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1、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=1.510衬砌材料为C25混凝土，弹性模量E=2.9510,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=0.452 =0.4521+i(B-5) =0.45218.51+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=0.4170=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
2、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=0.487110 （）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.
3、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 2066.485
4、3 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
5、，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： =0.487110864.0000=4.208510 =0.4871102643.1776=1.287510 =0.48711014338.9160=6.984510 计算精度校核为： +2+=(0.42085+21.2875+6.9845) 10=9.980310 =0.48711020489.2712=9.980310 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
6、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
7、.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
8、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 1.018
9、0 761.6385100.9770-2514.811263.7037949.2258171.12880.7565 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s
10、incos (Q+G)Esin(Q+G)cosE00.00001.00000.00000.00000.00000.00000.000010.22370.9747268.225211.403659.989911.114748.875220.43600.9000523.700445.0364228.323240.5308187.792430.62620.7796754.321699.1916472.368377.3347395.033640.78470.6198949.2258171.1288744.8817106.0731638.808750.90350.42861099.4710257.203
11、2993.3489110.2456883.103360.97650.21571198.1212353.05601169.915276.15661093.758671.0000-0.00591241.1134453.78441241.0921-2.65561243.747781.00000.00001257.6366550.91561257.63660.00001257.6366（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/Iy/I(1+y)/I00.000096.00000.00000.00000.00000.00001-187.694696.00001
12、5.4944-18018.6863-2908.2160-20926.90222-722.232796.000061.1808-69334.3422-44186.7763-113521.11843-1534.428096.0000134.7456-147305.0868-206757.4199-354062.50674-2514.811296.0000232.4736-241421.8711-584627.2030-826049.07405-3533.078096.0000349.4016-339175.4891-1234463.1100-1573638.59906-4468.675696.00
13、00479.6064-428992.8602-2143205.4300-2572198.29027-5222.130596.0000616.5024-501324.5258-3219455.9725-3720780.49838-5784.466596.0000753.7728-555308.7812-4360173.4886-4915482.2698-2300881.6426-11795777.616-14096659.259 则：= = -0.48712300881.6426 = -0.1121 = = -0.487111795777.616 = -0.5746计算精度校核： += -0.1
14、121-0.5746=-0.6867 =-0.487114096659.259=-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
15、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 0.51
16、82 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
17、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 ()()()()()()40.51150.1552-0.155251.94520.59020.67620.5942-1.184463.34611.01522.10981.85390.72580.9702-3.839374.64331.40883.50243.07762.15922.88620.80071.0612-8.433885.80181.76034.80584.22293.56164.76082.2362.96
18、361.0230.5545-14.2620 计算表 表3.8截面（）sin cos ()sin()()cos()()451.69530.78470.61980.15720.12340.25950.1608-0.0375564.61920.90350.42860.45450.41071.08640.4657-0.0550677.54300.97650.21570.62440.60972.41220.52030.0894790.33531.0000-0.00590.51010.51013.7327-0.02180.5319890.00001.00000.00000.37380.37384.2573
19、0.00000.3738（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)/I4-0.155296.0000232.4736-14.8982-36.0774-50.97555-1.184496.0000349.4016-113.6977-413.8140-527.51176-3.839396.0000479.6064-368.5694-1841.3360-2209.90547-8.433896.0000616.5024-809.6435-5199.4496-6009.09318-14.262096.0
20、000753.7728-1369.1495-10750.2878-12119.4373 -2675.9582-18240.9648-20916.9231 = =-0.48712675.9582 =-1.3035 = =-0.487118240.9648=-8.8852校核为： += -（1.3035+8.8852）=-1.0189 = -0.487120916.9231 =-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： =-5784.466564=-3.7021单位抗力及相应摩擦力作用下的转角： =-14.2620
21、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：=4.208510+64=6.82085=1.287510+7.851864=5.153910 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.
22、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
23、 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coscos00.0000678.8164678.81640.00002.14822.1482148.8752661.6208710.49600.00002.09382.09382187.7924610
24、.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
25、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()/I044416.546-255.26024.9015217707.6998-1251.1580136915.7118-221.97514.7401174984.1653-1052.1839216612.7314-123.83124.264270840.0091-528.04103-11421.023934.20123.4979-39949.5996119.63254-39198.4435229.2
26、4312.4799-97208.2200568.49995-57579.423381.62911.2619-72659.4736481.57786-59011.646406.4643-0.09445570.6994-38.3702 259285.2804-1700.0430位移值为：=0.4871259285.28040.9765=0.01233 = -0.48711700.04300.9765=-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.
27、08978450.36640.00001384.5387-325.794758.7439710.4960295.01511005.51110.05845639.4160910.20172173.0493-181.7481-8.6989798.6973272.40101071.0983-0.0081-835.0907-532.20333-118.969050.1975-68.7715924.2725235.98631160.2588-0.0593-6602.0684-9266.66334-408.3171336.4621-71.85501059.5685182.33531241.9038-0.0
28、579-6898.0833-16704.39855-599.7857560.1205-39.66521174.0660121.99011296.0561-0.0306-3807.8587-13859.08246-614.7046596.5712-18.13351240.184077.88041318.0644-0.0138-1740.8126-8696.92577-400.1674380.8281-19.33931239.775273.17871312.9540-0.0147-1856.5712-11922.714688.1361-7.55810.57811257.636652.6628131
29、0.29940.000455.4944435.7308-7595.2081-59636.0551 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，-0.48717595.2081=-3.6996 0.578164=3.6996闭合差：0 -0.487159636.0551=-2.90497.85183.6996=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）0.0897m2.4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:
