整体稳定计算

1、附件一围堰堰顶高程计算上游围堰堰顶高程计算1.1设计洪水位及堰顶超高计算公式根据 Tender documents, BOOK 3 OF 4, VOLUME W, PART 1, 1.3 （Hydrological Characteristics）, Fig. 4.3 （Discharge rating curves of the Nile river at the Merowe HPP tailrace可查 知全年3%洪水频率，相应流量为12300m3/s,厂房尾水处（靠近下游围堰）在左河道过流情 况下，相应水位为259.3m；根据水力学计算和水面线推求结果，推出上游围堰处相应水位为 259

2、.4m。为保证在发生设计洪水位时，不漫溢或溅过堰顶，堰顶高程要根据设计洪水位，考虑风 浪高和安全超高确定。堰顶超高可按下式计算：d = e + h + 6式中，d 围堰在静水位以上的超高，m；e 堰前因风吹而使静水位超出库水位的壅水高度，m；h 波浪在堰坡上的爬高，m； q6 一波浪以上的安全超高，m。下面分别确定e、h、6。1.2风雍水面高度q风雍水面高度可按下式计算：KW 2 D e = cos am式中W采用多年平均最大风速，m/s；D风区长度（吹程），m；H 堰前水深，m；K 综合摩阻系数，取3.6X10-6；a风向与围堰轴线的法线方向所成的交角。根据招标文件：MEROWE-03-B0

3、0K 3 OF 4-VOLUME W-SUPPORTING DATA水文气象和地质资料，风向：北风45%,东北风21%。20%频率暴风的年最大风速W为20m/s。水位为259.4m时，风区内水域平均深度H = 259 .4 - 244 = 15.4m吹程D取为从围堰算起沿库水面直到对岸的最大直线距离，约2000m。a取为20将以上参数代入公式，得=0.009 mKW 2D3.6 x 10 -6 x 20 2 x 2000。2gH 。以 一 2 x 9.8 x 15.41.3m波浪爬高1）波浪平均波高、平均波周期和平均波长计算波浪平均波高h采用莆田试验站公式 mgh= 0.13 thW 2th(

4、gD机奕 0.0018 | II W 2 )0.70.13 th0.7式中h 平均波高，m；W计算风速，m/s；D风区长度，m；0.0018h = 0.13 thm=0.13 th0.7 xth(9.8 x 15.4 0.7I 20 2(gH 0.70.7m W2 )0.450.13 th(W 0.0018(9.8 x 2000 (9.8 x 15.4 )0.70.7 xI 20 2)0.450.13 th1.20乙 y bH sin a58.009b.假定上游水位为407.5m,滑动面在水面以下，采用同样方法进行计算，如图2,计算 结果见表2。R=56.67m，b=1.6945m，c=0K=

5、ZY bH cos a tan o +Z cli iiii乙 y bH sin a65.43446.368=1.4111.20表2上游坡面局部稳定计算土条编号土条高度(m)容重 (tf/ m3)土条重量Wi=Y ibHia iSin a iCosa iNi=Y ib Hicos a iTi=Y ib Hisin a ilitgq iNi tgq i00.331.150.59910.4910.1820.9830.5890.1091.720.7810.46010.951.151.72412.2710.2130.9771.6850.3661.730.7811.31621.541.152.79513.

6、9950.2420.9702.7120.6761.740.7812.11832.051.153.72015.7660.2720.9623.5801.0111.760.7812.79742.511.154.55517.5530.3020.9534.3431.3741.780.7813.39352.921.155.29919.3570.3310.9434.9991.7561.810.7813.90663.101.155.62621.1820.3610.9325.2462.0331.830.7814.09873.541.156.42423.0290.3910.9205.9122.5131.850.7

7、814.61983.751.156.80524.9020.4210.9076.1732.8651.880.7814.82293.91.157.07726.8040.4510.8936.3173.1911.910.7814.935103.981.157.22328.7390.4810.8776.3333.4721.940.7814.947113.981.157.22330.710.5110.8606.2103.6881.970.7814.851123.91.157.07732.7220.5410.8415.9543.8252.010.7814.652133.741.156.78734.7810.

8、5700.8215.5753.8712.050.7814.355143.481.156.31536.8920.6000.8005.0513.7912.090.7813.946153.131.155.68039.0630.6300.7764.4103.5792.140.7813.445162.661.154.82741.3040.6600.7513.6263.1862.190.7812.833172.081.153.77543.6240.6900.7242.7322.6042.260.7812.135181.361.152.46846.0380.7200.6941.7131.7762.320.7

9、811.338190.51.150.90748.5620.7500.6620.6010.6802.380.7810.469合计46.36865.434迎水面部分浸水，部分干坡，如图3所示，计算结果见表3。R=67.41m, b0=1.368m, c=0y bH cos a tan 中 + Z c I 1zK =111z y bH sin a74.56356.686=1.315 1.20表3上游坡面局部稳定计算土条编号土条高度(m)容重 (tf/m3)土条 重量 Wi=yi bHia .isina .icosaiN.i=YibHicosaiTi=yibHisinail.itg iNjtgq i0

10、0.291.150.52613.4420.2320.9730.5120.1221.760.7810.40010.841.151.52414.9460.2580.9661.4730.3931.780.7811.15121.341.152.43216.4620.2830.9592.3320.6891.790.7811.82231.781.153.23017.9890.3090.9513.0720.9981.80.7812.40042.181.153.95619.5240.3340.9433.7291.3221.820.7812.91352.531.154.59121.0840.3600.9334.

11、2841.6521.840.7813.34762.821.155.11722.6560.3850.9234.7231.9711.860.7813.68973.061.155.55324.2460.4110.9125.0632.2801.880.7813.95583.231.155.86125.8560.4360.9005.2752.5561.910.7814.12193.351.156.07927.4850.4610.8875.3932.8051.930.7814.213103.411.9010.22429.1450.4870.8738.9304.9791.960.7816.976113.41

12、.9010.19430.8290.5120.8598.7545.22420.7816.838123.321.909.95432.5780.5380.8438.3885.3592.040.7816.553133.171.909.50434.2910.5630.8267.8535.3542.080.7816.134142.941.908.81536.0750.5890.8087.1255.1902.120.7815.566152.631.907.88537.9020.6140.7896.2224.8442.170.7814.861162.231.906.68639.7740.6400.7695.1

13、394.2772.230.7814.015171.731.905.18741.6990.6650.7473.8733.4502.300.7813.026181.131.903.38843.6840.6910.7232.4502.3402.370.7811.914190.411.901.22945.7360.7160.6980.8580.8802.470.7810.670合计56.68674.5631.2上游围堰下游坡面局部稳定性计算对于上游围堰下游边坡，如图4,按干坡考虑，计算方法同上，计算结果见表4。R=52.86m, b=1.5615m, c=0表4上游围堰下游坡面局部稳定计算土条编号土条

14、高度(m)容重(tf/m3)土条重量Wi=yibHia .isina .icosaiN.i=YibHicosaiTi=yibHisinailitgq iNjtgw i00.661.91.97913.7620.2380.9711.9220.4711.610.7811.50110.971.92.90815.5110.2670.9642.8020.7781.620.7812.18921.551.94.64717.2760.2970.9554.4381.3801.640.7813.46732.081.96.23619.0570.3260.9455.8952.0361.650.7814.60542.55

15、1.97.64520.8580.3560.9347.1442.7221.670.7815.58152.971.98.90522.680.3860.9238.2163.4331.690.7816.41963.331.99.98424.5270.4150.9109.0834.1441.720.7817.09673.631.910.88326.4020.4450.8969.7484.8391.740.7817.61683.861.911.57328.3080.4740.88010.1895.4881.770.7817.96094.031.912.08330.2480.5040.86410.4386.

16、0861.810.7818.154104.121.912.35332.2270.5330.84610.4506.5871.850.7818.163114.141.912.41334.2510.5630.82710.2606.9861.890.7818.015124.121.912.35336.3250.5920.8069.9527.3171.940.7817.775133.921.911.75338.4550.6220.7839.2047.3091.990.7817.190143.671.911.00340.6500.6510.7598.3497.1682.060.7816.522153.51

17、1.910.52442.920.6810.7327.7077.1662.130.7816.021162.851.98.54545.2770.7100.7046.0136.0712.220.7814.698172.411.97.22647.7360.7400.6734.8605.3472.320.7813.797181.481.94.43750.3170.7700.6392.8343.4152.450.7812.214190.551.91.64953.0470.7990.6010.9911.3182.570.7810.774合计90.059109.757109.757、C=1.219 1.209

18、0.059顶宽10m.ZY bH cos a tan 中 +Z cl.K =1i =2 y bH sin a1.3上游围堰整体滑苛稳起分析如图5,上游围堰上下游坡比m=1.75, 河床底部为35m厚中细砂覆盖层，砂的内摩擦角取甲=25 由于tan =tan25 =0.466,取摩擦系数f=0.4,凝聚力c=0 堆石容重Y 1=1.9 tf/m3心墙容重Y =2.1 tf/m3反滤层及过渡层容重Y 3=1.8 tf/m3堆石面积A1=(10+159.3)X42.1/2-57.17X2-5.41X 13.6-(18.71X2-1.5X 13.6)/2X 13.6+21.32*18.6 =3656.

19、67.63m2心墙面积 A = (379.5-353) X 0.8=21.2im2反滤层及过渡层面积A =57.17X2+5.41X 13.6+(18.71X2-1.5X 13.6)/2X 13.6=303.65im3垂直水流方向取单位宽度(1m)，则堆石重量 W1=Y 1XA1=6947.66tf心墙重量 w2=Y 2XA；=44.52tf反滤层及过渡层重量W3=y 3XA3= 546.57tfU =y H x 30.2 + 理 x 146.5 扬压力2式中Y为水的容重，取1 tf/m3H为上游水深，这里考虑3%频率洪水Q=21200m3/s，此时上游水位为407.5m,相应水深H=407.

20、5-365.9=41.6mx 41.6 = 4303.52 tf=865.28 tfU = 1 x 30.2 *41.6 + - x 146.5 2迎水面水压力xH1 x 41.6 x 41.62抗滑稳定安全系数:0.4 x (6947.66 + 44.52 + 546.57 - 4303.52) =1.50 1.20865.28此种情况为最不利情况，可见在各种水位下，围堰均无沿地基面整体滑动的可能。1.4上游围堰沿地基面的局部滑动分析由于上游围堰堰基为砂砾石覆盖层，其抗剪强度较低，可视为软弱层，因此考虑围堰沿 地基面的局部滑动，如图6所示:滑裂面为圆弧abc，对堰体下游坡面应用瑞典圆弧法计算

21、围 堰下游坡面的安全系数。堆石容重Y取19kN/m3，甲=38 ， c=0砼防渗墙容重Y取21kN/m3,甲=15，c=10kPa河床底部砂层Y取15kN/m3,甲=25 ，c=04.5H图6瑞典圆弧法稳定分析示意图假定土体里只有垂直力，不计水平力及剪应力，土条两侧的压i， ac不考虑土条间的作用力 力互相取消。假定滑裂面圆弧圆心为0，半径为R，土条高度为Hi，分条宽度为b，土条重Wi=Y ibHi， 法向分力为Ni，切向分力为Ti，Ni与Wi之交角为a i，ac弧长为l=li0其中N.=W.cosa .=y -bHcosa iT = W sina =Y bH sina 坍滑土体沿abc之总法

22、向分力及总切向分力为：N=bY .H.cosa .T=bY .H.sina在滑裂面上，抵抗滑动的力为：i i i总凝聚力=CL 总摩擦力=Ntgw 对圆心0的抗滑力矩为：Mr=R(Nitg i+Cili) 对圆心0的滑动力矩为：1 1M =RT 堰坡稳定安全系数为：式中 l=bseca .K= r = MS Tsi计算用列表法进行。计算步骤为：按比例作出堰体横断面图，取其厚度为1.0m，在堰体横断面上作出圆弧滑裂面。将滑裂面内的土体分成垂直土条。分条时，以铅直线Ob为零点，以等宽度直接向Ob两侧量取，即得各条块的中心线位置，并依顺序编号，O1b以左为1, 2, 3, ., 6。O1b 以右为-

23、1，-2，-3。O b处为零条。量出每一条块中心线的各种不同容重土体的高度，填入表中，逐条进行计算，最后用公 式求出安全系数。确定最危险滑动圆弧圆心位置的方法：首先按一定比例画出围堰的横剖面图，然后在下游坡面中点C,作一铅垂线及另一与坝坡 成85角的直线，同时以C为圆心，分别以R1=0.75H=12.75m,R2=1.7H=28.9m为半径作出圆 弧，与以上两直线围成扇形。最危险滑弧圆心位置大致在此扇形区域内的M1M2延长线附近， M1M2直线的确定方法如图所示。试算时，首先在M1M2延长线上取01、02、03各点为圆心，作通过B1点的圆弧，求出各 滑弧的安全系数K，并作出其变化曲线。然后通过

24、K值最小的点01作垂线N1N2，在N1N2线上01点附近，取03、04各点，分别以 各点为圆心，仍作通过B1点的圆弧，求出各滑动面的安全系数，绘制其变化曲线，从中找出 最小的圆心0点.然后改变B1,让滑弧通过B2,B3等各点，求出各情况下的K值。所求得的最 小K值，即为所求围堰下游坡面的最小稳定安全系数。经过多次试算，确定如图所示滑动面，为沿地基的最危险滑动面，圆弧半径R=35.20mb=2.25m计算结果见表5。K,bH . cos 气 tan 中.+ S 3269 .246 + 99.9771 4961 30E Y bH sin a2252 .168 综合分析以上各种可能的滑动形式，围堰边

25、坡部分浸水时最危险，此时安全系数K最小， 为1.35，满足规范要求。由于围堰上下游有垂直厚度为0.5m的护坡，而计算时没考虑，故计 算结果偏于保守，因此上游围堰上下游边坡采用1： 1.8是安全的。下游预围堰稳定分析对于下游预围堰，主要分析其迎水面粘土斜墙的抗滑稳定性。粘土料容重Y 取 16.5kN/m3, ip =15，c=10kPa,浮容重Y 取10kN/m3，采用条分法计算其抗滑稳定安全系数。假定不同的滑裂面，求得其最小安全系数。安全系数随水位的不同而变，计算时假定几 种水位，先求得某一水位的最小安全系数，然后找出最危险水位的最小安全系数。2.1圆弧法假设土体沿圆弧面发生滑动，考虑圆弧滑动

26、土体分条间推力，采用不考虑分条间的摩擦 力之差的简化毕肖普法计算其抗滑稳定安全系数，计算公式为E (W tg + c l cos a )i i i ii mE W sin aii式中， m a = cos a. + (tg 9 x sin a / F )a计算时通过试算方法，首先假定F =1,求出m.，再代入上面公式中求F，若F 1， 则用此F值求出新的m及F。如此反复进行下去:直至假设的F和算出的F接近为止。 通过假定多个滑动面和几种水位分别计算，确定如图7（下游预围堰稳定分析示意图1）所示。土条编号土条高 度(m)容重(t/m3)土条重量Wi=Y ibHia isina icosa iNi

27、=Y ibHicosa iTi=Y ibHisina iliCi-60.551518.563-22.69-0.3860.92317.325-7.2402.4390-51.491550.288-19.39-0.3320.94347.986-16.8802.3850-42.941599.225-14.81-0.2550.96797.040-25.6442.3270-34.7715160.988-11.02-0.1910.982159.848-31.1132.2920-26.43815217.283-7.28-0.1270.992218.023-27.8382.2680-17.9415267.975

28、-3.59-0.0630.998270.540-16.9652.254009.2816334.08000.0001.000337.9400.0002.2500110.4617400.0953.770.0660.998403.84326.5972.2550211.4818464.9407.460.1300.992466.33661.0322.2690312.3218498.96010.960.1900.982495.52995.9122.2920413.02418527.47214.770.2550.967515.954135.9602.3270513.518.5561.93818.920.32

29、40.946537.751184.2222.3780613.8418.5576.09022.930.3890.921536.745226.9332.4430713.9419595.93526.890.4520.892537.707272.5162.5220813.819589.95031.310.5190.855509.945309.9802.6330913.2418536.22035.980.5870.809439.037318.5312.78001011.2116.5416.17141.080.6570.754317.432276.5162.98410118.7416.5324.47346

30、.640.7270.687225.449238.5423.27610125.6516.5209.75653.020.7990.602127.714169.4393.73810131.521861.56060.960.8740.48630.25754.4264.6310合计6275.0782252.168最危险圆弧面。详细计算过程见简化毕肖普法计算表(表6)。圆弧半径R=63m，分条宽度b=1.95m,水位以上粘土取干容重，水位以下粘土取浮容重。计算所得稳定安全系数为Z (W tg + c l cos a )1i i i ii m494.931=2.67 1.30185.440Z W sin a

31、图7下游预围堰稳定分析示意图1sC1460.11 U811211.6块石碴混、石.二合料2.2折线法假设土体沿折线滑动面发生滑动，其折点一般为下游水位与滑动面的交点。不考虑土条 间的作用力传递时，计算偏于安全，各土块的抗滑力En和滑动力Ea的水平分力总和为=Z (W tg 中 cos 2 a + c l cos a )ii i iiE = Z (W sin a. cos a.)f EI抗滑稳定安全系数K为E Z (W tg 中 cos 2 a + c l cos a )K = n =ii1EZ (W sin a cos a )式中W各土块的重量；.一各土块的内摩擦角；c.、l.一各土块滑裂面上

32、的凝聚力和滑裂面长度；a i各土块滑裂面与水平面的夹角。2.2.1折线滑动面1假设土体沿如图8所示折线滑动面(下游预围堰稳定分析示意图2)发生滑动，此时的下 游水位为251m。取土条宽度b=2m，列表进行计算，水位以上粘土取干容重，水位以下粘土取浮容重。(见表 7:折线法计算表1)该滑动面的抗滑稳定安全系数为K = En = 394.339 = 4.066 1.30E 96.995J;,块石、石. :碴混合料图8下游预围堰稳定分析示意图22.2.2折线滑动面2假设土体沿如图9所示折线滑动面（下游预围堰稳定分析示意图3）发生滑动，此时的下 游水位为250.3m。取土条宽度b=2m，采用同样方法，

33、列表进行计算。（见表8:折线法计算表2）该滑动面的抗滑稳定安全系数为415.961115.644=3.597 1.3014 616_ 一253河床地面线、过渡层/250.312 13 弋反滤层 垫层图9下游预围堰稳定分析示意图3综合分析以上各种可能的滑动形式，预围堰最小的安全系数K为2.67,满足规范要求。 由于计算中没有考虑水平厚度为1m的砂砾石垫层和垂直厚度为0.5m的块石护坡对粘土斜墙 的保护作用，并且所取计算参数如粘土凝聚力等偏于保守，因此下游预围堰粘土斜墙是安全 的。辅助围堰稳定分析对于辅助围堰A-B段及B-C段，其结构与下游预围堰类似，可采用与预围堰同样的方法 进行稳定计算。经验证

34、，均满足稳定性要求。土条编号土条高度(m)容重Y(kN/m3)土条重量W=y.bH.1a .1sina .1cosa .il.1C1(k Pa)C l cos .1 1 aitgviW1tg 11/10.42816.5i13.7632.9710.0520.9991.9531019.5010.2683.68850.20.80016.525.7564.7480.0830.9971.9571019.5010.2686.90270.31.25816.540.4766.5310.1140.9941.9631019.5010.26810.84760.41.6541238.7028.3190.1450.98

35、91.9711019.5010.26810.37210.51.9871038.75710.1160.1760.9841.9811019.5010.26810.38680.62.2581044.02811.9230.2070.9781.9931019.5010.26811.79941.72.4641048.04113.7420.2380.9712.0081019.5010.26812.87511.82.6031050.77015.5750.2690.9632.0241019.5010.26813.60641.92.6761052.18217.4250.2990.9542.0441019.5010

36、.26813.98471.102.6791052.23819.2940.3300.9442.0661019.5010.26813.99971.112.6101050.89321.1840.3610.9322.0911019.5010.26813.63921.122.4661048.09523.0990.3920.9202.1201019.5010.26812.88951.132.2451043.78425.0410.4230.9062.1521019.5010.26811.73411.141.9431037.88927.0150.4540.8912.1891019.5010.26810.154

37、31.151.5551030.32829.0240.4850.8742.2301019.5010.2688.127931.161.0771021.00531.0730.5160.8572.2771019.5010.2685.629371.合计312.02170.637土条编号土条高度Hi(m)容重Yi(kN/m3)土条重量Wi=yibiHia .isinaicosa；N. w.i=Wi cos . aiTi=Wi sin . ail.iCi (kPa)C10.62716.520.68033.6900.5550.83217.20711.4712.4041024.(21.66716.555.000

38、33.6900.5550.83245.76330.5092.4041024.(31.55216.551.20715.4220.2660.96449.36313.6172.0751020.741.4371028.73615.4220.2660.96427.7017.6422.0751020.751.3221026.43715.4220.2660.96425.4857.0302.0751020.761.2071024.13315.4220.2660.96423.2646.4182.0751020.771.0921021.84015.4220.2660.96421.0545.8082.0751020.780.9771019.54015.4220.2660.96418.8365.1962.0751020.790.8621017.24015.4220.2660.96416.6194.5852.0751020.7100.7471014.93315.4220.2660.96414.3963.9712.0751020.7110.63