某隧道支護(hù)工程的襯砌內(nèi)力計(jì)算案例目錄TOC\o"1-3"\h\u23559某隧道支護(hù)工程的襯砌內(nèi)力計(jì)算案例 1199141.1斷面1：Ⅴ級(jí)圍巖淺埋 1320621.2斷面2：Ⅴ級(jí)圍巖深埋 6220381.3Ⅳ級(jí)圍巖深埋 121.1斷面1：Ⅴ級(jí)圍巖淺埋1.建模取隧道二次襯砌中軸線，等分為80個(gè)單元，80個(gè)節(jié)點(diǎn)。2.定義材料（1）定義單元類型荷載-結(jié)構(gòu)模型中的二次襯砌采用梁?jiǎn)卧?，本隧道設(shè)計(jì)計(jì)算采用Beam3單元類型，計(jì)算后可直接讀取彎矩與軸力。（2）設(shè)置單元實(shí)常數(shù)單元截面面積:（3）定義材料特性；；。（4）施加約束對(duì)于圍巖彈性反力進(jìn)行模擬，施加徑向桿單元，選擇Link10單元，長(zhǎng)度為1m，彈性模量，將桿單元外端采用固端約束。通過(guò)計(jì)算得出的襯砌內(nèi)力，將垂直、水平的面荷載轉(zhuǎn)換為節(jié)點(diǎn)荷載并將荷載施加到模型中，如下表所示：表5-7Ⅴ級(jí)圍巖淺埋節(jié)點(diǎn)荷載序號(hào)fx（N）fy（N）113668.7358561.05222729.3755536.1934510.0853879.9046290.7851931.9058064.7149019.9069828.8644774.20711594.0140279.68813351.3938498.97915094.2134604.21017029.4429502.141118554.5324082.271225248.6719634.401340178.5917037.211454501.9811601.791561594.696104.161663529.9258561.051764206.4355536.191864789.6353879.901965450.59-2400.62064704.09-8330.0822163724.32-15507.872261251.55-21761.432361998.04-29731.432462417.95-37534.382558561.05-43270.812655536.19-48864.212753879.90-55909.972851931.90-62667.662949019.90-65956.483044774.20-72570.133140279.68-78799.693238498.97-80864.213334604.2-84969.233429502.14-89566.383524082.27-93227.303619634.40-95671.913717037.21-94704.673811601.79-98604.64396104.16-101977.484058561.05-100154.034155536.19-99732.924253879.90-99600.8943-11889.50-98928.7244-16461.79-96936.2245-20971.87-94831.7046-25380.86-92231.0547-29657.66-89158.2848-33764.39-85594.3949-36788.25-82748.6850-41446.08-77144.2851-45870.62-71117.7752-48242.30-67060.7653-51267.16-61491.3654-54019.87-55574.8955-56694.81-49512.3756-58669.92-42910.7257-60334.98-36081.0158-62071.80-29347.3359-63288.86-22301.5760-64171.32-15159.7861-64719.64-7934.9862-64921.82-2148.5363-64781.8558561.0564-64291.9655536.1965-63471.4853879.9066-61368.1951931.9067-53891.4549019.9068-39214.3644774.2069-24852.0940279.6870-18452.4438498.9771-16726.1734604.272-14992.1229502.1473-13250.3024082.2774-11500.7019634.4075-9731.5517037.2176-7962.6211601.7977-6632.926104.1678-4416.7658561.0579-2181.0555536.1980-864.1353879.90將荷載添加到每個(gè)單元：圖1.1節(jié)點(diǎn)荷載圖4.求解及計(jì)算結(jié)果分析（1）變形圖圖1.2變形圖（2）軸力圖圖1.3軸力圖(N)（3）剪力圖圖1.4剪力圖(N)（4）彎矩圖圖1.5彎矩圖(N?m)查詢計(jì)算的襯砌軸力，仰拱底部為軸力最大部位，其大小為1732kN，拱頂為軸力最小部位，其值為1184.6kN，軸力總體上可看做從拱底至拱頂逐漸減小的變化趨勢(shì)。分析襯砌彎矩，拱頂為正彎矩最大部位，其值為202kN?m，負(fù)彎矩最大部位為拱肩，為-310kN?m。（內(nèi)側(cè)拉為正，壓為負(fù)）各節(jié)點(diǎn)軸力及彎矩見(jiàn)下表：挑選具有代表性的襯砌受力如拱底、拱頂?shù)冗M(jìn)行分析及計(jì)算，得到以下結(jié)果：表5-8典型節(jié)點(diǎn)內(nèi)力、安全系數(shù)表位置單元混凝土結(jié)構(gòu)厚度（m）軸力（kN）彎矩（kN?m）安全系數(shù)拉壓控制是否安全拱頂40C300.5-1184.62021.69拉否拱肩30C300.5-1220-201.379.59壓是邊墻20C300.5-1521.211.458.55壓是拱腳10C300.5-1637134.457.97拉是拱底1C300.5-173254.727.51壓是由以上結(jié)果可知，隧道襯砌拱頂?shù)陌踩禂?shù)小于規(guī)范規(guī)定值，受拉控制，因此應(yīng)進(jìn)行配筋來(lái)保證安全系數(shù)，以保證結(jié)構(gòu)安全。1.2斷面2：Ⅴ級(jí)圍巖深埋1.建模取隧道二次襯砌中軸線，等分為80個(gè)單元，80個(gè)節(jié)點(diǎn)。2.定義材料（1）定義單元類型荷載-結(jié)構(gòu)模型中的二次襯砌采用梁?jiǎn)卧舅淼涝O(shè)計(jì)計(jì)算采用Beam3單元類型，計(jì)算后可直接讀取彎矩與軸力。（2）設(shè)置單元實(shí)常數(shù)；；。（3）定義材料特性；；。4.施加約束模擬圍巖彈性反力，施加徑向桿單元，選擇Link10單元，長(zhǎng)度為1m，彈性模量，將桿單元外端采用固端約束。通過(guò)計(jì)算得出的襯砌內(nèi)力，將垂直、水平的面荷載轉(zhuǎn)換為節(jié)點(diǎn)荷載并將荷載施加到模型中，見(jiàn)下表5-9所示：表5-9Ⅴ級(jí)圍巖深埋節(jié)點(diǎn)荷載序號(hào)fx(N)fy(N)136696.80-20034.98216619.51-21828.83326676.12-24592.62436732.72-27217.98546784.71-28621.2565832.09-30420.1076879.47-32054.4587922.23-33640.6798951.77-34812.631010104.66-35800.021111009.00-36834.561214981.65-37554.341323840.53-38079.341432339.52-38402.321536547.49-38522.281637696.38-38439.231738097.79-38148.551838444.84-37664.081938836.03-2306.882038394.09-8004.872137811.73-14902.442236344.47-20911.862336787.42-28570.702437036.57-36068.062534748.03-41581.512632954.18-46956.542731970.40-53727.232830816.90-60221.102929086.65-63381.523026567.41-69736.983123900.52-75724.333222844.91-77707.253320532.3-81652.013417501.51-86069.693514289.55-89587.683611650.35-91940.703710109.27-91006.41386884.08-94751.09393621.99-97996.26401361.13-96244.0341-1421.11-95839.3242-4267.95-95712.4543-7054.80-95066.5244-9767.83-93151.8145-12444.95-91134.2946-15060.09-88630.3247-17597.79-85677.5248-20034.98-82251.8049-21828.83-79518.1550-24592.62-74131.5851-27217.98-68341.3252-28621.25-64442.6953-30420.10-59090.7354-32054.45-53404.2755-33640.67-47579.456-34812.63-41231.4857-35800.02-34672.4058-36834.56-28201.6059-37554.34-21430.9160-38079.34-14567.9461-38402.32-7624.2362-38522.28-2064.6563-38439.23-20034.9864-38148.55-21828.8365-37664.08-24592.6266-36414.68-27217.9867-31979.63-28621.2568-23268.40-30420.1069-14746.34-32054.4570-10949.02-33640.6771-9924.71-34812.6372-8891.79-35800.0273-7862.25-36834.5674-6824.10-37554.3475-5776.72-38079.3476-4724.73-38402.3277-3931.74-38522.2878-2620.75-38439.2379-1296.53-38148.5580-512.15-37664.08將荷載添加到每個(gè)單元后計(jì)算得到：4.求解及計(jì)算結(jié)果分析（1）變形圖圖1.6變形圖（2）軸力圖圖1.7軸力圖(N)（3）剪力圖圖1.8剪力圖(N)（4）彎矩圖圖1.9彎矩圖(N?m)分析襯砌軸力，仰拱底部為軸力最大部位，其大小為1692.1kN，拱頂為軸力最小部位，其值為1024.1kN，軸力總體上可看做從拱底至拱頂逐漸減小的變化趨勢(shì)。分析襯砌彎矩，拱頂為正彎矩最大部位，其值為244.53kN?m，負(fù)彎矩最大部位為拱肩，為-290.35kN?m。（內(nèi)側(cè)拉為正，壓為負(fù)）挑選具有代表性的襯砌受力如拱底、拱頂?shù)冗M(jìn)行分析及計(jì)算，得到以下結(jié)果：表5-10典型節(jié)點(diǎn)內(nèi)力、安全系數(shù)表位置單元混凝土結(jié)構(gòu)厚度（m）軸力（kN）彎矩（kN?m）安全系數(shù)拉壓控制是否安全拱頂40C300.5-1024.10244.530.84拉否拱肩30C300.5-1271.20-168.291.95拉否邊墻20C300.5-1508.9040.967.75壓是拱腳10C300.5-1564.10-141.841.78拉是拱底1C300.5-1624.3024.697.20壓是由以上結(jié)果可知，明洞襯砌拱頂?shù)陌踩禂?shù)小于規(guī)范規(guī)定值，受拉控制，因此應(yīng)進(jìn)行配筋來(lái)保證安全系數(shù)，以保證結(jié)構(gòu)安全。1.3Ⅳ級(jí)圍巖深埋1.3.1Ⅳ級(jí)圍巖深埋手算（結(jié)構(gòu)力學(xué)方法）1.建模取隧道二次襯砌中軸線，等分為80個(gè)單元，80個(gè)節(jié)點(diǎn)。2.定義材料（1）定義單元類型荷載-結(jié)構(gòu)模型中的二次襯砌采用梁?jiǎn)卧?，本隧道設(shè)計(jì)計(jì)算采用Beam3單元類型，計(jì)算后可直接讀取彎矩與軸力。（2）設(shè)置單元實(shí)常數(shù)單元截面面積：；截面慣性矩：；截面高度：。（3）定義材料特性C30混凝土彈性模量；泊松比；材料密度：。3.施加約束模擬圍巖彈性反力，施加徑向桿單元，選擇Link10單元，長(zhǎng)度為1m，彈性模量，將桿單元外端采用固端約束。通過(guò)計(jì)算得出的襯砌內(nèi)力，將垂直、水平的面荷載轉(zhuǎn)換為節(jié)點(diǎn)荷載并將荷載施加到模型中，如下表所示：表5-11Ⅳ級(jí)圍巖深埋節(jié)點(diǎn)荷載序號(hào)fx(N)fy(N)115509.59-50341.17245547.31-48962.44315539.15-47331.21413330.98-45438.73513321.55-43928.56616310.84-40952.84713900.13-37754.1821848.14-35600.36924473.61-32643.751024790.93-29502.361130440.71-26284.51241437.97-22779.9136584.82-19154.23148932.26-15579.541510094.52-11839.171610411.84-50341.171710522.72-48962.441810618.30-47331.211910726.62-1274.42010604.28-4422.162110443.70-8232.622210038.44-11552.432310160.79-15783.442410229.60-19921.24259597.50-22971.06269101.76-25940.41278830.31-29680.77288511.71-33268.21298033.81-35014.14307337.99-38521.11316601.39-41832.18326309.55-42928.16335671.08-45107.38344831.07-47547.86353946.81-49491.32363217.86-50791.21372792.21-50271.08381901.40-52341.98391000.40-54136.5140371.94-53167.9641-392.51-52944.9442-1178.82-52874.8543-1948.55-52518.0244-2697.90-51460.2745-3437.05-50341.1746-4159.64-48962.4447-4860.56-47331.2148-5533.44-45438.7349-6029.18-43928.5650-6792.55-40952.8451-7517.68-37754.152-7906.37-35600.3653-8402.11-32643.7554-8853.25-29502.3655-9291.65-26284.556-9611.34-22779.957-9888.06-19154.2358-10173.53-15579.5459-10372.34-11839.1760-10517.62-8047.8361-10606.83-4211.8962-10639.96-1140.5863-10617.02-50341.1764-10536.73-48962.4465-10402.92-47331.2166-10057.56-45438.7367-8832.86-43928.5668-6426.79-40952.8469-4072.98-37754.170-3024.15-35600.3671-2741.23-32643.7572-2457.04-29502.3673-2171.57-26284.574-1884.83-22779.975-1591.54-19154.2376-1304.98-15579.5477-1087.06-11839.1778-723.85-50341.1779-358.10-48962.4480-141.45-47331.21將荷載添加到每個(gè)單元。4.求解及計(jì)算結(jié)果分析（1）變形圖圖1.10變形圖（2）軸力圖圖1.11軸力圖(N)（3）剪力圖圖1.12剪力圖(N)（4）彎矩圖圖1.13彎矩圖(N?m)分析襯砌軸力，仰拱底部為軸力最大部位，其大小為567.54kN，拱頂為軸力最小部位，其值為960.45kN，軸力總體上可看做從拱底至拱頂逐漸減小的變化趨勢(shì)。分析襯砌彎矩，拱頂為正彎矩最大部位，其值為119.76kN?m，負(fù)彎矩最大部位為拱肩，為-126.29kN?m。（內(nèi)側(cè)拉為正，壓為負(fù)）各節(jié)點(diǎn)軸力及彎矩如下表：挑選具有代表性的襯砌受力如拱底、拱頂?shù)冗M(jìn)行分析及計(jì)算，得到以下結(jié)果：表5-12典型節(jié)點(diǎn)內(nèi)力、安全系數(shù)表位置單元混凝土結(jié)構(gòu)厚度（m）軸力（kN）彎矩（kN?m）安全系數(shù)拉壓控制是否安全拱頂40C300.4-567.54119.761.37拉否拱肩30C300.4-744.50-102.212.13拉否邊墻20C300.4-922.672911.27壓是拱腳10C300.4--936.73-80.716.13拉是拱底1C300.4-960.27-1.4510.83壓是由以上結(jié)果可知，襯砌拱頂、拱肩的安全系數(shù)小于規(guī)范規(guī)定值，受拉控制，因此應(yīng)進(jìn)行配筋來(lái)保證安全系數(shù)，以保證結(jié)構(gòu)安全。1.1襯砌結(jié)構(gòu)計(jì)算1.1.1襯砌幾何要素（1）擬定襯砌幾何尺寸內(nèi)輪廓線半徑；內(nèi)徑所畫(huà)圓曲線的終點(diǎn)截面與豎直軸的夾角截面厚度外輪廓線半徑：拱軸線半徑：拱軸線各段圓弧中心角：（2）半拱軸線長(zhǎng)度及分段軸長(zhǎng)分段軸線長(zhǎng)度：半拱軸線長(zhǎng)度：將半拱軸線等分為8段，每段軸長(zhǎng)為：（3）各分塊接縫（截面）中心幾何要素①與豎直軸夾角另一方面，角度閉合差。圖5-14襯砌結(jié)構(gòu)計(jì)算圖示1.2位移計(jì)算（1）單位位移單位位移值計(jì)算如下：表5-13單位位移計(jì)算表截面σsinαcosσxydI00°0.001.000.000.000.600.0251.560.000.0051.56111.820.270.961.390.190.600.0251.5610.732.0779.08231.470.520.852.680.760.600.0251.5642.1031.90171.66341.620.710.703.771.630.600.0251.5690.72148.13381.12459.770.860.504.632.750.600.0251.56152.78420.14781.25573.930.960.281.184.040.600.0251.56224.52901.381411.98688.081.000.031.401.430.600.0251.56301.591631.212291.947102.230.98-0.211.276.760.600.0251.56371.822542.293349.48890°1.000.004.088.150.600.0251.56452.943692.774654.20444.441651.199381.8913184.26計(jì)算精度校核為：（2）載位移①每一楔塊上的作用力豎向力：（校核）水平壓力：自重力：②外荷載在基本結(jié)構(gòu)中產(chǎn)生的內(nèi)力的計(jì)算見(jiàn)表5-14及表5-15。表5-14載位移計(jì)算表截面集中力力臂00.000.000.000.000.000.000.000.000.000.000.000.000.000.001178.0019.426.340.750.800.11-134.19-11.50-0.680.000.000.000.00-150.372162.0719.4218.220.690.810.31-111.25-11.67-1.62191.426.34-253.70-3.58-540.203131.1819.4221.960.580.790.47-79.70-11.29-13.24378.9124.56-416.24-21.49-1086.164104.8519.4231.450.440.710.60-46.57-13.73-21.29531.5152.52-451.72-58.66-1682.12566.4919.4240.810.280.580.69-18.72-11.19-28.17659.7881.96-364.33-113.60-2218.13624.0919.4243.59-0.100.410.732.51-1.97-31.65741.69128.77-163.75-178.63-2591.6270.1819.4243.83-0.160.230.740.03-4.46-32.27789.21172.3699.60-230.30-2761.0280.0019.4231.270.00-0.060.630.001.13-23.53808.81216.19371.69-300.12-2711.86表5-15載位移計(jì)算表截面00.00001.0000.00000.00000.00000.00000.000010.27260.9621191.41896.339353.81646.099041.717420.52200.8530378.912724.5576191.792420.9476176.844830.71470.6994531.509552.5151382.728636.7291341.999640.86400.5034659.783981.9629570.053344.2805521.772850.96090.2769741.6916128.7702716.535131.6565680.878660.99940.0335789.2071172.3636788.73361.7742782.959470.9773-0.2119808.8055216.1931790.4456-41.8113836.256981.00000.0000828.2268253.4648828.22680.0000828.2268基本結(jié)構(gòu)中，主動(dòng)荷載產(chǎn)生彎矩的校核為：另外，從表1-4中得到閉合差0③主動(dòng)荷載位移計(jì)算過(guò)程見(jiàn)表5-16表5-16主動(dòng)荷載位移計(jì)算表截面00.000051.55560.000010.00000.00000.00001-150.371451.555610.72781.1931-8353.9733-1613.1543-9961.12552-540.197951.555642.10001.7578-30011.0185-22742.3316-52753.36833-1086.156851.555690.71672.6329-60342.0927-98532.5606-158874.69594-1682.124551.5556152.77793.7500-93451.4359-256991.4486-350442.88465-2218.131151.5556224.52241.0414-123229.6041-498020.1181-621249.72616-2591.624151.5556301.58916.4286-144312.5654-783411.1145-927721.75797-2761.022851.5556371.81701.7647-153612.5007-1039142.5736-1192754.98428-2711.856951.5556452.93939.1529-150658.8372-1228306.5660-1378961.2710-7639728673-4692731.8136所以閉合差（3）載位移—單位彈性抗力及相應(yīng)的摩擦力引起的位移①各接縫處的抗力強(qiáng)度抗力上的零點(diǎn)假定在接縫3處，最大抗力值假定在接縫5處，；各截面最大抗力值由下式計(jì)算：最大抗力值以下各截面抗力值計(jì)算：②各楔塊上抗力集中力按下式近似計(jì)算：③抗力集中力與摩擦力的合力按下式計(jì)算：其作用方向與抗力集中力的夾角。將的延長(zhǎng)線與豎直軸有兩個(gè)夾角，將分解為水平力與豎直力：以上計(jì)算列入表5-17。表5-17彈性抗力及摩擦力計(jì)算表截面30.000.000.000.000.000.000.000.000.000.0040.570.291.500.430.4461.370.920.380.400.1751.000.791.491.171.2079.850.980.181.180.2160.880.941.491.401.4393.201.00-0.061.43-0.0870.510.691.501.041.06101.010.96-0.291.01-0.3180.000.251.350.340.35119.000.87-0.480.31-0.17④單位抗力所引起相應(yīng)的摩擦力在基本結(jié)構(gòu)中產(chǎn)生的內(nèi)力計(jì)算：彎矩：軸力：計(jì)算見(jiàn)表5-18及表5-19。表5-18計(jì)算表截面40.48-0.21-0.2151.97-0.860.66-0.79-1.6563.42-1.492.15-2.580.75-1.08-1.1574.75-2.073.59-4.292.25-3.220.81-0.86-10.4481.71-2.494.75-1.693.53-1.062.15-2.280.90-0.32-11.83表5-19計(jì)算表截面459.77240.86400.50340.16790.14510.40270.2027-0.0576573.92610.96090.27690.37890.36411.58140.4379-0.0738688.07970.99940.03350.29110.29093.01000.10080.19017102.23330.9773-0.2119-0.0105-0.01034.0222-0.85230.8418890°1.00000.0000-0.1796-0.17964.32730.0000-0.1796⑤單位抗力及相應(yīng)摩擦力產(chǎn)生的載位移計(jì)算見(jiàn)表5-20。表5-20單位抗力所引起的相應(yīng)摩擦力產(chǎn)生的載位移計(jì)算表截面積分系數(shù)1/34-0.207551.5556152.77793.75-11.5278-31.7014-43.229325-1.652951.5556224.52241.0414-91.8279-371.1131-462.941246-1.150851.5556301.58916.4286-286.1558-1553.4251-1839.581227-10.444451.5556371.8171.7647-580.2449-3921.1831-4501.427648-11.827951.5556452.93939.1529-879.3285-7169.0779-8048.40581-1849.0848-13050.5006-14899.5850校核為：（4）墻底（彈性地基上的剛性梁）位移單位彎矩作用下的轉(zhuǎn)角：主動(dòng)荷載作用下的轉(zhuǎn)角：?jiǎn)挝豢沽跋鄳?yīng)摩擦力作用下的轉(zhuǎn)角：1.3解力法方程襯砌矢高：計(jì)算力法方程的系數(shù)為：求解方程為：1.4計(jì)算主動(dòng)荷載和被動(dòng)荷載分別產(chǎn)生的襯砌內(nèi)力計(jì)算公式為：計(jì)算過(guò)程列入表5-1、5-22表5-21主、被動(dòng)荷載作用下襯砌彎矩計(jì)算表截面00.0000632.15090.0000632.15090.0000-3.9520.0000-3.9521-150.3714632.150949.8358531.61530.0000-3.9520.4647-3.48732-540.1979632.1509191.5754281.52840.0000-3.9521.8238-2.12823-1086.1568632.1509421.4239-32.5820.0000-3.9523.9299-0.02214-1682.1245632.1509709.7285-340.2451-0.2075-3.9526.61842.45895-2218.1311632.15091043.0170-542.9632-1.6529-3.9529.72644.12156-2591.6241632.15091401.0299-564.4433-1.1508-3.95213.06503.96227-2761.0228632.15091741.8547-381.0172-10.4444-3.95216.28061.88428-2711.8569632.15092104.125724.4197-11.8279-3.95219.6216-0.1583表5-22主、被動(dòng)荷載作用下所引起的襯砌軸力計(jì)算表截面00.0000258.0831258.08310.00002.46072.4607141.7174248.3018296.01920.00002.36742.36742176.8448220.1449396.98970.0