【《某隧道工程的隧道设计衬砌计算案例》6200字】

某隧道工程的隧道设计衬砌计算案例目录TOC\o"1-3"\h\u1516某隧道工程的隧道设计衬砌计算案例 1276271.1拟定衬砌尺寸 186621.2衬砌材料参数 2133271.3半拱轴线长度S及分段轴心线长△S 3241661.3.1计算半拱轴线长度S及分段轴线长度△S 314221.3.2各分块截面中心几何要素 35081.4计算位移 6188661.4.1单位位移 6172771.4.2载位移——主动荷载在基本结构中引起的位移 729521.4.3载位移 13231901.4.4墙底（弹性地基上的刚性梁）位移计算 18249751.5解力法方程 19294801.6主动荷载与被动荷载（σh=1）分别产生的衬砌内力 205121.7最大抗力值 2194701.8计算衬砌总内力 22159101.8.1总内力校核 22230941.9强度校核 23178211.10理正软件Ⅲ级围岩计算 2487181.10.1衬砌计算 24226501.10.2中间结果 291.1拟定衬砌尺寸以Ⅲ级围岩为例，拟定衬砌长度。内轮廓线半径r1=1.35m，外轮廓线半径R1=1.95m，C30级防腐钢筋混凝土拱墙厚度35cm，预留变形量10cm，C25喷射混凝土厚10cm。图1.1复合式衬砌设计图1.2衬砌材料参数围岩为Ⅲ级，根据《公路隧道设计规范》（JTGD70-2004），围岩重度取γ=23.5KN/m3,围岩的弹性系数取K=550MPa/m，弹性模量E=7.5GPa。衬砌采取C30钢筋混凝土为二次衬砌，C25喷射混凝土作为初期支护。内轮廓半径r1=1.35m，r2=1.20m外轮廓半径R1=1.95m，R2=1.80m拱轴线半径r01=1.65m，r02=1.50m拱轴线各段圆弧中心角：θ1=107.094°，θ2=54.853°1.3半拱轴线长度S及分段轴心线长△S1.3.1计算半拱轴线长度S及分段轴线长度△SS1=S2=θS=S1一共将衬砌分为10段，则分段长度：∆S=S101.3.2各分块截面中心几何要素1、与竖直夹角α1=∆αi=ααααααα∆Sα∆αθ校核：角度闭合差∆=0.012°≈02、接缝中心点坐标计算横坐标计算x=rxxxxxxxxx其中a1为小圆圆心到中轴线的横向距离x纵坐标计算yi=yyyyyyyyy其中a2是小圆圆心到中心点的竖直坐标y表1.SEQ表5.\*ARABIC4各截面中心几何要素截面α（°）sinαcosαxy112.1650.2110.9781.1910.127224.3300.4120.9112.3280.502336.4950.5950.8043.3601.108448.6600.7510.6614.2421.918560.8250.8730.4874.9332.896672.9900.9560.2931.4033.997781.1550.9960.0851.6301.173897.3200.992-0.1271.6046.3689116.1130.898-0.4401.2977.54010161.9350.310-0.9514.4158.307图1.2衬砌结构计算图示1.4计算位移1.4.1单位位移隧道的单位位移计算中：d衬砌过程中使用的C30混凝土和C25喷射混凝土的总厚度；I惯性矩，取值为bd3/12矩形惯性矩；且b取单位长度；具体计算的数值如表1.5中所示。表1.SEQ表5.\*ARABIC5单位位移截面d(m)I1/Iy/Iy2/I(y+1)2/I10.60.01851.5567.0560.89670.56320.60.01851.55627.88914.000121.33430.60.01851.55661.55668.204246.87040.60.01851.556106.556204.374473.04050.60.01851.556160.890461.937843.26860.60.01851.556222.057887.5621387.22370.60.01851.556287.3911486.6742116.99680.60.01851.556353.7812252.8773011.96890.60.01851.556418.8923158.4464051.756100.60.01851.556461.5043833.7144812.236∑611.1162107.57212372.68417143.254由上表的计算数据进行单位位移求解：δ11=δ12=δ22=δss=校核：δ11+2闭合差Δ≈0，计算结果正确。1.4.2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：Qi=q（上式中：bi——衬砌外缘相邻两截面之间的水平投影长度，由上图中衬砌结构示意图量测可得）水平压力：Ei=e(上式中：hi——衬砌外缘相邻两截面之间的竖直投影长度,由上式中衬砌结构示意图测量可得）自重力：G=d×∆S×γ（5-16）式中：d——接缝i的衬砌截面厚度。钢筋混凝土构件的重度为25kN/m3。 此段深埋隧道的竖向均布（压力）作用：q=γh（5-17）h=0.45×2s−1取S=3，γ=23.5kN/m3，ω=1+iq=γh=23.5×0.45×H/B=5/10=0.5<1.7此段水平均布围岩压力：e=（1.6表中e取25KN)单位位移计算完后计算单元集中力；表中bi衬砌外缘相邻两截面之间的水平投影长度；Hi衬砌外缘相邻两截面之间的竖直投影长度；d接缝i的衬砌截面厚度；（衬砌的厚度为C30混凝土和C25喷射混凝土的总厚度）其中bi可用bi=hi可用hi=计算结果保留你小数点后三位，具体计算结果如下表。表1.SEQ表5.\*ARABIC6单元集中作用力截面bi(m)hi(m)di(m)QEG11.2560.1340.60079.6933.35018.36921.2000.3960.60076.1409.90018.36931.0890.6400.60069.09716.00018.36940.9290.8550.60058.94521.37518.36950.7271.0320.60046.12821.80018.36960.4931.1620.60031.28029.05018.36970.2371.2400.60011.03831.00018.369801.2620.600031.55018.369901.3330.600033.32518.3691000.8650.600021.62518.369(2)外荷载在基本结构中产生的内力楔块上备集中力对下一接缝的力臂由上图衬砌结构计算图中量得，分别记为：QaQ、GaG、EaE，上部受拉记为负；表1.SEQ表5.\*ARABIC7各个分块的外力计算截面集中力(KN)力臂(m)-QaQ-EaE-GaGQEGaQaEaG179.6933.3518.3690.5650.5930.36-41.027-1.987-6.613276.149.918.3690.4760.5590.471-36.242-1.534-8.652369.0971618.3690.3660.5010.561-21.29-8.016-10.305458.94521.37518.3690.2390.4190.626-14.088-8.956-11.499546.12821.818.3690.0940.3190.662-4.336-8.2302-12.160631.2829.0518.369-0.0350.2050.6681.0948-1.955-12.270711.0383118.369-0.1810.0810.6452.722-2.511-11.8488031.5518.3690-0.0460.59201.4513-10.8749033.32518.3690-0.2120.51907.0649-9.53410021.62518.3690-0.5540.141011.980-2.590图1.3单元主动荷载示意图外荷载在基本结构中产生的内力计算原理如下弯矩：Mip0轴力：Nip0注：为相邻两截面中心点的坐标增量按下式计算：∆x=∆xi表1.SEQ表5.\*ARABIC8计算过程表截面i−1i−1∆∆−∆-∆−QM10.0000.0001.1910.1270.0000.000-53.627-53.627298.0623.351.1370.375-111.496-1.256-50.428-216.8073192.57113.251.0320.606-198.733-8.03-43.611-467.1814280.03729.250.8820.810-246.993-23.692-34.543-772.4095357.35150.6250.6910.978-546.930-49.511-24.726-1393.5766421.84876.4250.4701.101-198.269-84.144-17.130-1693.1197471.497101.4750.2271.176-107.030-124.039-11.639-1931.8278504.904136.475-0.0261.19513.128-163.088-9.423-2091.2109523.273168.025-0.3071.172160.645-196.825-2.469-2133.85910541.642201.350-0.8820.767477.728-154.4359.39-1801.176表1.9计算表截面sincosQ+GEsincosN10.2110.97898.0623.3520.691-3.27617.41520.4120.911192.57113.2579.339-12.07167.26830.5950.804280.03729.25166.622-23.517143.10540.7510.661357.35150.625268.371-33.463234.90850.8730.487421.84876.425368.273-37.219331.05460.9560.293471.497101.475450.751-30.904419.84770.9960.085504.904136.475502.884-11.6491.28480.992-0.127523.273168.025519.08721.337540.42490.898-0.440541.642201.350486.39588.594574.989100.310-0.951560.011222.975173.603212.049381.652基本结构中，主动荷载产生弯矩的校核为：M10e0M10q0M10g0M10e0从计算表中得出：M闭合差:∆=符合规范误差。（3）主动荷载位移表1.SEQ表5.\*ARABIC10主动荷载位移截面M1/Iy/I1+yMMM1-53.62751.5567.0561.127-2979.302-378.392-3357.6732-216.80751.55627.8891.502-12044.930-6046.530-18091.4843-467.18151.55661.5562.108-25954.708-28757.794-54712.5244-772.40951.556106.5562.918-42911.954-82304.813-125217.0835-1393.57651.556160.8903.896-77421.508-224212.443-301634.1966-1693.11951.556222.0574.997-94062.919-375968.926-470032.4077-1931.82751.556287.3916.173-107546.805-556339.257-663886.4268-2091.21051.556353.7817.368-116401.487-741241.489-857646.1549-2133.85951.556418.8928.540-118548.671-893856.464-1012401.64710-1801.17651.556461.5049.307-100066.134-831249.929-931311.508Σ-697938.417-3740360103主动位移的计算：∆1p=∆2p校核：∆1p+∆3p≈闭合差≈01.4.3载位移（1)单位弹性抗力及相应的摩擦力引起的位移;抗力上零点假定在接缝4，α4最大抗力值假定在接缝6，α6BH弧最大抗力值以上各截面抗力强度按下式计算:σi=所以计算可得：σσσAH弧最大抗力值以下各截面抗力强度按下式计算:σi=式中：--所考察截面外缘点到h点的垂直距离；--墙角外缘点到h点的垂直距离。由图测量可得：y7由(5-33)公式计算得：σσσσ（2）各楔块上的力各楔块上抗力集中力按下式近似计算：Ri'式中：——楔块i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。(3)抗力集中力与摩接力的合力按下式计算：Ri=式中：μ—围岩与衬砌间的摩擦系数，此处取μ＝0.3。则：Ri=将的方向线延长，使之交于竖直轴，量取夹角，将分解为水平与竖直两个分力：RRV=表1.SEQ表5.\*ARABIC11弹性抗力及摩擦力计算表截面σσ∆SRΨsincosRR40.0000.0001.26500.0000.0001.0000050.5690.2851.2650.36168.4490.9300.3670.3350.13261.0000.7851.2650.99378.7820.9810.1950.9740.19470.9300.9651.2651.22190.2660.999-0.0051.220-0.00680.7170.8241.2651.042102.2620.977-0.2131.018-0.22290.3340.5261.2650.665113.9840.914-0.4070.608-0.271100.0000.1671.2650.211131.6170.748-0.6640.158-0.140（4）计算单位抗力及其相应的摩接力在基本结构中产生的内力弯矩：（5-38）轴力：（5-39）式中：rji——力Ri至接缝中心点Aj的力臂,可由上衬砌计算图测量得。表1.SEQ表5.\*ARABIC12计算表截面R5=0.360R6=0.992R7=1.221R8=1.015R9=0.665R10=0.212Mr5iR5r5ir6iR6r6ir7iR7r7ir8iR8r8ir9iR9r9ir10iR10r10i1.000.40.170.000.000.000.000.000.000.000.000.000.00-0.176.001.620.580.630.630.000.000.000.000.000.000.000.00-1.227.002.821.011.801.790.690.840.000.000.000.000.000.00-3.678.003.991.433.002.971.872.280.710.720.000.000.000.00-7.449.001.121.844.174.143.073.751.891.920.760.500.000.00-12.1910.001.952.141.101.064.111.023.053.102.031.351.330.28-16.99表1.SEQ表5.\*ARABIC13计算表截面αsincosRRsincosN560.8250.8730.4870.3350.1320.2930.0640.229672.9900.9560.2931.3090.3261.2510.0961.155781.1550.9960.0852.5900.3202.5800.0272.553897.3200.992-0.1273.5470.0983.519-0.0133.5329116.1130.898-0.4404.156-0.1733.7320.0763.65610161.9350.310-0.9514.314-0.1401.3370.1331.204(5)单位抗力及相应摩擦力产生的载位移表1.SEQ表5.\*ARABIC14载位移计算表截面M1y1+yMMM5-0.1751.556160.8903.896-9.445-27.351-36.7966-1.2251.556222.0574.997-67.778-270.910-338.6887-3.6751.556287.3916.173-203.891-1054.725-1258.6168-7.4451.556353.7817.368-413.337-2632.131-3041.4649-12.1951.556418.8928.540-677.228-5106.294-5783.52410-16.9951.556461.5049.307-943.896-7840.953-8784.844∑-2311.574-16932.363-19247.933∆1σ=∆2σ=校核：∆∆sσ≈闭合差1.4.4墙底（弹性地基上的刚性梁）位移计算单位弯矩作用下墙底截面产生的转角:β1=(K为三级围岩的弹性抗力系数，550MPa/m)β0=单位抗力及相应摩擦力作用下的转角:βσ=1.5解力法方程衬砌矢高:f力法方程系数如下：a11=a12=a22a10=a（5-50）以上将单位抗力及相应摩擦力产生的位移乘以бh，即为被动荷载的载位移。解得：XX可得X1.6主动荷载与被动荷载（σh=1）分别产生的衬砌内力计算公式：（5-51）表1.SEQ表5.\*ARABIC15主、被动荷载产生的衬砌内力计算表（一）截面MXXMMXXM00.000369.7420.000369.7420.000-3.2370.000-3.2371-53.627369.74223.740339.8550.000-3.2370.295-2.9422-216.807369.74293.837246.7720.000-3.2371.165-2.0723-467.181369.742207.115109.6760.000-3.2372.572-0.6654-772.409369.742358.526-44.1410.000-3.2374.4521.2155-1393.576369.742541.341-482.493-0.17-3.2376.7223.3156-1693.119369.742747.147-576.230-1.22-3.2379.2774.8207-1931.827369.742966.973-599.112-3.67-3.23712.0071.1008-2091.210369.7421190.351-531.117-7.44-3.23714.7804.1039-2133.859369.7421409.430-354.687-12.19-3.23717.5002.07310-1801.176369.7421552.803121.369-16.99-3.23719.281-0.947表1.SEQ表5.\*ARABIC16主、被动荷载产生的衬砌内力计算表（二）截面NXXNNXXN117.415186.927182.815200.2300.002.3212.2702.270267.268186.927170.291237.5590.002.3212.1142.1143143.105186.927150.289293.3940.002.3211.8661.8664234.908186.927123.559358.4670.002.3211.5341.5345331.054186.92791.033422.0870.2292.3211.1301.3596419.847186.92754.770474.6171.1552.3210.6801.8357491.284186.92711.889507.1732.5532.3210.1972.7508540.424186.927-23.740516.6843.5322.321-0.2953.2379574.989186.927-82.248492.7413.6562.321-1.0212.63510381.652186.927-177.768207.8841.2042.321-2.207-1.0031.7最大抗力值首先求出最大抗力方向内的位移。考虑到接缝6的径向位移与水平方向有一定的偏离，下式可知：δδhσ=表1.SEQ表5.\*ARABIC17最大抗力位移修正计算表截面MMyyMM积分系数118880.969-163.4590.1273.87073069.351-632.5854213709.685-111.1040.5023.49547911.349-402.289236093.166-36.9631.1082.88917603.157-106.78744-2452.29867.4831.9182.079-5098.328140.29625-26801.404184.1472.8961.101-29512.750202.74646-32013.021267.7823.9970.000002∑103976.78-798.619位移值为：δδhσ=−则可得最大抗力:σh=1.8计算衬砌总内力1.8.1总内力校核按下式进行计算：（5-55）隧道中的衬砌总内力的求解基于上文中衬砌内力的计算，截面0-10，每个截面所表示的内力不同所以衬砌的总内力的求解具体数值表如下表所示；表1.SEQ表5.\*ARABIC18衬砌总内力计算表一截面MMMNNN0369.742-3.237-41.5261339.855-2.942-37.568200.2302.270491.4442246.772-2.072-19.041237.5592.114508.7603109.676-0.66524.365293.3941.866532.7794-44.1411.215111.729358.4671.534551.2615-482.4933.315-57.218422.0871.359596.4306-576.2304.82042.118474.6171.835710.0267-599.1121.10051.157507.1732.750859.9658-531.1174.103-8.751516.6843.237931.9529-354.6872.073-88.746492.7412.635830.78010121.369-0.947-0.120207.884-1.00379.211表1.SEQ表5.\*ARABIC19表二截面MM积分系数0-2529.2570.0001-2087.144-321.2331.33332-1057.827-1047.7420.666731353.593-1172.0721.333346207.2122596.1820.66675-3178.81917976.0661.333362339.916-12701.7200.666773064.29112104.3801.33338-486.18919513.4280.66679-4930.371-3661.8651.333310-6.652-40956.6230.3333Σ-1293.59533288.4241.9强度校核根据拱顶切开点的相对转角和相对水平位移应为零的条件来检查：拱顶转角为0；（5-56）式中：∆βa=闭合差：∆=误差在5%内，符合要求。1.10理正软件Ⅲ级围岩计算1.10.1衬砌计算图1.4计算简图计算基本参数见表7.1表1.20基本参数规范标准混凝土规范GB50010-2010结构重要性系数1.00衬砌断面类型拱形每段计算的分段数10计算迭代次数10抗力验证要求低表1.21衬砌参数拱半径1.350（m）半拱角90.000（°）拱脚厚度0.600（m）拱顶厚度0.600（m）支座类型固定支座围岩弹性抗力系数550.000（MN/m3）衬砌的弹性模量30000.000（MPa）表1.22荷载参数顶部山岩压力（侧）51.350（KN/m）顶部山岩压力（中）51.350（KN/m）顶部山岩压力（上）13.000（KN/m）顶部山岩压力（下）13.000（KN/m）内水压力水头0.000（m）外水压力水头0.000（m）外水压力折减系数（β）0.000顶拱灌浆压力0.000（kpa）顶拱灌浆压力作用范围角0.000（°）衬砌容重21.000（KN/m3）表1.23荷载组合参数编号荷载名称是否计算分项系数1衬砌自重√1.002顶岩压力√1.003底岩压力√1.004侧岩压力√1.005内水压力√1.006外水压力√1.007顶部灌浆压力√1.008其余灌浆压力√1.00表1.24配筋参数对称配筋：是混凝土等级：C30纵筋等级：HRB335(fy=300MPa,fyk=335MPa)拉结筋计算：计算拉结筋等级：HPB300(fy=270MPa,fyk=300MPa)拉结筋间距：100(mm)配筋计算as：65(mm)配筋调整系数：1.00裂缝计算：计算最大裂缝宽度允许值：0.40(mm)单侧拟采用纵筋直径：22(mm)砼保护层厚度：20(mm)图1.5衬砌内外侧纵筋示意图表1.25内力配筋计算分段轴向力N/kN剪力Q/kN弯矩M/kN.m切向位移U/mm法向位移V/mm0-474.705106.87673.8880.0000.0001-471.51249.5028.947-0.0240.032-456.08116.259-17.026-0.0540.0723-433.4431.848-21.026-0.0870.0894-380.9524.948-29.689-0.1200.0685-380.952-4.581-31.163-0.1450.0046-353.145-20.896-19.794-0.154-0.1037-326.899-26.7610.938-0.144-0.2348-301.499-23.46122.605-0.112-0.3619-291.544-13.48838.492-0.061-0.45210-286.7010.00044.280.000-0.485表1.26内力配筋计算分段转角W/度围岩抗力/kPa单侧纵筋(配筋率)As/mm²拉结筋面积Av/mm2截面验算00.0000.01200.0(0.22%)173.9满足10.00316.41200.0(0.22%)173.9满足20.00339.71200.0(0.22%)173.9满足30.00149.11200.0(0.22%)173.9满足4-0.00237.51200.0(0.22%)173.9满足5-0.00