曲墙衬砌计算二次衬砌结构设计 一、基本计算数据公路等级为二级公路 围岩类别 V 类围岩容重 rs=1.85t/m ³=18.5kN/m ³围岩弹性抗力系数 K=150MPa=0.15×510t/m ³=1.5×510kN/m ³ 衬砌材料为C25混凝土,弹性模量m kN MPaE h /1095.21095.264⨯=⨯=,容重h r =18.5t/m ³=18.5kN/m³二、 荷载确定1、围岩竖向均布压力:10.452s q γω-=⨯S---围岩类别,此处s=5γ--围岩容重,此处γ=18.53/k n m ω--跨度影响系数,1(15),i m ω=+-毛洞跨度1m=3. 1m 3.7520.75210.1211.2=⨯+⨯++⨯=,1m 在5—15之间,取i=0.1,故有:10.1ω=+⨯(11.2-5)=1.62 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,对本隧道安照35%折减,即:q=(1-35%)65%129.18215.784s q k p a=⨯=,2、围岩水平均布力:e=0.4q=0.4×140.2596=56.10384 3、计算位移: (3)单位位移:(所以尺寸见图)Q 7Q 6Q 5Q 4Q 3Q 2Q 1XYE 1G 1G 2G 3G 4G 5G 6G 7G 8R 4R 5R 6R 7R 8E 1E 2E 3E 4E 5E 6E 7E 8半拱轴线长度米7122.11=s轴线段圆弧的中心角 108.956°×2=217.912° 半轴线长度SS=︒⨯956.108180/01r π=3.1416×6.159/180×108.956°=11. 7122m △ S=S/8=11.7122/8=1.464025m△ S/E=1.464025/2.95×710=0.4963×710-m/kpa计算衬砌的几何参数,如拱部各截面与垂直轴之间夹角Φ和截面中心垂直坐标X,Y 等,见表1表1 单位位移的计算表截面 φ Sin φ Cos φ X Y d0 0.0000 0.0000 1.0000 0.0000 0.0000 0.45001 13.6195 0.2355 0.9719 1.4504 0.1731 0.45002 27.239 0.4577 0.8891 2.8190 0.6830 0.45003 40.8505 0.6542 0.7563 4.0292 1.5009 0.45004 54.478 0.8139 0.5810 5.0128 2.5806 0.45005 68.0975 0.9278 0.3730 5.7143 3.8617 0.45006 82.717 0.9919 0.1268 6.1091 5.3780 0.45007 95.3365 0.9957 -0.0930 6.1325 6.7318 0.45008 108.956 0.9458 -0.3248 5.8252 8.1594 0.4500∑1/J Y/J JY/2()IY /12+131.6872 0.0000 0.0000 131.6872 131.6872 22.795 3.9458 181.2231 131.6872 89.9424 61.4307 373.0025 131.6872 197.6493 296.6518 823.6377 131.6872 339.8320 876.9705 1668.3216 131.6872508.53651963.8154 3112.5754 131.6872 708.2138 3808.7738 5356.8883 131.6872886.49195567.6862 7872.3571 131.6872 1074.49428767.2280 11047.846 ∑3827.955121346.502230194.5364注:1、Ⅰ截面惯性矩,312b di =,b 取单位长度。
2、不考力的影响。
单位位移值用辛普森法近似计算,计算如下:74112020.4963106849.9499 2.973610shhMS Y M d s E E Iδ----∆=≈=⨯⨯=⨯∑⎰227422200.49631021346.502210.594310shhMS y d s E E Iδ---∆=≈=⨯⨯=⨯∑⎰444411122220.5882102 1.89981010.59431014.982110δδδ----++=⨯+⨯⨯+⨯=⨯2(1)ss hS y E Iδ∆+==∑闭合值0∆≈(2)载移——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:i Q q b i = 横向力:i E e h i=自重力:12i ihd d G i s γ-+=⨯∆⨯式中:i b衬砌外缘相邻两截面之间的水平投影长度;ih 衬砌外缘相邻两截面之间的竖直投影长度; id 接缝i 截面厚度。
作用在各楔块上的力均列入表-2中 2)外荷载在基本结构中产生的内力 内力按下式计算弯矩:001,11()ipi pi i g ei i MMx Q G y E Q a G a ---=-∆+-∆--∑∑轴力:11s in ()c o s ip i i i i N Q G Eϕϕ--=+-∑∑0ipM、ipN 的计算见表-3、-4载位移计算 表-2 截面 集中力 力臂gQ agG aQG Eqagaea0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 203.4325 15.1527 9.7116 0.7251 0.7201 0.0866 147.5089 10.9115 2 191.9593 15.1527 28.5737 0.6843 0.5808 0.21549 131.3577 10.1402 3 169.7422 15.1527 45.8873 0.6051 0.5808 0.4088 102.711 8.8007 4 137.9593 15.1527 60.5753 0.4917 0.4597 0.5398 67.8346 6.9657 5 98.3921 15.1527 71.8746 0.3509 0.3126 0.6404 34.5258 4.7367 6 55.3745 15.1527 85.0703 0.1976 0.1626 0.7584 10.9420 2.4638 7 3.2821 15.1527 75.9534 -0.0946 0.0245 0.6769 -0.3105 0.3712 8 43.101815.152780.0938-0.1537-0.16910.71416.6247-2.5623表3 轴力0pN的计算表eE a1()i Q G -+∑1i E-∑X∆ Y∆1()i x Q G -∆+∑1i YE-∆∑0pM0.0000 0.0000 0.0000 0.0000 0.00000 0.0000 0.0000 0.0000 0.841 0.0000 0.0000 1.4504 0.1731 0.0000 0.0000 -79.6307 7.2834218.58529.71161.3686 0.5099299.1557 4.9519 -306.07515 18.7587 425.6972 38.2853 1.2102 0.8179 515.1788 31.3135-644.456532.6985 610.5921 84.1726 0.9836 1.0797 600.5784 90.8812 -1043.9357 46.0285 763.7041 144.7479 0.7015 1.2811 535.7384 185.4365 -1447.1687 64.5173 877.2489 216.6225 0.3948 1.5163 346.3379 328.4647 -1823.5315 51.4129 947.7761 301.6928 0.0234 1.3538 22.178 408.4317 -2064.7284 57.195 966.2109 377.6462 -0.3073 1.4276-293.4383539.1277 -2214.88945单位变位可利用表1的计算结果代入下列公式得表4 轴力0pN的计算表截面号SinφCosφ∑(Q+G)Sinφ∑(Q+G)Cosφ∑(Q+G)Cosφ∑EpN0 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.00001 0.2355 0.9719 218.5852 9.7116 51.4768 9.4387 42.03212 0.4577 0.8891 425.6972 38.7853 194.8416 34.0395 160.80213 0.6542 0.7563 610.5921 84.1726 399.4494 63.6597 335.78974 0.8139 0.5810 763.7041 144.7479 621.5788 84.0985 537.48035 0.9278 0.3730 877.2489 216.6225 813.9115 80.8002 733.11136 0.9919 0.1268 947.7161 301.6928 940.0991 38.2546 901.84457 0.9957 0.0930 966.2109 377.6462 962.0562 -35.1211 997.17738 0.9458 -0.3248 1024.4654 457.74 968.9394 -148.674 1117.6134计算结果见表—5截面PM1IyIpMIpM yI0(1)pM yI+0 0.0000 131.6872 0.0000 131.6872 0.0000 0.00001 -79.6307 131.6872 22.795 -10486.3439 -1815.1818 -120301.52582 -306.7515 131.6872 89.9424 -40306.1795 27529.1336 -135670.62613 -644.4565 131.6872 197.6493 -84866.672 127376.3761 -212243.04814 -1043.9357 131.6872 339.8320 -1374729693 364762.7568 -492235.72615 -1447.168 131.6872 508.5365 -190573.5875 735938.08 -92651.66756 -1823.3325 131.6872 708.2138 -240135.7574 1291450.117- -1531585.937 -2064.7284 131.6872 886.4919 -2714695.862 1830365.003 -2102262.7348 -2214.88945 131.6872 1074.4942 -291672.59 2379885.868 -2671558.458131.6872∑10459332.53则:00811 4.9063103710209.9620.1835spp h M Ms p M d s E IEI-∆∆=≈=-⨯⨯=∑⎰00822 4.9631016749122.570.335spp h M Ms p M d s yE IEI-∆∆=≈=-⨯⨯=-∑⎰计算精度校核:12(0.18350.335)0.5185p p ∆+∆=-+=-0(1)ps p y M s EI+∆∆=84.9631010459332.530.519-=-⨯⨯=-闭合差∆≈0(3)载位移—单位弹性抗力图及相应是的摩擦力引起的位移 1) 各接缝处的弹性抗力强度抗力上零点假的在接缝3处,340.8585b ϕϕ== 最大抗力值假定在接缝6处, 682.717h ϕϕ== 最大抗力值以上各截面抗力强度按下式计算:2222c o s c o s c o s c o s b i i hb h ϕϕϕσϕϕ⎛⎫-= ⎪-⎝⎭2222c o s 40.2585c o s c o s 40.8585c o s 82.717ih ϕσ⎛⎫-= ⎪-⎝⎭220.572c o s c o s (1.029)0.5720.01610.5559i i hh ϕϕσσ⎛⎫-==-⎪-⎝⎭有计算可得: 30,σ= 40.3927h σϕ= 50.7787h σϕ=6hσσ=最大抗力值以下各截面抗力强度按下式计算:`2`21i ihhσσσσ⎛⎫=-⎪⎝⎭式中:`i y -所考察截面外缘点到h 点的垂直距离;`h y -墙脚外缘点到h 点的垂直距离。