某公路隧道的二次襯砌結(jié)構(gòu)設(shè)計計算案例目錄TOC\o"1-3"\h\u3994某公路隧道的二次襯砌結(jié)構(gòu)設(shè)計計算案例 1280871.1Ⅲ級圍巖襯砌驗算 1194751.2Ⅳ級圍巖襯砌驗算 105281.3Ⅴ級圍巖襯砌驗算 461.1Ⅲ級圍巖襯砌驗算對其二次襯砌支護(hù)結(jié)構(gòu)內(nèi)力進(jìn)行數(shù)值分析，計算采用ANSYS19.1有限元軟件計算。襯砌設(shè)計圖，如圖1.3所示。圖1.3Ⅲ級圍巖襯砌支護(hù)設(shè)計（單位：cm）1.設(shè)計基本資料（1）巖體特征巖體為Ⅲ級圍巖，圍巖的彈性抗力系數(shù)，計算摩察角，巖體重度，變形模量，泊松比，粘聚力，內(nèi)摩察角。（2）襯砌材料二襯選用C30防水混凝土；重度，彈性模量，混凝土襯砌軸心抗壓強(qiáng)度標(biāo)準(zhǔn)值：，混凝土軸心抗拉強(qiáng)度標(biāo)準(zhǔn)值：（3）圍巖壓力的計算a.支護(hù)參數(shù)b.豎向圍巖壓力c.水平圍巖壓力2.內(nèi)力數(shù)值計算分析用ANSYS進(jìn)行計算。單元實常數(shù)、，；材料屬性，。單元網(wǎng)格劃分：拱部半圓弧劃分為左右各25個，共50個單元。單元劃分見圖圖1.4單元劃分圖對節(jié)點施加荷載如圖1.5所示圖1.5節(jié)點施加荷載圖對于拱形結(jié)構(gòu)，需要約束墻底的水平位移。同時為避免結(jié)構(gòu)整體沉降過大，使彈簧全部受拉，也要對墻底的垂直位移進(jìn)行約束、本模型選取節(jié)點2、27進(jìn)行約束。地層彈簧單元，選擇單元實常數(shù)，長度。慣性荷載（重力加速度）Gravity取9.8。施加徑向彈簧如圖1.6所示圖1.6徑向施加彈簧圖查看求解后的彈簧受力表，分批多次除去受拉彈簧（正值受拉，負(fù)值受壓），在重新計算，保證彈簧全部處于受壓狀態(tài)。確定抗力分布范圍，最終計算模型見圖1.7圖1.7采用生死單元法殺死受拉彈簧后的變形軸力結(jié)果圖如圖1.8所示圖1.8軸力圖剪力結(jié)果圖如圖1.9所示。圖1.9剪力圖彎矩結(jié)果圖如圖1.10所示。圖1.10彎矩圖如圖1.7所示，最大變形出現(xiàn)在拱頂位置處。殺死受拉彈簧后的變形值為：0.048128m。如圖1.8所示，正值受拉，負(fù)值受壓，圖中的軸力值全為負(fù)值，全部受壓。其中最大值出現(xiàn)在邊墻底角處，最小值出現(xiàn)在拱頂處，關(guān)于軸力分布關(guān)于隧道中線軸對稱。如圖1.9所示，剪力值最大值出現(xiàn)在距拱頂大約22.5°兩側(cè)，拱頂處剪力為零，最小負(fù)值出現(xiàn)在拱墻處，關(guān)于隧道中線反對稱。如圖1.10所示，最大正彎矩出現(xiàn)在距離拱頂45°兩側(cè)，最大負(fù)彎矩出現(xiàn)在拱頂位置，關(guān)于隧道中線軸對稱。ANSYS分析結(jié)果見表1.5。表1.5單元內(nèi)力數(shù)值分析結(jié)果STATCURRENTCURRENTCURRENTCURRENTCURRENTCURRENTELEMNINJQIQJMIMJ1-0.83113E+006-0.83142E+006-53190-13081.0-0.27878E+006-0.26972E+0062-0.83804E+006-0.83890E+006-23067-30792.0-0.26972E+006-0.24319E+0063-0.84144E+006-0.84287E+006-40778-48418.0-0.24319E+006-0.19926E+0064-0.85188E+006-0.85386E+006-56703-64217.0-0.19926E+006-0.13970E+0065-0.86893E+006-0.87147E+006-69542-76889.0-0.13970E+006-67570.06-0.89199E+006-0.89506E+006-78073-85213.0-67570.012857.07-0.92023E+006-0.92381E+006-81186-88082.012857.096231.08-0.95267E+006-0.95675E+006-77912-84521.096231.00.17624E+0069-0.98818E+006-0.99274E+006-67445-73739.00.17624E+0060.24578E+00610-0.10255E+007-0.10305E+007-49163-55104.00.24578E+0060.29714E+00611-0.10633E+007-0.10687E+007-22647-28202.00.29714E+0060.32219E+00612-0.11001E+007-0.11060E+007123087168.50.32219E+0060.31259E+00613-0.11346E+007-0.11408E+0075568550989.00.31259E+0060.26005E+00614-0.11652E+007-0.11717E+0070.10724E+0060.10301E+0060.26005E+0060.15649E+00615-0.11906E+007-0.11974E+0070.16651E+0060.16278E+0060.15649E+006-5708.316-0.12095E+007-0.12166E+0070.23282E+0060.22960E+006-5708.3-0.23348E+00617-0.12206E+007-0.12279E+0070.30528E+0060.30259E+006-0.23348E+006-0.53288E+00618-0.12511E+007-0.12586E+007-0.46901E+006-0.47116E+006-0.53288E+006-69793.019-0.12970E+007-0.13046E+007-0.10386E+006-0.10545E+006-69793.033307.020-0.13187E+007-0.13264E+007421304110333307.0-7689.921-0.13288E+007-0.13365E+0077371073253-7689.90-80077.022-0.13397E+007-0.13474E+007-0.13581E+006-0.13569E+006-80077.053651.023-0.13538E+007-0.13616E+007-36587-35898.053651.089351.024-0.13607E+007-0.13684E+0076319964456.089351.026477.025-0.13934E+007-0.14010E+0072596827787.026477.0-0.66223E-01126-0.13783E+007-0.13707E+007-0.12028E+006-0.11846E+0060.38256E-0100.11759E+00627-0.13754E+007-0.13677E+007-19237-17979.00.11759E+0060.13592E+00628-0.13652E+007-0.13575E+0078151182200.00.13592E+00655286.029-0.13477E+007-0.13399E+0070.18145E+0060.18157E+00655286.0-0.12352E+00630-0.13366E+007-0.13288E+007-0.10977E+006-0.11022E+006-0.12352E+006-15163.031-0.13281E+007-0.13204E+007-50933-51960.0-15163.035518.032-0.13066E+007-0.12990E+0070.10673E+0060.10514E+00635518.0-68836.033-0.12612E+007-0.12538E+0070.47213E+0060.46998E+006-68836.0-0.53288E+00634-0.12279E+007-0.12206E+007-0.30259E+006-0.30528E+006-0.53288E+006-0.23347E+00635-0.12166E+007-0.12095E+007-0.22960E+006-0.23282E+006-0.23347E+006-5703.236-0.11974E+007-0.11906E+007-0.16278E+006-0.16651E+006-5703.20.15649E+00637-0.11717E+007-0.11652E+007-0.10301E+006-0.10724E+0060.15649E+0060.26005E+00638-0.11408E+007-0.11346E+007-50989-55681.00.26005E+0060.31260E+00639-0.11060E+007-0.11001E+007-7168.2-12308.00.31260E+0060.32219E+00640-0.10687E+007-0.10633E+0072820322647.00.32219E+0060.29714E+00641-0.10305E+007-0.10255E+0075510449164.00.29714E+0060.24579E+00642-0.99274E+006-0.98818E+0067373967446.00.24579E+0060.17624E+00643-0.95675E+006-0.95267E+0068452577913.00.17624E+00696234.044-0.92381E+006-0.92023E+0068808281187.096234.012860.045-0.89506E+006-0.89199E+0068521478073.012860.0-67568.046-0.87147E+006-0.86893E+0067689069542.0-67568.0-0.13969E+00647-0.85386E+006-0.85188E+0066421856704.0-0.13969E+006-0.19926E+00648-0.84287E+006-0.84144E+0064841840778.0-0.19926E+006-0.24319E+00649-0.83890E+006-0.83804E+0063079223068.0-0.24319E+006-0.26972E+00650-0.83142E+006-0.83113E+006130865319.5-0.26972E+006-0.27878E+0061.2Ⅳ級圍巖襯砌驗算對于Ⅳ級圍巖，在根據(jù)經(jīng)驗選定支護(hù)參數(shù)后，仍需進(jìn)行驗算。Ⅳ級圍巖的內(nèi)力求解，參考地下結(jié)構(gòu)設(shè)計，先采用手算法，然后用ANSYS19.1進(jìn)行驗證。1.計算參數(shù)（1）巖體特征計算摩察角，圍巖的彈性抗力系數(shù)，基底圍巖彈性反力系數(shù)：，巖體重度，變形模量，泊松比，粘聚力，內(nèi)摩察角。（2）襯砌材料二襯選用C30防水混凝土材料；重度，彈性模量，混凝土襯砌軸心抗壓強(qiáng)度標(biāo)準(zhǔn)值：，混凝土軸心抗拉強(qiáng)度標(biāo)準(zhǔn)值：。二襯設(shè)計如圖1.11所示。圖1.11Ⅳ級圍巖襯砌支護(hù)設(shè)計（單位：cm）（3）結(jié)構(gòu)尺寸2.主動荷載隧道處于Ⅳ級圍巖中，為深埋隧道，圍巖壓力為松散荷載。作用在其結(jié)構(gòu)上的荷載形式為：垂直均布荷載q、水平均布側(cè)向荷載e，側(cè)壓力系數(shù)0.25。3.繪制分塊圖取左半部，及半跨結(jié)構(gòu)，見圖1.12。圖1.12分塊圖（1）計算半拱軸線長度s和分塊軸線長度a.計算半拱軸線長度s式中為各圓弧軸線半徑半拱軸線長度。b.計算分塊軸線長度分塊長度4.計算各分段截面中心的幾何要素a求各截面、豎直軸的夾角角度校核：1.各截面的中心坐標(biāo)（單位：cm）曲墻拱結(jié)構(gòu)幾何要素計算過程，見表1.6。表1.6曲墻拱幾何要素截面00.00000.00001.00000.00000.00000.35114.19530.39420.9694138.145317.19580.35228.52970.57940.8798267.850467.72910.35342.36710.69970.7364381.2126148.52290.35456.34910.83710.5481471.3119254.63540.35570.95100.93540.3263532.6491379.60530.35681.14500.97340.0846546.4821511.78890.35797.69780.9913-0.1093558.4743651.11160.358101.13990.9164-0.2439531.7460777.92850.356.計算基本結(jié)構(gòu)的單位位移慣性矩，b取單位長度，計算過程見表1.7。表1.7曲墻拱結(jié)構(gòu)的單位位移計算過程表（單位：m）截面積分系數(shù)00.003572279.88330.00000.0000279.3124110.003572279.883348.12978.2495384.4036420.003572279.8833189.5624128.8474787.8263230.003572279.8833411.6395617.65571728.6984440.003572279.8833712.26491814.08973519.9093250.003572279.88331062.27294033.25076437.9291460.003572279.88331443.67137441.994710613.6093270.003572279.88331833.593012011.802415958.8730480.003572279.88332177.255216937.762621572.44331∑279.883320308.6815102398.3092149732.1730注：的計算按式辛普森法進(jìn)行，以下各表均同。如圖1.13所示，求曲線在上的曲邊體型的面積，可應(yīng)用精度較高的——辛普森方法計算，即把分成n等分，n必須為偶數(shù)。分別求出n個小段曲邊體型的面積（每3點組成的曲線用拋物線代替），然后求和：圖1.13辛普森法計算變位將各分點的坐標(biāo)代入得：校核:計算變位結(jié)果正確。7.計算主動荷載在基本結(jié)構(gòu)中產(chǎn)生的位移和（1）襯砌每一塊上的作用力豎向力：式中：——相鄰兩截面之間的襯砌外緣的水平投影（由分塊圖量?。﹤?cè)向水平力：式中：——相鄰兩截面之間的襯砌外緣的垂直投影（由分塊圖量?。┳灾亓Γ?。以上各集中力均通過相應(yīng)荷載圖形的形心,襯砌每一塊上的作用力計算過程，見表1.8。表1.8計算過程表（一）截面集中力(KN)力臂（m）(KN*m)(KN*m)-Eiae(KN*m)00.00000.00000.00000.00000.00000.00000.00000.00000.00001200.078411.23486.14770.66880.28670.6865-133.8170-7.7131-1.76262187.854711.234818.33740.60200.42990.6589-113.0944-7.4033-7.88363164.191111.234829.32730.46610.57600.5659-76.5348-6.3584-16.89454130.486711.234838.50130.31810.64280.4196-41.5150-4.7151-24.7489588.830311.234842.41200.15070.71680.3091-13.3956-3.4728-30.0272641.751811.234849.4113-0.01570.73110.1745-0.6578-1.9614-36.124773.371211.234850.5578-0.16190.69920.0212-0.5472-0.2385-31.323080.000011.234846.69640.00000.6508-0.10540.00001.1845-30.3977分塊上個集中力對下一分點的截面形心的力臂由分塊圖上量取，見圖1.14，并分別記為、、。圖1.14單元主動荷載模式彎矩：軸力：式中：——相鄰兩截面中心點的坐標(biāo)增量：校核：計算誤差：0.53126%<5%計算誤差表明計算結(jié)果在誤差范圍內(nèi)。計算過程見表1.9，的計算過程見表1.10。表1.9計算過程截面(KN)(KN)(m)(m)（KN*m）(KN*m)(KN*m)00.00000.00000.00000.00000.00000.00000.000010.00000.00001.84390.17180.00000.0000-143.29762211.33746.14691.20520.5396-274084-3.0695-548.64593410.024724.48521.16050.8046-461.2642-19.7647-1133.67194581.880753.89120.75111.1253-527.0287-57.1187-1789.58075727.557392.33970.61371.2478-446.6759-111.6423-2398.44836827.2175134.76570.18371.3635-114.4558-183.4708-2733.30727880.6809184.35940.14371.392-101.6057-256.5456-3131.057178891.1178234.9133-0.26281.28912392752-288.2452-3209.2368表1.10的計算過程截面(KN)(KN)(KN)(KN)(KN)00.00001.00000.00000.00000.00000.00000.000010.24270.9697211.3132-6.147651.8097-1.965741.447420.47890.8745410.4087-24.4836191.0703-21.5839173.535430.64090.7363581.8215-53.8365396.3228-39.6292356.666340.83980.586127.5544-92.3191608.5295-50.5984557.925150.94920.3266827.6217-134.7676782.3101-43.9341738.343960.95160.0844880.6801-184.5131854.0340-11.5909838.423470.9978-0.1096891.2179-234.6895892.5841-21.6703918.256780.9691-0.2439906.4619-281.3296879.7371-68.6309947.7060（2）主動荷載位移和計算過程，見表1.11。表1.11、計算過程截面(KN*m)(m-4)(m)(m)i(KN*m-3)(KN*m-2)（KN*m-2）積分系數(shù)00.0000279.88330.00001.00000.00000.00000000000.000000000011143.2928279.88330.17191.1719-40101.2960-6896.4420-47001.731542548.8647279.88330.67721.6772-153618.1119-104044.2868-257662.388323-1133.6965279.88331.48522.4852-317302.8166-471267.4851-788570.308444-1789.5805279.88332.524523.52452-500873.8574-1264469.5234-1765343.380925-2398.4747279.88333.79604.7960-671293.2222-2548264.9764-3219558.118746-2733.113279.88331.157886.1578-765162.9008-3946621.5676-4711788.468427-3131.0577279.88336.55117.5511-8763319411-6617279.979548-3209.2360279.88337.77928.7792-898211.8330-6987441.8398-7885657.67281∑-11357651974-64044887.742校核:故計算正確。（3）墻底（彈性地基上的剛性梁）位移計算單位彎矩作用下墻底截面產(chǎn)生的轉(zhuǎn)角主動荷載作用下墻底截面的轉(zhuǎn)角8.解主動荷載作用下的力法方程式中：其中——拱矢高，解得：9.求主動荷載作用下各截面的內(nèi)力，并校核計算精度主動荷載作用下各截面的內(nèi)力的計算過程，見表1.12。表1.12和計算過程截面(KN*m)(KN*m)(KN*m)(KN*m)(KN*m-3)(KN*m-2)積分系數(shù)(KN)(KN)(KN)00.000000501.49040.000000501.4994141481.02280.00001.00000.0000351.1685351.13851-143.2981501.490460.3813422.5836118271.360620338.41484.000041.8448340.4208386.23062-548.8137501.4904237.8273194.454954421.244136861.76872.0000173.5570308.9310482.46803-1133.6522501.4904521.5017-106.6818-29857.6282-44341.42384.0000356.6929258.5843611.20724-1789.5853501.4904886.4543-397.6296-111289.4207-280953.12512.0000557.9492192.4687750.38795-2398.4742501.49041332.9740-560.0478-156746.5626-595019.07704.0000738.3463114.5977852.91606-2733.8631501.49041811.1586-417.2491-116779.0477-602333.38722.0000838.428329.7302868.15867-3131.7773501.49042300.3375-321.2225-91024.4933-596312.28744.0000918.2572-38.4056879.84668-3209.2369501.49042731.585927.85947791.457760642.68061.0000947.7946-81.6487862.0639∑835424.31046493560.333610.求單位彈性反力、相應(yīng)摩擦力作用下，基本結(jié)構(gòu)中產(chǎn)生的變位，a.各截面的彈性反力強(qiáng)度最大彈性反力零點，假定在截面2，即；最大彈性反力值，假定在截面4，即拱圈任意截面的外緣彈性反力強(qiáng)度，見圖1.15圖1.15單元單位彈性反力荷載示意圖邊墻任意截面外緣的彈性反力強(qiáng)度b.各分塊上的彈性反力集中力作用方向垂直襯砌外緣，并通過分塊上彈性反力圖形的形心。各點彈性反力的計算過程，見表1.13。截面(m)30.48920.27751.46330.357842.57270.67600.73620.247441.00000.74421.46331.080856.76270.83180.54810.915451.40941.20381.46331.768370.95300.99240.34821.383161.61891.51321.46332.279381.14370.99930.08042.271271.60341.69121.46332.350796.28750.9934-0.10662.382581.50851.55431.46332.1286104.17520.9696-0.26792.0606表1.13各點彈性反力的計算過程c.彈性反力集中力與摩擦力集中力的合力本設(shè)計不考慮摩擦力d.計算作用下基本結(jié)構(gòu)內(nèi)力式中：——到截面中心點的距離計算過程見表1.14、1.15。表1.14的計算過程截面30.42530.1522-0.152441.71830.61530.53510.6358-1.204453.09601.10821.85902.02550.51890.9907-4.126064.25561.52343.15283.44021.85043.26980.58721.3019-9.354371.19281.85894.36624.72533.17831.49591.86484.13810.58951.3871-17.605581.93892.12591.40681.89064.30807.61653.17057.03561.85784.37160.59641.2675-28.3080表1.15的計算過程截面v342.57200.67160.73680.26250.18470.24780.17840.0000456.76240.83610.54180.86700.70321.15540.63270.0874570.95330.94510.34441.43761.35572.81910.92610.4386681.14740.96000.08691.62361.54571.02780.42501.1451796.28540.9962-0.10971.36191.36857.3686-0.80832.16438104.11730.9698-0.24330.84060.84739.4273-2.29453.1223e.計算作用下產(chǎn)生的荷載位移和計算結(jié)果,見表1.16。表1.16和計算過程截面(m-4)(m)(m)積分系數(shù)3-0.1528279.83191.48592.4854-42.6197-63.2880-101.808444-1.2095279.83192.52693.5469-350.1149-883.8851-1234.020025-4.1791279.83193.79354.7965-1154.4097-4382.2453-5536.609446-9.45271279.83191.17936.1593-2668.7876-13761.2827-16434.070327-17.6021279.83196.55717.5504-4927.4942-32280.6268-37208.168048-28.3025279.83197.77978.7750-7922.9562-61634.9122-69557.86641∑-38458.8345-237837.7130-276296.5446校核：經(jīng)校核，故計算正確11.解單位彈性反力、摩擦力作用下的力法方程式中均同前,計算解、：代入原方程檢驗，計算正確單位彈性反力圖、摩擦力作用下截面的內(nèi)力，并校核計算精度計算過程，見表1.17。表1.17和計算過程截面積分系數(shù)00.0000-1.57020.0000-1.5705-1559.12280.000010.00004.30204.352110.0000-1.57020.7478-4.8303-1351.9241-232.476940.00004.17354.178320.0000-1.57022.9168-2.6572-743.0151-503.235720.00003.78753.78773-0.1581-1.57026.39410.6730187.9031279.076240.00003.04963.17794-1.2555-1.570210.86084.04641132.75572859.505120.07412.35912.45205-4.1241-1.570216.31646.64931860.55037062.758140.48641.40461.82666-9.5471-1.570222.20257.09941987.138010249.446221.19010.34951.51707-17.6401-1.570228.20891.01481407.20139218.746742.1852-0.47061.62868-28.3085-1.570233.4995-0.3890-108.3642-843.015613.1229-1.05092.0711∑11501.105889680.834212.最大彈性反力值的計算先求出位移和式中：計算過程見表1.18。表1.18計算過程截面積分系數(shù)4279.88190.0000-397.62654.04760.00000000.000025279.88191.2667-560.04816.6463-196934.57532337.573646279.88192.5072-417.24147.0644-297819.83814982.695727279.88193.8193-321.24741.0148-346434.24825363.461548279.88191.026927.8522-0.379039088.2666-543.37431∑-2723426.922640226.105413.計算贅余力和14.計算襯砌截面總的內(nèi)力，并校核計算精度a.襯砌各截面內(nèi)力截面積分系數(shù)0501.4999-424.710381.2875351.1486327.3642678.35420.234422751.57350.000011422.5838-367.848154.7536386.2735317.5737704.38520.015715324.64592631.201042194.4647-202.1726-7.7374482.6342288.3542770.1235-0.0099-2156.4341-1460.534823-106.678851.1253-51.5534611.7534241.3452856.1541-0.0648-15548.4522-23093.137844-397.6365308.1875-89.4453750.3757186.4623936.3452-0.0954-25032.3757-63194.48130.000025-560.0485506.2421-53.8453852.7865140.3752993.3754-0.0541-15063.2537-57180.3568-18921.468546-417.2465540.6543123.4785868.3642111.7542983.37850.125534543.9458178173.745986617.848627-321.2248382.853457.6453879.2477129.38511009.8750.057116131.8477105707.564861500.26154827.8354-29.4512-1.6364862.7352157.37541019.985-0.0016-456.7451-3553.4682-2290.14691∑40400.1345335760.4866341247.3258計算過程，見表1.19。表1.19和計算過程b.校核計算精度墻底截面最終轉(zhuǎn)角：校核：相對誤差是遠(yuǎn)小于5%，計算結(jié)果正確11.繪制內(nèi)力圖計算結(jié)果按一定比例繪制如圖1.16圖1.16內(nèi)力圖（16）內(nèi)力數(shù)值計算分析單元實常數(shù)，，材料屬性，，。單元網(wǎng)格劃分：拱部半圓弧劃分為50份，邊墻每段劃分為4份，仰拱劃分為20份，一共78個單元。單元劃分見圖1.17圖1.17單元劃分圖計算時將均布荷載轉(zhuǎn)化為節(jié)點荷載，具體荷載。對節(jié)點施加荷載如圖1.18圖1.18節(jié)點施加荷載圖對于拱形結(jié)構(gòu)，需要約束墻底的水平位移。同時為避免結(jié)構(gòu)整體沉降過大，使彈簧全部受拉，也要對墻底的垂直位移進(jìn)行約束、本模型選取節(jié)點29、52進(jìn)行約束REF_Ref41410935\r\h錯誤!未找到引用源。。見圖1.19圖1.19徑向彈簧、墻底約束施加牛頓-拉普森求解后的變形如圖1.20圖1.20全牛頓-拉普森求解后的變形查看求解后的彈簧受力表，分批多次除去受拉彈簧（正值受拉，負(fù)值受壓），在重新計算，保證彈簧全部處于受壓狀態(tài)。確定抗力分布范圍，最終除去受拉彈簧后的變形圖。如圖1.21圖1.21采用生死單元法殺死受拉彈簧后的變形軸力結(jié)果圖如圖1.22圖1.22軸力結(jié)果剪力結(jié)果圖如圖1.23圖1.23剪力圖彎矩結(jié)果圖如圖1.24圖1.24彎矩圖如圖1.24所示，最大正彎矩出現(xiàn)在距離拱頂45°兩側(cè)，最大負(fù)彎矩出現(xiàn)在拱頂位置，彎矩關(guān)于拱頂垂線呈軸對稱。如圖1.22所示，軸力值全為負(fù)值，即全部受壓。其中最大值出現(xiàn)在邊墻底角處，最小值出現(xiàn)在拱頂處，軸力關(guān)于拱頂垂線呈軸對稱。如圖1.23所示，剪力在拱頂處為零，并關(guān)于拱頂垂線呈反對稱。17.結(jié)構(gòu)驗算（1）按偏心要求，對于整體式混凝土襯砌，其偏心受壓構(gòu)件，軸向力的偏心距和截面厚度應(yīng)滿足。（2）按抗壓要求，混凝土軸心、偏心受壓構(gòu)件的抗壓強(qiáng)度應(yīng)按下式計算：式中：（3）按抗裂要求，對于混凝土矩形截面，偏心受壓構(gòu)件的抗拉強(qiáng)度按下式計算：式中：當(dāng)時，系抗壓強(qiáng)度控制承載力，可不必按抗裂公式計算；時，系抗拉強(qiáng)度控制承載能力，可不必按抗壓計算。①拱頂驗算a.偏心驗算滿足要求。b.抗壓驗算（可不必計算）滿足要求。c.抗裂驗算可見左邊大于右邊（滿足）。②側(cè)墻驗算a.偏心檢驗滿足要求。b.抗壓驗算滿足要求。c.抗裂驗算（可不必計算）③底墻驗算a.偏心檢驗滿足要求。b.抗壓驗算滿足要求。c.抗裂驗算（可不必計算）18.驗算結(jié)論本設(shè)計按最不利情況，二次襯砌承擔(dān)100%荷載。經(jīng)過以上驗算，二次襯砌支護(hù)結(jié)構(gòu)強(qiáng)度，結(jié)構(gòu)拱頂處滿足抗裂和抗壓的要求，結(jié)構(gòu)不需需要進(jìn)行配筋計算。1.3Ⅴ級圍巖襯砌驗算對于Ⅴ級圍巖，在根據(jù)經(jīng)驗選定支護(hù)參數(shù)后，仍需進(jìn)行驗算，對于Ⅴ級圍巖的內(nèi)力求解，采用ANSYS19.1軟件數(shù)值法計算，襯砌設(shè)計圖1.25，圖1.25Ⅴ級圍巖襯砌支護(hù)設(shè)計（單位：cm）1.設(shè)計基本資料a.巖體特征巖體為Ⅴ級圍巖，圍巖的彈性抗力系數(shù)，計算摩察角，巖體重度，變形模量，泊松比，粘聚力，內(nèi)摩察角。b.襯砌材料初襯采用初襯選用C25混凝土；重度，彈性模量，混凝土襯砌軸心抗壓強(qiáng)度標(biāo)準(zhǔn)值：，混凝土軸心抗拉強(qiáng)度標(biāo)準(zhǔn)值：。二襯選用C30防水混凝土；重度，彈性模量，混凝土襯砌軸心抗壓強(qiáng)度標(biāo)準(zhǔn)值：，混凝土軸心抗拉強(qiáng)度標(biāo)準(zhǔn)值：。2.主動荷載隧道處于Ⅴ級圍巖中，為深埋隧道，圍巖壓力為松散荷載。作用在其結(jié)構(gòu)上的荷載形式為：垂直均布荷載q、水平均布側(cè)向荷載e，側(cè)壓力系數(shù)0.4。豎向圍巖壓力水平圍巖壓力邊墻底部水平圍巖壓力3.內(nèi)力分析采用荷載結(jié)構(gòu)法進(jìn)行計算。荷載結(jié)構(gòu)法基本假定：①按平面應(yīng)變問題進(jìn)行處理②結(jié)構(gòu)屬于小變形③彈簧單元只受壓。按照隧道斷面幾何數(shù)據(jù)建立分析模型。單元實常數(shù)、材料屬性，、。單元網(wǎng)格劃分：拱部半圓弧劃分為50份，邊墻每段劃分為4份，仰拱劃分為20份，一共78個單元。對于拱形結(jié)構(gòu)需要約束墻底的水平位移，同時為避免結(jié)構(gòu)整體沉降過大，使彈簧全部受拉，往往也要對墻底的垂直位移進(jìn)行約束、本模型選取節(jié)點29、52進(jìn)行約束。首先在CAD中建立模型，根據(jù)規(guī)范標(biāo)準(zhǔn)斷面的建議，建立二次襯砌結(jié)構(gòu)幾何模型，然后導(dǎo)入ANSYS。選用Beam單元模擬襯砌結(jié)構(gòu)，對模型施加圍巖垂直、水平荷載、重力，圍巖、二次襯砌之間施加徑向彈簧，添加邊墻底端垂直、水平位移約束。數(shù)值求解，采用全牛頓-拉普森法，進(jìn)行分析求解。求解后采用生死單元命令殺死全部受拉彈簧，進(jìn)行第二次求解。最后，處理數(shù)據(jù)結(jié)構(gòu)，得到彎矩、軸力、剪力。ANSYS數(shù)值分析過程。結(jié)構(gòu)劃分見圖1.26圖1.26單元結(jié)構(gòu)劃分對節(jié)點施加荷載如圖1.27圖1.27節(jié)點荷載施加對于拱形結(jié)構(gòu)，需要約束墻底的水平位移。同時為避免結(jié)構(gòu)整體沉降過大，使彈簧全部受拉，也要對墻底的垂直位移進(jìn)行約束、本模型選取節(jié)點29，52進(jìn)行約束。地層彈簧單元，選擇單元實常數(shù)，長度1m。慣性荷載（重力加速度）Gravity取9.8。施加徑向彈簧如圖1.28所示。圖1.28徑向彈簧，墻底約束施加查看求解后的彈簧受力表，分批多次除去受拉彈簧（正值受拉，負(fù)值受拉），在重新計算，保證彈簧全部處于受壓狀態(tài)。確定抗力分布范圍，最終計算模型。如圖1.29所示。圖1.29采用生死單元法殺死受拉彈簧后的變形彎矩結(jié)果如圖1.30圖1.30彎矩圖軸力圖如圖1.31圖1.31軸力圖剪力圖如圖1.32圖1.32剪力圖如圖1.30所示，最大正彎矩出現(xiàn)在距離拱頂45°兩側(cè)，最大負(fù)彎矩出現(xiàn)在拱頂位置，彎矩關(guān)于拱頂垂線呈軸對稱。如圖1.31所示，拱墻與上部拱圈軸力值全為負(fù)值，即拱墻以上全部受壓，其中最大值出現(xiàn)在邊墻底角處，最小值出現(xiàn)在拱頂處；拱墻以下與仰拱全部為正值，即全部受拉。軸力關(guān)于拱頂垂線呈軸對稱。如圖1.32所示，剪力在拱頂處為零，并關(guān)于拱頂垂線呈反對稱。節(jié)點坐標(biāo)與荷載如表1.20表1.20節(jié)點坐標(biāo)與荷載STATCURRENTCURRENTCURRENTCURRENTCURRENTCURRENTELEMNINJQIQJMIMJ1-0.23436E+007-0.23440E+007-37217.0-47202.0-0.13338E+007-0.12922E+0072-0.23683E+007-0.23694E+007-0.11937E+006-0.12930E+006-0.12922E+007-0.11697E+0073-0.24077E+007-0.24096E+007-0.19651E+006-0.20634E+006-0.11697E+007-0.97128E+0064-0.24705E+007-0.24730E+007-0.26386E+006-0.27352E+006-0.97128E+006-0.70659E+0065-0.25546E+007-0.25579E+007-0.31724E+006-0.32668E+006-0.70659E+006-0.38942E+0066-0.26575E+007-0.26614E+007-0.35281E+006-0.36200E+006-0.38942E+006-37334.07-0.27760E+007-0.27806E+007-0.36721E+006-0.37608E+006-37334.00.32878E+0068-0.29064E+007-0.29117E+007-0.35759E+006-0.36609E+0060.32878E+0060.68523E+0069-0.30446E+007-0.30504E+007-0.32169E+006-0.32979E+0060.68523E+0060.10061E+00710-0.31860E+007-0.31925E+007-0.25796E+006-0.26559E+0060.10061E+0070.12640E+00711-0.33261E+007-0.33331E+007-0.16551E+006-0.17265E+0060.12640E+0070.14306E+00712-0.34599E+007-0.34674E+007-44231.0-50843.00.14306E+0070.14774E+00713-0.35827E+007-0.35906E+0070.10524E+00699199.00.14774E+0070.13767E+00714-0.36896E+007-0.36980E+0070.28152E+0060.27609E+0060.13767E+0070.11020E+00715-0.37763E+007-0.37851E+0070.48251E+0060.47770E+0060.11020E+0070.62909E+00616-0.38385E+007-0.38476E+0070.70539E+0060.70125E+0060.62909E+006-63759.017-0.38725E+007-0.38819E+0070.94672E+0060.94326E+006-63759.0-0.99468E+00618-0.38750E+007-0.38846E+0070.12025E+0070.11997E+007-0.99468E+006-0.21779E+00719-0.39362E+007-0.39460E+007-0.13045E+007-0.13066E+007-0.21779E+007-0.89179E+00620-0.40659E+007-0.40758E+007-0.82126E+006-0.82258E+006-0.89179E+006-82102.21-0.41374E+007-0.41473E+007-0.18491E+006-0.18550E+006-82102.00.10035E+00622-0.41574E+007-0.41674E+00753894.054044.00.10035E+00647183.023-0.41622E+007-0.41722E+00771631.072516.047183.0-23818.024-0.41690E+007-0.41788E+0071307.72924.2-23818.0-25903.025-0.41877E+007-0.41974E+007-0.19664E+006-0.19430E+006-25903.00.16666E+00626-0.42482E+007-0.42549E+007-87649.-84789.00.16666E+0060.22884E+00627-0.42235E+007-0.42293E+0070.58572E+0060.59019E+0060.22884E+006-0.19521E+00628-42103.0-46558.0-88901.0-83103.0-0.19521E+006-0.13318E+00629-66162.0-68991.0-68530.0-61781.0-0.13318E+006-86186.030-85459.0-88289.0-53591.0-42766.0-86186.0-33011.031-89408.0-91946.0-40371.0-29473.0-33011.05521.932-0.10331E+006-0.10555E+006-29157.0-18191.05521.9031652.033-0.11671E+006-0.11866E+006-17237.0-6214.531652.044592.034-0.12960E+006-0.13125E+006-4631.76439.644592.043591.035-0.14192E+006-0.14328E+0068642.719754.043591.027921.036-0.15365E+006-0.15471E+00622566.033710.027921.0-3127.5037-0.16476E+006-0.16551E+00637118.048287.0-3127.50-50253.038-0.17661E+006-0.17707E+006-34496.0-23311.0-50253.0-18356.039-0.24342E+006-0.24357E+006-19971.0-8778.4-18356.0-2492.2040-0.24352E+006-0.24337E+00610240.021433.-2492.2-19969.041-0.19909E+006-0.19864E+00626029.037214.0-19969.-54866.042-0.18804E+006-0.18729E+006-51002.0-39833.0-54866.-4744.043-0.17731E+006-0.17625E+006-35818.0-24674.0-4744.028631.044-0.16592E+006-0.16457E+006-21253.0-10142.028631.045958.045-0.15393E+006-0.15228E+006-7328.63742.6045958.047937.046-0.14136E+006-0.13941E+0065936.016959.047937.035304.047-0.12824E+006-0.12600E+00618523.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