隧道畢業(yè)設(shè)計(jì)之明洞計(jì)算示例

1、精選優(yōu)質(zhì)文檔-傾情為你奉上第4章 明洞設(shè)計(jì)4.1明洞長(zhǎng)度確定進(jìn)口端圍巖等級(jí)為級(jí)，坡度比較平緩，因此有很長(zhǎng)的超淺埋段。為了施工上的方便，考慮把超淺埋段設(shè)為明洞。坍落拱高度按下式計(jì)算當(dāng)埋深時(shí),即為超淺埋隧道。洞口段Xm處埋深為；斜坡坡度為，路面縱坡為1.2%。則有得在考慮巖石巖性考慮取明洞長(zhǎng)度為50m。4.2明洞設(shè)置由于明洞圍巖級(jí)別很差，垂直壓力和側(cè)向壓力較大，故采用拱式明洞，并假設(shè)仰拱，明洞內(nèi)輪廓線與暗洞內(nèi)輪廓線一致。襯砌厚度為60m。襯砌材料采用鋼筋混凝土結(jié)構(gòu)，C25級(jí)混凝土，直徑25mmHRB335級(jí)鋼筋。明洞邊墻用5#漿砌石片回填，拱部用挖土回填，最低回填土不小于1.5m，填土坡度設(shè)為，以

2、利于排水。明洞配筋圖如下：4.3襯砌內(nèi)力計(jì)算4.3.1基本資料回填土=18kN/m3，重度，計(jì)算內(nèi)摩擦角，混凝土彈性模量，。4.3.2荷載確定 =6.336時(shí)屬于淺埋。 4.3.3襯砌幾何要素 計(jì)算圖示如下圖4.1級(jí)圍巖內(nèi)力計(jì)算圖示1、襯砌幾何尺寸內(nèi)輪廓線半徑：r1=5.70m，r2=8.20m內(nèi)徑所畫(huà)圓曲線的終點(diǎn)截面與豎直軸的夾角：1=90°，2=101.5725°截面厚度：d=0.60m外輪廓線半徑 R1=6.3m，R2=8.80m拱軸線半徑 r1=6.00m，r2=8.50m拱軸線各段圓弧中心角 1=90°，2=11.5725°2、半拱軸線長(zhǎng)度S及

3、分段軸長(zhǎng)S分段軸線長(zhǎng)度半拱軸線長(zhǎng)度將半拱軸線等分為8段，每段軸長(zhǎng)為3、各分塊接縫（截面）中心幾何要素與豎直軸夾角另一方面 角度閉合差： 接縫中心點(diǎn)坐標(biāo)計(jì)算4.3.4計(jì)算位移1、單位位移單位位移值計(jì)算如下計(jì)算精度校核為：閉合差 用辛普生近似計(jì)算，按計(jì)算列表4.1進(jìn)行。表4.1單位位移計(jì)算表截面sincosxydI1/Iy/Iy2/I(1+y)2/I積分系數(shù)1/300.00000.00001.00000.00000.00000.600.018055.5560.00000.000055.55561113.2930.23000.97321.38020.16090.600.018055.5568.938

4、91.438374.87174226.5960.44770.89422.68640.63500.600.018055.55635.27722.401148.51262339.8990.64140.76723.84851.39690.600.018055.55677.606108.41319.17414453.1920.80070.59914.80422.40560.600.018055.556133.46321.50644.34002566.4950.91700.39885.50223.60720.600.018055.556200.40722.881179.23944679.7980.984

5、20.17725.90514.93710.600.018055.556274.281354.21958.28802792.1880.9993-0.03815.99386.32400.600.018055.556351.332221.82980.05664890.0001.00000.00005.82727.70520.600.018055.556428.063298.34210.03151444.481289.96304.29327.07852、載位移 （主動(dòng)荷載在基本結(jié)構(gòu)中引起的位移）豎向力 式中為襯砌外緣相鄰兩截面之間的水平投影長(zhǎng)度水平壓力 式中為襯砌外緣相鄰兩截面之間的豎直投影長(zhǎng)度自重力

6、 式中為接縫的襯砌截面厚度。作用在各楔塊上的力均列入表4.2，各集中力均通過(guò)相應(yīng)圖形的形心。（1）外荷載在基本結(jié)構(gòu)中產(chǎn)生的內(nèi)力楔塊上各集中力對(duì)下一接縫的力臂由圖中量得，分別記為內(nèi)力按下式計(jì)算彎矩 (4-1) 軸力 (4-2) 式中為相鄰兩接縫中心點(diǎn)的坐標(biāo)增值，按下式計(jì)算 （4-3） 第一截面的的計(jì)算見(jiàn)表4.2及表4.3專心-專注-專業(yè)表4.2彎矩計(jì)算表截面集中力力臂-Qaq-Gag-Eae(Q+G)Exy-x(Q+G)-yEMp0QGEaqagae00.0 000.0000.0000.00000.00000.00000.0000.0000.0000.0000.0000.00000.00000.

7、0000.0000.0001199.26820.89021.0320.65560.68640.3764-130.640-14.339-7.9170.0000.0001.38020.1090.0000.000-152.8962184.52820.89060.1230.53810.62860.5105-99.294-13.131-30.693220.15821.0321.30620.4741-287.570-9.971-593.5563171.83620.890101.3790.43240.57700.6375-74.302-12.054-64.629425.57681.1551.16210.76

8、19-494.562-61.832-1300.9344137.98320.890131.8200.26150.45470.7093-36.083-9.499-93.500618.302182.5340.95571.0087-590.911-184.122-2215.0485100.77520.890157.0090.09130.32140.7505-9.201-6.714-117.835777.175314.3530.69801.2016-542.468-377.727-3268.993658.1 6320.890173.785-0.08370.17090.75134.868-3.570-13

9、0.564898.840471.3620.40291.3299-362.143-626.864-4387.266713.6 9520.890180.655-0.25640.00900.71433.511-0.188-129.042977.894645.1470.08871.3869-86.739-894.754-5494.47780.0 0020.890177.9540.0000-0.10570.65480.0002.208-116.5241012.479825.801-0.16661.3812168.679-1140.597-6580.711表4.3軸力計(jì)算表截面sincos(Q+G)Esi

10、n(Q+G)cosENp000.00001.00000.0000.0000.0000.0000.00010.23000.9732220.15821.03250.63620.46930.16820.44770.8942425.57681.155190.53072.569117.96130.64140.7672618.302182.534396.579140.040256.53940.80070.5991777.175314.353622.284188.329433.95550.91700.3988898.840471.362824.237187.979636.25860.98420.177297

11、7.894645.147962.443114.320848.12370.9993-0.03811012.479825.8011011.770-31.4631043.23381.00000.00001033.3691003.7551033.3690.0001033.369基本結(jié)構(gòu)中，主動(dòng)荷載產(chǎn)生彎矩的校核為另一方面，從表12中得到閉合差 （2）主動(dòng)荷載位移計(jì)算過(guò)程見(jiàn)表4.4。 表4.4主動(dòng)荷載位移計(jì)算表截面Mp01/Iy/I1+yMp0/IMp0y/IMp0(1+y)/I積分系數(shù)1/300.00055.55560.00001.00000.0000.0000.00011-152.89655.555

12、68.93891.1609-8494.206-1366.718-9860.92442-593.55655.555635.27781.6350-32975.354-20939.350-53914.70323-1300.93455.555677.60562.3969-72274.163-.778-.94044-2215.04855.5556133.64463.4056-.307-.063-.37025-3268.99355.5556200.40024.6072-.855-.677-.53246-4387.26655.5556274.28365.9371-.204-.950-.15427-5494.

13、47755.5556351.33367.3240-.990-.610-.59948-6580.71155.5556428.06708.7052-.362-.385-.7471-.648-.413-.061截面計(jì)算精度校核閉合差 3、載位移（單位彈性抗力及相應(yīng)的摩擦力引起的位移）（1）各接縫處的抗力強(qiáng)度抗力上零點(diǎn)假定在接縫3處，；最大抗力值假定在接縫5處，；最大抗力值以上各截面抗力強(qiáng)度按下式計(jì)算 （4-4）查表算得，最大抗力值以下各截面抗力強(qiáng)度按下式計(jì)算 （4-5） 式中 為所考察截面外緣點(diǎn)到h點(diǎn)的垂直距離； 為墻腳外緣點(diǎn)到h點(diǎn)的垂直距離。由圖中量得則 按比例將所求得的抗力繪于圖上。（2）各楔塊

14、上抗力集中力按下式近似計(jì)算 （4-6） 式中為楔塊i的外緣長(zhǎng)度，可通過(guò)量取夾角，用弧長(zhǎng)公式求得，的方向垂直于襯砌外緣，并通過(guò)楔塊上抗力圖形的形心。（3）抗力集中力與摩擦力的合力按下式計(jì)算 （4-7） 式中為圍巖于襯砌間的摩擦系數(shù)，此處則 其作用方向與抗力集中力的夾角。由于摩擦阻力的方向與襯砌位移的方向相反，其方向向上，畫(huà)圖時(shí)也可取 切向/徑向=3/10的比例求出合力的方向.的作用點(diǎn)即為與襯砌外緣的交點(diǎn)。將的方向線延長(zhǎng)，使之交于豎直軸，量取夾角，將分解為水平與豎直兩個(gè)分力。 （4-8） 以上計(jì)算列入表4.5中。表4.5分解為水平與豎直兩個(gè)分力計(jì)算表截面(h)R(h)ksinkcoskRH(h)R

15、v(h)30.00000.00000.00000.00000.00000.00000.00000.00000.000040.53470.26741.46230.408265.86610.91260.40890.37250.166951.00000.76741.46231.171577.32790.97560.21941.14290.257060.90570.95291.46231.454789.71600.99990.00501.45460.007370.56950.73761.45761.1224106.52500.9587-0.28441.0760-0.319280.00000.28481

16、.44180.4106111.82480.9283-0.37180.3812-0.1527（4）計(jì)算單位抗力及其相應(yīng)的摩擦力在基本結(jié)構(gòu)中產(chǎn)生的內(nèi)力彎矩 （4-9） 軸力 （4-10）式中為力至接縫中心點(diǎn)的力臂，有圖上量得計(jì)算見(jiàn)表4.6及表4.7。表4.6單位抗力及其相應(yīng)的摩擦力在基本結(jié)構(gòu)中產(chǎn)生彎矩計(jì)算表截面R4=0.4082hR5=1.1715hR6=1.4547hR7=1.1224hR8=0.4106hM0(h)r4i-R4r4i(h)r5i-R5r5i(h)r6i-R6r6i(h)r7i-R7r7i(h)r8i-R8r8i(h)40.4944-0.2018-0.201851.8763-0.

17、76590.6829-0.8000-1.565963.2547-1.32862.0686-2.42340.7766-1.1297-4.881774.5567-1.86003.4413-4.03152.1640-3.14800.8268-0.9280-9.967585.7490-2.34674.7522-5.56723.5443-5.15592.2112-2.48191.0158-0.4171-15.9688表4.7單位抗力及其相應(yīng)的摩擦力在基本結(jié)構(gòu)中產(chǎn)生軸力計(jì)算表截面sincosRv(h)sinRv(h)RH(h)cosRH(h)N0(h)453.19720.80070.59910.16690

18、.13360.37250.2232-0.0895566.49650.91700.39880.42390.38881.51540.6044-0.2156679.79580.98420.17720.43120.42442.97000.5263-0.1019792.18480.9993-0.03810.11200.11194.0460-0.15420.2661890.00001.00000.0000-0.0407-0.04074.42720.0000-0.0407（5）單位抗力及相應(yīng)摩擦力產(chǎn)生的載位移計(jì)算見(jiàn)表4.8。表4.8載位移計(jì)算表截面M0(h)1/Iy/I1+yM0/IM0y/IM0(1+y)

19、/I積分系數(shù)1/34-0.201855.5556133.64463.4056-11.2119-26.9714-38.183325-1.565955.5556200.40024.6072-86.9958-313.8112-400.807046-4.881755.5556274.28365.9371-271.2032-1338.9573-1610.160427-9.967555.5556351.33367.3240-553.7504-3501.9175-4055.667848-15.968855.5556428.06708.7052-887.1549-6835.7060-7722.86101-13

20、38.3233-8276.8260-9615.1493校核為閉合差 4、墻底（彈性地基上的剛性梁）位移單位位移作用下的轉(zhuǎn)角主動(dòng)荷載作用下的轉(zhuǎn)角截面單位抗力及相應(yīng)摩擦力作用下的轉(zhuǎn)角4.3.5解力法方程襯砌矢高 計(jì)算力法方程系數(shù)為截面 以上將單位抗力及相應(yīng)摩擦力產(chǎn)生的位移乘以，即為被動(dòng)荷載的載位移。求解方程為式中 式中 以上解得的值代入原方程，校核計(jì)算是否正確。4.3.6計(jì)算主動(dòng)荷載和被動(dòng)荷載計(jì)算公式為 （4-11） （4-12） 截面計(jì)算過(guò)程列入表4.9和表4.10。表4.9主動(dòng)荷載和被動(dòng)荷載的彎矩計(jì)算表截面Mp0X1pX2pyMpM0(h)X1(h)X2y(h)M(h)00.000111.57

21、950.0000111.57950.0000-3.24780.0000-3.24781-152.896111.5795135.198193.88200.0000-3.24780.3977-2.85012-593.556111.5795533.566251.58980.0000-3.24781.5695-1.67833-1300.934111.57951173.7616-15.59280.0000-3.24783.45270.20494-2215.048111.57952021.3335-82.1347-0.2018-3.24785.94592.49635-3268.993111.5795303

22、0.9920-126.4213-1.5659-3.24788.91594.10226-4387.266111.57954148.4560-127.2306-4.8817-3.247812.20304.07367-5494.477111.57955313.8150-69.0829-9.9675-3.247815.63102.41578-6580.711111.57956474.38455.2527-15.9688-3.247819.0449-0.1716表4.10主動(dòng)荷載和被動(dòng)荷載的軸力計(jì)算表截面Np0X2pcosNpN0(h)X2cosN00.000840.2617840.26170.0000

23、2.47172.4717130.168817.7427847.91030.00002.40552.40552117.961751.3620869.32330.00002.21022.21023256.539644.6488901.18770.00001.89631.89634433.955503.4008937.3559-0.08951.48081.39135636.258335.0964971.3539-0.21560.98570.77016848.123148.8944997.0174-0.10190.43800.336171043.233-32.01401011.21930.2661-0

24、.09750.168681033.3690.00001033.3690-0.04070.0000-0.04074.3.7最大抗力值的求解首先求出最大抗力方向內(nèi)的位移考慮到接縫5的徑向位移與水平方向有一定的偏離，因此修正后有 （4-13） 截面計(jì)算過(guò)程列入表4.11。表4.11位移值計(jì)算表截面Mp/IM/I (h)y5-yiMp(y5-yi)/IM(y5-yi)/I積分系數(shù)1/306198.8661-180.43353.607222360.5497-650.8596115215.6719-158.33923.446317974.7702-545.6844422866.1016-93.23732.

25、97228518.6270-277.120023-866.268211.38432.2103-1914.712725.162844-4563.0429138.68391.2016-5482.9523166.642525-7023.4097227.89980.00000.00000.0000430890.7098-984.6337位移值為最大抗力值為4.3.8計(jì)算襯砌總內(nèi)力按下式計(jì)算襯砌總內(nèi)力 （4-14） 截面計(jì)算過(guò)程列入表4.12。表4.12總內(nèi)力計(jì)算表截面MpMMNpNNeM/IMy/I積分系數(shù)1/30111.5795-97.326214.2533840.261774.0689914.33

26、060.0156791.85210.00001193.8820-85.40858.4735847.910372.0839919.99420.0092470.752675.74414251.5898-50.29241.2974869.323366.2324935.55580.001472.077345.769123-15.59286.1407-9.4521901.187756.8257958.0134-0.0099-525.1164-733.535144-82.134774.8063-7.3284937.355941.6917979.0476-0.0075-407.1315-979.395425-126.4213122.9296-3.4917971.353923.0777994.4316-0.0035-193.9818-699.731246-127.2306122.0721-5.1586997.01