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盾构隧道衬砌设计计算书060987李博一、设计资料如图所示，为一软土地区地铁盾构隧道横断面，有一块封顶块K，两块邻接块L，两块标准块B以及一块封底块D六块管片组成。35062005500138350B1138DB273L1K73L288500q=20kN/m21280灰色淤泥质粘土g=17.1kN/mc=12.kPaj=7.229253褐黄色粘土g=19.1kN/m10003500灰色淤泥质粉质粘土g=18kN/mc=12.2kPaj=8.916453灰色砂质粉土g=18.7kN/m33人工填土g=18kN/m1500350700部分数据地面超载2/20mkNq=超地层基床系数2/20000mkNk=衬砌外径mD2.60=衬砌内径mD5.5=管片厚度mmt350=管片宽度mb2.1=管片裂缝宽度允许值[]mm2.0=v接缝张开允许值[]mm3=D混凝土抗压强度设计值MPafc1.23=混凝土抗压强度设计值MPaft89.1=钢筋抗拉强度设计值（II级钢）MPafy300=钢筋抗拉强度设计值（II级钢）MPafy300'=管片混凝土保护层厚度mmaass50'==钢筋抗拉强度设计值（I级钢）MPafy210=混凝土弹性模量27/1045.3mkNE´=钢筋弹性模量（II级钢）28/100.2mkNE´=钢M30螺栓有效面积26.560mmAg=M30螺栓设计强度MPaRg210=M30螺栓弹性模量28/101.2mkNE´=螺栓M30螺栓长度cml5.18=螺栓二、荷载计算1、自重kNRDDgHh81.1602)(41220=×-=pgp2、竖向土压力由于隧道上覆土层为灰色淤泥质粉质粘土，地层基床系数2/20000mkNk=，推测应为硬黏性土，且隧道埋深超过隧道半径很多倍，故竖向土压力应按照太沙基公式计算。衬砌圆环顶部的松弛宽度mDB73.6)48cot(200=+=jp地面超载2/20mkNq=超，且Hqg/超，H为覆土厚度，即56.7m。松弛高度mKBHKBcBh05.29tantanexp1)1(0010000=úûùêëé÷÷øöççèæ---=jjg‘1H为修正覆土厚度，即将上部土柱重量按浮重度折算而成的覆土厚度mqlHHw83.59820185.082.56'1=+´+´=+×+=‘超ggg22'0/200/38.232mkNmkNhq==g土，取2/38.232mkNq=土3、拱背土压计算半径mmRH292523506200=-=。土层重度取拱背覆土所在土层的浮重度3/8mkN×=‘g，并将其简化为竖向均布荷载22/03.5243.02mkNRRRGqHHH=×=×=’拱g4、净水压力隧道顶面处净水压力2/00.562mkNHqww=×=g顶水隧道底面处净水压力2/50.6202mkNRHqHww=+×=）（底水g5、侧向水土压力侧向水土压力采用水土分算的方法，按朗肯主动土压力计算。土压力aaKcKhqp2)(-×+=g，水压力1wwHp×=g其中q为上部土层产生的竖向压力；g为计算土层的重度，因计算位置位于地下水位以下，故取浮重度；h为计算处至隧道顶面的距离；1wH为计算处至地下水面的距离。计算结果如下土压力（2/mkN）水压力（2/mkN）隧道顶面A149.23隧道顶面A562.00粉质粘土下表面B158.87淤泥质黏土上表面C169.51土层分界面B578.45隧道底面D192.72ABCD隧道底面D620.50ABD6、侧向土壤抗力由于土层变化引起的土压力突变比较小，可以将侧向水土压力近似看做是均匀变化的。取隧道顶面侧向压力21/97.706mkNp=，隧道底面侧向压力22/69.808mkNp=取衬砌圆环抗弯刚度折减系数7.0=h，管片弹性模量27/1045.3mkNE´=，管片的截面惯性矩mmI/10573.343×´=-，弹性基床系数3/20000mkNk=。衬砌圆环在水平直径处变形量mmRkIERgppqqqHH985.1)0454.0(242224421=×+×××+--++=hpd）（拱顶水土侧向抗力21/70.39mkNkpk=×=d7、荷载组合竖向荷载2/29.959)(2.1mkNqqqq=++=拱顶水土自重21/50.102.1mkNgg==水平荷载水土压力（2/mkN）隧道顶面A853.48粉质粘土下表面B884.78淤泥质黏土上表面C897.56隧道底面D975.86ABCD侧向抗力21/52.482.1mkNppkk==三、内力计算1、按惯用修正法公式表格进行计算侧向压力因土层改变所引起的变化很小，可以近似按照均匀变化计算a、管片内力计算结果弯矩（mkN×）角度垂直荷载水平荷载弹性抗力水平三角荷载自重每米内力02051.83-1825.51-40.42-108.1830.97108.69101928.09-1715.42-38.59-103.2529.39100.22201571.79-1398.42-33.18-88.6224.7676.33301025.92-912.76-24.33-64.9117.4841.4140356.30-317.00-12.32-33.368.171.7950-356.30317.002.483.80-2.34-35.3560-1025.92912.7618.9443.27-13.07-64.0270-1571.791398.4234.7380.70-22.91-80.8480-1928.091715.4246.69111.16-30.69-85.5190-2051.831825.5151.39129.81-35.28-80.39100-1928.091715.4246.69132.80-35.61-68.79110-1571.791398.4234.73118.18-31.14-51.61120-1025.92912.7618.9486.54-22.21-29.89130-356.30317.002.4841.28-9.91-5.45140356.30-317.00-12.32-11.724.0819.331501025.92-912.76-24.33-64.9117.8041.721601571.79-1398.42-33.18-110.2629.2959.221701928.09-1715.42-38.59-140.7236.9170.271802051.83-1825.51-40.42-151.4539.5874.04管片弯矩图（mkN×）剪力（kN）角度垂直荷载水平荷载弹性抗力水平三角荷载自重每米内力00.000.000.000.000.000.0010-479.84426.917.1319.266.17-20.3720-901.81802.3414.0437.8411.82-35.7630-1215.001080.9920.5354.6816.49-42.3240-1381.651229.2526.3968.1919.72-38.0950-1381.651229.2531.1976.3221.15-23.7460-1215.001080.9932.5176.8720.51-4.1370-901.81802.3428.3068.1517.6414.6280-479.84426.9117.4249.5712.4926.55900.000.000.0022.19-5.1217.07100479.84-426.9117.42-11.144.0163.22110901.81-802.3428.30-45.9613.3795.171201215.00-1080.9932.51-76.8721.27110.921301381.65-1229.2531.19-98.5126.36111.441401381.65-1229.2526.39-106.6327.7999.961501215.00-1080.9920.53-99.0625.2980.78160901.81-802.3414.04-76.2719.1956.43170479.84-426.917.13-41.4510.3328.941800.000.000.000.000.000.00管片剪力图（kN）轴力（kN）角度垂直荷载水平荷载弹性抗力水平三角荷载自重每米内力00.002496.4341.06110.95-5.122643.321084.612421.1540.44109.24-4.112651.3320328.232204.4038.58103.95-1.142674.0330701.481872.3235.5694.703.612707.67401159.341464.9631.4581.279.862746.89501646.581031.4626.1764.0417.242785.50602104.44624.1118.7744.3825.292816.99702477.69292.0310.3024.8033.512838.33802721.3175.283.078.7441.342849.75902805.920.000.000.0048.242854.171002721.3175.283.071.9652.232853.861102477.69292.0310.3016.7351.692848.441202104.44624.1118.7744.3847.072838.771301646.581031.4626.1782.6639.382826.251401159.341464.9631.45127.0730.002812.84150701.481872.3235.56171.5720.512801.45160328.232204.4038.58209.5512.432793.2017084.612421.1540.44235.097.022788.311800.002496.4341.06244.095.122786.70管片轴力图（kN）b、接缝内力计算值位置弯矩（mkN×）剪力（kN）轴力（kN）8103.24-26.462648.4773-83.46-13.522842.7113814.47102.972815.432、同济曙光荷载结构法计算用单向受压弹簧模拟地层抗力。a、计算模型b、管片弯矩图（mkN×）c、管片剪力图（kN）d、管片轴力图（kN）四、管片配筋和接头设计隧道采用通缝拼接，标准块即在73°~138°范围内。由内力计算结果可知：最大弯矩发生在80°处，为mkN×51.85，考虑到管片并非是理想的匀质圆环，对此弯矩乘以弯矩传递系数1.3，则设计控制弯矩为mkN×16.111，相应截面上的轴力为kN75.2849。最大轴力发生在90°截面，为kN17.2854，对应的弯矩乘以传递系数后为mkN×51.104。最大剪力发生在130°截面，为kN44.111。管片中受弯钢筋和分布钢筋使用II级钢，抗剪钢筋采用I级钢。1、标准块的受弯钢筋管片按照偏心受压构件进行设计，并且采用对称配筋。截面有效高度mmh300503500=-=；附加偏心距mmea7.11350301=´=，取mm20a、最大弯矩截面轴向力偏心距mmNMe0.390==；实际初始偏心距mmeeeai0.590=+=；偏心增大系数33.1=h，mmaheesi3.2032=-+=h。55.0411.00=×=bhfNcx为大偏心受压，'021004.123sammmmh==x2,02201332)()5.0(mmahfbhfNeAsycs-=---=xxb、最大轴力截面2,02201421)()5.0(mmahfbhfNeAsycs-=---=xx按照公式计算所得的钢筋面积均为负值，说明轴力很大，在管片工作过程中，全界面受压，不存在受拉破坏。考虑到管片装配、运输、不均匀沉降等影响，采用构造配筋。2min945mmbhAs==r，选用200@16钢筋，实际21131mmAs=。