道路工程毕业设计边坡稳定性分析

1、第二章边坡稳定性分析本设计任务段为包头至茂名高速公路湖南省怀化至通道K167+000K169+000段，总长2000m,其中填方路堤的K167+920的横断面虽然地面线较缓，但填方高度 较大，并采用了二级边坡，所以路堤边坡稳定性验算采用此断面为验算对象。如图所示，此断面高度为21.20m,顶宽为26m，边坡坡度采用1: 1.5,二级边 坡为1: 1.75,o其横段面如图2.1所示图2.1边坡验算的横断面本次稳定性验算分为三个部分：(1)计算参数的的选用；(2) 确定最危险滑动面；(3) 利用Bishop法进行路堤稳定性验算。2.1计算参数的选用：对本段路堤所填的土为粉质粘土 (取值见路基设计手

2、册)，路堤填土为粘土，土的 粘聚力G=25kPa,摩擦角;:1为300,天然容重为！ =18kN/m3;地基土也为粘土，土的 粘聚力c2=20kPa,摩擦角为200,天然容重为2=16kN/m3，荷载为公路I级。2.2最危险滑动面的确定2.2.1荷载当量高度计算将车辆荷载换算成土柱高(当量高度)，按以下公式换算土柱高度为(2-1)NQ hoBL式(2-1)中：N 横向分布并列的车辆数，单车道N=1，双车道N=2 ；本设计为双向4车道,N=2Q每一辆重车的重力(标准车辆荷载为 550kN)；L 前后轮最大轴距，按公路工程技术标准(JTG B012003)规定对标准车辆荷载为12.8m；路基填料的

3、容重；B荷载横向分布宽度，表示如下：B=Nb+( N-1)m+d式中：b后轮轮距，取1.8m；m 相邻两辆车后轮的中心间距，取 1.3m；d轮胎着地宽度，取0.6m。贝B=Nb+(N-1)m+d=2 1.8+(2-1) 1.3+0.6=5.5m(2-2)故h0 二 NQ =(2 550)/(18 5 X2.8)=0.867m VBl2.2.2危险滑弧圆心位置的确定(1) 按4.5H法确定滑动圆心辅助线。近似取边坡1: 1.5,边坡角30度由表查得1 =260， 2=350，再根据荷载换算得到 6和填土高度计算H=22.068,从而得到G点 具体步骤如下：a. 由坡脚A向下引竖线，在竖线上截取高

4、度H=h+h (h为边坡高度，为换算土层高)b. 自G点向右引水平线，在水平线上截取 4.5H,得E点。根据两角分别自坡角 和左点作直线相交于F点，EF的延长线即为滑动圆心辅助线。c.连接边坡坡脚A和顶点B，求得AB的斜度i=1/m，据此查路基路面工程表4-1得|.匚,|為。(2) 在EF的延长线上取4点分别画出4通过坡脚的滑动面，如图2(3) 将圆弧范围土体分成13段。(4) 算出滑动曲线每一分段中点与圆心竖曲线之间的偏角:.;sin a =X/R(2-4)式(2-4)中：X分段中心距圆心竖曲线的水平距离，圆心竖曲线左侧为负, 右侧为正；R滑动曲线半径(5) 对4个滑动面分别利用简化的Bis

5、hop法计算稳定系数K。图2 4.5H法确定滑动圆心的位置2.2.3 Bishop 法计算过程如下(1) 每一分段的滑动弧曲线可近似取直线，将各段图形简化为梯形或三角形，分段 计算面积，其中包括荷载换算成土柱部分的面积在内。(2) 计算稳定系数：根据迭代法计算，首先假定一个 Fs值算出m,代入公式算出一个Fs值，这个Fs与设定Fs值相比较如小于所设Fs值的百分之一就可确定所设Fs值为 此的边坡稳定性Fs值。当土条i滑弧位于地基中时:Cdibj +W tan di +U (W+QtandiK i 二ma中：Wd 第i 土条地基部分的重力；(2-5)式Wt 第i 土条路堤部分的重力;bi 第i 土

6、条宽度;U地基平均固结度；令U=1。Cd、;：di 第i 土条滑弧所在地基土层的粘结力和内摩擦角;当土条i滑弧位于路堤中时(2-6)式中：Cti、 ti 第i 土条滑弧所在路堤土的粘结力和内摩擦角。其中：l sin ai tan 卩，mai - cos : i(2-7)Fsmai Ctibi +(Wti+Qi)tan tiK iFK i (WiQi) sin q(2-8)(3)同理可求出其他滑动曲线的稳定系数。2.2.4具体计算过程及图表2.241 以O 1为圆心过坡脚做一滑动面，R=51.37m见下图2.1图2.1 以01为圆心的滑动面计算简图假设Fs=1.80,计算结果如表2-1所示表2-

7、1计算土坡的稳定安全系数12345678910111213土 条 编 号土条宽(m)i(路 堤 部 分 面 积地 基 部 分 面 积Wti(kN)Wdi(KN)WixsinotiQi Xsin%Cti biCdibimaiKiFs=1.80Fs =1.8012.53533.5063050.314012.477963.250.000.8578116.109222.53487.430133.74099.38820.000063.250.000.9073154.756232.53449.890178.020123.66310.000063.250.000.9420176.183342.534011.

8、510207.180133.17270.000063.250.000.9721188.040452.533712.350222.30133.78350.000063.250.000.9916193.149162.53；3314.260256.680139.79790.000063.250.001.0133208.589072.53：3015.40277.20138.60000.000063.250.001.0263217.474182.53：2714.120254.160115.38620.000063.250.001.0365202.501892.532412.410223.38090.85

9、680.000063.250.001.0439184.0552102.532110.280185.04066.31240.000063.250.001.0485162.1602112.53：187.760139.68043.16350.000063.250.001.0501136.9808122.53154.88087.84022.73470.000063.250.001.0489108.6229132.49312| 1.65029.706.1750 |0.000062.3250.001.0448 |76.0550142124.677115送 +Qj) sin g1175.8260计算Fs21

10、42 .5457=1.8070(WiQi )sin :. i 1171 .73371.8070 -1.80100 % = 0.39% 1.35所以此边坡满足稳定行要求。图2.2以02为圆心的滑动面计算简图(1)假设Fs=1.70,计算结果如表2-2-1所示表2-2-1计算土坡的稳定安全系数12345678910111213土 条 编 号土条宽(m)Gi()路 堤 部 分 面 积地 基 部 分 面 积Wti(kN)Wd(KN)WiXsi notjQi Xsina iCti biCdibimaiKiFs=1.70Fs=1.7012.88555.930106.74087.436312.798472.

11、000.000.8516156.867122.884916.630299.340225.914811.791672.000.000.9122268.268832.88：4422.280401.040278.58580.000072.000.000.9551317.658242.88：3924.030432.540272.20620.000072.000.000.9907324.579752.883424.640443.520248.01320.000072.000.001.0188321.849362.8813024.30437.40218.70000.000072.000.001.03573

12、13.189172.88：2625.420457.560200.58110.000072.000.001.0476320.750182.882224.630443.340166.07810.000072.000.001.0543310.915292.881821.440385.920119.25580.000072.000.001.0559279.0648102.881417.630317.34076.77150.000072.000.001.0524242.4017112.881013.240238.32041.38380.000072.000.001.0437200.7295122.886

13、8.280149.04015.57890.000072.000.001.0300153.3942132.828732.78050.0402.61890.000070.720.001.016497.984314Z Ki3307.652015送(Wi +Qsini1977.7145 Ki计算i3307 .6520(WiQi )sin1977 .7145Fs=1.67251.7 1.6725100 % =1.62% 1%1.7故必须重新用计算Fs。(2)假设fs=1.68，计算结果如表2-2-2所示表2-2-2计算土坡的稳定安全系数12345678910111213土 条 编 号土条宽(m)i()路

14、 堤 部 分 面 积地 基 部 分 面 积Wti(kN)Wd(KN)Wi xsin ot iQi xsince iCti biCdibimKiFs=1.68Fs =1.6812.88555.930106.74087.436312.798472.000.000.8549156.259722.884916.630299.340225.914811.791672.000.000.9153267.375032.88：4422.280401.040278.58580.000072.000.000.9579316.727442.883924.030432.540272.20620.000072.000.0

15、00.9933323.748752.883424.640443.520248.01320.000072.000.001.0211321.137162.88；3024.30437.40218.70000.000072.000.001.0378312.579472.882625.420457.560200.58110.000072.000.001.0494320.208782.88：2224.630443.340166.07810.000072.000.001.0558310.469592.881821.440385.920119.25580.000072.000.001.0572278.7352

16、102.881417.630317.34076.77150.000072.000.001.0534242.1767112.88：1013.240238.32041.38380.000072.000.001.0444200.5947122.8868.280149.04015.57890.000072.000.001.0304153.3314132.8332.78050.0402.61890.000070.720.001.016697.963914Z Ki3301.307415送(Wi +C)sini1977.7145Z Ki3301.3074Fs=1.6693瓦(Wi +Qi )sin Gj 1

17、977 .7145计算1 .68 -1.66931.68100 % =0.64% 1.35所以此边坡满足稳定行要求2.243以O 3为圆心过坡脚做一滑动面，R=40.94m。见下图2.3图2.3以03为圆心的滑动面计算简图(1)假设Fs=1.80,计算结果如表2-3-1所示E表2-3-1计算土坡的稳定安全系数12345678910111213土条编号土条宽(m)i(路 堤 部 分 面 积地 基 部 分 面 积Wti(kN)Wdi(KN)Wixsin %Qi Xsin%Cti biCdibimaiKiFs=1.70Fs=1.7013.21578.140146.520.00122.882013.1

18、03480.2500.8293209.584523.215022.40403.200.00：308.869111.968780.2500.9028356.573233.214333.390601.02 ,0.00 .409.894710.655580.2500.9628452.88654r 3.213739.10P 703.800.00：423.55740.000080.2501.0029484.937053.213239.7101714.780.00378.77570.000080.2501.0279479.301363.212738.650695.700.00315.84120.00008

19、0.2501.0451460.88477P 3.212236.540:657.720.00：246.38620.000080.2501.0543436.063283.211736.660659.880.00；192.93020.000080.2501.0555436.744393.211232.530585.540.00121.74060.000080.2501.0487398.6846103.21826.610.17478.982.7266.66110.000080.2532.11.0375344.6841113.21319.130.96344.3415.3618.02140.000080.

20、2564.21.0164279.936213.21011.481.15206.6418.400.00000.000080.2564.21.0000206.178921-63.840.5233.2269.128.32-7.22500.000080.5064.40.9590128.6810144675.139515Z (Wi+ Qi) si ng2634.0623计算Z Ki4675 .1395F=sZ (Wi +Qi )sinoti 2634 .0623=1.7749故需要重新假设计算Fs值(2)假设Fs=1.78，计算结果如表2-3-2所示表2-3-2计算土坡的稳定安全系数1234567891

21、0111213路地土土堤基Qi XmaiKi条编条 宽8(部分部分Wti(kN)Wdi(KN)Wixsin%sin%CtibiCdibi号(m)面积面积Fs=1.78Fs=1.7813.21578.140146.520.00122.882013.103480.250.000.8165212.868423.215022.40403.200.00 1308.869111.968780.250.000.8911361.249133.214333.390601.020.00409.894710.655580.250.000.9524457.83344:3.213739.10703.800.00 142

22、3.55740.000080.250.00P 0.9937489.417053.213239.710714.780.00 1378.77570.000080.250.001.0198483.100563.212738.650695.700.00315.84120.000080.250.001.0382463.95927:3.212236.540657.720.00 1246.38620.000080.250.00P 1.0486438.439683.211736.660659.880.00192.93020.000080.250.001.0511438.597693.211232.530585

23、.540.00121.74060.000080.250.001.0455399.893910:3.21826.610.17：478.982.72 166.66110.000080.2532.10P 1.0354345.3909113.21319.130.96344.3415.3618.02140.000080.2564.201.0156280.1563123.21011.481.15206.6418.400.00000.000080.2564.201.0000206.1789133.22-63.840.5269.128.32-7.22500.000080.5064.400.9606128.46

24、7414Z Ki4705.552115Z +QJsin 码2634.06231 .7749 -1 .701.70100 % = 4.4% 1%计算可得F=1.7864送 K i_ 4705.5521 (Wi - Qi)sin : i 2634 .06231 .7864 _1 .781.78100 % = 0.36% 1.35所以此边坡满足稳定行要求。224.4以0 4为圆心过坡脚做一滑动面，R=38.37m。见下图2.4- - - 一图2.4以04为圆心的滑动面计算简图(1)假设Fs=1.90,计算结果如表2-4-1所示表2-4-1计算土坡的稳定安全系数12345678910111213土条编

25、号土条宽(m)i(路 堤 部 分 面 积地 基 部 分 面 积Wti(kN)Wdi(KN)Wi xsi n码Qi xsin%Cti biCdibimaiKiFs=1.90Fs =1.9013.586011.480206.640.00178.955513.530889.500.000.7630285.382523.585130.90P 556.200.00432.248612.142189.500.000.8653484.721133.584344.840807.120.00550.454510.655589.500.000.9385601.218843.583655.530999.540.00

26、587.51499.183689.500.000.9875683.784653.583060.730P 1093.140.00：546.57000.000089.500.001.0179707.598863.582458.7601057.680.00：430.19720.000089.500.001.0371674.771073.581854.910.29988.384.64305.42620.000089.5028.201.0449633.05988P 3.581248.292.89P 869.2246.24；180.72100.000089.5071.601.0413583.769293.

27、58742.975.11773.4681.76：94.26110.000089.5071.601.0296549.3116103.58233.486.09602.6497.4421.03180.000089.5071.601.0100468.0163113.58-423.985.87431.6493.92-30.10970.000089.5071.600.9764381.7603123.58-914.474.43260.4670.88-40.74490.000089.5071.600.9402282.4834133.66-154.971.7489.4627.84-23.15400.000091

28、.5073.200.8873172.712314Z Ki6508.589615Z (Wi+ Qi) sin %3278.88421 .9850 -1.901.90100 % = 4.47% 1%二.Ki6508 .5896Fs=1.9850送(Wi +Qj )sin 83278 .8842故需要重新假设计算Fs值(2)假设Fs=1.98，计算结果如表2-4-2所示表2-4-2计算土坡的稳定安全系数12345678910111213土 条 编 号土条宽(m)i(路 堤 部 分 面 积地 基 部 分 面 积Wti(kN)Wdi(KN)Wixsi notjQi Xsin%CtibiCdibimaiK

29、iFs=1.98Fs =1.9813.586011.480206.640.00178.955513.530889.500.000.7524289.413123.585130.90556.200.00 :432.248612.142189.500.000.8558490.122133.584344.840807.120.00550.454510.655589.500.000.9301606.62804P 3.583655.530999.540.00 ：587.51499.183689.50:0.00P 0.9803688.815253.583060.7301093.140.00546.57000

30、.000089.500.001.0117711.889663.582458.7601057.680.00 1430.19720.000089.500.001.0321678.033973.581854.910.29988.384.64305.42620.000089.50:28.201.0411635.365383.581248.292.89869.2246.24180.72100.000089.5071.601.0387585.202993.58742.975.11773.4681.7694.26110.000089.5071.601.0281550.1106103.58：233.486.0

31、9602.6497.4421.0318:0.000089.5071.601.0096468.2148113.58-423.985.87431.6493.92-30.10970.000089.5071.600.9772381.4259123.58-914.474.43260.4670.88-40.74490.000089.5071.600.9421281.9079133.66；-154.971.7489.4627.84-23.1540:0.000091.5073.200.8905172.096314工Ki6539.225715送+Ch) sin oti3278.8842计算可得FsZ Ki_ 6

32、539.22577 (WiQi)sin :匚 3278 .8842=1.99431.9943 -1.981.98100 % = 0.72% 1.35所以此边坡满足稳定行要求。2.2.5最危险滑动面圆心Omi n的确定现在通过已经找到O1、O2、O3、O4对应的Fs值画圆弧找到最小Fs值，并且可以确 定最危险滑动面的圆心 Omin,以Omin为圆心画一个坡面圆弧和一个过坡脚外的圆弧（如下图）并根据简化Bishop法验算这两个滑动面，计算如下：以Omin为圆心画两个圆弧简图:225.1以Omin为圆心过坡脚外做一滑动面， R=47.68m见下图过坡脚外的圆弧滑动面的稳定系数计算简图:(1)假设Fs

33、=1.98，计算结果如表5-1-1所示表5-1-1计算土坡的稳定安全系数12345678910111213土条编号土条宽(m)i(路 堤 部 分 面 积地 基 部 分 面 积Wti(kN)Wdi(KN)Wi xsin码Qi Xsina iCti biCdibimaiKiFs=1.98Fs =1.9814.425611.380204.800.00178.9555169.7902110.500.000.8008285.559324.424836.310:653.51：0.00：432.2486485.6511110.500.000.8857550.499834.424024.140434.500.

34、00 1550.4545279.2925110.500.000.9534378.877844.423450.620911.230.00587.5149509.5545110.500.000.9920641.415954.422749.640:893.500.00：546.5700405.6414110.500.001.0233611.792464.422250.250904.430.51 1430.1972338.8047110.508.601.0363618.992674.421639.170.03705.0855.02305.4262194.3458110.5088.401.0416603

35、.825184.421024.683.44444.29128.46180.721077.1508110.5088.401.0354487.247894.42510.208.03183.51 1171.23 194.261115.9940110.5088.401.0216360.7208104.4200.3010.705.42184.5321.03180.0000110.5088.401.0000157.540314.42-60.0011.50.00168.69-30.10970.0000110.5088.400.9641155.386913124.42-110.0010.540.00123.2

36、6-40.74490.0000110.5088.400.9260143.9145134.46-160.007.700.0046.99-23.15400.0000111.5089.200.8809120.672714送Ki5116.445815送(Wi+ QJsi ng2500.7888 Ki计算Fs5116 .4458 =2.0459、 (Wi Qi )sin : i 2500 .78882.0459 -1.981.98100 % = 3.33% 1%故需要重新假设计算Fs值(2)假设Fs=2.04,计算结果如表5-1-2所示表5-1-2计算土坡的稳定安全系数12345678910111213

37、土条编号土条宽(m)i(路 堤 部 分 面 积地基 部 分 面 积Wti(kN)Wdi(KN)Wixsin ot jQi Xsina iCti biCdibimaiKiFs=1.98Fs =1.9814.425611.380204.800.00178.9555169.7902110.500.000.7937288.115824.424836.310653.510.00432.2486485.6511110.500.000.8793554.487434.424024.140434.500.00：550.4545279.2925110.500.000.9479381.080044.423450.6

38、20911.230.00 1587.5149509.5545110.500.000.9872644.529954.422749.640893.500.00546.5700405.6414110.500.001.0194614.12766P 4.422250.250P 904.430.5430.1972338.8047110.508.601.0331620.906871 4.421639.170.03705.0855.02：305.4262194.3458110.5088.401.0392605.112284.421024.683.44444.29128.46180.721077.1508110

39、.5088.401.0339487.880794.42510.208.03：183.51：171.2394.261115.9940110.5088.401.0208360.9451104.4200.3010.705.42184.5321.03180.0000110.5088.401.0000157.5403114.42-60.0011.530.00168.69-30.10970.0000110.5088.400.9650155.2426124.42-110.0010.540.00123.26-40.74490.0000110.5088.400.9277143.660814.46-160.007.700.0046.99-23.15400.0000111.5089.200.8833120.35005133.9794计算、 (Wi QJsin ：2500.7888Z Ki5133 .9794F=瓦(Wi +Qi )sin 82500 .7888=2.05292.0529 -2.042.04100 % = 0.63% 1.35所以此边坡满足稳定行要求2.2.5.2以Omin为圆心过坡面做一滑动面，R=43.25m见下图过坡面的圆弧滑动面的稳定系数计算简图:假设Fs=1.8，计算结果如表5-1-3所示表5-1-3计算土坡的稳定安全系数123