衬砌计算1.doc

目 录一、 二次衬砌结构计算.1 (一)基本参数 .2 (二)荷载确定.2 (三)计算衬砌几何要素.3 (四)位移计算.4 1.单位位移.5 2.载位移主动荷载在基本结构中引起的位移.6 3.载位移单位弹性抗力及相应的摩擦力引起的位移.8 4.墙底（弹性地基梁上的刚性梁）位移.12 (五)解力法方程.12 (六)计算主动荷载和被动荷载分别产生的衬砌内力13 (七)最大抗力值的求解.14 (八)计算衬砌总内力16 (九)衬砌截面强度检算.17 (十)内力图.18参考资料.19 二次衬砌结构计算一、二次衬砌结构计算选取五级级围岩复合式衬砌的二次衬砌作为典型衬砌，做结构计算。（一）基本参数1. 围岩级别：2. 围岩容重：；3. 围岩弹性抗力系数：；4. 衬砌材料为C25混凝土，弹性模量，容重。5. 抗压极限强度：，；6. 衬砌拱厚度：；（二）荷载确定1. 围岩垂直均布压力按矿山法施工的隧道围岩荷载为：式中： s围岩类别，此处s=5; 围岩容重，此处=18.5kN/m3; 跨度影响系数，=1+i(B-5),隧道跨度B=12.72m,B=515m时，i取0.1。考虑到初期支护承担大部分围岩压力，而二次衬砌一般作为安全储备，故对围岩 压力进行折减，本隧道按25%折减，取为177.02kN/m。 围岩水平均布压力e=0.4qs=70.808kN/m2。浅埋隧道围岩垂直均布压力按矿山法施工的隧道围岩荷载为: =3.27 =0.303 =65.3 则经过计算最终取在深埋情况下的围岩压力=e=0.4qs=0.4177.02=70.808kN/m2（三）计算衬砌几何要素1. 几何尺寸：内轮廓半径r=5.60m, 拱截面厚度d=0.50m 则外轮廓半径R=r+d=5.6+0.50=6.10m, 拱轴线半径r=r+0.5d=5.6+0.50.50=5.85m, 拱轴线圆弧中心角=1102. 半拱轴线长度S及分段轴长S： ， 将半拱轴平均分为8段，每段轴长为：3. 各分块接缝（截面）中心几何要素：（1） 与竖直轴夹角 另外，角度闭合差=0。（四）位移计算1.单位位移（所有尺寸见图1）衬砌几何要素、拱部各截面与垂直轴之间的夹角和截面中心垂直坐标汇总于表1图1 二次衬砌结构计算图单位位移计算表 表1截面积分系数000.00001.00000.00000.00000.596.15380.00000.000096.15383113.750.23760.97131.44990.41770.596.153840.163416.7762193.25692227.50.46170.88702.70120.9110.596.153887.596179.8351.14601341.250.65930.75183.85721.70170.596.1538163.6249278.4405701.844124550.81910.57354.7922.74460.596.1538263.9037724.3101348.2712568.750.93200.36245.45233.97970.596.1538382.66321522.8852384.3651682.50.99140.13055.85.33640.596.1538513.11512738.18763860.5712796.250.9940-0.10885.81526.73690.596.1538647.77854364.01925755.73003890105.49728.10010.596.1538778.85536308.80657962.67111769.23042877.700516033.225422557.8569注：1.I截面惯性矩，I=bd3/12,b取单位长度。 2.不考虑轴力的影响。计算精度校核为：闭合差=0.000000022.载位移主动荷载在基本结构中引起的位移(1).每一楔块上的作用力：竖向力：Qi=qbi 侧向力：Ei=ehi 自重力：式中：bi衬砌外缘相邻两截面之间的水平投影长度，由图1中量得； hi衬砌外缘相邻两截面之间的竖直投影长度，由图1中量得；di接缝i的衬砌截面厚度。作用在各楔块上的力计算如表2所示; 载位移计算表 表2截面集中力力臂QaqGagQGEaqagae0000000001256.661216.134512.37720.68340.68340.0874175.402311.02632241.950916.134536.42360.60270.60260.2572145.82389.72263213.362216.134558.38110.48740.48740.4123103.99277.86394172.559016.134576.99660.34420.34420.543759.39485.55345121.860516.134591.19360.17710.17710.643921.58152.8574662.718116.1345100.17200.05210.03020.70733.27320.48727016.1345103.40090-0.06050.73010-0.97658016.1345100.70310-0.08560.71110-1.3811(2).外荷载在基本结构中产生的内力内力按下式计算（见图2所示）弯矩： 图二：轴力： 式中：xi、yi相邻两接缝中心点坐标增量值，按右式计算：xi=xixi-1 yi=yiyi-1、的计算见表3，表4. 载位移计算表 表3EaeQ+GExyxQ+GyE000000001.0817001.38410.184600-187.5109.368272.795712.37721.33010.4933362.84566.1056-721.376424.0705530.881248.80081.15590.7907613.645638.5868-1509.53641.8630760.3779107.180.93481.0428710.8012111.7694-2438.91858.7195949.7153184.17860.66021.2351626.5770227.4790-3376.132970.85171087.0666275.37230.34771.3566377.9730373.5700-4202.288375.49301165.9192375.54430.0231.398726.81614525.2739-4828.895271.61001182.05478.9453-0.3181.3656-375.893654.0477-5177.2787载位移计算表 表4截面sincosQ+GEsinQ+GcosE0010000010.23760.9713272.795 12.377264.839712.02252.817120.46170.8870530.88148.8008245.13343.2869201.846730.65930.7518760.377107.182501.352080.583420.768240.81910.5735949.0715184.17777.4338105.640671.793350.93200.36241087.066275.3721013.154699.80540913.349260.99140.13051165.919375.5441155.94449.01831106.92670.9940-0.10881182.0537478.94531175.0280-52.14121227.169380.939601198.188579.64841125.928601125.928 (3).主动荷载位移计算结果见表5所示主动荷载位移计算表 表5截面1/I(m4)y/I(m4)/Iy/I (1+y)/I积分系数1/30096.15380.000000011-187.51096.153840.1634-18029.83933-7531.063886-25560.9032142-721.376496.153887.5961-69363.08588-63189.77124-132552.857123-1509.53696.1538163.6249-145147.639-246997.7373-392145.376344-2438.91896.1538263.9037-234511.2652-643639.6183-878150.883525-3376.132996.1538382.6632-324628103-1616550.11646-4202.288396.1538513.1151-404065.9913-2156257.756-2560323.74727-4828.895296.1538647.7785-464316.6314-3128054.714-3592371.34548-5177.278796.1538778.8553-497815515-4530166.5441769.23042877.7005-2157877.494-11569944.28-13727821.77则：计算精度校核：闭合差=0.0009。3.载位移单位弹性抗力及相应的摩擦力引起的位移各接缝处的弹性抗力强度抗力上零点假定在接缝2处，最大抗力值假定在接缝5处，拱部任一截面截面外缘的抗力强度按下式计算：算出：最大抗力值以下各截面抗力强度按下式计算：式中：所考察截面外缘点到到h点的垂直距离;墙角外缘点到到h点的垂直距离;由图1 中量得:，;按比例将所求的抗力绘在分块图上(2).各楔块上抗力集中力Ri按下式近似计算：式中：Si外楔块外缘长度。(3).抗力集中力与摩擦力的合力Ri按下式计算：式中：围岩与衬砌间的摩擦系数，此处取u=0.2。则：其作用方向与抗力集中力的夹角=arctan=11.3099。由于摩擦阻力的方向与衬砌位移的方向相反，其方向向上。将Ri的方向线延长，使之交与竖直轴，量取夹角k，将Ri分解为水平与竖直两个分力：RH=RisinkRV=Ricosk 以上计算列于表6.弹性抗力及摩擦力计算表 表6截面(h)(i-1+i)/2Si外R(h)KsinKcosKRH(h)RV(h)30.3320.1661.4630.247641.020.65630.75440.16250.186840.6910.51151.4630.763149.230.7570.65300.57790.4983510.84551.4631.261460.30.86860.49541.09570.625060.89160.94581.4631.411176.120.97080.23981.36980.33870.55260.72211.4631.0773890.99980.01741.07710.0188800.27631.4630.412298.040.9901-0.13980.4081-0.0576 (4).计算单位抗力及其相应的摩擦力在基本结构中产生的内力弯矩： 轴力：式中：力Ri至接缝中心点K的力臂，由图1量得。计算见表7及表8.计算表 表7截面R3=0.2476hR4=0.7631hR5=1.2614hR6=1.4111hR7=1.0773h R8=0.4122h(h)30.04950.0122-0.01241.32761.01300.52310.3991-0.727852.56353.23352.5533.22030.86631.0927-3.675663.91915.53023.2444.57762.21743.12890.72121.0176-7.260575.31965.73084.82315.19593.80124.09502.14452.31020.76730.8266-13.645486.68382.75505.83752.40624.98732.05573.51631.44942.13340.8791.1460.4738-20.1343计算表 表8截面 ()sincosRV (h)sinRV (h)RH (h)cosRH (h) (h)341.250.65930.75180.18680.12310.16250.12210.00094550.81910.57350.68510.56110.73950.42410.1369568.750.93200.36241.311.2201.83520.66500.5549682.50.99140.13051.64011.6253.2050.41821.2067796.250.9940-0.10881.65891.64894.282-0.46582.1148900.939601.60121.50444.690201.5044(5).单位抗力及相应摩擦力产生的载位移计算见表9单位抗力及相应摩擦力产生的载位移计算表 表9截面M0 (h)1/ I y/I M0/IM0y/IM0(1+y)/I积分系数1/33-0.01296.1538163.6249-1.1784-0.4922-1.670724-0.727896.1538263.9037-69.9895-63.760-133.749945-3.675696.1538382.6632-353.4294-601.4308-954.860226-7.260596.1538513.1151-698.1322-1916.0938-2614.226147-13.645496.1538647.7785-1312.036-5221.5133-6533.550218-20.134396.1538778.8553-1936.0099-10331.32-12267.33343-4370.7765-18134.614-22505.3908计算精度校核：闭合差=0.0000001。4.墙底（弹性地基梁上的刚性梁）位移单位弯矩作用下的转角：主动荷载作用下的转角：单位抗力及相应摩擦力作用下的转角：（5） 解力法方程 衬砌计算矢高 计算力法方程的系数 以上将单位抗力图及相应摩擦力产生的位移乘以倍，即被动荷载的载位移。求解方程：式中式中（六）计算主动荷载和被动荷载分别产生的衬砌内力计算公式为, , 计算过程见表10和表11 主被动荷载作用下衬砌弯矩计算表 表10截面 yy00273.4680273.4680-2.51450-2.51451-187.510273.468250.6187336.57670-2.51451.1459-1.36852-721.3764273.468546.597298.68880-2.51452.4992-0.01523-1509.536273.4681021.014-215.053-0.012-2.51454.66842.14194-2438.918273.4681646.751-518.698-0.7278-2.51457.52954.28725-3376.132273.4682387.808-714.856-3.6756-2.514510.91794.72786-4202.288273.4683928.822-326.996-7.2605-2.514514.63984.86487-4828.8952273.4684432.119-123.3074-13.6454-2.514518.48202.32218-5177.2787273.4684860.03543.7750-20.1343-2.514522.2218-0.4269 主被动荷载作用下衬砌轴力计算表 表11截面 00599.997599.997O2.74342.7434152.8171582.8023635.619402.66472.6642201.8467532.2038734.050502.43342.43343420.7682451.1016871.86980.00092.06252.06344671.7933344.14411015.93740.13691.57351.71045913.3492217.46171130.81090.55490.99431.549261106.92678.31531185.24131.20670.35801.564771227.1693-65.31971161.84952.114-0.29861.815381125.92801125.9281.504401.5044（七）最大抗力值的求解首先求出最大抗力方向内的位移。考虑到接缝6处的径向位移与水平方向有一定的偏离，因此修正后有：, 计算过程见表12最大抗力位移修正计算表 表12截面/I/I(-)(-)/I（-)/I积分系数1/3026294.987-241.77875.3364140320.5706-1290.2281132363.1287-201.58644.9187159184.5211-991.5430429489.3031-67.46154.425441993.9621-298.544123-20678.1631205.95183.6347-75158.9196748.573044-49874.7837322.23052.5918-129265.4645835.15725-68736.120454.59591.3567-93254.2951616.750346-69903.427467.769000043820.3745-379.8347位移值为：最大抗力值为： （八）计算衬砌总内力按下式计算衬砌总内力：, 计算过程见表13衬砌总内力计算表 表13截面 /I/I积分系数1/30273.468-2.514546.8612599.99798.771026.636-0.01654505.8882221882.1095111336.5767-1.3685213.247635.6194 98.771049.91136-0.022120504.5555418679.65014298.6888-0.015297.3189734.050598.771112.480-0.02439357.58935515923.809823-215.0532.1419-22.0249871.869898.771192.7590.0121-2117.784753-5812.47203244-518.6984.2872-132.33551015.937498.771281.93020.1103-12724.56466-50639.9499825-714.8564.7278