【某高速公路隧道工程的衬砌内力计算过程案例分析3000字】

某高速公路隧道工程的衬砌内力计算过程案例分析1.1基本情况此公路隧道，结构断面尺寸如下图，内轮廓半径为5.88m，二衬厚度为0.450m。围岩为=5\*ROMANV级，重度为18.6kN/m3，围岩弹性抗力系数为1.6×105kN/m3。二衬材料为C25混凝土，弹性模量为2.8*10⁴MPa，重度为23kN/m3。考虑到初支和二衬分别承担部分荷载，二衬作为安全储备，对其围岩压力进行折减，对本隧道按照52%进行折减。图3-1围岩基本情况图1.2荷载确定：1.1.1围岩竖向均布压力围岩重度γ=18.6KN/m³跨度影响系数ω=1+i(lm-5)Lm=12.66+2*0.06=12.78m其中0.06m为一侧平均超挖量因为lm=5～15mi=0.1此处ω=1+0.1*（12.78-5）=1.778q=0.45*2⁴*18.6*1.778=238.11kpa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，对本隧道按照52%折减，取为121.82kN/m2此处超挖回填层忽略不计。1.1.2围岩水平均布压力e=0.46q=0.46*121.82=56.96kpa1.3衬砌几何要素计算：1.1.1衬砌几何尺寸内轮廓线半径r1=5.88mr2=11.8m内径r1r2所画圆曲线的终点截面与竖直轴的夹角φ1=90°φ2=110°拱顶截面厚度d0=0.45m墙底截面厚度dn=0.45m此处墙底截面为自内轮廓半径d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。外轮廓线半径：R1=r1+d0=6.33mR2=r2+d0=12.25m拱轴线半径：r′1=r1+0.5*d0=6.105mr′2=r2+0.5*d0=12.025m拱轴线各段圆弧中心角：θ1=90°θ2=14.2°1.1.2半拱轴线长度S及分段轴长ΔS分段轴线长度：S1=9.58S2=2.98半拱线长度：S=S1+S2=12.56将半拱轴线等分为8段，每段轴长为：Δs=S/8=1.571.1.3各分块接缝（截面）中心几何要素与竖直轴夹角αiα1=Δθ1=14.73°Δθ2=7.47°表3-1夹角计算表α1α2α3α4α5α6α7α814.7329.4644.1958.9271.6588.3896.72114.2Δ S1=7*ΔS-S1=1.41α7=96.72°α8=114.2°则角度闭合差为Δ～0接缝中心点坐标计算X1X2X3X4X5X61.271321852.4590790861.4851998394.2822366834.7977999934.998001538Y1Y2Y3Y4Y5Y60.1643262360.6465036981.4148386252.4188279811.592479054.858647166表3-2接缝中点计算表X7X84.9656493164.560600581Y7Y85.585087067.0496151691.4计算位移：1.4.1单位位移计算：本题采用辛普胜法进行近似值计算，得下表；表3-3单位位移计算表截面αsinαcosαxydI1/Iy/Iy2/I(1+y)2/I积分系数1/30001000.450.01131.690.000.00131.691.00114.730.250.971.270.160.450.01131.6921.071.37177.204.00219.460.490.872.460.650.450.01131.6985.6055.64358.522.00344.190.700.721.491.410.450.01131.69185.68261.81764.854.00458.920.860.524.282.410.450.01131.69317.37764.851531.272.00571.650.960.284.801.590.450.01131.69472.761697.202774.404.00688.381.000.035.004.860.450.01131.69640.003110.404522.092.00796.720.99-0.124.975.590.450.01131.69736.134114.985718.934.008114.200.91-0.414.567.050.450.01131.69928.406545.198531.661.00Σ1051.502892.2912905.4619741.541/Iy/Iy2/I(1+y)2/I积分系数1/3131.690.000.00131.691.00131.6921.071.37177.204.00131.6985.6055.64358.522.00131.69185.68261.81764.854.00131.69317.37764.851531.272.00131.69472.761697.202774.404.00131.69640.003110.404522.092.00131.69807.244948.406694.574.00131.69965.277075.419137.631.001051.502999.4014191.4321245.72（∑）1.4.2精度校核表3-4精度校核表S/Ehδ11δ12δ22δ和δss4.59064E-084.83623E-050.0001376920.000651570.0009753150.000975315由上面计算结果可知闭合差为0图3-2衬砌计算图1.4.2载位移计算：1.4.2.1主动荷载在基本结构中引起的位移每一块楔块上的作用力竖向与水平压力计算表3-5竖直/水平压力计算表b11.33h10.17b21.24h20.5b31.07h30.8b40.83h41.05b50.54h51.23b60.21h61.32b70h71.33b80h81.15总和5.22总和7.56B/25.23H7.56自重力:1.4.2.2外荷载在基本结构中产生的内力楔块上各集中力对下一接缝的力臂由图中量得，分别记为aqaeag。内力按下式计算。弯矩：如上所示计算步骤进行计算，列出以下计算表：表3-6Mp计算表截面集中力力臂QGEaqagae00000001164.6811.549.680.620.640.312151.5411.5428.480.520.590.463132.4911.5445.570.380.500.574102.7711.5459.810.220.370.65566.8611.5470.060.040.220.69626.0011.5475.19-0.140.050.6870.0011.5475.760.00-0.120.6280.0011.5465.500.00-0.270.57-Qaq-Gag-EaeΣ(G+Q)ΣExy0000000-101.76-8.71-2.970.000.001.270.16-79.47-8.00-12.98178.229.681.190.49-50.61-6.75-26.17345.3038.161.030.76-22.64-5.04-39.09491.3381.730.791.00-2.92-2.98-48.22607.64141.540.521.181.54-0.73-50.84688.04211.600.201.270.001.58-46.81727.59288.79-0.131.270.001.68-37.59741.13364.54-0.451.20-xΣ(Q+G)-YΣEM0p0000.000.00-111.43-212.08-4.74-430.71-355.66-29.00-898.90-388.15-81.73-1437.55-315.97-169.38-1977.02-137.61-271.27-2431.9394.59-366.76-2751.34331.51-437.45-2889.19表3-7载位移N0p计算表截面sinαcosαΣ(Q+G)ΣEsinαΣ(Q+G)cosαΣEN0p0010000010.260.97178.229.6846.139.3536.7720.500.87345.3038.16172.6531.05139.6030.710.71491.3381.73347.4259.21288.2140.870.50607.64141.54526.2371.77454.4650.970.26688.04211.60664.6055.28609.3261.000.00727.59288.79727.590.00727.5970.97-0.26741.13364.54715.88-94.35810.2381.000.00754.67430.05754.670.00754.671.4.2.3基本结构中，主动荷载产生的弯矩的校核：M8q=-qB/2(x8-B/4)M8e=-e/2H²M8g=-∑Gi（x8-xi+agi)M8p=M8q+M8e+M8gΔ为闭合差表3-8闭合差计算表M08qM08eiM08gM08p闭合差-1169.379296-1699.5618-51.36047171-91.53194396-2960.473040.0246721171.4.3主动荷载位移：1.4.1.1计算过程如下表表3-9主动荷载位移计算表截面M0p1/Iy/I(1+y)M0p/IM0py/IM0p(1+y)/I积分系数1/30.000.00131.690.001.000.000.000.001.001.00-111.43131.6921.071.16-14937.69-2390.03-17327.724.002.00-430.71131.6985.601.65-56719.41-36867.62-93587.032.001.00-898.90131.69185.682.41-118371.52-166906.67-285280.194.004.00-1437.55131.69317.371.41-189306.77-456229.32-645536.102.005.00-1977.02131.69472.764.59-260348.86-934652.42-1195001.294.006.00-2431.93131.69640.005.86-320517.98-1557717.39-1878235.372.007.00-2751.34131.69807.247.13-362316.07-2220997.51-2583311.584.008.00-2889.19131.69965.278.33-380469.54-2788841.75-3169311.291.00Σ-1512487.49-6730085.64-8242571.131.4.1.2精度校核：表3-10精度校核表Δ1p-0.069432905Δ2p-0.308954224Δ1p+Δ2p-0.378387129Δsp-0.378387129闭合差0.00载位移单位弹性抗力及相对应的摩擦力引起的位移载位移—单位弹性抗力及相应的摩擦力引起的位移1.5各接缝处的抗力强度抗力上零点假定在接缝3α3=44.19°最大抗力值假定在接缝5α5=71.65°最大抗力值以上各截面抗力强度按下式计算：查前表可算得σ3=0α4=0.57σ5=σh最大抗力值以下各截面抗力强度按下式计算式中：y'i--所考察截面外缘点到h点的垂直距离； y'h--墙角外缘点到h点的垂直距离。1.6各楔块上抗力集中力R′i1.6.1弹性抗力及摩擦力计算表3-11弹性抗力及摩擦力计算表截面σ（σh）（σi-1+σi)/2（σh）S外R（σh）ψksinψkcosψkRH（σh）RV（σh）30.000.000.000.000.000.000.000.000.0040.570.281.450.421.170.920.390.390.1751.000.781.451.161.390.980.181.140.2160.880.941.451.391.631.00-0.061.38-0.0970.550.711.451.051.890.95-0.311.00-0.3380.000.281.450.412.100.86-0.510.35-0.211.6.2计算单位抗力及其相应的摩擦力在基本结构中的内力：Mσ与Nσ计算如下表：表3-12M0σ计算表截面R4R5R6R7R8M0σ（σh）r4i-R4r4i（σh）r5i-R5r5i（σh）r6i-R6r6i（σh）r7i-R7r7i（σh）r8i-R8r8i（σh）40.43-0.18-0.1851.74-0.730.62-0.72-1.4562.99-1.261.93-2.240.71-0.98-4.4874.12-1.731.17-1.682.01-2.790.76-0.80-9.0085.03-2.124.26-4.951.25-4.512.06-2.180.99-0.40-14.15表3-13N0σ计算表截面αsinαcosαΣRv（σh）sinαΣRv（σh）ΣRh（σh）cosαΣRh（σh）N0σ（σh）458.920.860.520.170.140.390.20-0.06571.650.960.280.380.361.530.43-0.07688.381.000.030.290.292.910.090.207101.110.97-0.23-0.04-0.041.92-0.900.868117.840.88-0.47-0.24-0.224.27-2.011.791.6.3单位抗力及相应摩擦力产生的载位移计算见下表表3-14单位抗力与摩擦力产生的载位移计算表截面M0p（σh）1/Iy/I(1+y)M0p/IM0py/IM0p(1+y)/I积分系数1/34-0.18131.69317.371.41-21.98-57.79-81.762.005-1.45131.69472.764.59-191.53-687.60-879.134.006-4.48131.69640.005.86-590.09-2867.82-3457.912.007-9.00131.69807.247.13-1185.82-7269.07-8454.894.008-14.15131.69965.278.33-1861.12-13656.64-15519.751.00Σ-2866.88-17111.50-19978.38校核步骤如下：经校核结果如下表表3-15校核计算表Δ1σ-0.000131608Δ2σ-0.000785528Δ1σ+Δ2σ-0.000917136Δsσ-0.000917136闭合差0.00综上所述计算经检验合格。1.6.4墙底（弹性地基上的刚性梁）位移表3-16位移计算表βa0.000823045β0ap-2.377934644β0aσ-0.0116444721.7解力法方程：1.7.1衬砌失高f=7.331.7.2计算立法方程的系数为：表3-17解力法方程表a110.000871408a120.006170613a220.044872887σha10-2.447367549-0.01177608a20-17.73921517-0.086139505XpXσX1349.4846218-1.027844431X2347.262722.3360022031.8计算主动荷载和被动荷载（σh=1）分别产生时的衬砌内力计算公式如上所列计算结果见下表：表3-18主、被动荷载作用下衬砌弯矩计算表截面M0pX1pX2p·y[Mp]M0σ（σh）X1σ（σh）X2σ·y（σh）[Mσ]（σh）00.0000349.48460.0000349.48460.0000-1.02780.0000-1.02781-111.4331349.484655.5620291.61360.0000-1.02780.3738-2.65412-430.7130349.4846225.7208144.49230.0000-1.02781.5184-1.50943-898.8989349.4846489.6404-59.77390.0000-1.02781.29380.26594-1437.5483349.4846836.9032-251.1605-0.1821-1.02785.62982.41985-1977.0242349.48461246.6732-380.8664-1.4544-1.02788.38621.90406-2431.9334349.48461687.6968-396.7520-4.4810-1.027811.35301.84427-2751.3377349.48462128.7205-271.1326-9.0048-1.027814.31972.28708-2889.1906349.48462545.43575.7298-14.1480-1.027817.1229-0.0530表3-19主、被动荷载作用下衬砌轴力计算表截面N0pX2pcosα[Np]N0p（σh）X2σcosα（σh）Nσ（σh）00.0000347.2627347.26270.00002.33602.3360136.7740336.8448371.61880.00002.25642.25642139.5996302.1186441.71820.00002.02302.02303288.2149250.0292538.24400.00001.65181.65184454.4624180.5766635.0390-0.05861.16801.10945609.316297.2336706.5497-0.06780.60460.53686727.587910.4179738.00580.20030.00000.20037810.2267-79.8704730.35630.8633-0.60460.25878754.6704-161.2135591.45691.79020.00001.79021.9最大抗力值求解：根据公式计算过程计算结果如下表所示位移值及最大抗力值如下：表3-20最大抗力位移修正计算表截面Mp/IMσ/I（σh）Risin(α5-αi)Mp/I·Risin(α5-αi)Mσ/IRisin(α5-αi)（σh）积分系数1/3046022.6662-398.72854.7978220807.5478-1911.01951138401.7898-349.50904.2822164445.5530-1496.68034219027.7980-198.77441.485266315.6784-692.768523-7871.458235.01812.4591-19356.538386.112344-33074.6382318.66191.2713-42048.5102405.121925-50155.2468514.10240.00000.00000.00004Σ271901.3418-2601.7872最大抗力值为：表3-21最大抗力值计算表δhp0.0125δhσ-0.0001σh99.30971.10计算衬砌总内力表3-22衬砌总内力计算表截面MpMσ[M]NpNσ[N]e0349.4846-300.694348.7903347.2627231.9877579.25040.08421291.6136-261.576328.0373371.6188224.0829597.70170.04692144.4923-149.9023-5.4100441.7182200.9072642.6254-0.00843-59.773926.4083-31.3656538.2440164.0400702.2841-0.04754-251.1605240.3135-10.8471635.0390110.1739745.2129-0.01465-380.8664387.70166.8352706.549751.3102759.86000.00906-396