压力隧洞的衬砌计算

1、压力隧洞的衬砌计算一、基本资料某水电站压力隧洞，为三级建筑物，拟进行设计的断面桩号为0+320，该设计断面围 岩属III类，岩石容重Y r = 25 kN / m 3，铅直向和水平向围岩压力系数分别为S = 0.2， 七=0，相应的单位弹性抗力系数k 0=5 X 106 kN / m 3，隧洞的过水流量Q =12.2 m 3 / s， 在正常运行情况下，计算断面内壁洞顶静水头H = 42.5m，调压井产生最高涌浪时使洞 内增加的静水压力 H = 17.5m，隧洞内直径D = 2.10m。采用C20砼衬砌，其设计抗裂 强度Rf = 1600kPa，相应的弹模Eh = 2.6 x 10 7 kPa

2、 ;采用3#钢筋，其设计强度 R = 2.4 x 10 5 kPa，相应的弹模 E = 2.1 x 10 8 kPa，钢筋砼容重y” = 25 kN / m 3，泊 松比H= 。对于三级建筑物，钢筋砼结构构件的抗裂安全系数Kf = 1.20 ;砼结构构件 的强度安全系数K = 1.50，考虑隧洞超挖 h = 0.15 m。LTN单位:解:（一）衬砌厚度计算h = r : A 9 g+- 1。 - P*gh式中：A =*o(1 + *)= (2.18*108-5*106 ( 1+1/6)/(2.18*108+5*106( 1+1/6) E + k (1 + * )(1 - 2 *)(1-2/6)

3、 =0.9545 3 =Rf/Kf=1600/1.2=1333.3Kpagh均匀内压力 P=rw (H+AH) =9.81*(42.5+17.5)=588.6Kpa1.05、:0.95451333 .3 + 588 .61333 .3 - 588 .6一 1 =0.60m（二）荷载计算：均匀内水压力p :P=（H+AH） Y w=588.6Kpa围岩压力q：q=SyDY R=0.2*2.1*25=10.5Kka单位面积衬砌自重g：在计算断面上沿着长度方向取1米长的衬砌计算其自重g。g=h - Y gh= （0.6+0.1） *25=18.75Kpa（三）衬砌内力计算：1.由均匀内水压力作用，在

4、衬砌中产生的轴向拉力：N = Pr - pr=588.6*1.05-588.6*1.65*(1-0.9545)/(1.65/1.05)2-0.9545)(re )2 - A ri=588.85KN/M2.由围岩垂直压力作用，使衬砌各断面产生的弯矩和轴向力按下式计算:M = qr r A a + B + Cn (1 + a ) eN = qr D a + F + Gn (1 + a)bh 3J = 3 =1*0.6 3/12=0.018 M 412取计算宽度b=1米式中系数A、B、C、D、F、G可由表查出，K =如=5*106/1.65=3 . 03*106KN/M 2rea = 2 - re

5、=2-1.65/1.35=0.7778r0.06416 + EhJ=2.69r3 r KbM = qr r A a + B + Cn (1 + a)计算表 e断面AAaBCCnAa +B+Cn(1+a )M =00.1630.1270.087-0.007-0.0190.1804.202(P =n /4-0.025-0.0200.025-0.001-0.0020.0010.034 =n /2-0.125-0.097-0.1250.0080.022-0.182-4.256 =3n /40.0250.020-0.0250.0000.001-0.005-0.106 =n0.0870.0680.163-

6、0.008-0.0230.1904.435N = qr D a + F + Gn (1 + a)计算表断面DDaFGGnDa +F+Gn(1+a )N =00.2120.165-0.2120.0210.0570.0550.946 =n /40.1500.1170.3500.0150.0400.5399.316 =n /20.0000.0001.0000.0060.0161.02817.775 =3n /4-0.150-0.1170.9000.0140.0380.85014.698 =n-0.212-0.1650.7120.0220.0610.65511.3313.由衬砌自重g作用下，衬砌各断面

7、产生的弯矩和轴向力按下式计算:M=gr2 (A1+B1n)N=gr(C1+D1n)列表计算M=gr2 R+B)计算表断面A 1B 1B1nA1+B1nM=gr2 (A1+B1n) =00.345-0.022-0.0600.2859.680 =n /40.033-0.003-0.0070.0260.893 =n /2-0.3930.0260.070-0.322-10.943 =3n /4-0.0340.0010.002-0.032-1.076 =n0.441-0.026-0.0720.36912.533Nugrlq+Dn)计算表断面C 1D 1D,nC,+D,nM=gr (C,+D,n) =0-

8、0.1670.0660.1790.0130.320(P =n /40.4370.0470.1270.56414.212 =n /21.5710.0180.0491.62040.797 =3n /41.9190.0430.1182.03751.286 =n1.7370.0700.1911.92948.570由无水头洞内满水水压力作用下，衬砌各断面产生的弯矩和轴向力按下式计算:M=y r.2r(A2+B2n)N=y r.2 (C2+D2n)列表计算M=y wrj2r(A2+B2n)计算表断面A 2B 21 w i22qB2nA2+B2nM=y r 2r(A +B n) :_-i2 2 =00.17

9、2-0.011-0.0300.1432.077 =n /40.017-0.001-0.0040.0130.192 =n /2-0.1960.0130.035-0.161-2.347 =3n /4-0.0170.0000.001-0.016-0.231 =n0.220-0.013-0.0360.1852.688N=y片 阳+叩)计，算表断面C 2wiD 222D2nC2+D2nN=y r 2 (C +D n) :i22 =0-0.5830.0330.090-0.494-5.334 =n /4-0.4280.0230.063-0.364-3.936 =n /2-0.2150.0090.025-0.

10、190-2.053 =3n /4-0.3940.0220.059-0.335-3.623 =n-0.6310.0350.096-0.536-5.7875.除均匀内水压力外，其荷载产生的内力总和:断面弯矩M轴向力N围岩压力衬砌自重非均匀内 水压力 M围岩压力衬砌自重非均匀内 水压力 NMM 2M 3M+M +M 123NN 2N 3N+N +N 123 =04.2029.6802.07715.9590.9460.320-5.334-4.069 =n /40.0340.8930.1921.1199.31614.212-3.93619.592 =n /2-4.256-10.943-2.347-17.

11、54617.77540.797-2.05456.518 =3n /4-0.106-1.076-0.231-1.41314.69851.286-3.62362.362 =n4.43512.5331.96018.92811.33148.570-5.78754.115配筋计算:内层：3 J =Rg/Kg= (588.85-54.29)*(0.6-0.05-0.05)+2*19.8)(N - E N )( h - a ) + 2 M2。( h o - a )/(2*1.6*105*(0.6-0.05-0.05)(m2)=1918MM2外层：(N, - N )( h, - a) - 2 M = (588 .85 二