某公路隧道工程的隧道支護(hù)結(jié)構(gòu)設(shè)計(jì)計(jì)算案例目錄TOC\o"1-3"\h\u21859某公路隧道工程的隧道支護(hù)結(jié)構(gòu)設(shè)計(jì)計(jì)算案例 1125361.1深淺埋判定 1141361.1.1隧道深淺埋判定 1188611.1.2圍巖壓力的計(jì)算 246401.2初期支護(hù)設(shè)計(jì) 5110131.2.1軸對(duì)稱條件下噴層上圍巖壓力的計(jì)算 5298371.2.2錨噴支護(hù)的計(jì)算與設(shè)計(jì) 8231701.2.3Ⅳ級(jí)圍巖錨噴支護(hù)驗(yàn)算 990651.2.4Ⅴ級(jí)圍巖錨噴支護(hù)驗(yàn)算 12207541.3二次襯砌結(jié)構(gòu)設(shè)計(jì) 1612641.3.1Ⅲ級(jí)圍巖襯砌驗(yàn)算 16289181.3.2Ⅳ級(jí)圍巖襯砌驗(yàn)算 2370211.3.3Ⅴ級(jí)圍巖襯砌驗(yàn)算 631.1深淺埋判定1.1.1隧道深淺埋判定左幅隧道：全長(zhǎng)1766m；隧道平面位于曲線～直線上；所在路段縱坡為-1.200%；最大埋深約為229m。右輻隧道：全長(zhǎng)1754m；隧道平面位于曲線～直線上；所在路段縱坡為-1.200%；最大埋深約為219m。右輻隧道深淺埋判定（1）Ⅲ級(jí)圍巖深淺埋判定均布豎直荷載：式中：——圍巖級(jí)別——；Bi——B每增加1m時(shí)的圍巖壓力增減率；當(dāng)B小于5m時(shí)，i取0.2；當(dāng)B＞5m時(shí),取i=0.1淺埋隧道分界深度：所以，Ⅲ級(jí)圍巖均為深埋。（2）Ⅳ級(jí)圍巖深淺埋判定均布豎直荷載：所以，Ⅳ圍巖均為深埋。（3）Ⅴ級(jí)圍巖深淺埋判定均布垂直荷載:所以Ⅴ級(jí)圍巖均為深埋1.1.2圍巖壓力的計(jì)算（1）深埋隧道拱部豎向圍巖壓力可按經(jīng)驗(yàn)公式計(jì)算：式中：q--垂直均布?jí)毫Γ↘N/m2）；h--荷載等效高度（m）；γ--圍巖重度（KN/m3）；S--圍巖級(jí)別；ω--寬度影響系數(shù)；Bt--隧道最大開(kāi)挖跨度，應(yīng)考慮超挖影響（m）。(2）Ⅲ級(jí)圍巖水平圍巖壓力荷載計(jì)算按均布荷載算式中：——。（3）Ⅳ、Ⅴ級(jí)圍巖水平圍巖壓力計(jì)算；按梯形荷載拱頂水平壓力按：邊墻底部水平壓力可按下式計(jì)算：式中——表1.1圍巖側(cè)壓力系數(shù)圍巖級(jí)別ⅢⅣⅤ側(cè)壓力系數(shù)<0.150.15~0.300.30~0.50（4）支護(hù)參數(shù)式中:1.Ⅲ級(jí)圍巖（1）支護(hù)參數(shù)（2）豎向圍巖壓力水平圍巖壓力2.Ⅳ級(jí)圍巖(1)支護(hù)參數(shù)(2)豎向圍巖壓力（3）水平圍巖壓力（4）邊墻底部水平圍巖壓力3.Ⅴ級(jí)圍巖(1)支護(hù)參數(shù)（2）豎向圍巖壓力（3）水平圍巖壓力（4）邊墻底部水平圍巖壓力

1.2初期支護(hù)設(shè)計(jì)對(duì)隧道初期支護(hù)設(shè)計(jì)進(jìn)行驗(yàn)算，詳細(xì)過(guò)程如下：1.2.1軸對(duì)稱條件下噴層上圍巖壓力的計(jì)算圖1.2點(diǎn)錨式錨桿的分布力點(diǎn)錨式錨桿可以視為錨桿的兩端作用有集中力，如圖1.2假設(shè)集中力分布于錨固區(qū)內(nèi)外端2個(gè)同心圓上，由此在洞壁上產(chǎn)生支護(hù)的附加阻力，而錨桿內(nèi)端分布力為（為錨桿加固圈的內(nèi)半徑，為錨桿加固區(qū)的外半徑），為初始豎向地應(yīng)力，，其中H為隧道埋深A(yù)DDINEN.CITE<EndNote><Cite><Author>蘇永華</Author><Year>2020</Year><RecNum>128</RecNum><DisplayText><styleface="superscript">[7]</style></DisplayText><record><rec-number>128</rec-number><foreign-keys><keyapp="EN"db-id="5wztzpre9tvfvbexvam50tf7v2prpfwrde0a"timestamp="1621577006">128</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>蘇永華,</author><author>肖峰,湖南大學(xué)巖土工程研究所</author></authors></contributors><titles><title>基于突變理論的隧道自穩(wěn)能力量化研究</title><secondary-title>公路工程</secondary-title></titles><periodical><full-title>公路工程</full-title></periodical><pages>63-67+89%@1674-0610%L43-1481/U%WCNKI</pages><volume>45</volume><number>05</number><keywords><keyword>強(qiáng)度折減法</keyword><keyword>突變理論</keyword><keyword>穩(wěn)定性分析</keyword><keyword>失穩(wěn)判據(jù)</keyword><keyword>深埋隧道</keyword></keywords><dates><year>2020</year></dates><urls></urls></record></Cite></EndNote>[7]REF_Ref6724\r\h錯(cuò)誤!未找到引用源。。平衡方程及塑性方程為：式中、——加固后圍巖的、值，一般可取，按c和由錨桿抗剪力折算而得。得由時(shí)，得積分常數(shù)代入有令錨桿內(nèi)端點(diǎn)的徑向應(yīng)力為并位于塑性區(qū)內(nèi)，則彈塑性界面上有式中——有錨桿時(shí)的塑性區(qū)半徑。由此得此外，考慮錨桿內(nèi)端的分布力，則有錨桿時(shí)的塑性區(qū)半徑當(dāng)錨桿內(nèi)端位于塑性區(qū)內(nèi)，且在松動(dòng)區(qū)之外時(shí)，有錨桿時(shí)的最大松動(dòng)區(qū)半徑為當(dāng)錨桿內(nèi)端位于松動(dòng)區(qū)時(shí)，則有有錨桿時(shí)的洞壁位移及圍巖位移式中對(duì)于點(diǎn)錨式錨桿，可按錨桿與圍巖共同變形理論錨桿軸力式中——————、——圖1.3加錨區(qū)與非加錨區(qū)洞壁位移比較因?yàn)殄^桿是集中加載，其圍巖變位是不均勻的，如圖1.2所示，因此在計(jì)算錨桿拉力時(shí)應(yīng)乘以一個(gè)小于1的系數(shù)，即式子中的k和巖質(zhì)、錨桿間距有關(guān)系，當(dāng)巖石較好時(shí)可以取1，巖質(zhì)較差時(shí)取4/5，1/2。由Q即能算出，即式中、——錨桿的橫向和縱向間距。當(dāng)錨桿有預(yù)拉力作用時(shí)，則顯然，上述式子要求錨桿拉力小于錨桿錨固力。計(jì)算時(shí)，需要通過(guò)試求出、及，并按下式求出洞壁位移及錨桿拉力1.2.2錨噴支護(hù)的計(jì)算與設(shè)計(jì)1.為讓錨桿充分發(fā)揮作用，應(yīng)使錨桿應(yīng)力盡量接近鋼材設(shè)計(jì)抗拉強(qiáng)度，即錨桿的抗拉安全系數(shù)K1應(yīng)在1-1.5之間。為防止錨桿和圍巖一起塌落，錨桿長(zhǎng)度必須大于松動(dòng)區(qū)厚度，而且有一定安全儲(chǔ)備，即要求錨桿間距、應(yīng)滿足下列要求：，此外，、的合理選擇還應(yīng)是噴層具有適當(dāng)?shù)暮穸?，這樣才能充分發(fā)揮噴層的作用。2.噴層的計(jì)算與設(shè)計(jì)，噴層除作為結(jié)構(gòu)要起到承載作用外，還要求向圍巖提供足夠的支護(hù)助力，以維持圍巖的穩(wěn)定。為了驗(yàn)證圍巖的穩(wěn)定，需要計(jì)算最小支護(hù)助力以及圍巖穩(wěn)定安全系數(shù)。松動(dòng)區(qū)內(nèi)滑移體的重力為即能求出，由此得要求值應(yīng)在2～4.5之間。作為噴層強(qiáng)度校核，要求噴層內(nèi)壁切向應(yīng)力小于噴混凝土抗壓強(qiáng)度。有式中，其中為混凝土內(nèi)壁半徑；——由此可算噴層厚度式中K3——噴層的安全系數(shù)1.2.3Ⅳ級(jí)圍巖錨噴支護(hù)驗(yàn)算1.計(jì)算參數(shù)圍巖參數(shù)如表1.2。表1.2圍巖參數(shù)取值圍巖級(jí)別重度γ（KN/m3）彈性抗力系數(shù)K(Mpa/m)變形模量E(Gpa)泊松比μ內(nèi)摩擦角(゜)黏聚力c(Mpa)Ⅲ24～25850～120010.7～20.00.25～0.2644～501.1～1.5Ⅳ21～23200～5001.3～7.00.30～0.3127～390.2～0.7Ⅴ18～20100～2001～20.35～0.4520～270.05～0.12（1）圍巖參數(shù)：重度，粘聚力，內(nèi)摩擦角，變形模量，泊松比。初始應(yīng)力場(chǎng)支護(hù)參數(shù)則有rc=9.89m錨桿間距所以。采用錨桿，單根錨桿截面面積,彈性模量=2.0×105MPa,桿體極限拉力值=180kN,抗剪度,抗拉強(qiáng)度=188,安全系數(shù),錨桿間距=0.5m,=1.0m,噴層采用C25混凝土=0.2,=11.9MPa,噴層厚度=0.15m,剪切模量，彈性模量；無(wú)錨桿時(shí)，圍巖位移值按經(jīng)驗(yàn)確定，取預(yù)留變形量的0.3倍；錨固前毛洞四周位移=(0.5~0.8)，即=0.03m,=0.8=0.024m，。2.確定圍巖塑性區(qū)加錨后的、值3.計(jì)算、、、及由于噴層厚度因此采用薄壁圓筒公式計(jì)算噴混凝土結(jié)構(gòu)的剛度。聯(lián)立解得=8.695m,,,,滿足要求。4.驗(yàn)算錨桿長(zhǎng)度1.計(jì)算圍巖穩(wěn)定性安全度 解之得滿足要求。6.驗(yàn)算噴層強(qiáng)度7.驗(yàn)算噴層厚度滿足要求。1.2.4Ⅴ級(jí)圍巖錨噴支護(hù)驗(yàn)算計(jì)算參數(shù)（1）圍巖參數(shù)重度，粘聚力，內(nèi)摩擦角，變形模量，泊松比。（2）初始應(yīng)力場(chǎng)（3）支護(hù)參數(shù)則，。（4）錨桿間距所以采用錨桿，單根錨桿截面面積,彈性模量=2.0×105,桿體極限拉力值=180kN,抗剪強(qiáng)度,抗拉強(qiáng)度=188MPa,安全系數(shù)錨桿間距=0.5m,=1.0m,噴層采用C30混凝土=0.167,=14.3MPa,噴層厚度=0.15m,剪切模量Mpa，彈性模量Mpa無(wú)錨桿時(shí)，圍巖位移值按經(jīng)驗(yàn)確定，取預(yù)留變形量的0.3倍；錨固前毛洞四周位移=(0.5~0.8)，即=0.04m,=0.8=0.032m。2.確定圍巖塑性區(qū)加錨后的。3.計(jì)算因?yàn)閲妼雍穸?0.21m<0.04=0.2508m。所以采用薄壁圓筒公式計(jì)算噴混凝土結(jié)構(gòu)的剛度。解之得、、、滿足要求。4.驗(yàn)算錨桿長(zhǎng)度1.計(jì)算圍巖穩(wěn)定性安全度解之得滿足要求。6.驗(yàn)算噴層強(qiáng)度7.驗(yàn)算噴層厚度滿足要求。

1.3二次襯砌結(jié)構(gòu)設(shè)計(jì)1.3.1Ⅲ級(jí)圍巖襯砌驗(yàn)算1.設(shè)計(jì)基本資料（1）巖體特征當(dāng)巖體等級(jí)為Ⅲ級(jí)時(shí)，Ⅲ級(jí)圍巖的彈性抗力系數(shù)，計(jì)算摩擦角為，巖體的重度，變形模量，泊松比，粘聚力，內(nèi)摩察角。（2）襯砌材料第二次襯砌選用C30防水混凝土；重度，彈性模量，混凝土襯砌軸心抗壓強(qiáng)度標(biāo)準(zhǔn)值：，混凝土軸心抗拉強(qiáng)度標(biāo)準(zhǔn)值：（3）圍巖壓力的計(jì)算e=0.05m，γ=24KN/m3，d1=0.12m，d2=0.35m，λ=0.15a支護(hù)參數(shù)Bt=2R1+2d1+2d2+e=2×7.08+2×0.12+2×0.35+0.05=11.15(m)b豎向圍巖壓力ω=1+i（Bt-5）=1+0.1×(11.15-5)=2.015h=0.45×2s-1×ω=0.45×4×2.015=3.627mq=γh=24×3.627=87.048kpac水平圍巖壓力e=λq=0.15×87.048=13.0572kpa3.內(nèi)力數(shù)值計(jì)算分析用ANSYS進(jìn)行計(jì)算。單元實(shí)常數(shù)、，；材料屬性，。單元網(wǎng)格劃分：拱部O1圓弧劃分為15個(gè)、邊墻每段劃分為17個(gè)，共64個(gè)單元。單元?jiǎng)澐忠?jiàn)圖1.4圖1.4ansys網(wǎng)格劃分圖對(duì)節(jié)點(diǎn)施加荷載如圖1.5所示圖1.5ansys節(jié)點(diǎn)施加荷載圖對(duì)于拱形結(jié)構(gòu)，需要約束墻底的水平位移。同時(shí)為避免結(jié)構(gòu)整體沉降過(guò)大，使彈簧全部受拉，也要對(duì)墻底的垂直位移進(jìn)行約束，本模型選取節(jié)點(diǎn)46、48進(jìn)行約束。地層彈簧單元，選擇單元實(shí)常數(shù)K=800000000，長(zhǎng)度1m。慣性荷載（重力加速度）Gravity取9.8，施加徑向彈簧如圖1.6所示圖1.6ansys徑向施加彈簧圖查看求解后的彈簧受力表，分批多次除去受拉彈簧（正值受拉，負(fù)值受壓），在重新計(jì)算，保證彈簧全部處于受壓狀態(tài)。確定抗力分布范圍，最終計(jì)算模型見(jiàn)圖1.7圖1.7采用生死單元法殺死受拉彈簧后的變形軸力結(jié)果圖如圖1.8所示圖1.8ansys軸力圖剪力結(jié)果圖如圖1.9所示圖1.9ansys剪力圖彎矩結(jié)果圖如圖1.10所示圖1.10ansys彎矩圖如圖1.7所示，最大變形出現(xiàn)在拱頂位置處。殺死受拉彈簧后的變形值為：0.00218957m。如圖1.8所示，正值受拉，負(fù)值受壓，圖中的軸力值全為負(fù)值，全部受壓。其中最大值出現(xiàn)在邊墻底角處，最小值出現(xiàn)在拱頂處，關(guān)于軸力分布關(guān)于隧道中線軸對(duì)稱。如圖1.9所示，剪力值最大值出現(xiàn)在距拱頂大約45°兩側(cè)，拱頂處剪力為零，最小負(fù)值出現(xiàn)在拱墻處，關(guān)于隧道中線反對(duì)稱。如圖1.10所示，最大正彎矩出現(xiàn)在距離拱頂45°兩側(cè)，最大負(fù)彎矩出現(xiàn)在拱頂位置，關(guān)于隧道中線軸對(duì)稱。ANSYS分析結(jié)果見(jiàn)表1.11。表1.11單元內(nèi)力數(shù)值分析結(jié)果STATCURRENTCURRENTCURRENTCURRENTCURRENTCURRENTELEMNINJQIQJMIMJ10.10578E+0080.10575E+0080.11377E+0060.11734E+0060.20103E+0070.20825E+00720.10309E+0080.10306E+0080.12533E+0060.12158E+0060.20825E+0070.20054E+00730.10033E+0080.10030E+0080.32196E+0060.31805E+0060.20054E+0070.18056E+00740.97562E+0070.97534E+0070.47660E+0060.47254E+0060.18056E+0070.15093E+00750.94831E+0070.94805E+0070.59029E+0060.58609E+0060.15093E+0070.11421E+00760.92186E+0070.92162E+0070.66462E+0060.66030E+0060.11421E+0070.72850E+00670.89672E+0070.89651E+0070.70170E+0060.69725E+0060.72850E+0060.29181E+00680.87332E+0070.87314E+0070.70412E+0060.69957E+0060.29181E+0060.14637E+00690.85206E+0070.85190E+0070.67494E+0060.67030E+0060.14637E+0060.56630E+006100.83329E+0070.83315E+0070.61762E+0060.61290E+0060.56630E+0060.95042E+006110.81732E+0070.81720E+0070.53600E+0060.53121E+0060.95042E+0060.12836E+007120.80440E+0070.80431E+0070.43422E+0060.42938E+0060.12836E+0070.15531E+007130.79476E+0070.79469E+0070.31669E+0060.31181E+0060.15531E+0070.17493E+007140.78854E+0070.78850E+0070.18802E+0060.18311E+0060.17493E+0070.18652E+007150.78586E+0070.78584E+00752978.48051.0.18652E+0070.18967E+007160.78594E+0070.78595E+00783818.88741.0.18967E+0070.18429E+007170.78878E+0070.78882E+0070.21878E+0060.22369E+0060.18429E+0070.17047E+007180.79516E+0070.79523E+0070.34727E+0060.35216E+0060.17047E+0070.14864E+007190.80497E+0070.80506E+0070.46455E+0060.46939E+0060.14864E+0070.11949E+007200.81804E+0070.81815E+0070.56600E+0060.57079E+0060.11949E+0070.84000E+006210.83417E+0070.83431E+0070.64720E+0060.65192E+0060.84000E+0060.43447E+006220.85309E+0070.85326E+0070.70402E+0060.70866E+0060.43447E+0066517.4230.87450E+0070.87469E+0070.73262E+0060.73717E+0066517.40.46533E+006240.89805E+0070.89826E+0070.72954E+0060.73399E+0060.46533E+0060.92218E+006250.92333E+0070.92356E+0070.69173E+0060.69606E+0060.92218E+0060.13554E+007260.94992E+0070.95018E+0070.61660E+0060.62080E+0060.13554E+0070.17417E+007270.97737E+0070.97765E+0070.50203E+0060.50608E+0060.17417E+0070.20564E+007280.10052E+00810054901.0.34643E+0060.35034E+0060.20564E+0070.22739E+0072910328843.0.10332E+0080.14879E+0060.15253E+0060.22739E+0070.23679E+007300.10599E+0080.10603E+00891392.87819.0.23679E+0070.23120E+007310.10845E+0080.10848E+0080.53082E+0060.52762E+0060.23120E+0070.19951E+007320.11034E+0080.11038E+0080.11798E+0070.11769E+0070.19951E+0070.12895E+007330.11160E+0080.11164E+0080.18823E+0070.18797E+0070.12895E+0070.16323E+006340.11213E+0080.11217E+0080.26309E+0070.26286E+0070.16323E+0060.14114E+007350.11182E+0080.11187E+0080.34162E+0070.34143E+0070.14114E+0070.34563E+007360.10217E+0080.10221E+0080.19479E+0070.19495E+0070.34563E+0070.22895E+007370.10376E+0080.10380E+0080.23635E+0070.23647E+0070.22895E+0070.87393E+006380.10665E+0080.10670E+0080.13183E+0070.13192E+0070.87393E+00684314.390.10819E+0080.10823E+0080.37886E+0060.37936E+00684314.0.14268E+0064010856601.0.10861E+0080.15214E+0060.15202E+0060.14268E+00651624.410.10850E+0080.10855E+0080.40915E+0060.40940E+00651624.0.19344E+006420.10858E+0080.10863E+0080.43360E+0060.43423E+0060.19344E+0060.45325E+006430.10960E+0080.10965E+00880672.79669.0.45325E+0060.40525E+006440.11339E+0080.11343E+0080.17543E+0070.17530E+0070.40525E+0060.64478E+006450.12943E+0080.12949E+0080.25633E+0070.25600E+0070.64478E+0060.27142E+007460.12770E+0080.12774E+0080.33571E+0070.33625E+0070.27142E+0070.99965E470.12731E+0080.12727E+0080.32630E+0070.32576E+0070.14318E008480.12867E+0080.12861E+0080.26307E+0070.26341E+0070.26338E+0070.50721E+006490.11943E+0080.11939E+0080.40078E+0060.40215E+0060.50721E+0060.26683E+006500.11868E+0080.11864E+0080.13524E+0070.13534E+0070.26683E+0060.54327E+006510.11815E+0080.11811E+0080.11648E+0060.11585E+0060.54327E+0060.47371E+006520.11834E+0080.11829E+0080.46290E+0060.46264E+0060.47371E+0060.19662E+006530.11854E+0080.11849E+0080.35959E+0060.35971E+0060.19662E+00618730.540.11833E+0080.11829E+0080.11451E+0060.11501E+00618730.87441.550.11746E+0080.11742E+0080.28320E+0060.28233E+00687441.81866.560.11579E+0080.11575E+0080.92841E+0060.92717E+00681866.0.63740E+006570.11324E+0080.11320E+0080.15994E+0070.15978E+0070.63740E+0060.15946E+007580.11024E+0080.11020E+0080.11724E+0070.11705E+0070.15946E+0070.22960E+007590.10861E+00810856888.0.28319E+0070.28342E+0070.22960E+0070.59972E+006600.10826E+0080.10822E+0080.21108E+0070.21134E+0070.59972E+0060.66493E+006610.10719E+0080.10715E+0080.14343E+0070.14372E+0070.66493E+0060.15246E+007620.10551E+0080.10547E+0080.80960E+0060.81280E+0060.15246E+0070.20103E+007

1.3.2Ⅳ級(jí)圍巖襯砌驗(yàn)算對(duì)于Ⅳ級(jí)圍巖，在根據(jù)經(jīng)驗(yàn)選定支護(hù)參數(shù)后，仍需進(jìn)行驗(yàn)算。Ⅳ級(jí)圍巖的內(nèi)力求解，參考地下結(jié)構(gòu)設(shè)計(jì)，先采用手算法，然后用ansys進(jìn)行驗(yàn)證。計(jì)算參數(shù)（1）巖體特征計(jì)算摩察角，圍巖的彈性抗力系數(shù)，基底圍巖彈性反力系數(shù)：，巖體重度，變形模量，泊松比，粘聚力，內(nèi)摩察角。（2）襯砌材料二襯選用C30防水混凝土；重度，彈性模量，混凝土襯砌軸心抗壓強(qiáng)度標(biāo)準(zhǔn)值：，混凝土軸心抗拉強(qiáng)度標(biāo)準(zhǔn)值：。二襯設(shè)計(jì)如圖1.13所示。圖1.13Ⅳ級(jí)圍巖襯砌支護(hù)設(shè)計(jì)（單位：cm）（3）結(jié)構(gòu)尺寸,，，斷面加寬2.主動(dòng)荷載隧道處于Ⅳ級(jí)圍巖中，為深埋隧道，圍巖壓力為松散荷載。作用在其結(jié)構(gòu)上的荷載形式為：垂直均布荷載q、水平均布側(cè)向荷載e，側(cè)壓力系數(shù)0.25。3繪制分塊圖因結(jié)構(gòu)左右相同，荷載左右也形同，故取左半部，及半跨結(jié)構(gòu)，見(jiàn)圖1.14圖1.14分塊圖（4）計(jì)算半拱軸線長(zhǎng)度s和分塊軸線長(zhǎng)度a.計(jì)算半拱軸線長(zhǎng)度式中為各圓弧軸線半徑半拱軸線長(zhǎng)度b.計(jì)算分塊軸線長(zhǎng)度分塊長(zhǎng)度（5）計(jì)算各分段截面中心的幾何要素a.求各截面、豎直軸的夾角角度校核：

（2）各截面的中心坐標(biāo)（單位：cm）坐標(biāo)校核曲墻拱結(jié)構(gòu)幾何要素計(jì)算過(guò)程，見(jiàn)表1.15表1.15曲墻拱幾何要素截面φisinφicosφixiyi000100110.8390.1880498930.982159477151.380163714.3616212221.6790.3694061880.929268028297.37198156.93923715332.5180.5375645410.843222607432.7394556126.2058017443.3570.6865420290.72709012552.6663335219.6924536566.8440.9194375940.393235948422.9412932279.1114638681.8130.9973310690.073011912458.7722916426.41452067104.7820.966903592-0.255142009789.7756521718.36532418123.7510.831459916-0.555584745727.4715612846.56898266.計(jì)算基本結(jié)構(gòu)的單位位移 慣性矩，b取單位長(zhǎng)度，計(jì)算過(guò)程見(jiàn)表1.166.計(jì)算基本結(jié)構(gòu)的單位位移 慣性矩，b取單位長(zhǎng)度，計(jì)算過(guò)程見(jiàn)表1.16。表1.16曲墻拱結(jié)構(gòu)的單位位移計(jì)算過(guò)程表（單位：m）截面Ii1/Iiyi/Iiyi2/I(1+yi)2/Ii積分系數(shù)00.003572917279.883379300279.8833793110.003572917279.88337934019.57907557727.6720766046.7136420.003572917279.883379315936.34611907403.3903939551.9659230.003572917279.883379335322.906284457951.7064528881.402440.003572917279.883379361488.2663313508508.113631764.52250.003572917279.883379378118.6596921803813.4621960330.66460.003572917279.8833793119346.33750891011.0851129983.63270.003572917279.8833793201058.5145144433464.9144835861.8480.003572917279.8833793236940.5877200586552.2201060713.312518.95041475223.11966436646.4365438153.4179注：的計(jì)算按式辛普森法進(jìn)行，以下各表均同。如圖1.17所示，求曲線在上的曲邊體型的面積，可應(yīng)用精度較高的——辛普森方法計(jì)算，即把分成n等分，n必須為偶數(shù)。分別求出n個(gè)小段曲邊體型的面積（每3點(diǎn)組成的曲線用拋物線代替），然后求和REF_Ref6724\r\h錯(cuò)誤!未找到引用源。：圖1.17辛普森法計(jì)算變位將各分點(diǎn)的坐標(biāo)代入得：校核;計(jì)算變位結(jié)果正確。7.計(jì)算主動(dòng)荷載在基本結(jié)構(gòu)中產(chǎn)生的位移和（1）襯砌每一塊上的作用力豎向力：式中：——相鄰兩截面之間的襯砌外緣的水平投影（由分塊圖量?。﹤?cè)向水平力：式中：——相鄰兩截面之間的襯砌外緣的垂直投影（由分塊圖量取）自重力：以上各集中力均通過(guò)相應(yīng)荷載圖形的形心,襯砌每一塊上的作用力計(jì)算過(guò)程，見(jiàn)表1.18表1.18計(jì)算過(guò)程表（一）截面集中力力臂-Qiaq-Wiaw-EiaeQiWiEiaqaeaw0012.25322700000001266.446160612.2532276.63348060.76090.29380.7477-202.7388836-0.916173783-0.0004788942251.97909812.25322719.7376570.67570.43290.6714-172.9650765-0.822681661-0.0020995653231.468213212.25322731.7430360.57550.54330.5732-131.5119567-0.702354972-0.004237744201.678594812.25322742.85309860.42860.65450.4724-88.15384573-0.578842443-0.0068918855154.759509412.25322754.439306740.24270.74980.314-37.56013292-0.384751328-0.010030075681.392412.25322763.612230220.01030.80840.1815-0.83834172-0.22239607-0.0126361710.4833411212.25322766.78653382-0.26680.7944-0.16742.7969554110.20511902-0.0130368988012.25322763.6610656600.7822-0.470400.576391798-0.012235955分塊上個(gè)集中力對(duì)下一分點(diǎn)的截面形心的力臂由分塊圖上量取，見(jiàn)圖1.19，并分別記為、、。圖1.19單元主動(dòng)荷載模式彎矩：軸力：式中：、——相鄰兩截面中心點(diǎn)的坐標(biāo)增量：校核：。計(jì)算誤差：1.18775%<5%計(jì)算誤差表明計(jì)算結(jié)果在誤差范圍內(nèi)。計(jì)算過(guò)程，見(jiàn)表1.20。的計(jì)算過(guò)程見(jiàn)表1.2。計(jì)算誤差：1.18775%<5%計(jì)算誤差表明計(jì)算結(jié)果在誤差范圍內(nèi)。計(jì)算過(guò)程，見(jiàn)表1.20。的計(jì)算過(guò)程見(jiàn)表1.2。表1.20計(jì)算過(guò)程截面000000001001.57930.155800-203.655542268.23236.63348061.51940.4619-40.75521946-0.306400469-418.507013511.953826.3711381.40920.7433-72.70820459-1.960166658-629.393934733.885658.1141741.20811.0294-88.66071777-1.98227303-812.776515900.8983100.967270.92121.2904-82.99075355-13.0288168-946.750996994.544151.406580.4931.509-49.03101675-23.45085276-1020.306271017.281219.018810.0051.538-0.508640259-33.68509285-1051.510981029.534281.80534-0.54341.590551.94486373-41.4573398-1040.4592表1.21的計(jì)算過(guò)程截面0010000010.1880498930.982159477278.6994-6.6334852.40938998-6.5151358441.8942520.3694061880.929268028546.9317-26.3711202.0399588-24.505855177.534130.5375645410.843222607794.6532-58.1142427.1773574-49.0031849378.174240.6865420290.727090121012.585-100.967691.1821432-73.412306621.769850.9194375940.3932359481179.598-151.4071084.566481-61.11145341023.45560.9973310690.0730119121273.243-219.0191269.845139-11.9909821253.85470.966903592-0.255142011291.98-281.8051253.08762672.920949341326.00980.831459916-0.555584741308.233-349.4661087.743411194902（2）主動(dòng)荷載位移和計(jì)算過(guò)程，見(jiàn)表1.22表1.22、計(jì)算過(guò)程截面積分系數(shù)00279.88340100011-203.6555279.88340.1436161.143616-56999.7997-8186.09532-65181.8950442-418.507279.88340.5693921.569392-117133.157-66694.7262-183827.883623-629.3939279.88341.2620582.262058-176156.901-222320.23-398477.13144-812.7765279.88342.1969253.196925-227482.635-499762.182-727244.817425-946.751279.88342.7911153.791115-264979.866-739589.184-1004569.05146-1020.306279.88344.2641451.264145-285566.757-1217698.12-1503264.87327-1051.511279.88347.1836538.183653-294300.432-2114152.25-2408452.68648-1040.459279.88348.465699.46569-291207.251-2465270.26-2756477.5111-4721320.35-18370571.4-23091891.71校核:故計(jì)算正確（3）墻底（彈性地基上的剛性梁）位移計(jì)算單位彎矩作用下墻底截面產(chǎn)生的轉(zhuǎn)角主動(dòng)荷載作用下墻底截面的轉(zhuǎn)角8.解主動(dòng)荷載作用下的力法方程式中：其中——拱矢高，解得：9.求主動(dòng)荷載作用下各截面的內(nèi)力，并校核計(jì)算精度主動(dòng)荷載作用下各截面的內(nèi)力的計(jì)算過(guò)程，見(jiàn)表1.23表1.23和計(jì)算過(guò)程截面積分系數(shù)0703.7880440703.788196978.5801351.136185351.13621703.78804450.42884884550.5614154092.972213024.914344.871732390.7662703.788044199.9342652481.2153135803.77732558.882326.299631503.83373703.788044443.1542378517.5483144853.1818281311.84296.085969674.26014703.788044771.419701662.4312185403.4940731748.52251.307651877.07755703.788044980.0613467737.0984206301.5957581139.14138.0793711161.5346703.7880441497.2956811180.777330479.99140921468221.63712421279.4917703.7880442522.4405952174.718608667.344372455124-89.5895921236.4198703.7880442972.6100312631.939737751.476245608941-191.085911086.8166693768.8306461639810.求單位彈性反力、相應(yīng)摩擦力作用下，基本結(jié)構(gòu)中產(chǎn)生的變位，a各截面的彈性反力強(qiáng)度最大彈性反力零點(diǎn)，假定在截面2，即；最大彈性反力值，假定在截面4，即拱圈任意截面的外緣彈性反力強(qiáng)度，見(jiàn)圖1.24圖1.24單元單位彈性反力荷載示意圖邊墻任意截面外緣的彈性反力強(qiáng)度b各分塊上的彈性反力集中力作用方向垂直襯砌外緣，并通過(guò)分塊上彈性反力圖形的形心。各點(diǎn)彈性反力的計(jì)算過(guò)程，見(jiàn)表1.25表1.25各點(diǎn)彈性反力的計(jì)算過(guò)程截面30.4554322380.2277161191.64758750.37518220.5375650.8432230.20168470.3163621410.7277161191.64758751.1989760.6865420.727090.82314740.871763652.1168974521.5584487261.64758752.56768060.9194380.3932362.36082211.009704362.5627413532.3398194021.64758753.85505720.9973310.0730123.84476830.281465172.3842688282.4735050911.64758754.07531610.966904-0.255143.9404377-1.03978481.6569107532.0205897911.64758753.32909850.83146-0.555582.7680119-1.849596c.彈性反力集中力與摩擦力集中力的合力本設(shè)計(jì)不考慮摩擦力d.計(jì)算作用下基本結(jié)構(gòu)內(nèi)力式中：計(jì)算過(guò)程見(jiàn)表1.26.表1.26的計(jì)算過(guò)程截面0.3751822311.1989759812.567680643.85505724.0753160693.329098482M0iσ(σ-h)r3kR3r3kr4kR4r4kr5kR5r5kr6kR6r6kr7kR7r7kr8kR8r8k30.780.29264214-0.2926421442.35890.8850173650.79380.946984334-1.83200169953.9011.4635858832.37032.8277109680.79042.029494778-6.32079162961.35642.0096261023.89434.6458063632.36326.0679428880.77953.0050170-11.7283924476.68342.5074929231.32416.351523423.87889.9595196662.35359.07287710.78963.21786957-31.109282787.89972.9638270716.68677.9770724921.37313.796148083.953811.2421252.45249.994305130.90193.002513921-52.97599185表1.27的計(jì)算過(guò)程截面332.5180.5375650.8432230.3163620.1700650680.2016850.1700650680443.3570.6865420.727091.1881260.8156982481.0248320.745145270.070553566.8440.9194380.3932362.197832.0207675823.3856541.331360930.689407681.8130.9973310.0730122.4792952.4726780877.2304220.5279069691.9447717104.7820.966904-0.255141.4395111.39186818911.17086-2.850155724.2420248123.7510.83146-0.55558-0.41009-0.3409696613.93887-7.744224747.403255e.計(jì)算作用下產(chǎn)生的荷載位移和計(jì)算結(jié)果,見(jiàn)表1.28表1.28和計(jì)算過(guò)程截面1/Ii積分系數(shù)3-0.29264214279.88341.2620580172.262058-81.90567113-103.3697089-181.2753844-1.8320017279.88342.1969245363.196925-512.7468263-1126.466084-1639.2129125-6.32079163279.88342.7911146383.791115-1769.084521-4937.717703-6706.80222346-11.7283924279.88344.2641452061.264145-4402.115627-18771.26025-23173.3758827-31.1092827279.88347.1836532418.183653-8706.971169-62547.86165-71254.8328248-52.9759918279.88348.4656898269.46569-14827.09962-125521.6264-140348.7261-66888.66997-435672.8753-502561.5453校核：經(jīng)校核，故計(jì)算正確11.解單位彈性反力、摩擦力作用下的力法方程式中均同前,計(jì)算解、：代入原方程檢驗(yàn)，計(jì)算正確單位彈性反力圖、摩擦力作用下截面的內(nèi)力，并校核計(jì)算精度計(jì)算過(guò)程，見(jiàn)表1.29表1.29和計(jì)算過(guò)程截面積分系數(shù)00-23.883090-23.8831-6684.4810750102.961526392.96152610-23.883090.425323202-23.4578-6561.44018-942.903649402.908691212.90869120-23.883091.686270536-22.1968-6212.521979-3537.362622202.752051792.7520523-0.292642-23.883093.737618127-20.4381-5720.289554-7219.337293402.4972262.4972264-1.832002-23.883096.506249996-19.2088-5376.236666-11811.1862420.0705532.153296582.223855-6.320792-23.883098.265959664-21.9379-6140.060872-17137.6137840.6894071.164578641.8539856-11.72839-23.8830912.62837857-26.9831-7552.123434-32203.3509321.9447710.21622672.1609987-31.10928-23.8830921.27457866-33.7178-9437.051274-67792.5039744.242024-0.75560983.4864148-52.97599-23.8830921.07136385-51.7877-14494.52266-122706.13317.403255-1.64537891.757876-170912.1354-590179.3674（12）最大彈性反力值的計(jì)算先求出位移和式中：計(jì)算過(guò)程見(jiàn)表1.30表1.30計(jì)算過(guò)程截面1/IiMipMiσM-ikMip/IiM-ikMiσ/Ii積分系數(shù)40279.88338662.43124-1.832001700251.2907279.88338737.0984-6.32079163266273.4638-2283.357391462.2997279.883381180.77749-11.7283924760004.8433-10123.54531274.3877279.883382174.71771-31.10928272670649.695-38203.5774481.9782279.883382631.93883-52.97599184410449.728-88639.36695117678152.05-270834.1967（13）計(jì)算贅余力和（14）計(jì)算襯砌截面總的內(nèi)力，并校核計(jì)算精度a.襯砌各截面內(nèi)力計(jì)算過(guò)程，見(jiàn)表1.3。表1.31和計(jì)算過(guò)程截面MipMiσσhMi(KN*m)NipNiσσhNi(KN)e（m）Mi/IiMiyi/IiMiyih/Ii積分系數(shù)070.788044-23.88309410351.136192.961526400.2015971210001150.6366006-23.4577709-203.6555390.765992.908691241.8942540.129582928-56999.79971-8186.09532042-28.7279597-22.1968235-418.507503.833732.7520518177.5341-0.05701873-117133.1573-66694.7262023-78.823933-20.4381181-629.3939674.260142.497226378.17417-0.116904334-176156.9013-222320.23044-101.277256-19.2088458-812.7765877.077492.2238496621.76984-0.115471276-227482.635-499762.182025-233.166134-21.937926-946.7511161.53441.85398531023.455-0.200739758-264979.8665-739589.184-342009.51446-301.55104-26.9831079-1020.3061279.49132.16099781253.8542-0.235680418-285566.7566-1217698.12-656717.8727-212.508262-33.7177981-1051.5111236.4193.48641411326.0086-0.171873989-294300.4322-2114152.25-1291302.014898.95663409-51.7877221-1040.4591086.81571.75787621281.90160.091051899-291207.2507-2465270.26-1740891.191∑-4721320.348-18370571.4-9587577.007b.校核計(jì)算精度墻底截面最終轉(zhuǎn)角：校核：相對(duì)誤差是遠(yuǎn)小于5%，計(jì)算結(jié)果正確（15）繪制內(nèi)力圖計(jì)算結(jié)果按一定比例繪制如圖1.32。圖1.32內(nèi)力圖（16）內(nèi)力數(shù)值計(jì)算分析單元實(shí)常數(shù)，，材料屬性，，單元網(wǎng)格劃分：拱部半圓弧劃分為15份，邊墻每段劃分為14份，仰拱劃分為17份，一共92個(gè)單元。單元?jiǎng)澐忠?jiàn)圖1.32圖1.32ansys網(wǎng)格劃分圖計(jì)算時(shí)將均布荷載轉(zhuǎn)化為節(jié)點(diǎn)荷載，具體荷載對(duì)節(jié)點(diǎn)施加荷載如圖1.33圖1.34ansys節(jié)點(diǎn)施加荷載圖對(duì)于拱形結(jié)構(gòu)，需要約束墻底的水平位移。同時(shí)為避免結(jié)構(gòu)整體沉降過(guò)大，使彈簧全部受拉，也要對(duì)墻底的垂直位移進(jìn)行約束、本模型選取節(jié)點(diǎn)78、32進(jìn)行約束ADDINEN.CITE<EndNote><Cite><Author>郭紅軍</Author><Year>2018</Year><RecNum>130</RecNum><DisplayText><styleface="superscript">[8]</style></DisplayText><record><rec-number>130</rec-number><foreign-keys><keyapp="EN"db-id="5wztzpre9tvfvbexvam50tf7v2prpfwrde0a"timestamp="1621577006">130</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>郭紅軍,中鐵建大橋工程局集團(tuán)第六工程有限公司</author></authors></contributors><titles><title>基于ANSYS有限元軟件的隧道結(jié)構(gòu)受力分析</title><secondary-title>中國(guó)礦業(yè)</secondary-title></titles><periodical><full-title>中國(guó)礦業(yè)</full-title></periodical><pages>276-278+281%@1004-4051%L11-3033/TD%WCNKI</pages><volume>27</volume><number>S2</number><keywords><keyword>ANSYS</keyword><keyword>數(shù)值模擬</keyword><keyword>隧道結(jié)構(gòu)</keyword><keyword>水壓</keyword></keywords><dates><year>2018</year></dates><urls></urls></record></Cite></EndNote>[8]。見(jiàn)圖1.35。圖1.35ansys徑向彈簧、墻底約束施加牛頓-拉普森求解后的變形如圖1.36圖1.36ansys全牛頓-拉普森求解后的變形查看求解后的彈簧受力表，分批多次除去受拉彈簧（正值受拉，負(fù)值受壓），在重新計(jì)算，保證彈簧全部處于受壓狀態(tài)。確定抗力分布范圍，最終除去受拉彈簧后的變形圖。如圖1.37圖1.37ansys采用生死單元法殺死受拉彈簧后的變形軸力結(jié)果圖如圖1.38圖1.38ansys軸力結(jié)果剪力結(jié)果圖如圖1.39。圖1.39ansys剪力圖彎矩結(jié)果圖如圖1.40圖1.40ansys彎矩圖節(jié)點(diǎn)坐標(biāo)與荷載如表1.32。STATCURRENTCURRENTCURRENTCURRENTCURRENTCURRENTELEMNINJQIQJMIMJ1-0.19885E+007-0.19851E+00756304.52731.0.48794E+0060.45390E+0062-0.19450E+007-0.19418E+00786881.83140.0.45390E+0060.40083E+0063-0.19024E+007-0.18994E+0070.11000E+0060.10609E+0060.40083E+0060.33337E+0064-0.18616E+007-0.18588E+0070.12597E+0060.12192E+0060.33337E+0060.25599E+0065-0.18235E+007-0.18209E+0070.13525E+0060.13105E+0060.25599E+0060.17286E+0066-0.17889E+007-0.17866E+0070.13836E+0060.13403E+0060.17286E+00687834.7-0.17586E+007-0.17565E+0070.13590E+0060.13146E+00687834.4374.78-0.17331E+007-0.17312E+0070.12858E+0060.12403E+0064374.7-74478.9-0.17130E+007-0.17114E+0070.11714E+0060.11250E+006-74478.-0.14616E+00610-0.16989E+007-0.16975E+0070.10241E+00697684.-0.14616E+006-0.20862E+00611-0.16910E+007-0.16898E+00785241.80452.-0.20862E+006-0.26034E+00612-0.16896E+007-0.16887E+00766543.61700.-0.26034E+006-0.30038E+00613-0.16950E+007-0.16943E+00747238.42351.-0.30038E+006-0.32834E+00614-0.17070E+007-0.17066E+00728262.23352.-0.32834E+006-0.34446E+00615-0.17258E+007-0.17257E+00710551.5631.0-0.34446E+006-0.34951E+00616-0.17257E+007-0.17258E+007-5622.5-10546.-0.34951E+006-0.34446E+00617-0.17066E+007-0.17070E+007-23343.-28254.-0.34446E+006-0.32836E+00618-0.16943E+007-0.16950E+007-42346.-47229.-0.32836E+006-0.30039E+00619-0.16887E+007-0.16896E+007-61692.-66531.-0.30039E+006-0.26037E+00620-0.16898E+007-0.16910E+007-80444.-85233.-0.26037E+006-0.20865E+00621-0.16975E+007-0.16989E+007-97676.-0.10240E+006-0.20865E+006-0.14619E+00622-0.17114E+007-0.17130E+007-0.11249E+006-0.11713E+006-0.14619E+006-74511.23-0.17312E+007-0.17331E+007-0.12402E+006-0.12857E+006-74511.4333.524-0.17565E+007-0.17586E+007-0.13145E+006-0.13589E+0064333.587788.25-0.17866E+007-0.17889E+007-0.13402E+006-0.13835E+00687788.0.17281E+00626-0.18209E+007-0.18235E+007-0.13105E+006-0.13525E+0060.17281E+0060.25594E+00627-0.18588E+007-0.18616E+007-0.12191E+006-0.12597E+0060.25594E+0060.33331E+00628-0.18994E+007-0.19024E+007-0.10608E+006-0.10999E+0060.33331E+0060.40076E+00629-0.19418E+007-0.19450E+007-83133.-86879.0.40076E+0060.45383E+00630-0.19851E+007-0.19885E+007-52721.-56298.0.45383E+0060.48787E+00631-0.20274E+007-0.20309E+00715013.11809.0.48787E+0060.47984E+00632-0.20634E+007-0.20671E+0070.12256E+0060.11964E+0060.47984E+0060.40733E+00633-0.20906E+007-0.20945E+0070.24095E+0060.23834E+0060.40733E+0060.26383E+00634-0.21069E+007-0.21110E+0070.36933E+0060.36704E+0060.26383E+00643378.35-0.21103E+007-0.21146E+0070.50645E+0060.50450E+00643378.-0.25929E+00636-0.20989E+007-0.21034E+0070.65073E+0060.64913E+006-0.25929E+006-0.64845E+00637-0.21273E+007-0.21319E+007-0.31505E+006-0.31629E+006-0.64845E+006-0.45943E+00638-0.21849E+007-0.21895E+007-0.42970E+006-0.43057E+006-0.45943E+006-0.20188E+00639-0.22310E+007-0.22357E+007-0.26767E+006-0.26817E+006-0.20188E+006-41458.40-0.22574E+007-0.22621E+007-0.10971E+006-0.10983E+006-41458.24267.41-0.22705E+007-0.22752E+007-29139.-28883.24267.41638.42-0.22790E+007-0.22837E+007-4872.5-4241.441638.44366.43-0.22863E+007-0.22909E+00718603.19606.44366.32927.44-2289156.-0.22937E+0070.10058E+0060.10195E+00632927.-27708.456649.51250.6-3790.0-403.61-27708.-26014.46-18292.-21666.-12917.-7510.7-26014.-17762.47-47382.-48918.-10358.-5733.0-17762.-12792.48-71920.-73353.-11691.-7032.9-12792.-7008.049-96684.-98014.-11988.-7298.7-7008.0-1050.650-0.12163E+006-0.12286E+006-11232.-6514.9-1050.64431.451-0.14672E+006-0.14784E+006-9410.7-4667.74431.48780.252-0.17179E+006-0.17281E+0062712.37478.98780.25632.153-0.19685E+006-0.19776E+0063451.98243.95632.12018.154-0.22202E+006-0.22282E+006918.715721.62018.1-34.32155-0.24732E+006-0.24802E+006-1299.83523.7-34.321-721.2956-0.27271E+006-0.27330E+006-2460.92376.9-721.29-691.3357-0.29814E+006-0.29862E+006-2910.91938.8-691.33-391.0658-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