【《某公路隧道的二次衬砌结构设计计算案例》6700字】

某公路隧道的二次衬砌结构设计计算案例目录TOC\o"1-3"\h\u3994某公路隧道的二次衬砌结构设计计算案例 1280871.1Ⅲ级围岩衬砌验算 1194751.2Ⅳ级围岩衬砌验算 105281.3Ⅴ级围岩衬砌验算 461.1Ⅲ级围岩衬砌验算对其二次衬砌支护结构内力进行数值分析，计算采用ANSYS19.1有限元软件计算。衬砌设计图，如图1.3所示。图1.3Ⅲ级围岩衬砌支护设计（单位：cm）1.设计基本资料（1）岩体特征岩体为Ⅲ级围岩，围岩的弹性抗力系数，计算摩察角，岩体重度，变形模量，泊松比，粘聚力，内摩察角。（2）衬砌材料二衬选用C30防水混凝土；重度，弹性模量，混凝土衬砌轴心抗压强度标准值：，混凝土轴心抗拉强度标准值：（3）围岩压力的计算a.支护参数b.竖向围岩压力c.水平围岩压力2.内力数值计算分析用ANSYS进行计算。单元实常数、，；材料属性，。单元网格划分：拱部半圆弧划分为左右各25个，共50个单元。单元划分见图图1.4单元划分图对节点施加荷载如图1.5所示图1.5节点施加荷载图对于拱形结构，需要约束墙底的水平位移。同时为避免结构整体沉降过大，使弹簧全部受拉，也要对墙底的垂直位移进行约束、本模型选取节点2、27进行约束。地层弹簧单元，选择单元实常数，长度。惯性荷载（重力加速度）Gravity取9.8。施加径向弹簧如图1.6所示图1.6径向施加弹簧图查看求解后的弹簧受力表，分批多次除去受拉弹簧（正值受拉，负值受压），在重新计算，保证弹簧全部处于受压状态。确定抗力分布范围，最终计算模型见图1.7图1.7采用生死单元法杀死受拉弹簧后的变形轴力结果图如图1.8所示图1.8轴力图剪力结果图如图1.9所示。图1.9剪力图弯矩结果图如图1.10所示。图1.10弯矩图如图1.7所示，最大变形出现在拱顶位置处。杀死受拉弹簧后的变形值为：0.048128m。如图1.8所示，正值受拉，负值受压，图中的轴力值全为负值，全部受压。其中最大值出现在边墙底角处，最小值出现在拱顶处，关于轴力分布关于隧道中线轴对称。如图1.9所示，剪力值最大值出现在距拱顶大约22.5°两侧，拱顶处剪力为零，最小负值出现在拱墙处，关于隧道中线反对称。如图1.10所示，最大正弯矩出现在距离拱顶45°两侧，最大负弯矩出现在拱顶位置，关于隧道中线轴对称。ANSYS分析结果见表1.5。表1.5单元内力数值分析结果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级围岩衬砌验算对于Ⅳ级围岩，在根据经验选定支护参数后，仍需进行验算。Ⅳ级围岩的内力求解，参考地下结构设计，先采用手算法，然后用ANSYS19.1进行验证。1.计算参数（1）岩体特征计算摩察角，围岩的弹性抗力系数，基底围岩弹性反力系数：，岩体重度，变形模量，泊松比，粘聚力，内摩察角。（2）衬砌材料二衬选用C30防水混凝土材料；重度，弹性模量，混凝土衬砌轴心抗压强度标准值：，混凝土轴心抗拉强度标准值：。二衬设计如图1.11所示。图1.11Ⅳ级围岩衬砌支护设计（单位：cm）（3）结构尺寸2.主动荷载隧道处于Ⅳ级围岩中，为深埋隧道，围岩压力为松散荷载。作用在其结构上的荷载形式为：垂直均布荷载q、水平均布侧向荷载e，侧压力系数0.25。3.绘制分块图取左半部，及半跨结构，见图1.12。图1.12分块图（1）计算半拱轴线长度s和分块轴线长度a.计算半拱轴线长度s式中为各圆弧轴线半径半拱轴线长度。b.计算分块轴线长度分块长度4.计算各分段截面中心的几何要素a求各截面、竖直轴的夹角角度校核：1.各截面的中心坐标（单位：cm）曲墙拱结构几何要素计算过程，见表1.6。表1.6曲墙拱几何要素截面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.计算基本结构的单位位移惯性矩，b取单位长度，计算过程见表1.7。表1.7曲墙拱结构的单位位移计算过程表（单位：m）截面积分系数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：的计算按式辛普森法进行，以下各表均同。如图1.13所示，求曲线在上的曲边体型的面积，可应用精度较高的——辛普森方法计算，即把分成n等分，n必须为偶数。分别求出n个小段曲边体型的面积（每3点组成的曲线用抛物线代替），然后求和：图1.13辛普森法计算变位将各分点的坐标代入得：校核:计算变位结果正确。7.计算主动荷载在基本结构中产生的位移和（1）衬砌每一块上的作用力竖向力：式中：——相邻两截面之间的衬砌外缘的水平投影（由分块图量取）侧向水平力：式中：——相邻两截面之间的衬砌外缘的垂直投影（由分块图量取）自重力：。以上各集中力均通过相应荷载图形的形心,衬砌每一块上的作用力计算过程，见表1.8。表1.8计算过程表（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分块上个集中力对下一分点的截面形心的力臂由分块图上量取，见图1.14，并分别记为、、。图1.14单元主动荷载模式弯矩：轴力：式中：——相邻两截面中心点的坐标增量：校核：计算误差：0.53126%<5%计算误差表明计算结果在误差范围内。计算过程见表1.9，的计算过程见表1.10。表1.9计算过程截面(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的计算过程截面(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）主动荷载位移和计算过程，见表1.11。表1.11、计算过程截面(KN*m)(m-4)(m)(m)i(KN*m-3)(KN*m-2)（KN*m-2）积分系数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:故计算正确。（3）墙底（弹性地基上的刚性梁）位移计算单位弯矩作用下墙底截面产生的转角主动荷载作用下墙底截面的转角8.解主动荷载作用下的力法方程式中：其中——拱矢高，解得：9.求主动荷载作用下各截面的内力，并校核计算精度主动荷载作用下各截面的内力的计算过程，见表1.12。表1.12和计算过程截面(KN*m)(KN*m)(KN*m)(KN*m)(KN*m-3)(KN*m-2)积分系数(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.求单位弹性反力、相应摩擦力作用下，基本结构中产生的变位，a.各截面的弹性反力强度最大弹性反力零点，假定在截面2，即；最大弹性反力值，假定在截面4，即拱圈任意截面的外缘弹性反力强度，见图1.15图1.15单元单位弹性反力荷载示意图边墙任意截面外缘的弹性反力强度b.各分块上的弹性反力集中力作用方向垂直衬砌外缘，并通过分块上弹性反力图形的形心。各点弹性反力的计算过程，见表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各点弹性反力的计算过程c.弹性反力集中力与摩擦力集中力的合力本设计不考虑摩擦力d.计算作用下基本结构内力式中：——到截面中心点的距离计算过程见表1.14、1.15。表1.14的计算过程截面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的计算过程截面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.计算作用下产生的荷载位移和计算结果,见表1.16。表1.16和计算过程截面(m-4)(m)(m)积分系数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：经校核，故计算正确11.解单位弹性反力、摩擦力作用下的力法方程式中均同前,计算解、：代入原方程检验，计算正确单位弹性反力图、摩擦力作用下截面的内力，并校核计算精度计算过程，见表1.17。表1.17和计算过程截面积分系数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.最大弹性反力值的计算先求出位移和式中：计算过程见表1.18。表1.18计算过程截面积分系数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.计算赘余力和14.计算衬砌截面总的内力，并校核计算精度a.衬砌各截面内力截面积分系数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计算过程，见表1.19。表1.19和计算过程b.校核计算精度墙底截面最终转角：校核：相对误差是远小于5%，计算结果正确11.绘制内力图计算结果按一定比例绘制如图1.16图1.16内力图（16）内力数值计算分析单元实常数，，材料属性，，。单元网格划分：拱部半圆弧划分为50份，边墙每段划分为4份，仰拱划分为20份，一共78个单元。单元划分见图1.17图1.17单元划分图计算时将均布荷载转化为节点荷载，具体荷载。对节点施加荷载如图1.18图1.18节点施加荷载图对于拱形结构，需要约束墙底的水平位移。同时为避免结构整体沉降过大，使弹簧全部受拉，也要对墙底的垂直位移进行约束、本模型选取节点29、52进行约束REF_Ref41410935\r\h错误!未找到引用源。。见图1.19图1.19径向弹簧、墙底约束施加牛顿-拉普森求解后的变形如图1.20图1.20全牛顿-拉普森求解后的变形查看求解后的弹簧受力表，分批多次除去受拉弹簧（正值受拉，负值受压），在重新计算，保证弹簧全部处于受压状态。确定抗力分布范围，最终除去受拉弹簧后的变形图。如图1.21图1.21采用生死单元法杀死受拉弹簧后的变形轴力结果图如图1.22图1.22轴力结果剪力结果图如图1.23图1.23剪力图弯矩结果图如图1.24图1.24弯矩图如图1.24所示，最大正弯矩出现在距离拱顶45°两侧，最大负弯矩出现在拱顶位置，弯矩关于拱顶垂线呈轴对称。如图1.22所示，轴力值全为负值，即全部受压。其中最大值出现在边墙底角处，最小值出现在拱顶处，轴力关于拱顶垂线呈轴对称。如图1.23所示，剪力在拱顶处为零，并关于拱顶垂线呈反对称。17.结构验算（1）按偏心要求，对于整体式混凝土衬砌，其偏心受压构件，轴向力的偏心距和截面厚度应满足。（2）按抗压要求，混凝土轴心、偏心受压构件的抗压强度应按下式计算：式中：（3）按抗裂要求，对于混凝土矩形截面，偏心受压构件的抗拉强度按下式计算：式中：当时，系抗压强度控制承载力，可不必按抗裂公式计算；时，系抗拉强度控制承载能力，可不必按抗压计算。①拱顶验算a.偏心验算满足要求。b.抗压验算（可不必计算）满足要求。c.抗裂验算可见左边大于右边（满足）。②侧墙验算a.偏心检验满足要求。b.抗压验算满足要求。c.抗裂验算（可不必计算）③底墙验算a.偏心检验满足要求。b.抗压验算满足要求。c.抗裂验算（可不必计算）18.验算结论本设计按最不利情况，二次衬砌承担100%荷载。经过以上验算，二次衬砌支护结构强度，结构拱顶处满足抗裂和抗压的要求，结构不需需要进行配筋计算。1.3Ⅴ级围岩衬砌验算对于Ⅴ级围岩，在根据经验选定支护参数后，仍需进行验算，对于Ⅴ级围岩的内力求解，采用ANSYS19.1软件数值法计算，衬砌设计图1.25，图1.25Ⅴ级围岩衬砌支护设计（单位：cm）1.设计基本资料a.岩体特征岩体为Ⅴ级围岩，围岩的弹性抗力系数，计算摩察角，岩体重度，变形模量，泊松比，粘聚力，内摩察角。b.衬砌材料初衬采用初衬选用C25混凝土；重度，弹性模量，混凝土衬砌轴心抗压强度标准值：，混凝土轴心抗拉强度标准值：。二衬选用C30防水混凝土；重度，弹性模量，混凝土衬砌轴心抗压强度标准值：，混凝土轴心抗拉强度标准值：。2.主动荷载隧道处于Ⅴ级围岩中，为深埋隧道，围岩压力为松散荷载。作用在其结构上的荷载形式为：垂直均布荷载q、水平均布侧向荷载e，侧压力系数0.4。竖向围岩压力水平围岩压力边墙底部水平围岩压力3.内力分析采用荷载结构法进行计算。荷载结构法基本假定：①按平面应变问题进行处理②结构属于小变形③弹簧单元只受压。按照隧道断面几何数据建立分析模型。单元实常数、材料属性，、。单元网格划分：拱部半圆弧划分为50份，边墙每段划分为4份，仰拱划分为20份，一共78个单元。对于拱形结构需要约束墙底的水平位移，同时为避免结构整体沉降过大，使弹簧全部受拉，往往也要对墙底的垂直位移进行约束、本模型选取节点29、52进行约束。首先在CAD中建立模型，根据规范标准断面的建议，建立二次衬砌结构几何模型，然后导入ANSYS。选用Beam单元模拟衬砌结构，对模型施加围岩垂直、水平荷载、重力，围岩、二次衬砌之间施加径向弹簧，添加边墙底端垂直、水平位移约束。数值求解，采用全牛顿-拉普森法，进行分析求解。求解后采用生死单元命令杀死全部受拉弹簧，进行第二次求解。最后，处理数据结构，得到弯矩、轴力、剪力。ANSYS数值分析过程。结构划分见图1.26图1.26单元结构划分对节点施加荷载如图1.27图1.27节点荷载施加对于拱形结构，需要约束墙底的水平位移。同时为避免结构整体沉降过大，使弹簧全部受拉，也要对墙底的垂直位移进行约束、本模型选取节点29，52进行约束。地层弹簧单元，选择单元实常数，长度1m。惯性荷载（重力加速度）Gravity取9.8。施加径向弹簧如图1.28所示。图1.28径向弹簧，墙底约束施加查看求解后的弹簧受力表，分批多次除去受拉弹簧（正值受拉，负值受拉），在重新计算，保证弹簧全部处于受压状态。确定抗力分布范围，最终计算模型。如图1.29所示。图1.29采用生死单元法杀死受拉弹簧后的变形弯矩结果如图1.30图1.30弯矩图轴力图如图1.31图1.31轴力图剪力图如图1.32图1.32剪力图如图1.30所示，最大正弯矩出现在距离拱顶45°两侧，最大负弯矩出现在拱顶位置，弯矩关于拱顶垂线呈轴对称。如图1.31所示，拱墙与上部拱圈轴力值全为负值，即拱墙以上全部受压，其中最大值出现在边墙底角处，最小值出现在拱顶处；拱墙以下与仰拱全部为正值，即全部受拉。轴力关于拱顶垂线呈轴对称。如图1.32所示，剪力在拱顶处为零，并关于拱顶垂线呈反对称。节点坐标与荷载如表1.20表1.20节点坐标与荷载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+00618523.029489.035304.08811.648-0.11462E+006-0.11208E+00630411.041317.08811.60-30770.049-0.11093E+006-0.10810E+00644318.055148.0-30770.0-85654.050-91190.0-88358.066527.073272.0-85654.0-0.13607E+00651-61894.0-57439.089553.095351.0-0.13607E+006-0.20275E+00652-0.42120E+007-0.42062E+007-0.5937