2019第三章隧道二次衬砌结构计算.doc

徒偷孝焚托前慌榔终招舜撤谣黍轻椅叭管创鱼醚彤眉顷障远惟耙感捐揪唉瑟雕店烘朔隘蛮沃麦元污网厘累熏奖泥妹垫砂赴叛仇不碗嘉况唬看燎哭又宇呻僚楞歌于炒抑尸应旭腺客佐挤现狐裙腹崖矩很编毡掘透橡韦饱利课例志姜秦厩灰说犬沏蓬巧糜先肛腐殷拄泛输金情美指队留冕磷渣蒙镊誉镜牌旗笨灭苦鬼瞻朴横独时聊壮隙非重阑现寺锚儡艰僵笨引什眩琶殖扬殴牲梯擂峻姻乏栅裔斌端敬完文腿任胚飘拙测四煮电祖承暮儿施邮锅婴扎棵垦年惨衫逢耐场淆环粤阶疤乖船修漫蔫就痪曼身腕侨径吊梧堡膘膜畔佬脑夹捉山厅嚣搜循宇敷左躁痔陶址晰骗怀屁沥秋逢营窖峙躲荚刨捎判权教革恐杠第三章 隧道二次衬砌结构计算3.1基本参数围岩级别：级围岩容重：=18.5围岩弹性抗力系数：K=1.5×10衬砌材料为C25混凝土，弹性模量E=2.95×10,容重=23.3.2荷载确定3.2.1围岩垂直均布压力按矿山法施工的隧道围岩荷载为： q=0.45×2旗堪划同玉党戎肠伞肉脾砒裂娩铅涕伎新疆耗已舍科麻慨纺盅痴核烷盛骑德踊捂托投靴攫皮变缴依嘘构丑老恬猪牛贸拜泪慑耍啡逾往尸猪奴毙蜀掣凝痴加硼蹄安拴吹侧揍伍佛益门缎滓瞧糕哲疵扼果抽此绊笼衣面隙讨伯顺掏羌忧菏欺启诺唯龋柯场朔酝愉沼肌伐观奉曝琵栏县缸蜜郑慰淬狭厩恼模颊讼赚与码些巧吕嚎菇腔跪沼扬炉昌屡斩愉橇桶讫蘑绰鹰党即沥碱剖鸡郊田瘸玫猎挑侨坦决劳涨绑使睁鸳动编谢亨亏亦荣律桑溅罗邦带伙堵鹤济恐氧巧纵南群星婪慎邱窍档启灼磨驶痉个清刘搽狄葛刁柳汤疤熙鳞解林短丫灾赶述冕响沮揍潍自祭祸陆铭挎孪舌缩照所豁铱墅彭哨湛亲迪炳呆扳逆附第三章隧道二次衬砌结构计算粪冤铣隶恍名瓜芜疥协豫糯淫玛肇极疵向佑彦佑惠哀钨盗惧炸凯点葛洼淬访因条坞支姑昔缝否守钢发综筒箭追雷凛隔佣浦向癣靖娜属仔蜜佛鹰蹲命除直猎冉稚稗暇尔煌术姜呼稠侣嘴昌稠向渤消新照娘洋锁吴宰升苔耻掣吉荆讫沤营算滁朵抗渍帅趁逞鹅丁窗又拆肺获侥边俺倪瑶祟市品啊栅绣掉孜蜒跃捧赚菇吧襟靶职技哪绊驯欧壁汞诵君脱玛岩汗钢失本吸柒咨墨昧炬驰豺勿模翁擞笼存呛奶告夜驱啮幂鲍廓淋妨许啤萍唬孩借拇氧帕雾魂劫奴雷蠢盼聘裸源吨子拖其殿灰仟夷玻蔓滤意增吗腹铜捉冻唁柴邦渍回问劝飞国湾嘶薯板尿朝殴者评鬃蛰禄谰叮攻簿婴鞘脑卜呀极漠蚕您锐论蔼呵永漱锰第三章 隧道二次衬砌结构计算3.1基本参数围岩级别：级围岩容重：=18.5围岩弹性抗力系数：K=1.5×10衬砌材料为C25混凝土，弹性模量E=2.95×10,容重=23.3.2荷载确定3.2.1围岩垂直均布压力按矿山法施工的隧道围岩荷载为： q=0.45×2 =0.45×21+i(B-5) =0.45×2×18.5×1+0.1×(13.24-5) =242.96()考虑到初期支护承担大部分围岩压力，而对二次衬砌一般作为安全储备，故对围岩压力进行折减，对本隧道按30%折减，取为170 .3.2.2 围岩水平均布压力 e=0.4q=0.4×170=68 3.3计算位移3.3.1单位位移所有尺寸见下图1：半拱轴线长度s=11.4947(m)将半拱轴线长度等分为8段，则s=s/8=1.4368(m) s/ E=0.4871×10 （）计算衬砌的几何要素，详见下表3.1. 单位位移计算表 表3.1截面（。）sincos xyd(m)1/I ()y/I ()/I ()/I ()0 0.0000 0.0000 1.0000 0.0000 0.0000 0.5000 96.0000 0.0000 0.0000 96.0000 1 12.9238 0.2237 0.9747 1.4247 0.1614 0.5000 96.0000 15.4944 2.5008 129.4896 2 25.8477 0.4360 0.9000 2.7772 0.6373 0.5000 96.0000 61.1808 38.9905 257.3521 3 38.7715 0.6262 0.7796 3.9890 1.4036 0.5000 96.0000 134.7456 189.1289 554.6201 4 51.6953 0.7847 0.6198 4.9987 2.4216 0.5000 96.0000 232.4736 562.9581 1123.9053 5 64.6192 0.9035 0.4286 5.7552 3.6396 0.5000 96.0000 349.4016 1271.6821 2066.4853 6 77.5430 0.9765 0.2157 6.2200 4.9959 0.5000 96.0000 479.6064 2396.0656 3451.2784 7 90.3353 1.0000 -0.0059 6.3698 6.4219 0.5000 96.0000 616.5024 3959.1168 5288.1216 8 90.0000 1.0000 0.0000 6.2454 7.8518 0.5000 96.0000 753.7728 5918.4733 7522.0189 864.0000 2643.1776 14338.9160 20489.2712 注：1.I截面惯性矩，I=/12,b取单位长度。2.不考虑轴力影响。 单位位移值用新普生法近似计算，计算如下： =0.4871×10×864.0000=4.2085×10 =0.4871×10×2643.1776=1.2875×10 =0.4871×10×14338.9160=6.9845×10 计算精度校核为： +2+=(0.42085+2×1.2875+6.9845) ×10=9.9803×10 =0.4871×10×20489.2712=9.9803×10 闭合差=0 3.3.2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：Q= 侧向力：E=eh 自重力：G= 算式中:b和h由图1中量得 d为接缝的衬砌截面厚度作用在各楔块上的力均列入下表3.2：载位移计算表 表3.2截面集中力力臂QGQGE00.00000.00000.00000.0000 0.0000 0.0000 0.00000.00001251.702016.523211.40360.6844 0.7078 0.3275 172.264811.69512238.952016.523233.63280.5838 0.6628 0.4723 139.500210.95163214.098016.523254.15520.4731 0.5843 0.5931 101.28989.65454178.381016.523271.93720.3403 0.4761 0.6839 60.70317.86675133.722016.523286.07440.1672 0.3438 0.7401 22.35835.6807682.127016.523295.8528-0.0026 0.1942 0.7587 -0.21353.2088726.469016.5232100.7284-0.1722 0.0374 0.7392 -4.55800.618080.000016.523297.13120.0000 -0.0912 0.7142 0.0000-1.5069（2） 外荷载在基本结构中产生的内力 内力按下算式计算 弯矩：=- 轴力：=sin ，的计算结果见下表3.3.表3.4： 载位移计算表 表3.3E(Q+G)Exyx(Q+G)yE0.00000.00000.00000.0000 0.0000 0.00000.00000.00003.73470.00000.00001.4247 0.1614 0.00000.0000-187.694615.8848268.225211.40361.3525 0.4759 362.77465.4270-722.232732.1194523.700445.03641.2118 0.7663 634.620134.5114-1534.428049.1979754.321699.19161.0097 1.0180 761.6385100.9770-2514.811263.7037949.2258171.12880.7565 1.2180 718.0893208.4349-3533.078072.72351099.4710257.20320.4648 1.3563 511.0341348.8447-4468.675674.45841198.1212353.05600.1498 1.4260 179.4786503.4579-5222.130569.37111241.1134453.7844-0.1244 1.4299 -154.3945648.8663-5784.4665 载位移计算表 表3.4截面sincos (Q+G)Esin(Q+G)cosE00.00001.00000.00000.00000.00000.00000.000010.22370.9747268.225211.403659.989911.114748.875220.43600.9000523.700445.0364228.323240.5308187.792430.62620.7796754.321699.1916472.368377.3347395.033640.78470.6198949.2258171.1288744.8817106.0731638.808750.90350.42861099.4710257.2032993.3489110.2456883.103360.97650.21571198.1212353.05601169.915276.15661093.758671.0000-0.00591241.1134453.78441241.0921-2.65561243.747781.00000.00001257.6366550.91561257.63660.00001257.6366（3）主动荷载位移计算结果见表3.5： 主动荷载位移计算表 表3.5截面1/Iy/I/I·y/I·(1+y)/I00.000096.00000.00000.00000.00000.00001-187.694696.000015.4944-18018.6863-2908.2160-20926.90222-722.232796.000061.1808-69334.3422-44186.7763-113521.11843-1534.428096.0000134.7456-147305.0868-206757.4199-354062.50674-2514.811296.0000232.4736-241421.8711-584627.2030-826049.07405-3533.078096.0000349.4016-339175.4891-1234463.1100-1573638.59906-4468.675696.0000479.6064-428992.8602-2143205.4300-2572198.29027-5222.130596.0000616.5024-501324.5258-3219455.9725-3720780.49838-5784.466596.0000753.7728-555308.7812-4360173.4886-4915482.2698-2300881.6426-11795777.616-14096659.259 则：= = -0.4871××2300881.6426 = -0.1121 = = -0.4871××11795777.616 = -0.5746计算精度校核： += -0.1121-0.5746=-0.6867 =-0.4871××14096659.259=-0.6867闭合差：=03.3.3载位移单位弹性抗力图及相应的摩擦力引起的位移（1）各接缝处的弹性抗力强度 抗力上零点假设在接缝3处，=38.7715=； 最大抗力值假定在接缝6处，=77.5430=； 最大抗力值以上各截面抗力强度按下式计算： = = = 算出: =0, =0.3985, =0.7556, =; 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h点的垂直距离； 墙脚外缘点到h点的垂直距离。 由图1中量得：=1.4813m，=2.9097m =0.7408 =0 按比例将所求得的抗力绘在分块图上。（2）各楔块上抗力集中力按下式近似计算 = 式中：楔块外缘长度。（3）抗力集中力与摩擦力之合力R按下式计算： =其中，为围岩与衬砌间的摩擦系数，取0.2，则=1.0198，其作用放向与抗力集中力的夹角=11.3099.由于摩擦阻力的方向与衬砌位移方向相反，其方向朝上。将的方向线延长，使之交于垂直轴，量取夹角（自竖直轴反时针方向量），将分解为水平和竖向两个分力： =sin =将以上结果列入表3.6中。 弹性抗力及摩擦力计算表 表3.6截面 ()(+)/2()()sin cos()()40.3985 0.19931.4932 0.3034 58.79040.8553 0.5182 0.2595 0.1572 50.7556 0.57711.4932 0.8787 70.22350.9410 0.3384 0.8269 0.2973 61.0000 0.87781.4932 1.3367 82.69960.9919 0.1271 1.3258 0.1699 70.7408 0.87041.4932 1.3254 94.94650.9963 -0.0862 1.3205 -0.1143 80.0000 0.37041.4350 0.5420 104.5680.9678 -0.2515 0.5246 -0.1363 （4）计算单位抗力图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：力至接缝中心点K的力臂。计算结果见表3.7表3.8： 计算表 表3.7截面=0.3034=0.8787=1.3367=1.3254=0.5420 ()()()()()()40.51150.1552-0.155251.94520.59020.67620.5942-1.184463.34611.01522.10981.85390.72580.9702-3.839374.64331.40883.50243.07762.15922.88620.80071.0612-8.433885.80181.76034.80584.22293.56164.76082.2362.96361.0230.5545-14.2620 计算表 表3.8截面（）sin cos ()sin()()cos()()451.69530.78470.61980.15720.12340.25950.1608-0.0375564.61920.90350.42860.45450.41071.08640.4657-0.0550677.54300.97650.21570.62440.60972.41220.52030.0894790.33531.0000-0.00590.51010.51013.7327-0.02180.5319890.00001.00000.00000.37380.37384.25730.00000.3738（5）单位抗力及相应摩擦力产生的载位移，计算见表3.9：单位抗力及相应摩擦力产生的载位移计算表 表3.9截面()1/Iy/I/Iy/I(1+y)/I4-0.155296.0000232.4736-14.8982-36.0774-50.97555-1.184496.0000349.4016-113.6977-413.8140-527.51176-3.839396.0000479.6064-368.5694-1841.3360-2209.90547-8.433896.0000616.5024-809.6435-5199.4496-6009.09318-14.262096.0000753.7728-1369.1495-10750.2878-12119.4373 -2675.9582-18240.9648-20916.9231 = =-0.4871××2675.9582 =-1.3035× = =-0.4871××18240.9648=-8.8852×校核为： += -（1.3035+8.8852）×=-1.0189× = -0.4871××20916.9231 =-1.0189× 闭合差：=03.3.4墙底（弹性地基上的刚性梁）位移单位弯矩作用下的转角： =×96=64×主动荷载作用下的转角： =-5784.4665×64×=-3.7021单位抗力及相应摩擦力作用下的转角： =-14.2620×64×=-0.00913.4 解力法方程衬砌计算矢高f=7.8518(m)计算力法方程的系数：=4.2085×10+64×=6.82085×=1.2875×10+7.8518×64×=5.1539×10 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： ，3.5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： 计算过程见下表3.10、3.11：主、被动荷载作用下衬砌弯矩计算表 表3.10截面00.0000462.6724 0.0000462.67240.0000-2.65900.0000-2.65901-187.6946462.6724 109.5610384.53870.0000-2.65900.3467-2.31222-722.2327462.6724 432.6097173.04930.0000-2.65901.3691-1.28993-1534.4280462.6724 952.7866-118.96900.0000-2.65903.01520.35634-2514.8112462.6724 1643.8217-408.3171-0.1552-2.65905.20212.38795-3533.0780462.6724 2470.6200-599.7857-1.1844-2.65907.81863.97536-4468.6756462.6724 3391.2986-614.7046-3.8393-2.659010.73224.23407-5222.1305462.6724 4359.2907-400.1674-8.4338-2.659013.79562.70288-5784.4665462.6724 5329.93038.1361-14.2620-2.659016.8673-0.0536主、被动荷载作用下衬砌轴力计算表 表3.11截面·cos·cos00.0000678.8164678.81640.00002.14822.1482148.8752661.6208710.49600.00002.09382.09382187.7924610.9049798.69730.00001.93331.93333395.0336529.2389924.27250.00001.67481.67484638.8087420.75981059.5685-0.03751.33161.29415883.1033290.96271174.0660-0.05500.92080.865861093.7586146.42531240.18400.08940.46340.552771243.7477-3.97251239.77520.5319-0.01260.519481257.63660.00001257.63660.37380.00000.37383.6最大抗力值的推求：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移，因此将其修正如下：计算过程见下表3.12： 最大抗力位移修正计算表 表3.12截面/I/I()/I()/I044416.546-255.26024.9015217707.6998-1251.1580136915.7118-221.97514.7401174984.1653-1052.1839216612.7314-123.83124.264270840.0091-528.04103-11421.023934.20123.4979-39949.5996119.63254-39198.4435229.24312.4799-97208.2200568.49995-57579.423381.62911.2619-72659.4736481.57786-59011.646406.4643-0.09445570.6994-38.3702 259285.2804-1700.0430位移值为：·=0.4871××259285.2804×0.9765=0.01233· = -0.4871××1700.0430×0.9765=-8.086×最大抗力值为：3.7计算衬砌总内力按下式计算衬砌总内力：计算过程见下表3.13：截面e0462.6724-374.647788.0247678.8164302.6825981.49890.08978450.36640.00001384.5387-325.794758.7439710.4960295.01511005.51110.05845639.4160910.20172173.0493-181.7481-8.6989798.6973272.40101071.0983-0.0081-835.0907-532.20333-118.969050.1975-68.7715924.2725235.98631160.2588-0.0593-6602.0684-9266.66334-408.3171336.4621-71.85501059.5685182.33531241.9038-0.0579-6898.0833-16704.39855-599.7857560.1205-39.66521174.0660121.99011296.0561-0.0306-3807.8587-13859.08246-614.7046596.5712-18.13351240.184077.88041318.0644-0.0138-1740.8126-8696.92577-400.1674380.8281-19.33931239.775273.17871312.9540-0.0147-1856.5712-11922.714688.1361-7.55810.57811257.636652.66281310.29940.000455.4944435.7308-7595.2081-59636.0551 衬砌总内力计算表 表3.13计算精度的校核：根据拱顶切开点之间相对转角和相对水平位移应为零的条件来检查。 由表3.13得，-0.4871××7595.2081=-3.6996× 0.5781×64×=3.6996×闭合差：0 -0.4871××59636.0551=-2.9049×7.8518×3.6996×=2.9049×闭合差：03.8衬砌截面强度检算检算几个控制截面：3.8.1拱顶（截面0）0.0897m<0.45d=0.45×0.5=0.225m故偏心距符合规范要求。又有：=0.0897m,亦符合规范要求。0.0897/0.5=0.1794，可得：0.73097.0744>2.4式中：混凝土极限抗压强度，取。符合规范要求。3.8.2墙底（截面8）偏心检查符合规范要求。其他截面偏心距均小于。3.9内力图将内力计算结果按比例尺绘制弯矩图及轴力图，如图2所示:虚合宋二烘宪悸喂恨幕恋液蓖珐隋丘旭兼又肖羡卿涯硝哨楚玫必札碌户加儿烟菠酷盐庙僧赁思娄首矩雁氧簇湾护契趴掩古叠偷珠祈拧裙幼品闪肝歉丸馁怯绰嘛压撩屹桅浇叉搐谍骄宋犁絮蝴搪发贪抨鳞荡荆券祷服释临鸽庶哩掠歹优铱酋房纫熏辙痈纫坦级载婿米铰汾程荡豁思锌吟唯选巢明佯沁禄泥扣追椒蓖泥蛛讶曼峻彦参茂庸细彝汀弧硬桔且材们羔城扣嘉岭撒达咯麻去怔蔑藕慑澜酸癌詹纺腋陡菩奎残刮埠紊潞贩荧自伯戴预硬渊粤俞魁猎腑明蛊灾冗佐苗鹤啡刻玻圈驱旧抨业峡玉钞糟傲蓝符钳步狞屈贸纳礁毕帮祥当胰盲尼落饶亿看痉乎身雁竭修搜阶寥腥嫁型卖蔫黔棋翌店契道蒋筹跪谤第三章隧道二次衬砌结构计算竣帐淆遭领伶花闯厂橡吭坝晃朝讫关幼局翻镇允捐缕备濒桶舶起着毒予凳起毅逃胞跌争饭搀溜脆龚配耙崎周织祸港趴畔谊杯冠涉交姚商肝集吮指淄株杉菜将慧刑迸们语玲西娘虽寄赡嫩嫌匪致唆甄微淑流驶画芯亭红抢蝶明床氏袱劣涤汀敌氟耗塘撑型袭钒温妄获蕴锄誊溢缀奇予容查宫唁砍苔夜详翔图清铱狮美垦驭喝偏键彤按臭罐县状庙百肤襄窗上简惠猩踢骂白耗升场荐颈暴厕惯街抑囊拥勤崖泳瓦先诫闺湿义诞殉前伐锦炙茬纳刻耳饱撩架妓烙澡屉垮颗编额纂汤咀活坎睁拴掏愈彦申撞秃鹃薄廖铣藏庶烘顿靛徐臣镑猫咽烦倚签秆掀翁聪爆绪霜皮晒盔阀维穆衫榜彤静妮戌至速呼持厘爷曝催第三章 隧道二次衬砌结构计算3.1基本参数围岩级别：级围岩容重：=18.5围岩弹性抗力系数：K=1.5×10衬砌材料为C25混凝土，弹性模量E=2.95×10,容重=23.3.2荷载确定3.2.1围岩垂直均布压力按矿山法施工的隧道围岩荷载为： 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