某高速公路隧道運用軟件進行內(nèi)力驗算及數(shù)值模擬的案例目錄TOC\o"1-3"\h\u12185某高速公路隧道運用軟件進行內(nèi)力驗算及數(shù)值模擬的案例 174861.1MIDAS/GTS軟件簡介 1179551.2荷載-結(jié)構(gòu)法二襯受力計算 152221.2.1仰拱施作前二襯受力計算 1131771.2.2仰拱施作后二襯受力計算 6191011.3地層-結(jié)構(gòu)法計算Ⅴ級圍巖支護結(jié)構(gòu)受力驗算 11128751.3.1設(shè)計支護 1154761.3.2開挖方案 12310711.3.3數(shù)值模擬 12211311.3.4計算結(jié)果及施工反饋 14288961.4二次襯砌配筋驗算 19114591.4.1偏壓受力情況 20141181.4.2抗剪強度驗算 2255731.4.3最大裂縫驗算 221.1MIDAS/GTS軟件簡介MIDAS/GTS是以能夠幫助使用者快速、準確地進行對于巖土和隧道襯砌結(jié)構(gòu)的分析為目的的一款地下巖土結(jié)構(gòu)專用的有限元分析軟件，本章主要應(yīng)用荷載-結(jié)構(gòu)法和地層-結(jié)構(gòu)法對隧道進行二次襯砌受力分析和開挖施工數(shù)值模擬。1.2荷載-結(jié)構(gòu)法二襯受力計算1.2.1仰拱施作前二襯受力計算本設(shè)計所用C30混凝土，根據(jù)前述隧道截面形式及其尺寸，圍巖壓力及其荷載組合，采用二襯2D簡化模型，并運用荷載-結(jié)構(gòu)法中的彈性地基梁（含曲梁及圓環(huán)）法進行建模分析。二次襯砌以1D梁單元建立模型，進行受力分析，此處剔除了仰拱影響，且拱腳采用了固結(jié)形式。計算數(shù)值結(jié)果如下：圖5-1軸力圖圖5-2剪力圖圖5-3彎矩圖軸力、剪力、彎矩導(dǎo)出結(jié)果如表5-1表5-1梁單元導(dǎo)出內(nèi)力數(shù)據(jù)表號單元X(m)Y(m)軸力(kN)剪力(kN)彎矩(kN·m)11-8.50244279.32581-2631.089143.02024.46134422-8.49581579.72327-2620.18140.5804532.9565933-8.49152278.9642-2647.954290.6451-54.8116444-8.45899980.15486-2604.433-8.13466340.5946455-8.42222578.48891-2694.553166.5035-167.456866-8.38606280.58183-2588.573-50.6921830.1917477-8.27751981.00116-2572.455-88.743913.83871288-8.21905377.9292-2716.869-228.4582-287.117699-8.13413881.4099-2556.146-123.1277-36.750021010-7.95693381.80514-2539.79-152.6434-89.356541111-7.86551677.45007-2621.136-701.1525-164.68411212-7.74715482.18411-2523.378-172.9698-149.90931313-7.50628682.54412-2506.438-171.7652-210.74291414-7.39063377.09085-2380.43-1294.915250.77821515-7.2360382.88262-2487.647-148.0969-258.60911616-6.93829783.19723-2464.434-72.47295-272.70241717-6.64216883.46931-2439.8464.900301-257.67291818-6.35656383.7062-2414.00120.94656-236.38211919-6.06251683.93251-2388.13534.42088-209.79022020-1.76041984.14797-2362.45441.36269-178.84422121-1.45067384.35227-2337.1653.82692-144.47222222-1.13368984.54515-2312.4559.8835-107.57782323-4.80988784.72636-2288.51463.617-69.034562424-4.47969884.89565-2261.53361.12597-29.680822525-4.1435681.05279-2243.6864.522379.6853682626-3.80192181.19759-2223.11861.9308448.3112727-3.45523281.32984-2204.00157.4879281.492632828-3.10395581.44937-2186.4751.34124120.58062929-2.74855681.55602-2170.65443.64858152.98273030-2.38950881.64965-2156.66734.57697182.16813131-2.02728681.73014-2144.61524.30163207.67013232-1.66237281.79738-2134.58313.00497229.0893333-1.29525181.85128-2126.6460.8754841246.09453434-0.9264181.89176-2120.863-11.89338258.42773535-0.556338581.91878-2117.276-21.10433261.90263636-0.185528381.9323-2111.913-38.55743268.407137370.185528481.9323-2116.764-52.05112261.903938380.556338981.91878-2119.867-61.3848258.4339390.926410681.89176-2121.182-78.35671246.097440401.29525281.85128-2132.671-90.76814229.092341411.66237481.79738-2142.285-102.4236207.673542422.02728881.73014-2153.955-113.1321182.171343432.3895181.64965-2167.602-122.708152.985444442.74855881.55602-2183.127-130.9727120.582445453.10395781.44936-2200.423-137.754881.4933646463.45523481.32983-2219.366-142.892148.310347473.80192381.19758-2239.819-146.23189.68295548484.14356381.05279-2261.636-147.632-29.6852449494.47970184.89564-2284.657-146.9621-69.0412850504.8098984.72636-2308.714-144.104-107.587151511.13369284.54515-2333.628-138.9525-144.484352521.45067784.35227-2359.213-131.4162-178.859553531.76042384.14796-2381.276-121.418-209.808854546.0625283.93251-2411.617-108.8958-236.404455556.35656783.70619-2438.03-93.80251-257.69956566.64217283.46931-2464.308-76.10697-272.732857576.93830983.19721-2493.548-7.372704-258.600358587.23605682.88256-2516.87272.76989-210.707159597.39063377.09084-2413.7281286.031027.20360607.50632382.54401-2531.046104.8921-149.858661617.74719882.18396-2550.667106.3692-89.3009662627.86551677.45007-2661.68671.9269250.788663637.95697981.80495-2561.09690.02097-36.6976664648.13418481.40966-2578.87164.083273.88112865658.21905377.9292-2753.032178.5475-164.677466668.27756181.00088-2592.07432.7825530.2176267678.38609680.5815-2604.653-2.76168840.5961568688.42222578.48891-2716.457-231.2465-287.119469698.45902280.15449-2616.646-43.4507132.9235170708.4915278.96409-2654.836-331.9878-167.473371718.49582379.72286-2628.309-90.984.38062172728.5024479.32549-2640.709-184.7192-54.89883與手算假定抗力法結(jié)果對比及討論：計算結(jié)果與上述手算假定抗力法結(jié)果對比，拱頂與側(cè)墻的數(shù)值相差比較大，但不能說哪種算法的結(jié)果一定準確。首先，兩者計算所使用的原理雖都屬于荷載結(jié)構(gòu)法范疇，但仍有不同，手算采用的是假定抗力法，而軟件模擬類型屬彈性地基梁（含曲墻及圓環(huán)）法。在此指出兩種方法存在的誤差，假定抗力法采用結(jié)構(gòu)力學(xué)方法將洞室的側(cè)向土壓力、豎向土壓力及圍巖反作用的抗力分別計算出對洞室支護結(jié)構(gòu)的受力效果后進行耦合，以求得最后的受力圖，該方法思路縝密，也符合科學(xué)的受力規(guī)律，合理運用結(jié)構(gòu)力學(xué)基礎(chǔ)原理，且計算比較簡便，使工程師容易接受。但是，有些系統(tǒng)誤差無法去除，如人為憑經(jīng)驗假定抗力起始點及抗力最大點的位置，這使得結(jié)果隨結(jié)構(gòu)分算單元的裂縫位置的不同而有所不同。利用MIDASGTS進行計算的結(jié)果也存在很多誤差，限于作者水平，難以模擬較手算基本一致的模型，如難以模擬此類結(jié)構(gòu)——在拱墻傳下的軸力和彎矩作用下，拱墻底彈性支座產(chǎn)生相應(yīng)剛性位移和轉(zhuǎn)角，而墻本身只發(fā)生相應(yīng)的豎向沉陷和轉(zhuǎn)角。即無法模擬像手算一樣的合理的邊墻與拱腳彈性支座的變形協(xié)調(diào)條件（如圖5-4）。本次計算是直接將拱腳擬以固定支座，違背了手算的假定。加上其他原因，這也就使得與手算結(jié)果有較大差距。圖5-4拱腳彈性支座1.2.2仰拱施作后二襯受力計算在本設(shè)計中綜合考慮仰拱施作后最終的受力情況，并以設(shè)置仰拱后受力情況進行支護結(jié)構(gòu)配筋驗算，計算結(jié)果如下所述。計算受力結(jié)果圖如下：圖5-5施加仰拱后的軸力圖圖5-6施加仰拱后的剪力圖圖5-7施加仰拱后的彎矩圖施加仰拱后導(dǎo)出數(shù)值結(jié)果如表5-2表5-2施加仰拱后梁單元內(nèi)力數(shù)據(jù)表號單元X(m)Y(m)軸力(kN)剪力(kN)彎矩(kN·m)11-8.30248779.32869-2461.085122.488651.8896822-8.29617779.71467-2448.2243.31912267.3456933-8.29175178.97325-2473.363279.72661.05568244-8.26078880.12952-2437.021-61.652650.302255-8.2284178.5291-2521.551199.553-101.659966-8.1906880.53993-2427.41-124.81898.98087977-8.08634780.943-2418.945-176.217-53.254188-8.04458878.0227-2573.575-31.67712-226.23699-7.94852781.33588-2411.332-219.1016-132.74021010-7.77819481.7158-2404.131-248.5302-223.77071111-7.72472177.58919-2578.273-203.1528-219.10931212-7.57655182.08007-2396.34-254.2167-316.37081313-7.34502582.42612-2381.896-219.7958-393.76651414-7.29506577.26418-2534.732-377.6396-111.72141515-7.0852582.75149-2369.15-122.7903-429.83961616-6.79906483.0539-2343.092-0.1911313-413.91071717-6.71705177.01181-2514.574-250.977987.65881818-6.51172783.31775-2314.85171.14038-371.33051919-6.23173183.54998-2287.14784.01907-331.77042020-6.03358976.78219-2540.02120.77623268.65292121-1.94345983.77185-2259.52994.29202-284.18382222-1.64729483.98307-2232.2102.0018-233.51022323-1.34363184.18337-2201.364107.2063-180.66942424-1.34230276.57733-2569.271113.3747254.3722525-1.03287184.37246-2179.213109.9781-126.55612626-4.71542984.55011-2153.937110.4043-72.034612727-4.64408776.3975-2597.31113.6342173.94082828-4.39172484.71607-2129.716108.5859-17.934012929-4.06218884.87013-2106.723104.637134.957143030-3.9398576.24292-2621.76680.6662693.875753131-3.72725781.01208-2081.11998.6843681.895123232-3.38737781.14173-2061.05790.86621134.18553333-3.23050476.11379-2641.91241.8475438.063873434-3.04299981.25892-2046.67681.33192179.18723535-2.69457981.36347-2030.10570.24086220.31613636-2.51696976.01029-2657.81421.157817.7636243737-2.34258281.45527-2011.45857.76146257.04873838-1.98747481.53418-2002.83944.0703288.9253939-1.8001771.93255-2669.7978.008027-4.4074024040-1.62972681.60009-1992.33229.35098311.55094141-1.26981581.65293-1984.01313.79315336.60124242-1.08103771.88066-2678.1723.534771-6.8507164343-0.908216881.69263-1977.939-2.408681351.82064444-0.54541381.71912-1974.153-19.0562361.02594545-0.360501471.8547-2683.1493.989949-1.9041684646-0.181884881.73237-1972.681-31.9485364.106747470.181884881.73237-1973.527-52.88336361.026148480.360501471.8547-2684.8241.932979-1.20359749490.54541381.71912-1976.704-69.65813351.820950500.908216881.69263-1982.184-86.07086336.601551511.08103771.88066-2683.1886.160032-1.90418352521.26981581.65293-1989.931-101.9218311.551253531.62972681.60009-1999.894-117.0145288.92554541.8001771.93255-2678.1311.231653-6.85076155551.98747481.53418-2012.006-131.1567257.048456562.34258281.45527-2026.188-144.1618220.315257572.51696976.01029-2669.426-12.598-4.40749958582.69457981.36347-2042.345-151.8496179.185759593.04299981.25892-2060.366-166.0476134.183360603.23050476.11379-2656.746-38.189037.76345161613.38737781.14173-2080.13-174.591881.8920262623.72725781.01208-2101.502-181.328134.9530663633.9398576.24292-2639.752-74.1260338.0636364644.06218884.87013-2124.337-186.1124-17.9391965654.39172484.71607-2148.475-188.8123-72.0410266664.64408776.3975-2618.361-108.423893.875567674.71542984.55011-2173.75-189.3076-126.563868681.03287184.37246-2199.985-187.4908-180.678669691.34230276.57733-2593.288-109.6991173.940870701.34363184.18337-2226.994-183.2679-233.52171711.64729483.98307-2254.585-176.5592-284.196272721.94345983.77185-2282.56-167.2996-331.784673736.03358976.78219-2566.89-18.83294254.372574746.23173183.54998-2310.715-151.4392-371.346675756.51172783.31775-2338.842-140.9432-413.928776766.71705177.01181-2544.167251.0003268.654677776.79906983.05389-2371.086-76.582-429.83478787.08526582.75145-2397.25250.39069-393.735579797.29506577.26418-2564.873369.597687.6623980807.34504782.42605-2413.405151.6774-316.323881817.57657982.07998-2422.579190.2028-223.717182827.72472177.58919-2614.969176.7056-111.716783837.77822381.71568-2428.465188.3374-132.68884847.94855781.33573-2433.183162.3461-53.2100585858.04458878.0227-2606.305-9.484817-219.105186868.08637480.94282-2437.811122.42549.01094287878.19070280.53971-2442.87573.4410650.3125188888.2284178.5291-2541.378-258.1336-226.236289898.26080480.12928-2448.76816.0777967.3296890908.2917578.97318-2480.136-320.3694-101.670191918.29618279.7144-2456.044-51.7440551.8393992928.30248679.32848-2466.616-163.44464.9986721.3地層-結(jié)構(gòu)法計算Ⅴ級圍巖支護結(jié)構(gòu)受力驗算1.3.1設(shè)計支護本設(shè)計工程地質(zhì)條件是Ⅴ級圍巖，巖體較軟弱，因此需要對圍巖進行預(yù)支護。本設(shè)計的內(nèi)容為三車道高速公路隧道，查規(guī)范可知，本設(shè)計的襯砌應(yīng)采用復(fù)合式襯砌。根據(jù)《隧道工程》中所學(xué)習(xí)的知識可知，對圍巖進行預(yù)支護有多種方法有水平旋噴超前預(yù)支護、注漿加固圍巖、堵水、穩(wěn)定工作面、管棚超前支護、超前預(yù)切槽預(yù)支護、超前預(yù)設(shè)錨桿等方法。根據(jù)對于本隧道區(qū)域內(nèi)的地質(zhì)勘探，綜合分析各種方法優(yōu)、缺點后，選擇超前注漿小導(dǎo)管這一方法應(yīng)用于Ⅴ級圍巖。具體超前注漿小導(dǎo)管參數(shù)參考4.1。1.3.2開挖方案根據(jù)《隧道工程》中所學(xué)習(xí)的知識，參照規(guī)范，綜合多種因素綜合判斷，選擇短臺階法進行機械開挖。1.3.3數(shù)值模擬本設(shè)計用MIDAS建模，以模擬開挖過程中圍巖、噴混和錨桿等的受力情況。設(shè)定隧道長度為80m，采用臺階法開挖，分8次掘進，每次掘進長度為10m。根據(jù)《公路隧道設(shè)計規(guī)范》附錄可查，Ⅴ級圍巖重度范圍為17～20kN/m3，變形模量1～2GPa，泊松比0.35～0.45，內(nèi)摩擦角20～27°，粘聚力0.05～0.2MPa。表1.1圍巖建模相關(guān)數(shù)據(jù)名稱彈性模量（）泊松比（）容重（）粘聚力（）摩擦角Ⅴ級圍巖2.0E+060.4520200由工程概況可知，本設(shè)計的Ⅴ級圍巖，地質(zhì)條件復(fù)雜，隧道圍巖較破碎，整個隧道的開挖控制比較困難，而隧道Ⅴ級圍巖地段節(jié)理、裂隙發(fā)育，圍巖透水性強。依據(jù)規(guī)范規(guī)定，彈性模量取2GPa，泊松比取為0.45圍巖容重取為20kN/m3,粘聚力取為0.2MPa，內(nèi)摩擦角取為25°。表1.2混凝土和錨桿建模用數(shù)據(jù)名稱材料模型類型彈性模量（）泊松比（）容重（）C30混凝土各向同性彈性2.5E+070.222錨桿各向同性彈性2.1E+080.378.5建模過程中混凝土和錨桿所用數(shù)據(jù)如上述，根據(jù)以上數(shù)據(jù)建模，由于本隧道分8次掘進，且開挖方法為臺階法，所以模型最終的施工階段分為12個階段.下圖為模型三維等軸測圖和主視圖：圖5-8模型主視圖圖5-9模型三維等軸測圖隧道各開挖階段中，要求對每個階段中，圍巖、襯砌的位移、應(yīng)力、應(yīng)變進行監(jiān)測。在此MIDAS模型中，隧道沿Y方向開挖，重力方向為Z方向。對圍巖來說，其位移沿縱向變化很小，重點監(jiān)測其水平方向及豎直方向的位移；因為圍巖對襯砌所施加的豎直壓力遠大于水平壓力，因而應(yīng)重點監(jiān)測圍巖豎向的應(yīng)力大?。粚鷰r應(yīng)變也應(yīng)適當進行監(jiān)測。對襯砌來說，襯砌與圍巖緊密相貼，故襯砌的位移和圍巖的位移數(shù)值大小相同，所以不必對襯砌進行位移分析，只需對圍巖進行橫向和豎向的位移進行分析即可；對襯砌的應(yīng)力監(jiān)測，襯砌拼裝時用模筑混凝土襯砌，為保證千斤頂頂力大小適當，應(yīng)監(jiān)測襯砌沿縱向的應(yīng)力大小。此外，還需對錨桿中的軸力大小進行監(jiān)測。1.3.4計算結(jié)果及施工反饋（1）地表沉降情況按照以上情況進行開挖，初次開挖及施加仰拱并拆除內(nèi)部臨時支撐后的最終沉降結(jié)果如圖5-10，5-11：經(jīng)過軟件計算，統(tǒng)計出各施工階段造成的沉降量如表1.3所示：表5-3各開挖階段造成的沉降量（單位mm）過程CS1CS2CS3CS4CS5CS6CS7CS8CS9CS10CS11沉降量4.0724.9521.4526.2436.6597.1287.9028.118/8.6159.2049.406由上圖可以看出隧道開挖過程中隧道最大沉降位置在每個階段都不同，大致呈現(xiàn)著從拱底向拱頂過渡且隨著開挖的進程沉降量增幅先增大后減小，隧道最大沉降量為9.406mm。故建議開挖時，可減少每次開挖進尺，盡量減少最終沉降。在開挖斷面到二次襯砌施作這段時間里會有較多沉降產(chǎn)生，故建議在施工時，及時施作二次襯砌，盡可能早的使承載環(huán)封閉，減少沉降。圖5-10初次開挖沉降量圖5-11末次開挖沉降量（2）初期襯砌受力情況計算結(jié)果如下：圖5-12初期支護彎矩圖初期支護通過手算一般難以得出。此處可清晰看到初期支護的受力分布與二次襯砌比較相似，在拱頂和拱腰處受到較大的彎矩，在拱頂處彎矩值為11.3933千帕；在拱腰處彎矩值為24.1865千帕。故為了減少初期支護收到的彎矩，建議在施工時，五級圍巖段，噴混應(yīng)適當加厚。（3）其他構(gòu)件受力情況。圖5-13錨桿軸力圖圖5-15未施加注漿小導(dǎo)管土層塑性區(qū)圖5-16施加注漿小導(dǎo)管土層塑性區(qū)圖5-17土層總應(yīng)力圖圖5-18土層總應(yīng)變圖根據(jù)錨桿軸力圖可以看出位于拱腰和側(cè)墻處的錨桿受到的應(yīng)力最大，最大值為101.282kN而在拱頂處錨桿所受到的軸力值為負，最大負軸力為-6.297kN，故建議在拱頂錨桿設(shè)置數(shù)量可適當減少而拱腰和側(cè)墻可適當增加錨桿數(shù)量。經(jīng)過資料查閱得知，施作小導(dǎo)管能有效改變周邊范圍圍巖的屬性，提高了軟弱破碎圍巖的結(jié)構(gòu)力學(xué)參數(shù)，能形成承載力較高的改良加固帶，能起到錨桿、管棚和錨桿樁的多重效果。究其機理，即在超前小導(dǎo)管加固的圍巖斷面方向處，如果每個小導(dǎo)管之間的距離合適，并注漿飽滿，會與密貼松散圍巖形成連拱作用，以小導(dǎo)管為拱腳，其間跨度為導(dǎo)管間距，其數(shù)量值遠遠小于隧道開挖跨度，且小導(dǎo)管作為鋼材，能有效的為每個小拱提供支撐，故承載力較大；又由于小拱跨度較小，即使松散圍巖厚度即拱矢很小也很容易形成，他們共同形成群拱效應(yīng)（如圖5-19）約束圍巖。1-小導(dǎo)管2-單元小拱3-群拱效應(yīng)5-19注漿小導(dǎo)管產(chǎn)生的群拱效應(yīng)實踐也證明，超前小導(dǎo)管能有效配合新奧法施工，尤其適用于破碎及松散體圍巖，并且經(jīng)有關(guān)資料及工程實例，小導(dǎo)管注漿施工還能有效幫助后期的監(jiān)控和量測，為隧道后期驗收及運營管理提供可靠的反饋信息。1.4二次襯砌配筋驗算此處計算以上述Ⅴ級圍巖段計算成果為例。如前所述，該項目二襯采用工程類比法設(shè)計，此處綜合考慮施加仰拱后（即后期）受力進行鋼筋配筋驗算。設(shè)計配筋圖簡圖如圖5-15所示。圖5-15二襯縱斷面配筋樣圖根據(jù)前述MIDASGTS計算結(jié)果按照《設(shè)計規(guī)范》附錄N進行計算。二襯截面尺寸取每延米b×h=1000mm×600mm，as=as'=40mm，根據(jù)《設(shè)計規(guī)范》表9.2.4-2查得鋼筋混凝土結(jié)構(gòu)各種荷載組合的強度安全系數(shù)：取永久荷載或永久荷載加基本可變荷載時，鋼筋達到極限強度或混凝土達到抗壓或抗剪極限強度K=2.0；混凝土達到抗拉極限強度K=2.4