計算點處的作用水頭，m；γw—水（或含泥沙水）的重度，kN/m3；設(shè)計洪水位（319.98m）時上游面：截面Ⅰ：截面Ⅱ：截面Ⅲ：截面Ⅳ：截面Ⅴ：截面Ⅵ：下游面：截面Ⅴ處高程為279.8m，高于下游水位276.70，故截面Ⅵ的水平水壓力為：截面Ⅵ：b、校核洪水位（321.00m）時上游面：截面Ⅰ：截面Ⅱ：截面Ⅲ：截面Ⅳ：截面Ⅴ：截面Ⅵ：下游面：截面Ⅴ處高程為279.80m，高于校核洪水位時下游水位277.7m。所以：截面Ⅵ：垂直靜水壓力計算公式為：

（kN）（2.4）式中，—計算點的水深，m；—壩體上游面混凝土塊的徑向投影長度，m；—混凝土塊上游面水平弧長，m（近似取為1m）；設(shè)計洪水位319.98m時上游面：截面Ⅰ：截面Ⅱ：截面Ⅲ：截面Ⅳ：截面Ⅴ：截面Ⅵ：下游面：截面Ⅵ：b、校核洪水位時321.00m上游面：截面Ⅰ：截面Ⅱ：截面Ⅲ：截面Ⅳ：截面Ⅴ：截面Ⅵ：下游面沒有垂直靜水壓力。2.1.3泥沙壓力泥沙壓力Ps式中：為淤沙浮容重；為泥沙摩擦角；為壩前泥沙淤積高度，m。大壩壩前百年泥沙淤積高程約286.0m，泥沙浮容重取8KN/m3，摩擦角取13o。則泥沙壓力Ps2.1.4揚壓力揚壓力包括浮托力和滲透壓力，根據(jù)SL282—2003《混凝土拱壩設(shè)計規(guī)》附錄B·3，計算公式為：（2.5）（2.6）式中，—揚壓力，kN；—浮托力，kN；—單位混凝土塊所受的滲透壓力，kN；—計算水位至各計算點的水深m；—混凝土塊計算截面面積m2；—計算截面厚度m；r—計算截面平均半徑m；設(shè)計洪水位（319.98m）時截面Ⅱ：截面Ⅲ：截面Ⅳ：截面Ⅴ：截面Ⅵ：截面Ⅴ高于下游水位，所以下游沒有浮托力。b、校核蓄水位（321.00m）時截面Ⅱ：截面Ⅲ：截面Ⅳ：截面Ⅴ：截面Ⅵ：截面Ⅴ高于相應(yīng)下游水位，所以下游沒有浮托力。2.1.5溫度荷載由于此次設(shè)計所給資料有限，可按一下經(jīng)驗公式對溫度荷載進行簡化計算：（2.7）式中，—計算點處溫度荷載，℃；—計算高程處的拱圈厚度，；表2-1溫度荷載計算表截面拱圈厚度（m）溫度荷載（℃）Ⅰ3.59.36Ⅱ6.018.48Ⅲ8.596.75Ⅳ10.665.36Ⅴ12.614.05Ⅵ152.442.2地基位移計算拱壩的建基面既是梁的基礎(chǔ)又是拱的基礎(chǔ)。地基位移與建基面的形狀無關(guān)，建基面沿弧線展平后的不規(guī)則平面，用一個長寬比相似、面積相等的當(dāng)量矩形來代替展開后的面積。如圖：圖2-2建基面展開圖=而實際展開的面積比以上據(jù)算的要大得多，故可以近似看作、，即：根據(jù)已有資料查得系數(shù)：彈性模量、查表可得：K1=5.1、K2=2.18、K3=2.4、K4=7.2、K5=0.47由K3查表得=2.1（2.8）（2.9）（2.10）（2.11）（2.12）（2.13）式中——由于單位彎矩作用在基巖面所產(chǎn)生的平均角位移；——由于單位垂直壓力作用在基巖面上所產(chǎn)生的平均法向位移；——由于單位徑向剪力作用在基巖面所產(chǎn)生的平均徑向剪變位移；——由于單位扭矩作用在基巖面所產(chǎn)生的平均扭轉(zhuǎn)角變位移；——由于單位剪力作用在基巖面所產(chǎn)生的平均角位移；——由于單位彎矩作用在基巖面所產(chǎn)生的平均剪變位移；——基巖彈性模量；——壩底厚度；——當(dāng)量矩形邊長比及基巖泊松比的函數(shù)，由《水工設(shè)計手冊》差得。故有：拱座位移計算（2.14）（2.15）（2.16）式中、、及稱作拱座位移系數(shù)。梁基位移計算（2.17）（2.18）式中2.3拱冠應(yīng)力分析（拱冠梁法）拱壩是一個變厚度、變曲率而邊界條件又很復(fù)雜的空間殼體結(jié)構(gòu)，要進行嚴(yán)格的理論計算是有困難的。在實際工程中，通常要做一些必要的假定和簡化。2.3.1拱梁徑向變位一致關(guān)系式由拱冠梁和各層拱圈交點處徑向變位一致的條件可以列出關(guān)系式（梁截面在平均厚度處（中線處）弧長取為1m，則上游面弧長為ΔSu，拱截面取1m高的等厚圓弧拱圈）：（2.19）等式左邊為拱冠梁截面的徑向變位值,等式右端為第i層拱圈的拱冠徑向變位值,拱冠分為五段,即梁、拱徑向變位一致的關(guān)系式為:式中，i—拱冠梁與水平拱交點的序列，即拱的層數(shù)，i=1～5；j—單位荷載作用點的序列；Pi—在i層截面上總的水平徑向荷載（如靜水壓力等）；xi—在i層截面上梁所分配到的水平徑向均勻荷載；δi—作用于拱冠梁上的鉛直荷載所引起梁在i處的徑向變位；Pi-xi/ΔSui—i層截面拱圈所分配到的水平徑向均布荷載；—單位徑向均布荷載作用于i層拱圈時，在拱冠i處所引起的徑向變位，為拱的變位系數(shù)；—溫度荷載分別作用于拱和梁時，所引起拱對梁的徑向變位差。如只計均勻溫度變化，則不引起梁的徑向變位，相當(dāng)于純拱法計算所得拱在i點的變位。2.3.2設(shè)計洪水位和校核洪水位各項參數(shù)的計算先計算設(shè)計洪水位的各項參數(shù)，計算成果見下表：表2-2設(shè)計洪水位各項參數(shù)計算成果表編分名稱及算式截面號類1234561計算高程V323312.2301.4290.6279.82692拱厚T3.56.018.5910.6612.61153平均半徑r83.178.86547.6427.1616.584外半徑Ru=r+T/2=（3）+84.8581.8169.3052.9733.9224.085半徑Rd=r-t/2=（3）-81.3575.860.7142.3121.319.086中線弧長ΔS1.01.01.01.01.01.07外弧長ΔSu=ΔS=（6）1.021.041.071.111.131.2458弧長ΔSd=ΔS=（6）0.980.960.930.890.770.559梁截面積A=ΔS·T=（6）（2）3.56.018.5910.6612.6115拱梁截面慣性矩I=3.5718.0852.74100.53164.19262.07形心偏心距e1=0.0010.0040.0090.200.481.13形心至上游面的距離au=1.742.974.215.135.836.37冠形心至下游面的距離ad=1.763.054.395.536.798.63上核點至上游面的距離Ku=1.161.982.803.433.914.34下核點至下游面的距離Kd=1.172.032.933.694.555.89梁形心至上核點的距離eu=-0.58-0.99-1.41-1.7-1.92-2.03分段高度Δh=V上-V下10.810.810.810.810.8分塊上游面水平投影ΔTu3.082.431.130-1.35截分塊頂?shù)仔涡牡乃骄唳g1.851.190.21-0.7-1.89分塊重心至分塊底形心的水平距Δag=0.840.560.10-0.34-0.92分塊平均截面積=4.767.39.6311.6413.81面分塊重ΔWs=111.56171.08225.69272.80323.42分塊重對塊底形心的彎矩Δ=93.7195.8022.57-92.75-297.55分塊累計彎矩=9371.51119.33-178.22常累計重量Ws=111.56282.64508.33781.131104.55塊頂上自重對塊底形心的彎矩=132.7659.35-355.83-1476.34累計彎矩=132.76192.11-.72-1640.06數(shù)自重總彎矩Ms=+93.71322.27404.19-44.39-1818.28截面至水面深度hu07.7818.5829.3840.1850.98平均水深3.8913.1823.9834.7845.58分塊上游面上的水面寬度△Tu’(當(dāng)水位高于塊頂△Tu’=△Tu)3.082.431.130-1.35平均弧長1.031.061.091.171.34分塊三角形水重12.3413.916.650-10.85塊頂上矩形水重020.0422.88072.69分塊水重△Ww=△WWA+△WWb=(33)+(34)12.3433.0829.53061.84累積水重Ww=∑⊿Ww=∑(35)12.3445.4274.9574.95136.79三角形水重重心到塊底形心的距離1.943.44.755.836.82矩形水重重心到塊底形心的距離1.433.04.575.837.05三角形水重對塊底形心的彎矩△Mwa=△WWAbga=(33)(37)23.9447.3031.590-74矩形水重對塊底形心的彎矩MWb=△WWbbgb=(34)(38)060.12104.560-512.46壩頂以上水重對塊底形心的彎矩計算改正值△MWc=WW上△ag=(36)上(19)22.8354.0515.74-52.47-258.53每塊水重對底部形心的總彎△MW=△Mwa+△MWb+△MWc=(39)+(40)+(41)46.77161.47151.89-52.47.93累積水重的彎矩MW=∑△MW=∑(42)46.77208.24360.13307.66487.59下截面至水面深度hd7.7游平均水深3.85面分塊上游面上的水面寬度△Td’(當(dāng)水位高于塊頂△Td’=△Td)1.03水平均弧長0.970.950.910.830.66重分塊三角形水重2.62及塊頂上矩形水重其分塊水重△Ww’=△WWA’+△WWb’=(48)+(49)2.62彎累積水重Ww’=∑△Ww’=∑(50)2.62距三角形水重重心到塊底形心的距離bga’=ad下-1/3△Td’=(13)下-1//3(46)8.29矩形水重重心到塊底形心的距離bgb’=ad下-1/2△Td’=(13)下-1//2(46)8.12三角形水重對塊底形心的彎矩△MWA’=△WWA’bga’=(48)(52)21.72矩形水重對塊底形心的彎矩△MWb’==△WWb’bgb’=(49)(53)壩頂以上水重對塊底形心的彎矩計算改正值△MWc’=WW上’ag=(51)上(19)每塊水重對底部形心的總彎矩△MW’=△Mwa’+△MWb’+△MWc’=(54)(55)(56)21.72累積水重的彎矩MW’=∑△MW’=∑(57)21.72揚浮托力Wu1’=γmhdA=(44)(9)-115.5壓滲透壓力-23.68-81.56-162.44-272.62-373.54力揚壓力Wu1=Wu1’+Wu1〃=(59)+(60)-23.68-81.56-162.44-272.62-489.04及浮托力對塊底形心彎矩Mu1’=0其滲透壓力對塊底形心彎矩Mu1〃=Wu1〃eu=(60)(16)23.44115276.15523.43758.29彎揚壓力力矩Mu1=Mu1’+Mu1〃23.44115276.15523.43758.29距排水點至上游面距離ba1.5防滲排水后水頭折減系數(shù)a0.5防滲排水后減少的水頭h1=(hu-hd)(1-a-ba/T)=[(29)-(44)][1-(66)-(65)/(2)]17.31防滲排水減少的滲透壓力Wu2〃=-1/2Th1=-1/2(2)(67)-129.83防滲排水減少的滲透壓力的力臂eu2=1/3(T+ba)-au=1/3[(2)+(65)]-(12)-0.87防滲排水減少的彎矩Mu2〃=Wu2〃eu2=(68)(69)112.95設(shè)防滲排水時的揚壓力Wu=Wu1-Wu2〃=(61)-(68)-23.68-81.56-162.44-272.62-359.21設(shè)防滲排水時的揚壓力的彎矩Mu=Mu1-Mu2〃=(64)-(70)23.44115276.15523.43645.34總垂直力W=Ws+Ww+Ww’+Wu=(25)+(36)+(51)+(71)100.22246.5420.84583.46884.75總垂直力的彎矩M=Ms+Mw+Mw’+Mu=(28)+(43)+(58)+(72).92645.511040.47786.7-663.63表2-3設(shè)計洪水位拱冠梁單位三角形徑向荷載徑向變位系數(shù)計算成果表彎矩變位系數(shù)h4/12I2h4/12I3h4/12I4h4/12I5h4/12I6小計徑向變位系數(shù)62.7121.5011.286.914.33系數(shù)乘積系數(shù)乘積系數(shù)乘積系數(shù)乘積系數(shù)乘積1/Ema114250.832043048541.4488608.0863272.792103.14a122125.412451672892.16144995.04108467.642916.25a1348636406.0896663.3681350.731506.17a14667.684855.2854233.82633.18a158456.0627116.91172.19a164.519.491949a21162.711021532360.9666456.0649212.171306.9a220.531.361225848541.44108746.2884363.721940.8a2324324270.7272497.5263272.791084.03a24445.1236248.7642181.86475.74a25641.462190.93132.39a263.515.1615.16a312.553.7516180.4844304.0435151.55689.82a32364.524270.7272497.5260259.81092.54a330.510.7512.3648331.6845.85672.64a34222.5624165.8430129.9318.3a35427.641564.9592.59a362.510.8310.83a41445.1222152.022190.93288.07a42667.6836284.7636155.88472.32a43333.8424165.8427116.91316.59a440.55.641282.921877.94116.5a45213.82938.9752.79a461.56.506.50a515.538.01730.3168.32a52962.191251.96114.15a53641.46938.9780.43a54320.37625.9846.71a550.53.46321.9916.45a560.52.172.17剪力變位系數(shù)3⊿h2/A23⊿h2/A33⊿h2/A43⊿h2/A53⊿h2/A6徑向變位系數(shù)58.2240.7432.8327.7523.33小計系數(shù)乘積系數(shù)乘積系數(shù)乘積系數(shù)乘積系數(shù)乘積1/EmA110.526.110.520.370.516.4150.513.8750.255.83382.603A120.526.11140.74132.83127.750.511.665.095A130.520.37132.83127.750.511.66592.615A140.516.415127.750.511.66555.83A150.513.8750.511.66537.205A160.255.8335.833A210.2514.5550.520.370.516.4150.513.8750.255.83371.A220.2514.555140.74132.82127.750.511.665127054A230.520.37132.83127.750.511.66592.615A240.516.415127.750.511.66555.83A250.513.8350.511.66525.54A260.255.83350833A310.2510.1850.516.4150.513.8750.255.83346.308A320.520.37132.83127.750.511.66592.615A330.2510.185132.83127.750.511.66582.43A340.516.415127.750.511.66555.83A350.513.8750.511.66525.54A360.255.8335.833A410.258.2050.513.8750.255.83327.916A420.516.45127.750.511.66555.83A430.516.45127.750.511.66555.83A440.258.205127.750.511.66547.623A450.513.8750.511.66515.54A460.255.8335.833A510.256.9830.255.83312.771A520.513.8750.511.66525.54A530.513.8750.511.66525.54A540.513.8750.511.66525.54A550.256.9830.511.66518.613A560.255.8335.833基礎(chǔ)變位系數(shù)徑向變位系數(shù)21.914.714.7133.73小計小計系數(shù)乘積系數(shù)乘積系數(shù)乘積系數(shù)乘積1/Em1/EmA1111.67333.2.59.1252.338.5170.512.96363.692549.43A1220571518.25414.6125.92629.772685.12A1315428518.25310.95125.92483.372082.16A1410285.5518.2527.3125.92337.221026.23A155142.75518.2513.65125.92188.57397.97A160.83323.7912.59.1250.170.6080.512.9679.44104.76A219.333266.46727.32.338.5170.512.96295.241673.19A2216456.8414.6414.6125.92498.961567.3A2312342.6414.6310.95125.92394.071570.72A248228.4414.627.3125.92276.22807.79A254114.2414.613.65125.92158.37316.3A260.66719.03327.30.170.6080.512.9639.9060.89A317.851.55.4752.338.5170.512.96226.80963.23A3212342.6310.95414.6125.92394.071579.23A339256.95310.95310.95125.92304.771059.84A346171.3310.9527.3125.92215.47589.6A35385.65310.9513.65125.92.17244.3A360.514.2751.55.4750.170.6080.512.9633.3450.00A414.667.2313.652.33805170.512.96158.36474.35A428228.427.3414.6125.92276.22804.37A436171.327.3310.95125.92215.47743.62A444114.327.327.3125.92154.82368.94A45257.127.313.65125.9293.97162.3A460.3339.51713.650.170.6080.512.9626.7439.07A512.33366.6170.51.8252.338.5170.512.9689.92171.01A524114.313.65414.6125.92158.47298.16A53385.6513.65310.95125.92.17232.14A54257.113.6527.3125.9293.97166.22A55128.5513.6513.65125.9261.7796.82A560.1674.7580.51.8250.170.6080.512.9620.1528.15A612.338.5170.512.9621.4821.48A62414.6125.9240.5240.52A63310.95125.9236.8736.87A6427.3125.9233.2233.22A6513.65125.9229.5729.57A660.170.6080.512.9613.5713.57表2-4設(shè)計洪水位拱冠梁徑向變位δi的計算表彎矩產(chǎn)生的徑向變位（）01057.751427.611207.21558.87-295.36-162.46-20.79系數(shù)乘積系數(shù)乘積系數(shù)乘積系數(shù)乘積系數(shù)乘積系數(shù)乘積系數(shù)乘積系數(shù)乘積小計0.2501105.7522855.2233621.6342235.482.25-664.565-812.31-207.98272.180.25264.37511427.6122414.4231676.611.75-516.884-649.841-207.94595.510.25356.9011207.2121117.741.25-369.23-487.831-207.91804.480.25301.811558.870.75-221.522-324.921-207.9293.440.25192.1530.25-73.841-162.461-207.9-117.371-207.9-207.9下面計算校核洪水位的各項參數(shù)。其中拱冠梁單位三角形徑向荷載徑向變位系數(shù)計算表與正常蓄水位相同。計算成果見下表：表2-5校核洪水位各項參數(shù)計算成果表編分名稱及算式截面號類1234561計算高程V323312.2301.4290.6279.82692拱厚T3.56.018.5910.6612.61153平均半徑r83.178.86547.6427.6116.584外半徑Ru==84.858.8169.3052.9733.9224.085半徑Rd==81.3575.860.7142.3121.319.086中線弧長△S1.01.01.01.01.01.07外弧長△Su==1.021.041.071.111.231.458弧長△Sd=0.980.960.930.890.770.559梁截面積3.56.018.5910.6612.61151拱梁截面慣性矩3.5718.0852.74100.53164.19262.071形心偏心距0.010.040.090.200.481.131形心至上游面的距離1.742.974.215.135.836.371冠形心至下游面的距離1.763.054.395.536.798.631上核點至上游面的距離1.161.982.803.433.914.341下核點至下游面的距離1.172.032.933.694.555.891梁形心至上核點的距離eu=-(au-ku)=-[(12)-(14)]-0.58-0.99-1.41-1.7-1.92-2.031分段高度△h=V上-V下=(1)上-(1)下10.810.810.810.810.81分塊上游面水平投影⊿Tu3.082.431.130-1.351截分塊頂?shù)仔涡牡乃骄唷鱝g=au上+△Tu-aU下=(12)上+(18)-(12)下1.851.190.21-0.7-1.892分塊重心至分塊底形心水平距0.840.560.10-0.34-0.922分塊平均截面積4.767.39.6311.6413.812面分塊重111.56171.08225.69272.80323.422分塊重對塊底形心的彎矩93.7195.8022.57-92.75-297.552分塊累計彎矩Ms’=∑△Ms=∑(23)93.71.51212.08119.33-178.222常累積重量Ws=∑△Ws=∑(22)111.56282.64508.33781.131104.552塊頂上自重對塊底形心的彎矩△Ms〃=Ws上△ag下=(25)上(19)下132.7659.35-355.83-1476.342累積彎矩Ms〃=∑△Ms〃=∑(26)132.76192.11-.72-1640.062數(shù)自重總彎矩Ms=Ms’+Ms〃=(24)+(27)93.71322.27404.19-44.39-1818.282截面至水面深度hu08.819.630.441.2523平均水深4.414.22535.846.63分塊上游面上的水面寬度△Tu’(當(dāng)水位高于塊頂△Tu’=△Tu)3.082.431.130-1.353平均弧長1.031.061.091.171.343分塊三角形水重13.9613.916.650-10.853塊頂上矩形水重022.6724.14074.533分塊水重△Ww=△WWA+△WWb=(33)+(34)13.9636.5830.79063.683累積水重Ww=∑⊿Ww=∑(35)13.9650.5481.3381.33145.013三角形水重重心到塊底形心的距離1.943.44.755.836.823矩形水重重心到塊底形心的距離1.433.04.575.837.053三角形水重對塊底形心的彎矩△Mwa=△WWAbga=(33)(37)27.0847.3031.590-744矩形水重對塊底形心的彎矩△MWb=△WWbbgb=(34)(38)068.01110.320525.444壩頂以上水重對塊底形心的彎矩計算改正值△MWc=WW上△ag=(36)上(19)25.8360.1417.08-56.93-274.074每塊水重對底部形心的總彎△MW=△Mwa+△MWb+△MWc=(39)+(40)+(41)52.91175.45159-56.93177.374累積水重的彎矩MW=∑△MW=∑(42)52.91228.36387.36330.43507.84截面至水面深度hd8.84平均水深4.44分塊上游面上的水面寬度△Td’(當(dāng)水位高于塊頂△Td’=△Td)1.034平均弧長0.970.950.910.830.664分塊三角形水重2.994塊頂上矩形水重5分塊水重△Ww’=△WWA’+△WWb’=(48)+(49)2.995累積水重Ww’=∑△Ww’=∑(50)2.995三角形水重重心到塊底形心的距離bga’=ad下-1/3△Td’=(13)下-1/3(46)8.295矩形水重重心到塊底形心的距離bgb’=ad下-1/2△Td’=(13)下-1/2(46)8.125三角形水重對塊底形心的彎矩△MWA’=△WWA’bga’=(48)(52)24.795矩形水重對塊底形心的彎矩△MWb’==△WWb’bgb’=(49)(53)5壩頂以上水重對塊底形心的彎矩計算改正值△MWc’=WW上’ag=(51)上(19)5每塊水重對底部形心的總彎矩△MW’=△Mwa’+△MWb’+△MWc’=(54)+(55)+(56)24.795累積水重的彎矩MW’=∑△MW’=∑(57)24.795浮托力Wu1’=γmhdA=(44)(9)-1326滲透壓力-26.78-86.03-168.08-279.55-372.876揚壓力Wu1=Wu1’+Wu1〃=(59)+(60)-26.78-86.03-168.08-279.55-504.876浮托力對塊底形心彎矩Mu1’=06滲透壓力對塊底形心彎矩Mu1〃=Wu1〃eu=(60)(16)26.51121.30285.74536.74756.936揚壓力力矩Mu1=Mu1’+Mu1〃26.51121.30285.74536.74756.93排水點至上游面距離ba1.56防滲排水后水頭折減系數(shù)a0.56防滲排水后減少的水頭h1=(hu-hd)(1-a-ba/T)=[(29)-(44)][1-(66)-(65)/(2)]17.286防滲排水減少的滲透壓力Wu2〃=-1/2Th1=-1/2(2)(67)-129.66防滲排水減少的滲透壓力的力臂eu2=1/3(T+ba)-au=1/3[(2)+(65)]-(12)-0.877防滲排水減少的彎矩Mu2〃=Wu2〃eu2=(68)(69)112.757設(shè)防滲排水時的揚壓力Wu=Wu1-Wu2〃=(61)-(68)-26.78-86.03-168.08-279.55-375.277設(shè)防滲排水時的揚壓力的彎矩Mu=Mu1-Mu2〃=(64)-(70)26.51121.3285.74536.74644.187總垂直力W=Ws+Ww+Ww’+Wu=(25)+(36)+(51)+(71)98.74247.15421.58582.91877.287總垂直力的彎矩M=Ms+Mw+Mw’+Mu=(28)+(43)+(58)+(72)173.13671.931077.29822.78-641.51表2-6校核洪水位拱冠梁徑向變位δi的計算表彎矩產(chǎn)生的徑向變位（）2.2.3拱冠徑向變位系數(shù)的確定1）由下式確定：（均勻水壓）（2.20）（均勻溫降）（2.21）截面Ⅰ：n=1 查表得：截面Ⅱ：n=1 查表得：截面Ⅲ：n=1 查表得：面Ⅳ：n=1 查表得：截面Ⅴ：n=1 查表得：截面Ⅵ：n=1 查表得：2）系數(shù)計算：截面Ⅰ：截面Ⅱ：截面Ⅲ：截面Ⅳ：截面Ⅴ：截面Ⅵ：2.2.4拱冠梁變位的計算1)計算式a、拱冠梁由于垂直力（自重，水重，揚壓力）作用產(chǎn)生的徑向變位計算式：（2.22）拱冠分為五等段，則計算式為：式中，Mi—各截面在垂直力作用下產(chǎn)生的彎矩；Mx—梁基斷面的彎矩；Ii—各計算截面的慣性矩；Ti—各計算截面拱冠梁厚度；△hi—拱冠梁分段高；Em、Ef—壩體,壩基彈性摸量；n’=Em/Ef’—壩體彈性摸量與梁基鉛直方向彈性摸量之比；n〃=Em/Ef〃—壩體彈性摸量與梁基水平方向彈性摸量比值；k1,、k5—壩基變位系數(shù)；b、拱冠梁由于單位三角形徑向荷載作用在各計算截面產(chǎn)生的徑向變位系數(shù)aij：（2.23）式中，M、V——在某單位三角形荷載作用下各計算截面的彎矩和剪力；Mx、Vi——單位三角形荷載下，梁基面的彎矩和剪力；其他符號同前。2）由上式聯(lián)立方程式求得設(shè)計洪水位情況時，各梁各截面分荷為：x1=-3.69(T/m)x2=5.03(T/m)x3=10.12(T/m)x4=18.29(T/m)x5=27.6(T/m)x6=40.3(T/m) 拱冠梁分配的荷載強度（Xi=Xi／△Sui，如圖2-2所示）x1=-3.62(T/m2)x2=4.84(T/m2)x3=9.46(T/m2)x4=17.93(T/m2)x5=22.44(T/m2)x6=27.79(T/m2)圖2-3正常蓄水位拱梁分荷截面圖（單位：T/M2）校核洪水位情況時，各梁各截面分荷為：x1=-3.71(T/m)x2=5.14(T/m)x3=10.27(T/m)x4=18.42(T/m)x5=27.98(T/m)x6=41.23(T/m)拱冠梁分配的荷載強度（Xi=Xi／△Sui，如圖2-3所示）x1=-3.64(T/m2)x2=4.94(T/m2)x3=9.60(T/m2)x4=18.06(T/m2)x5=22.75(T/m2)x6=28.43(T/m2)圖2-4校核洪水位拱梁分荷截面圖（單位：T/M2）2.2.5拱冠梁應(yīng)力計算1）拱冠梁的水平荷載彎矩計算a、各段水平力及力臂圖2-5梁荷載計算簡圖設(shè)計洪水位 水平力：力臂:校核洪水位水平力：力臂:b、各截面水平荷載彎矩:設(shè)計洪水位截面Ⅰ：截面Ⅱ：截面Ⅲ：截面Ⅳ：截面Ⅴ截面Ⅵ校核洪水位截面Ⅰ：截面Ⅱ：截面Ⅲ：截面Ⅳ：截面Ⅴ截面Ⅵ表2-7各截面水平荷載彎矩成果表水位截面ⅠⅡⅢⅣⅤⅥ319.980-52.01552.482104.625957.3613095.27321.000-45.39435.342172.946086.4913336.852）拱冠梁的總垂直力及總力矩計算總垂直力:設(shè)計洪水位0100.22246.5420.84583.46884.75校核洪水位098.74247.15421.58582.91877.28總彎矩:垂直荷載彎矩+水平荷載彎矩（2.24）設(shè)計洪水位0+0=0.92-52.01=111.91645.51+552.48=1197.991040.47+2104.62=3145.09786.7+5957.36=6744.06-663.63+13095.27=12431.64校核洪水位0+0=0173.13-45.39=127.74671.93+435.34=1107.271077.29+2172.94=3250.23822.78+6086.49=6909.27-641.51+13336.85=12695.343）拱冠應(yīng)力計算（參見圖2-6）圖2-6拱冠應(yīng)力計算示意圖a、設(shè)計洪水位截面Ⅰ：截面Ⅱ：最大應(yīng)力（2.25）（2.26）截面Ⅲ：最大應(yīng)力截面Ⅳ：最大應(yīng)力截面Ⅴ：最大應(yīng)力截面Ⅵ：最大應(yīng)力b、校核洪水位截面Ⅰ：截面Ⅱ：最大應(yīng)力截面Ⅲ：最大應(yīng)力截面Ⅳ：最大應(yīng)力截面Ⅴ：最大應(yīng)力截面Ⅵ：最大應(yīng)力2.2.6拱圈應(yīng)力計算純拱法梁中的水壓產(chǎn)生的應(yīng)力乘以拱圈分荷強度比，即得分荷拱圈徑向均布荷載下的應(yīng)力；在溫度荷載下的拱圈應(yīng)力與純拱法相同，故拱圈總應(yīng)力為兩項之和，詳見下表：1）徑向均布荷載下的應(yīng)力（2.27）式中，——應(yīng)力系數(shù)（可由查表求得）表2-8正常蓄水位徑向分布荷載時的應(yīng)力計算成果表截面徑向力（t）應(yīng)力系數(shù)應(yīng)力（t/m2）拱冠拱端拱冠拱端上游下游上游下游上游下游上游下游13.6230.540622.905517.428927.3878110.55782.9179163.0926299.1438422.9418.18636.66005.303122.379053.4677219.580415.5911165.7942639.1212.24221.9684-1.094015.9029111.648917.95181-9.97728145.0344411.457.4993-1.5305-2.200510.266385.86699-17.5242-25.1957117.5491517.783.4843-0.9804-0.89844.099061.95085-17.4315-15.973672.88022623.191.2235-0.41980.15460.636728.37297-9.735163.58517414.76507表2-9校核洪水位徑向分布荷載時的應(yīng)力計算成果表截面徑向力（t）應(yīng)力系數(shù)應(yīng)力（t/m2）拱冠拱端拱冠拱端上游下游上游下游上游下游上游下游13.6430.540622.905517.428927.3878111.167883.3760263.441299.6915922.8418.18636.66005.303122.379051.6490918.914415.060863.5563638.9812.24221.9684-1.094015.9029109.93517.67623-9.82412142.808411.327.4993-1.5305-2.200510.266384.89208-17.3253-24.9097116.2145517.433.4843-0.9804-0.89844.099060.73135-17.0884-15.659171.44557622.551.2235-0.41980.15460.636727.58993-9.466493.4862314.357592）均勻溫降時溫度應(yīng)力計算：（2.28）式中，——溫度應(yīng)力系數(shù)（查表可得）表2-10均勻溫降時溫度應(yīng)力計算成果表截面溫度荷載應(yīng)力系數(shù)應(yīng)力（t/m2）拱冠拱端拱冠拱端上游下游上游下游上游下游上游下游110.170.201-0.173-0.3030.4345.11-4.39-7.711.0328.480.301-0.369-0.6120.5626.38-7.82-12.9711.9136.750.338-0.640-0.9510.77810.8-4.32-16.0513.1345.360.384-0.810-1.050.7105.15-10.85-14.079.5154.050.1280.711-0.7650.3221.30-7.20-7.753.2662.440.003-0.671-0.6230.04450.02-4.90-3.800.27第三章壩肩穩(wěn)定分析拱壩壩肩穩(wěn)定分析實際上是一個空間問題，嚴(yán)格說必須按空間問題進行分析才能反映實際情況，但以往中小型工程為簡化計算，大都采用平面分層計算來代替空間問題分析。3.1穩(wěn)定分析3.1.1計算式1）拱端傳來的軸力和剪力：（3.1）（3.2）式中，—軸向力；—剪力；—水平壓力強度，；—拱圈厚度，m；—軸力系數(shù)，查附表得；—剪力系數(shù)，查附表得。2）垂直和平行于線的分力：（3.3）（3.4）式中，—拱端傳來的軸力，kN；—拱端傳來的剪力（還包括梁底部傳來的剪力）；—水平徑向壓力，kN；—岸坡角，本工程為；—側(cè)滑面的傾角，本工程中為。梁底單位寬度的鉛直壓力G：（3.5）式中，—滑移體自重，T；—垂直水