【《某高速公路隧道Ⅴ级围岩支护结构受力验算计算案例》4900字】

某高速公路隧道Ⅴ级围岩支护结构受力验算计算案例目录TOC\o"1-3"\h\u9862某高速公路隧道Ⅴ级围岩支护结构受力验算计算案例 1145781.1衬砌设计 169171.2隧道Ⅴ级围岩支护结构内力计算 2249521.2.1基本资料 2240741.2.2深埋段围岩压力 3304061.2.3衬砌几何要素 5180911.3位移计算 8308171.4解力法方程 24286651.5计算主动荷载和被动荷载（）分别产生的衬砌内力 25205331.6最大抗力值的求解 27212231.7计算衬砌总内力 28141591.8内力图 291.1衬砌设计隧道衬砌结构型式均采用“新奥法”复合式衬砌，衬砌设计参数以工程类比法并结合计算分析确定，断面型式采用等截面单圆心，对于Ⅳ、Ⅴ级围岩均采用带仰拱衬砌。具体各级围岩下隧道衬砌参数设计如下表：表1.1隧道各围岩支护形式及参数围岩级别初期支护二次衬砌预留变形量喷射混凝土小导管锚杆钢筋网钢架（间距）Ⅴ级浅埋C30混凝土25cmΦ=20×5mmL=400cm环向间距80cm长度1.75mΦ25中空注浆L=450cm间距Φ=8mm@20cm×20cmH200×200mm型纵向间距70cmC30混凝土60cm抗渗等级P815cmⅤ级深埋C30混凝土25cmΦ=20×5mmL=400cm环向间距80cm长度1.75mΦ20中空注浆L=400cm间距Φ=8mm@20cm×20cmH200×200mm型纵向间距100cmC30混凝土60cm抗渗等级P815cmⅣ级C30混凝土20cmΦ20水泥砂浆锚杆，L=300cm间距Φ=8mm@20cm×20cmH200×200mm型纵向间距80cmC30混凝土50cm抗渗等级P810cm1.2隧道Ⅴ级围岩支护结构内力计算1.2.1基本资料某隧道高速公路隧道，围岩等级为V级，容重γ=20kN/m3，围岩的弹性抗力系数K=0.2×106kN/m3，衬砌材料为C30混凝土，弹性模量Eh=3.0×107kPa，容重γh=23kN/m3。图1.1Ⅴ级围岩衬砌断面图1.2.2深埋段围岩压力1.2.2.1.隧道深浅埋判断按荷载等效高度判定过程如下：根据规范公式：(1.1)Ⅴ级围岩取(1.2)则(1.3)经前述纵断面绘制，隧道埋深基本都在50米以上，故可判断该设计隧道为深埋隧道。1.2.2.2围岩竖向均布压力(1.4)式中：s——围岩类别，此处s=5；γ——围岩容重，此处γ=20kN/m3；ω——跨度影响系数，ω=1+i（B−5），跨度B=15.0m，im=5～15m时，i=0.1，此处ω=1+0.1×（15.0−5）=2.0。所以，有：q0=0.45×25-1×20×2.0=288kPa，此处超挖回填层忽略不计。1.2.2.3围岩水平均布压力根据规范取侧压力系数0.5则图1.2衬砌结构计算图示1.2.2.4荷载分担根据《公路隧道设计规范-2004》，隧道释放荷载分担比例建议值应按以下表格取值表4-2隧道释放荷载分担比例表围岩级别分担比例围岩＋初期支护二次衬砌Ⅳ0.20.8Ⅴ0.20.8按照分担比计算二衬承受的释放荷载：二衬受到的围岩水平均布压力竖向均布压力1.2.3衬砌几何要素1.衬砌几何尺寸内轮廓半径r1=9.58m，r2=1.55m，r3=11.25m，r4=1.5m；内径r1、r2所画圆曲线的终点截面与竖直轴的夹角φ1=42°，φ2=90°,φ3=94°,φ4=160°；拱顶截面厚度d0=0.60m；墙底截面厚度dn=0.60m。此处墙底截面为自内轮廓半径r2的圆心向内轮廓墙底做连线并延长至与外轮廓相交，其交点到内轮廓墙底间的连线。在此前提下，有如下三心圆变截面拱圈尺寸计算公式。外轮廓线与内轮廓线相应圆心的垂直距离为：(1.5)式中：带入数值，计算得到：m=0m外轮廓线半径：拱轴线与内轮廓线相应圆心的垂直距离为:(1.6)拱轴线半径：拱轴线各段圆弧中心角：2.半拱轴线长度S及分段轴长ΔS(1.7)分段轴线长度：(1.8)(1.9)(1.10)半拱轴线长度为：(1.11)将半拱轴线等分为12段，每段轴长为：(1.12)3.各分块接缝（截面）中心几何要素（1）与竖直轴夹角αi由于临近部分弧段均为同心圆，故每段弧对应角度相同。则有由于分割小弧段与原不同半径弧段接缝不重合，故对弧上的接缝7进行修正。第6小段弧中位于弧上的长度(1.13)(1.14)(1.15)同理对弧上的接缝10进行修正。(1.16)(1.17)对圆弧上的接缝，进行修正(1.18)(1.19)(1.20)(1.21)另一方面，(1.22)角度闭合差∆≈0。注意，因墙体底面水平，计算衬砌内力时用。（2）接缝中心点坐标计算在附图上直接量出xi、yi，整理于列表中。以后计算中，只取四位小数。计算过程如表所示。表4-3接缝中心点坐标计算点横坐标纵坐标1X11.1695Y10.06732X22.3227Y20.27333X33.4432Y30.6154X41.5152Y41.08745X55.5233Y51.68416X66.4533Y62.39647X77.2676Y73.26688X87.8305Y81.26619X98.1477Y95.391610X108.1986Y106.560611X117.8984Y117.704412X127.0218Y128.4094校核：经过CAD命令POINT/LINE进行各小段弧中线位置的校核，结果较精确。1.3位移计算（1）单位位移参照夏永旭主编的《隧道结构力学计算》中讲述的辛普森积分法：变位积分的近似计算——辛普森法，原理见图4-3所示。此方法是当截面和拱轴线以及荷载的变化规律所用的数学表达式比较复杂积分比较困难时，通常采用数值（图解）积分法来计算。辛普森积分法是用一系列抛物线来逼近附图所示的曲线而求得的定积分数值。若设为任意自变量x的函数，令、、、各为时函数的值，则此函数的近似积分公式可表达为：其中，为积分段的总长。每一分段长度为，则上式可改写为：此公式即为辛普森公式。图1.3Simpson原理示意（1）图1.4Simpson原理示意（2）利用此公式之前，首先用图解法以一定的比例绘出拱圈的断面，然后，用图解法（数值法）确定拱圈的轴线长，将其等分几段（偶数段）。利用此公式时，分段长（S——拱轴线长），分段数n必须为偶数。现用辛普森公式计算某高速公路隧道衬砌拱顶位移，取n=10，则带入公式有：将附表4-5中的数据带入上式得：用辛普生法近似计算，按计算列表进行。单位位移的计算见单位位移计算表4-4。单位位移值计算如下：(1.23)(1.24)(1.25)计算精度校核为：(1.26)闭合差Δ≈0表4-4单位位移计算表截面角度sincosxyd0001000.616.85170.11930.99291.16950.06730.6000213.70340.23690.97152.32270.27330.6000320.55510.35110.93633.44320.61500.6000427.40680.46030.88781.51521.08740.6000531.25850.56290.82655.52331.68410.6000641.11020.65750.75346.45332.39640.6000751.18920.81100.58517.26363.26680.6000868.14700.92810.37227.83051.26610.6000982.10480.99050.13748.14775.39160.60001092.55000.9990-0.04458.19866.56060.600011122.35500.8447-0.53527.89847.70440.60001290.00001.00000.00007.02188.40940.6000续表表4-4单位位移计算表截面I1/Iy/Iy^2/I(1+y)^2/I00.01855.55560.00000.000055.555610.018055.55563.73890.251663.285020.018055.555615.18331.149690.071830.018055.555631.166721.0125141.901440.018055.555660.411165.6910242.068850.018055.555693.5611157.5663400.244060.018055.5556133.1333319.0407640.862970.018055.5556181.4889592.88791011.421280.018055.5556237.00561011.08941540.656190.018055.5556299.53331611.96392269.5861100.018055.5556361.47782391.19293175.7040110.018055.5556428.02223297.65444209.2544120.018055.5556467.18893928.77824918.7116Ʃ722.22222317.911113401.278518762.3230注：1.I——截面贯性矩，，b取单位长度。2.不考虑轴力得影响。2.载位移——主动荷载在基本结构中z引起的位移（1）每一楔块上的作用力竖向力：(1.27)式中：——衬砌外缘相邻两截面之间的水平投影长度，由图4-2量得：表4-5衬砌外缘相邻两截面之间的水平投影长度（m）1.20521.18841.1431.11641.03890.95840.86020.59750.33680.0542∑bi=8.499m≈=8.5m(校核)水平压力：(1.28)式中：——衬砌外缘相邻两截面之间的竖向投影长度，由图4-2量得：表4-6衬砌外缘相邻两截面之间的竖直投影长度（m）0.06940.21220.38370.45530.61480.73400.82031.06081.1948∑hi=8.9902m≈H=9.0m(校核)自重力：(1.29)式中：——接缝i的衬砌截面厚度。注（作用在各楔块上的力均列入表4-7中，且各集中力均通过相应图形的形心。）2）外荷载在基本结构中产生的内力表中楔块上各集中力对下一接缝的力臂由图4-2中量得，分别记为、、。表4-7载位移计算表截面bhQ000000011.20520.0694277.678116.30477.99490.566221.18840.2122273.807416.304721.44540.522731.1430.3837263.347216.304741.20220.477541.11610.4553257.149416.304752.45060.425851.03890.6148239.362616.304770.82500.350260.95840.734220.815416.304781.55680.281670.86020.9203198.190116.3047106.01860.173280.59751.0608137.664016.3047122.20420.002190.33681.194877.598716.3047137.6410-0.1279100.05421.226612.487716.3047141.3043-0.27151101.29560.000016.3047149.253101200.82270.000016.304791.77500续表求和Q+G求和E000.00000.00000.000000.00000.58380.3326-9.5187-2.65910.00000-169.39910.57350.3978-9.3507-9.7244293.98287.99488-331.59340.55520.4415-9.0524-19.5153581.094832.44032-826.57720.52890.4945-8.6236-25.9368863.746776.64256-1636.19490.48960.5560-7.9828-39.37871137.2009129.09312-2729.52360.46720.5939-7.6176-50.21831392.8681199.91808-4072.98310.37190.6189-6.0637-65.61491629.9882281.47488-5616.75720.25750.6459-1.1985-78.93171841.4830390.49344-7268.56280.12470.6435-2.0332-88.57201998.4517512.6976-8785.10060.00230.6019-0.0375-85.05112092.3551650.33856-10077.7488-0.23820.46093.8838-68.79082121.1475791.64288-11009.4024-0.50570.13058.2453-12.36812137.4522940.896-11282.2379内力按下式计算，受力机理见图4-6所示。图1.5内力、计算图弯矩：(1.30)轴力：(1.31)式中:、——相邻两接缝中心点的坐标增值，按下式计算：、的计算见表1.7及表1.8。表4-8载位移截面0000000.000010.1193293.98287.994935.07217.937827.134320.2369581.094832.4403138.369631.5169106.852730.3511863.746776.6426303.268471.7631231.505340.46031137.2009129.0931523.4594111.6038408.855650.56291392.8681199.9181781.0838165.2335618.850360.65751629.9882281.47491071.7325211.3366857.396070.81101841.4830390.49341495.7900228.48181267.308280.92811998.4517512.69761851.8468190.83971661.007190.99052092.3551650.33862072.521689.33151983.1901100.99902121.1475791.64292119.0471-35.22112151.2682110.84472137.4522940.89601805.6095-503.53322309.1427121.00002153.75691035.67102153.75690.00002153.7569基本结构中，主动荷载产生弯矩的校核为：(1.31)(1.32)(1.33)另一方面，从表中得到闭合差符合（3）主动荷载位移计算过程见表。表4-9主动荷载位移计算表截面00.00001000-169.3991-169.39911.0673-9411.0692-633.3650-10041.4341-331.5934-331.59341.2733-18421.8680-5031.6965-23456.5645-826.5772-826.57721.615-45920.9918-28241.4100-74162.4018-1636.1949-1636.19492.0874-90899.7898-98841.4314-189741.2212-2729.5236-2729.52362.6841-151640.3205-255377.4637-407017.7842-4072.9831-4072.98313.3964-226277.0200-542250.2507-768527.2707-5616.7572-5616.75721.2668-312042.3189-1019379.8473-1331422.1662-7268.5628-7268.56285.2661-403809.3698-1722691.1527-2126500.5225-8785.1006-8785.10066.3916-488061.5358-2631432.5762-3119491.1120-10077.7488-10077.74887.5606-559875.3814-3673118.4273-4232993.8087-11009.4024-11009.40248.7044-611633.9581-4712272.6667-5323906.6247-11282.2379-11282.23799.4094-626791.4985-5270940.4272-5897731.9257-3544785.122-19960216.71-23505001.84(1.34)(1.34)计算精度校核：（1.35）闭合差：（4）载位移——单位弹性抗力及相应的摩擦力引起的位移1）各接缝处的抗力强度假定抗力上零点在接缝3，则：假定抗力上零点在接缝5，则：最大抗力值以上各截面抗力强度按下式计算：（1.36）查表，算得：，，最大抗力值以下各截面抗力强度按下式计算：(1.37)式中：——所考察截面外缘点到h点得垂直距离；——墙脚外缘点到h点得垂直距离。由附图量得：计算得：按比例将所求的抗力绘于下图1.6上。图1.6假定抗力图2）各楔块上抗力集中力按下式近似计算：（1.38）式中：——楔块外缘长度，可通过量取夹角，用弧长公式求得，的方向垂直于衬砌外缘，并通过楔块上抗力图形的形心。求每楔块抗力图形的形心的方法：方法一：近似图解法如图所示，先连接两个对角线与，再等分每一对角线，使，，得1、3两点，然后在每条对角线上，量取，得2、4两点，连接两条直线，其交点O即为四边形ABCD的形心。图1.7几何寻形心方法示意图方法二：使用AutoCAD精确查找形（质）心将每相邻两截面间的抗力四边形，使用PEDIT命令转化为多线，然后，使用REGION创建为面域，再使用MASSPROP分析查找形（质）心，将形（质心）心坐标利用POINT命令标注。图1.8运用CAD寻找质心3）抗力集中力与摩擦力得合力按下式计算：(1.39)式中：——围岩与衬砌间得摩擦系数，此处取。其作用方向与抗力集中力得夹角。由于摩擦阻力得方向与衬砌位移的方向相反，其方向向上。画图时，也可取切向：径向=1：5的比例求出合力的方向。的作用点即为与衬砌外缘的交点。将方向线延长，使之交于竖直轴，量取夹角：图1.9假定抗力与竖直夹角量取将分解为水平与竖直两个分力：(1.40)计算结果列入表1.10。表4-10弹性抗力及摩檫力计算表截面()()30000010040.45760.22881.20720.30290.74310.66910.22510.202751.00000.72881.20720.96480.80900.58780.78050.567160.95430.97721.20721.29360.88290.46951.14220.607370.81370.88401.25971.22110.94550.32561.15460.397680.60970.71171.21760.95030.99620.08720.94670.082890.37140.49061.24130.66770.9877-0.15640.6595-0.1045100.14890.26021.22780.35030.9272-0.37460.3248-0.13121100.07451.34160.10950.7771-0.62930.0851-0.06894）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：(1.41)轴力：(1.42)式中：——力至接缝中心点的力臂，由图1.10量得。图1.10力臂量取计算见表4-11及表4-12。表4-11计算表截面40.5857-0.177451.6510-0.50010.5201-0.501862.8043-0.84941.6284-1.57110.5483-0.709373.9960-1.21042.7925-2.69421.6755-2.16740.5505-0.672285.1134-1.54883.9543-3.81512.8448-3.68001.6786-2.049796.1582-1.86535.0512-1.87343.9789-5.14712.8460-3.4753107.0644-2.13986.0267-5.81465.0183-6.49173.9680-1.8453117.7020-2.33296.7754-6.53695.8611-7.58191.9345-6.0255续表表4-11计算表()()()()()-0.1774-1.0019-3.1298-6.74420.5255-0.4994-11.59311.6749-1.59170.5357-0.3577-17.31042.8438-2.70251.6844-1.12470.5437-0.1905-23.30903.9338-3.73832.8602-1.90981.8471-0.64700.5519-0.0604-28.8328表4-12计算表截面()()()()()427.40680.20270.09330.22510.1998-0.1065531.25850.76980.43331.00560.8312-0.3978641.11021.37710.90542.14781.6182-0.7128751.18921.77461.43913.30241.9323-0.4931868.14701.85741.72401.24911.58160.1424982.10481.75301.73641.90860.67421.06211092.55001.62181.62025.2333-0.23281.853011122.35501.55281.31185.3185-2.84622.1580（5）单位抗力及相应摩擦力产生的载位移计算见表1.13表4-13单位抗力及相应摩擦力产生的载位移计算表截面()4-0.17741.087460.41122.0874-9.8560-10.7175-20.57355-1.00191.684193.56122.6841-55.6601-93.7371-149.39726-3.12982.3964133.13343.3964-173.8770-416.6789-590.55597-6.74423.2668181.48901.2668-371.6800-1221.0047-1598.68478-11.59311.2661237.00575.2661-641.0623-2747.6341-3391.69649-17.31045.3916299.53366.3916-961.6906-5185.0509-6146.741510-23.30906.5606361.47817.5606-1291.9432-8495.6046-9790.547911-28.83287.7044428.02268.7044-1601.8233-12341.0875-13942.9108-5116.5925-30511.5153-35631.1078(1.43)(1.44)校核为：(1.45)闭合差1.墙底（弹性地基上的刚性梁）位移单位弯矩作用下的转角：(1.46)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：1.4解力法方程衬砌矢高：计算力法方程的系数为：(1.47)(1.48)(1.49)(1.50)(1.51)以上将单元抗力及相应摩擦力产生的位移乘以，即为被动荷载的载位移。求解方程为：(1.52)式中：，(1.53)其中：，以上解得的X1，X2值应代入原方程，校核计算是否正确，此处从略。1.5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：(1.54)(1.55)计算过程如表4-14、4-15所示。表4-14主、被动荷载作用下衬砌弯距计算表截面()()()0340.99960341.000-2.8500.000-2.8501340.999691.114265.714-2.8500.274-2.5762340.9996382.188391.594-2.8501.113-1.7373340.9996860.028371.450-2.8502.503-0.3464340.99961520.641225.445-2.8501.4261.4005340.99962355.077-33.447-2.8506.8553.0046340.99963351.171-380.812-2.8509.7553.7767340.99964568.355-707.403-2.85013.2983.7048340.99965965.795-961.768-2.85017.3662.9239340.99967539.715-901.386-2.85021.9481.78810340.99969171.467-562.282-2.85026.7060.54811340.999610773.979105.576-2.85031.362-0.32012340.999611759.864818.626-2.85031.232-0.383表4-15主、被动荷载作用下衬砌轴力计算表截面()()()01398.41890.00001.07071.070711388.43180.00001.04161.041621358.61300.00003.95483.954831309.38850.00003.81153.811541241.4614-0.10653.61383.507351155.8020-0.39783.36452.966761053.6336-0.71283.06712.35437818.2296-0.49312.38181.88878520.52860.14241.51521.65769192.08901.06210.55921.621310-62.21731.8530-0.18111.671911-748.38