某拱壩的設(shè)計(jì)計(jì)算案例目錄TOC\o"1-3"\h\u25082某拱壩的設(shè)計(jì)計(jì)算案例 1305701.1拱壩形式及布置 184771.1.1拱壩剖面設(shè)計(jì) 1201411.1.2拱壩的布置 3194421.2荷載及其組合 3287881.2.1荷載及計(jì)算 4254581.2.2荷載組合 822041.3計(jì)算原理和計(jì)算方法 9326751.1.1計(jì)算原理 910671.1.2計(jì)算步驟 1087411.4應(yīng)力強(qiáng)度分析（電算、手算） 10195061.4.1應(yīng)力控制指標(biāo) 10281731.4.2電算 11257671.4.3手算 11306621.5壩肩穩(wěn)定驗(yàn)算 17305501.5.1驗(yàn)算原理 17135191.5.2驗(yàn)算工況 19212731.5.3驗(yàn)算結(jié)果 191.1拱壩形式及布置1.1.1拱壩剖面設(shè)計(jì)拱冠梁主要剖面尺寸包括壩頂、壩底厚度，拱冠梁上游曲線參數(shù)。1．壩頂厚度（TC）：采用下列經(jīng)驗(yàn)公式設(shè)計(jì)：Tc=0.01H+(0.012～0.024)L1Tmin=3～5mH——壩高L1——壩頂高程處兩拱端新鮮基巖之間的直線距離Tc=0.01×101+（0.012~0.024）×305=(4.67~8.33)m＞Tmin=3~5m考慮交通要求、加大頂拱厚度以改善梁應(yīng)力，取Tc=8米。2．壩底厚度（TB）：控制拱壩斷面尺寸的重要參數(shù)用我國(guó)朱伯芳等建議公式：TB=K（L1+LK——經(jīng)驗(yàn)系數(shù)，一般可取K=0.0035L1、Ln-1——第一層和倒數(shù)第二層拱圈兩拱端新鮮基巖面之間的直線距離（m）〔σa〕——拱的允許壓應(yīng)力（t/m3）H——壩高TB=K(L1+L4)H/[σ]L1=305m，L4=142mH為壩高101m[σ]拱的允許壓應(yīng)力5～6MPa取為6MPaTB=0.0035×(305+142)×101/6=26.336m取26m上游面曲線：用黎展眉推薦的方程式：z=?式中:x1=2β1取β1=0.63β2=0.42經(jīng)計(jì)算得：x2=0.22×26/(2×0.63-1)=42x1=2×0.63×42=52.92算得:z=-52.95×y/101+42×(y/101)2下游面曲線按Tc、TB沿高程線性內(nèi)插得到。Ti=Tc+(TB-Tc)/H×yi為第i層拱圈的厚度代入Ti=8+(26-8)/101×yiZ下=Z上+Ti表4-1拱冠梁端面的幾層典型拱圈的幾何尺寸層12345高程193167.75142.5117.2592縱坐標(biāo)yi025.2550.575.75101上游面橫坐標(biāo)z10-7.6571-11.5873-11.8149-8.3206拱厚Ti812.51721.526下游面橫坐標(biāo)z284.84855.41279.685117.67941.1.2拱壩的布置1．由初擬斷面尺寸按下列步驟做平面布置：⑴根據(jù)地形地質(zhì)資料，找可利用巖石等高線。⑵定出平面壩軸線后在可利用等高線上，定出頂拱的中心角和圓心位置。⑶要求初擬拱冠懸臂梁的剖面形態(tài)及尺寸與各層拱圈拱冠斷面重合，試畫拱圈線。⑷按拱圈線切垂直剖面檢查垂直方向是否扭曲，是否滿足倒懸度要求。⑸初擬形式和尺寸后，計(jì)算拱梁上下游壩面應(yīng)力及壩肩穩(wěn)定性。2．布置原則：（1）力求壩面平順（2）有足夠的下游支撐巖體（3）剖面倒懸度低于1/3；（4）拱圈、拱端內(nèi)弧面切線與利用等高線夾角不小于30°；（5）盡可能順河向取頂部中心角70°～110°，各層中及左右半中心角相差小于5°。3．拱壩布置的結(jié)果:表4-2各層拱圈特性參數(shù)層數(shù)高程拱圈厚（米）左半中心角（度）右半中心角（度）上游拱圈半徑下游拱圈半徑拱軸線半徑1191.08.051.551195.25187.0191.252167.7512.549.649.9165.7151.2159.453142.51746.548141.1126.1134.64117.2521.554.549111.391.8102.55592.026.027.82989.361.376.31.2荷載及其組合1.2.1荷載及計(jì)算自重、靜水壓力、泥沙壓力、風(fēng)浪壓力、溫度和地震荷載。1.2.1.1自重計(jì)算本設(shè)計(jì)自重應(yīng)力全由梁承擔(dān)。壩塊簡(jiǎn)化計(jì)算公式如下：G=Rc×V式中：Rc——混凝土容重，取25kN/m3V在前面工程量比較處已經(jīng)計(jì)算出拱壩總重G=25×339789m3=8494950kN。1.2.1.2泥沙壓力50-100年泥沙淤積壓力計(jì)算公式如下：ps=γshstg2(45o-φs/2)式中：ps——泥沙對(duì)上游壩底的水平壓強(qiáng)；γs——浮容重。取為8.5kN/m3φs——內(nèi)摩擦角，為10ohs——淤積高度，為23mps=8.5×23×tg2(45o-10o/2)=129.5844kN/m21.2.1.3溫度荷載溫度變化對(duì)整體固結(jié)于基巖的拱壩的應(yīng)力影響顯著，故溫度荷載須列為主要荷載。表4-3溫度變化△θ=47/（T+1.39）截面溫升時(shí)△θ溫降時(shí)△θ14.13-4.1322.96-2.9632.31-2.3141.89-1.8951.60-1.601.2.1.4靜水壓力計(jì)算壩面上任意一點(diǎn)靜水壓力這一主要荷載：pi=γ0×y式中：γ0——水的容重y——計(jì)算點(diǎn)距水面的深度1.2.1.5地震荷載包括地震慣性力（忽略基礎(chǔ)影響）、地震動(dòng)水壓力和上游淤沙的地震土壓力。本工程用簡(jiǎn)化擬靜力法——取每層拱圈上的慣性力為αKhCzWi與地震加速度方向相反，α取2，所受最大動(dòng)水壓力q0=KhCzFyγH0，（1）.縱向地震慣性力：拱冠截面的內(nèi)力：H0=k·γc·T·r·Z1V0=0M0=k·γc·T·r2·Z0拱端截面的內(nèi)力：HA=k·γc·T·r·(Z1COSφA+φAsinφA);VA=k·γc·T·r·(-φAcosφA+Z1sinφA);MA=k·γc·T·r2·[-φAsinφA-cosφA+1+Z0+Z1(1-COSφA)]式中：γc——壩體容重k——地震系數(shù)（＝αKhCz）T——截面厚度r——中心軸線半徑φA——拱圈半中心角表4-4.1縱向地震慣性力截面拱冠拱端（左、右）H0(kN)V0(kN)M0(kN·m)HA(kN)VA(kN)MA(kN·m)11662.50202202241.6250472395.031561248.16602333797.49269422121.92674703498.2817633022.121886221.7689917541.084117232262.59381305940.1006433267.93858960.34763849-5720.92161141821.30089808265.1613112885.855915-214.2294593-11927.910845497.791725102196.168554730.1876605-301.8466311-4150.100326（2）.縱向地震激蕩力：拱冠截面的內(nèi)力：H0=q0·Ru·U1;V0=0;M0=q0·Ru·U0·r拱端截面的內(nèi)力：式中：Ru——拱圈外半徑。表4-4.2縱向地震激蕩力截面拱冠拱端（左、右）H0(KN)V0(KN)M0(KN·m)HA(KN)VA(KN)MA(KN·m)100000021757.08314501951.4368841775.22384762.33086701-939.097985431526.10625703101.4708541580.286767-42.6529702-4189.2257684857.843601903109.631011938.3593018-134.6263824-5147.2540115209.915011201912.18662281.5915279-282.7525842-3709.331606（3）.橫向地震慣性力：拱冠截面的內(nèi)力：H0=0V0=kγcTrY0M0=0拱端截面的內(nèi)力:表4-4.3橫向地震慣性力(力單位kN，彎矩kN·m)截面拱冠左拱端右拱端H0V0M0HAVAMAHAVAMA10319.85000-1319.26-1181.40-36472.991319.26-1181.4036472.9920377.94310-1686.21-1406.90-34331.061686.21-1406.9034331.0630391.03000-1888.27-1466.66-28545.691888.27-1466.6628545.6940368.41140-1809.15-1385.50-20331.641809.15-1385.5020331.645061.99400-570.09-237.77-1497.03570.09-237.771497.03(4).橫向地震激蕩力左半拱的內(nèi)力：H0=0V0=q0RuX0M0=0拱端截面的內(nèi)力：表4-4.4橫向地震激蕩力(力單位kN，彎矩kN·m)截面拱冠 左拱端右拱端H0V0M0HAVAMAHAVAMA100000000020146.9746081.0743-544.9665-13246.1977-81.0743-544.966513246.197730124.0682065.7899-460.1471-8855.3272-65.7899-460.14718855.32724080.9133040.9354-295.1390-4197.9265-40.9354-295.13904197.92655021.985305.2135-77.8414-397.7912-5.2135-77.8414397.7912計(jì)算結(jié)果匯總表4-4.5地震荷載產(chǎn)生的內(nèi)力匯總表截拱冠左拱端右拱端面軸力剪力彎矩軸力剪力彎矩軸力剪力彎矩11675.5322.32261.21067.4-925.9-32420.93695.5-928.340060.823909.4529.05494.53169.3-1654.8-47601.56367.2-1659.146931.533818.4519.19114.63002.1-1894.2-46942.56636.7-1899.227347.742700.1452.811464.12040.9-2011.7-41280.55561.3-2018.97415.65717.786.94118.4448.1-892.2-9734.31568.7-912.2-5954.6表4-5地震荷載產(chǎn)生的應(yīng)力匯總表地震應(yīng)力截面拱冠左拱端右拱端上游σ下游σ上游σ下游σ上游σ下游σ1414.54-4.01-2892.743219.724211.80-3338.092514.3597.60-1555.452111.971646.90-1959.673404.7930.74-780.761176.08444.84-692.224266.23-28.61-425.20651.18-0.68-191.89561.95-11.69-65.19109.08-84.6821.681.2.1.6揚(yáng)壓力拱壩揚(yáng)壓力很小,壩體應(yīng)力分析時(shí)可忽略。但拱座穩(wěn)定分析時(shí),要計(jì)滑裂面處揚(yáng)壓力。1.2.2荷載組合1、基本組合：（1）正常水位+溫降；（2）設(shè)計(jì)水位+溫升。2、特殊組合：（1）校核水位+溫升；（2）正常水位+溫降+地震。1.3計(jì)算原理和計(jì)算方法1.1.1計(jì)算原理1.圓桶法薄壁圓桶公式僅適用等截面圓形拱圈，本設(shè)計(jì)不宜采用。2.純拱法該法忽略壩的整體穩(wěn)定，誤差大也不宜采用。1.拱梁分載法部分考慮了拱壩的整體作用，荷載由水平拱圈和鉛直梁同承擔(dān)，據(jù)拱梁交點(diǎn)處變位一致來(lái)確定荷載分配。拱和梁分別按彈性拱的純拱法和靜力結(jié)構(gòu)計(jì)算應(yīng)力。1.拱冠梁法以拱冠梁所分配荷載代表梁系的受力情況。適用本工程。拱冠梁法計(jì)算應(yīng)力的變形協(xié)調(diào)方程：ai1x1+ai2x2+ai3x3+ai4x4+ai5x5+xiδi=Piδi+ΔAi-ΔBi式中：aij——梁的變位系數(shù)是單位荷載作用在梁上j點(diǎn)使i點(diǎn)產(chǎn)生的徑向變位；δi——拱的變位系數(shù)是在單位均勻徑向水平荷載作用下，第i層拱圈拱冠處的徑向變位ΔAi——第i層拱圈在該層均勻溫度變化Δθ時(shí)在拱冠處的徑向變位；ΔBi——作用于梁上豎直方向荷載引起的拱冠梁上i點(diǎn)的徑向變位；Pi、xi——分別為i層截面處水平徑向總荷載、梁分擔(dān)的荷載。1.1.2計(jì)算步驟拱冠梁法主要步驟：①選定若干拱圈，分別計(jì)算各拱圈拱頂以及拱冠梁與各拱圈交點(diǎn)在單位徑向荷載作用下的“單位變位”②根據(jù)變位協(xié)調(diào)的關(guān)系及荷載和等于總荷載建立變位協(xié)調(diào)方程組③求解，得出荷載分配；④根據(jù)分配值，計(jì)算拱冠梁的內(nèi)力和應(yīng)力。1.4應(yīng)力強(qiáng)度分析（電算、手算）1.4.1應(yīng)力控制指標(biāo)1.壓應(yīng)力容許值為混凝土極限抗壓強(qiáng)度除以安全系數(shù)，系數(shù)在基本和特殊荷載組合時(shí)分別采用4.5和4.0。2.拉應(yīng)力對(duì)于基本和特殊組合，容許拉應(yīng)力分別不得大于1.2Mpa和1.5MPa；考慮地震時(shí)各自可有不超過(guò)30%提高1.4.2電算⑴正常水位+溫降表4-6梁拱應(yīng)力電算結(jié)果（正常水位+溫降）（單位：t/m2）截面拱冠拱端懸臂梁上游下游上游下游上游下游1216.58130.2097.08254.240.000.002270.27102.1947.51224.5160.1652.533270.8140.53-16.39185.1486.86119.434210.88-20.03-48.71125.3749.74234.38591.49-70.74-47.4238.75-30.36371.83⑵設(shè)計(jì)水位+溫升表4-7表梁拱應(yīng)力電算結(jié)果（設(shè)計(jì)水位+溫升）（單位：t/m2）截面拱冠拱端懸臂梁上游下游上游下游上游下游1270.09210.49187.50296.620.000.002291.74165.50121.78256.5690.4824.543287.19100.6954.59215.70120.0789.724227.3636.9511.30155.2784.06200.735121.51-26.11-5.1570.5436.30298.55⑶校核水位+溫升表4-8梁拱應(yīng)力電算結(jié)果（校核水位+溫升）（單位：t/m2）截面拱冠拱端懸臂梁上游下游上游下游上游下游1305.99235.64208.50337.310.000.002329.68182.55134.68287.7898.4818.793315.79107.9356.54236.95116.0397.164244.7237.6211.90167.0666.78222.345127.51-28.81-6.6174.2511.41327.801.4.3手算1.4.1.1拱冠梁法計(jì)算拱梁荷載分配(1)變形協(xié)調(diào)方程為圖4—1變形協(xié)調(diào)方程如前計(jì)算原理所示(⒉)計(jì)算步驟拱圈變位系數(shù)δi及均勻溫降Δθ時(shí)的ΔAi的計(jì)算：式中:——拱冠徑向位移系數(shù)E——混凝土的彈性模量，取2.2×106R——第i層拱圈的平均半徑ΔAi=Δγ0（RCΔθ）式中：Δγ0——由ΦA(chǔ)、T/R查表得出；R——第i層拱圈的平均半徑；C——壩身材料線脹系數(shù)，取0.8×10-5；Δθ——第i層拱圈的均勻溫度下降值Δθ=47/（T+1.39）(oC)T——第i層拱圈的拱厚經(jīng)計(jì)算得：表4-9各層拱圈的δi與ΔAi的結(jié)果截面高程拱厚T半徑RT/R半中心角φiδi/1000δi/E均勻溫降△t系數(shù)Ci△Ai*E11938191.250.041852.25-52.883310100.714.13-1.8405255301.042167.7512.5159.450.078449.75-26.81814276.152.96-1.7662146605.763142.517134.60.126347.25-16.75292254.942.31-1.606587724.1344117.2521.5102.550.209746.75-10.14321040.191.89-1.355346190.9335922676.30.340828.4-1.1686241.761.60-0.40258641.73342.垂直荷載作用下梁的徑向變位ΔBi的計(jì)算：垂直荷載（壩重、水荷載）作用下彎矩引起的變位ΔBiIΔBiI=Ωiyi式中：Ωi——垂直荷載作用下i截面以下M/ECI圖的面積；yi——Ωi面積形心至i截面的距離。梁基變形產(chǎn)生的拱冠梁徑向變位ΔBiⅡΔBiⅡ=θxhi+Δγf僅垂直荷載時(shí)θx=MxαΔγf=Mxα2表4-10.1拱冠梁基本尺寸、垂直荷載及其彎矩計(jì)算表序計(jì)算項(xiàng)目拱冠梁計(jì)算界面編號(hào)號(hào)類別序號(hào)名稱單位123451△h拱冠梁分段高度m25.2525.2525.2525.252拱△Su上游面寬度m1.021.0351.0591.1031.1713冠△S平均寬度m111114梁e1截面形心偏心矩m0.030.0820.1790.3760.7345基aD形心至下游面距離m4.036.3398.67511.12111.7396本au形心至上游面距離m1.966.1718.32110.37412.2627尺△ae上游面水平投影m7.651.940.22-1.498寸△au頂?shù)仔涡乃骄嚯xm5.4541.787-1.833-5.3789Ia截面慣性矩m442.25162.677408.872825.1541450.49410拱A截面積m2812.51721.52611冠A平均平均截面積m210.2514.7519.2521.7512梁△W1分塊自重kN6470.319310.9412151.2514992.1913自分塊重心至上游面的水平距離m8.759.319.7810.2214重分塊重心到塊底形心的水平距離m2.5820.989-0.594-2.04215及W1累計(jì)自重kN06470.3115781.2527932.814292516彎△M1分塊自重對(duì)塊底形心的力矩kNm16706.349208.52-7218.03-30614.0517矩△M1’累記自重對(duì)塊底形心的力矩kNm0011562.44-28927.03-1550222.6518M1自重引起的力矩kNm016706.3437477.31332.24-179504.4619h分塊平均水頭m7.7528.12551.37578.62520水△W2每塊上游水重kN599.11681142.7286124.8702-3062.278421重W2累計(jì)水重kN0599.11681741.84541866.7156-1195.562822及bg每塊水重心至上游面的距離m2.3436.35110.26414.00723彎△M2每塊水重對(duì)塊底形心力矩kNm1401.737257.471281.67-42891.3324距△M2’累計(jì)水重對(duì)塊底形心的力矩kNm001070.62-3192.8-10039.196525M2水重引起的力矩m01401.739731.827820.69-45111.836526M2/IkPa08.62921.8029.478-31.101取拱壩Ec=Er=22×106kN/m2，即n=1α=5.352n/（Ec×T2）×n=5.352/(262×Ec)=0.0083/Ecα2=0.74n/(27×Ec)=0.74、（26×Ec)=0.0285/EcMx=-45111.8365kN·mΘf=Mx×αΔγf=Mx×α2ΔBiⅡ=Θfhi+Δγf表4-10.2垂直荷載作用下彎矩引起的變位ΔBi1截面坐標(biāo)Ωi(1/Ec)yiΩi*yi(1/Ec)△BiⅠ(1/Ec)距梁基高h(yuǎn)i△BiⅡ(1/Ec)△Bi(1/Ec)108.9411316.833331831.8423409.4413839.8438916311.737420.1661.313725761.56327.960177.716672172.9658-300.902294.55-28450.31017631.80717631.807101-37817.25-20185.45409.4413814.593895975.342420.1636.063715152.52327.960152.466671466.9732-300.902269.3-20852.52225.251742.31741742.317475.75-28362.94-26620.62420.1610.81374541.482927.960127.21667760.98072-300.902244.05-13254.74350.5-7950.277-7950.27750.5-18908.63-26858.927.96011.96666754.988197-300.902218.8-5656.961475.75-5601.973-5601.97325.25-9454.313-15056.2951010000000將ΔBiI和ΔBiⅡ迭加得ΔBiΔBi=ΔBiI+ΔBiⅡ表4-10.3垂直荷載作用下梁的徑向變位ΔBi截面△BiⅠ(1/Ec)△BiⅡ(1/Ec)△Bi(1/Ec)117631.81-37817.3-2018521742.317-28362.9-266213-7950.28-18908.6-268594-5601.97-9454.31-1505650001.計(jì)算pi正常水位183mH1=183-167.75=15.25m百年后水庫(kù)淤積高程為115mp1=0p2=γwH1=9.81×(183-167.75)=149.025kN/m2p3=γwH2=9.81×(183-142.5)=397.305kN/m2p4=γwH3=9.81×(183-117.25)=640.1025kN/m2p5w=γwH4=9.81×(183-92)=892.71kN/m2p5s=γshstg2(45o-φs/2)=8.5×23×tg2(45o-10o/2)=137.6492kN/m2p5=p5w+p5s=892.71+137.6492=1030.3592kN/m24.梁變位系數(shù)aij的計(jì)算結(jié)果：表4-11梁變位系數(shù)aija117061.68a214024.78a311811.82a41591.32a5171.44a129547.44a225996.62a322898.93a42989.09a52131.62a134519.27a233100.75a331798.53a43818.60a53135.20a141599.66a241164.99a34776.67a44466.47a54115.80a15235.36a25192.05a35145.76a45101.52a5547.665.根據(jù)變位協(xié)調(diào)方程列出五元一次方程組：16861.52x1+9140.66x2+4326.72x3+1531.5x4+235.357x5=275488.453962.86x1+10239.01x2+3051.05x3+1147.07x4+190.06x5=823435.771887.71x1+3020.350x2+4128.80x3+809.201x4+146.79x5=1016012.4650.119x1+1087.450x2+767.167x3+1477.34x4+102.52x5=734725.5178.5469x1+144.710x2+126.7120x3+108.516x4+289.978x5=258340.6求解此五元一次方程組得：梁所受的荷載：x1=-74.3416x2=-0.8474x3=179.9112x4=389.5644x5=687.0578拱所受的荷載：p1-x1=74.3416p2-x2=149.8724p3-x3=217.39383p4-x4=250.5381p5-x5=341.3014第i層截面處水平徑向總荷載pi的計(jì)算結(jié)果：p1=0kN/m2p2=149.8724kN/m2p3=367.2662kN/m2p4=617.8043kN/m2p5=961.1057kN/m21.1.1.2拱梁應(yīng)力分配表4-12梁拱應(yīng)力匯總表（正常水位+溫降+地震）（單位：kN/m2）截懸臂梁拱冠左拱端右拱端面上游下游上游下游上游下游上游下游1002844.711531.39-1731.096025.885390.60-531.942469.84538.973352.641171.83-1138.205658.032080.901565.083211.351676.113294.40380.42-1198.524975.0431.4973096.954128.032555.262512.58-255.44-1170.973637.34-744.222785.835-739.484329.151281.17-727.60-728.501501.60-748.421411.75經(jīng)計(jì)算，在左拱端上游面產(chǎn)生最大1731.09kN/m2的拉應(yīng)力，滿足規(guī)范要求。1.5壩肩穩(wěn)定驗(yàn)算1.5.1驗(yàn)算原理1.5.1.1基本資料壩肩穩(wěn)定必須保證。穩(wěn)定分析相對(duì)復(fù)雜，一般；①存在明顯滑裂面②不滑動(dòng)但下游有較大軟弱帶或斷層變形。對(duì)①滑動(dòng)體邊界常有滑裂面和臨空面。穩(wěn)定分析要在查勘后研究確定滑裂面后才進(jìn)行。對(duì)②種過(guò)有限元分析，比較論證后在必要時(shí)采取措施控制變形。穩(wěn)定分析前：①深入了解壩址情況；②了解當(dāng)?shù)貛r石力學(xué)特性等試驗(yàn)條件和參數(shù)；③研究和確定拱座上空間力系④選擇合理方法，本工程采用剛體極限平衡法分析。假定：①滑移體為剛體，無(wú)各部分相對(duì)位移②只考慮上力平衡，不考慮力矩和壩端彎矩③忽略內(nèi)力重分布，認(rèn)為拱端作用在巖體上的力系為定值；④滑移趨向與剪力平行反向，數(shù)值最大時(shí)值為極限平衡狀態(tài)。根據(jù)安全系數(shù)Kc驗(yàn)算整體穩(wěn)定：KC=Kc僅取決于兩岸地形地質(zhì)，該壩址處條件可免此驗(yàn)算。但因河谷兩岸有走向互相垂直的節(jié)理，仍應(yīng)進(jìn)行平面穩(wěn)定分析。圖4-1平面穩(wěn)定分析計(jì)算簡(jiǎn)圖1.4.5.1.2壩肩抗滑穩(wěn)定計(jì)算圖4-1平面穩(wěn)定分析計(jì)算簡(jiǎn)圖取任一高程單位高度拱圈驗(yàn)算。設(shè)滑動(dòng)面走向平行于河谷，傾角平行于岸坡，拱端軸力為Ha，剪力為Va，用拱梁分載法計(jì)算內(nèi)力時(shí)，V含懸臂梁底部水平力。并將Ha和Va投影到滑動(dòng)面上：S=HN=H式中：φ——軸力與滑動(dòng)面夾角在立視圖上，將N分解為平行和垂直拱座面的分力Q和P：Q=Nsinψ?GcosψP=Ncosψ+Gsinψ?U式中：ψ——岸坡（滑動(dòng)面）與垂線夾角G——拱端面上懸臂梁的自重U——拱端面上的揚(yáng)壓力抗滑穩(wěn)定安全系數(shù)計(jì)算公式為：K=(f式中：K——抗滑穩(wěn)定安全系數(shù)ffW——拱端下游巖體的重量c——凝聚力l——滑動(dòng)面的長(zhǎng)度1.5.2驗(yàn)算工況Ⅰ：校核水位+溫升；Ⅱ：正常水位+溫降+地震1.5.3驗(yàn)算結(jié)果對(duì)工況Ⅰ進(jìn)行穩(wěn)定驗(yàn)算（1）查表插值求ha,ua表4-11.1ha,ua數(shù)值表截面TT/RφA均勻水壓力均勻溫度升高h(yuǎn)auahaua180.041852.2526.8494-0.17790.0059340.007399212.50.078449.7511.0694-0.36440.021390.024993170.126347.257.8005-0.64160.062340.063787421.50.209746.754.4812-0.83410.117080.1190475260.340828.41.3029-1.14160.306390.165792（2）Ha、Va計(jì)算表4-11.2Va計(jì)算表拱厚Pi─Xi水壓引起的V1均勻溫升引起的V2Va=V1+V2UaV1=(Pi─Xi)TUaE?tCUaV2=E?tCTUa874.3416-0.1779-105.803726.25110.007398542.9854-62.817612.5228.9299-0.3644-1042.776520.578980.02499162.616-880.159817295.8738-0.6416-3227.155405.689060.063787439.921-2787.23421.5331.9231-0.8341-5988.293332.342310.119047850.634-5137.65926421.7814-1.1416-12519.15281.456280.1657921211.24-11305.90表4-11.3Ha計(jì)算表拱厚Pi─Xi水壓引起的H1均勻溫升引起的H2Ha=H1+H2haH1=(Pi─Xi)ThaE?tChaH2=E?tCTha874.341626.849415968.22726.25110.00593434.476616002.69512.5228.929911.069437399.71520.578980.02139139.189837538.89517295.87387.800539235.38405.689060.06234429.941239665.32221.5331.92314.481232172.09332.342310.11708836.578733008.66726421.78141.302914288.01281.456280.306392242.12016530.134表4-11.4滲透壓力計(jì)算截面水頭拱厚T5T右岸滲透壓力滑動(dòng)面長(zhǎng)度10840040221.2512.562.53007.83796962.5348.517858385.71062585471.7521.5107.515961.94297107.55992613025736.535130（3）S、N計(jì)算表4-11.5S、N計(jì)算表截面φφ弧度HaVaSN左岸136.50.63704516002.69543-62.8176151612901.241969468.271240.40.70511337538.89524-880.159835529157.7561423659.43341.50.75921839665.32196-2787.23401130690.8135825282.02445.50.79412533008.66691-5137.65941926800.518619942.41562.21.08559516530.13375-11305.9036217710.420979349.319右岸1390.68067816002.69543-62.8176151612475.9626510021.999240.10.69987737538.89524-880.159835529281.2363723506.435483420.73303839665.32196-2787.23401131342.1026624469.953444410.71558533008.66691-5137.65941928282.5652117778.193375611.06465116530.13375-11305.9036217902.3341419938.79129（4）Q、P計(jì)算表4-11.6Q、P計(jì)算表截面SNΨ弧度GQuP左岸112901.241969468.2710.785406695.07906695.066334229157.7561423659.430.78546470.3112154.543007.8418297.08115330690.8135825282.020.785415781.256718.0578385.7120650.39434426800.518619942.410.785427932.81-5650.0615961.9417890.96309517710.420979349.3190.785442925-23741.625736.5411227.02905右岸112475.9626510021.9990.785407086.62707086.610439229281.2363723506.435480.78546470.3112046.363007.8418188.89788331342.1026624469.953440.785415781.256141.8478385.712007656517778.190.785427932.81-7180.415961.9416360.63126517902.3348976.370.785442925-24005.325736.5410961.31477（5）抗滑穩(wěn)定安全系數(shù)K’計(jì)算表4-11.7工況Ⅰ的抗滑穩(wěn)定安全系數(shù)K’截面抗滑穩(wěn)定安全系數(shù)K’左半拱右半拱15.34915.663924.11461.929534.87934.976146.58386.0681511.330911.4853對(duì)工況Ⅱ進(jìn)行穩(wěn)定驗(yàn)算（1）查表插值求ha,ua，同工況Ⅰ。（2）Ha、Va計(jì)算 表4-14.1Va計(jì)算表拱厚Pi─Xi水壓引起的V1均勻溫升引起的V2Va=V1+V2UaV1=(Pi─Xi)TUaE?tCUaV2=E?tCTUa874.3416-0.1779-105.803-726.25110.0073985-42.985-148.78812.5149.8724-0.3644-682.669-520.57900.02499-162.616-845.28517217.3938-0.6416-2371.158-405.68910.063787-439.921-2811.07921.5250.5381-0.8341-4492.937-332.34230.119047-850.634-5341.57126341.3014-1.1416-10189.735-281.45630.165792-1211.243-11402.978表4-14.2Ha計(jì)算表拱厚Pi─Xi水壓引起的H1均勻溫升引起的H2Ha=H1+H2haH1=(Pi─Xi)ThaE?tChaH2=E?tC