道路工程毕业设计-边坡稳定性分析

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,。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(取值见路基设计手册)，路堤填土为粘土，土的粘聚力=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=20kPa，摩擦角为200，天然容重为=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)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。则：B=Nb+(N-1)m+d=21.8+(2-1)1.3+0.6=5.5m （2-2）故=(2550)/(185.512.8)=0.867m 2.2.2 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=260，=350 ，再根据荷载换算得到h0和填土高度计算H=22.068，从而得到G点。具体步骤如下：.由坡脚A向下引竖线，在竖线上截取高度H=h+h0（h为边坡高度，h0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（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=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Bishop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，首先假定一个值算出m，代入公式算出一个值，这个Fs与设定值相比较如小于所设值的百分之一就可确定所设值为此的边坡稳定性值。 当土条i滑弧位于地基中时： (2-5)式中：第i土条地基部分的重力； 第i土条路堤部分的重力； 第i土条宽度； U地基平均固结度；令U=1。 、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：、第i土条滑弧所在路堤土的粘结力和内摩擦角。其中： (2-7) (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2.2.4.1 以1为圆心过坡脚做一滑动面，R=51.37m。见下图2.1 图2.1 以O1为圆心的滑动面计算简图 假设=1.80，计算结果如表2-1所示表2-1 计算土坡的稳定安全系数12345678910111213土条 编号土条宽(m)()路堤部分面积地基部分面积Wti(kN)Wdi(KN)WisinQisinCtibiCdibi=1.80=1.8012.53533.5063050.3140 12.4779 63.250.00 0.8578 116.1092 22.53487.430133.74099.3882 0.0000 63.250.00 0.9073 154.7562 32.53449.890178.020123.6631 0.0000 63.250.00 0.9420 176.1833 42.534011.510207.180133.1727 0.0000 63.250.00 0.9721 188.0404 52.533712.350222.30133.7835 0.0000 63.250.00 0.9916 193.1491 62.533314.260256.680139.7979 0.0000 63.250.00 1.0133 208.5890 72.533015.40277.20138.6000 0.0000 63.250.00 1.0263 217.4741 82.532714.120254.160115.3862 0.0000 63.250.00 1.0365 202.5018 92.532412.410223.38090.8568 0.0000 63.250.00 1.0439 184.0552 102.532110.280185.04066.3124 0.0000 63.250.00 1.0485 162.1602 112.53187.760139.68043.1635 0.0000 63.250.00 1.0501 136.9808 122.53154.88087.84022.7347 0.0000 63.250.00 1.0489 108.6229 132.493121.65029.706.1750 0.0000 62.3250.00 1.0448 76.0550 142124.6771 151175.8260 计算可得=1.8070= 0.39% 1.35所以此边坡满足稳定行要求。2.2.4.2以2为圆心过坡脚做一滑动面，R=44.72m。见下图2.2 图2.2 以O2为圆心的滑动面计算简图（1）假设=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)()路堤部分面积地基部分面积Wti(kN)Wdi(KN)WisinQisinCtibiCdibi=1.70=1.7012.88555.930106.74087.4363 12.7984 72.00 0.00 0.8516 156.8671 22.884916.630299.340225.9148 11.7916 72.00 0.00 0.9122 268.2688 32.884422.280401.040278.5858 0.0000 72.00 0.00 0.9551 317.6582 42.883924.030432.540272.2062 0.0000 72.00 0.00 0.9907 324.5797 52.883424.640443.520248.0132 0.0000 72.00 0.00 1.0188 321.8493 62.883024.30437.40218.7000 0.0000 72.00 0.00 1.0357 313.1891 72.882625.420457.560200.5811 0.0000 72.00 0.00 1.0476 320.7501 82.882224.630443.340166.0781 0.0000 72.00 0.00 1.0543 310.9152 92.881821.440385.920119.2558 0.0000 72.00 0.00 1.0559 279.0648 102.881417.630317.34076.7715 0.0000 72.00 0.00 1.0524 242.4017 112.881013.240238.32041.3838 0.0000 72.00 0.00 1.0437 200.7295 122.8868.280149.04015.5789 0.0000 72.00 0.00 1.0300 153.3942 132.828732.78050.0402.6189 0.0000 70.72 0.00 1.0164 97.9843 143307.6520 151977.7145 计算可得=1.6725=1.62% 1%故必须重新用计算Fs。（2）假设=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)()路堤部分面积地基部分面积Wti(kN)Wdi(KN)WisinQisinCtibiCdibi=1.68=1.6812.88555.930106.74087.4363 12.7984 72.00 0.00 0.8549 156.2597 22.884916.630299.340225.9148 11.7916 72.00 0.00 0.9153 267.3750 32.884422.280401.040278.5858 0.0000 72.00 0.00 0.9579 316.7274 42.883924.030432.540272.2062 0.0000 72.00 0.00 0.9933 323.7487 52.883424.640443.520248.0132 0.0000 72.00 0.00 1.0211 321.1371 62.883024.30437.40218.7000 0.0000 72.00 0.00 1.0378 312.5794 72.882625.420457.560200.5811 0.0000 72.00 0.00 1.0494 320.2087 82.882224.630443.340166.0781 0.0000 72.00 0.00 1.0558 310.4695 92.881821.440385.920119.2558 0.0000 72.00 0.00 1.0572 278.7352 102.881417.630317.34076.7715 0.0000 72.00 0.00 1.0534 242.1767 112.881013.240238.32041.3838 0.0000 72.00 0.00 1.0444 200.5947 122.8868.280149.04015.5789 0.0000 72.00 0.00 1.0304 153.3314 13 2.8332.78050.0402.6189 0.0000 70.72 0.00 1.0166 97.9639 143301.3074 151977.7145 计算可得=1.6693=0.64% 1.35所以此边坡满足稳定行要求。2.2.4.3以3为圆心过坡脚做一滑动面，R=40.94m。见下图2.3图2.3 以O3为圆心的滑动面计算简图（1）假设=1.80，计算结果如表2-3-1所示 表2-3-1 计算土坡的稳定安全系数12345678910111213土条 编号土条宽(m)()路堤部分面积地基部分面积Wti(kN)Wdi(KN)WisinQisinCtibiCdibi=1.70=1.7013.21578.140146.52 0.00 122.8820 13.1034 80.25 00.8293 209.5845 23.215022.40403.20 0.00 308.8691 11.9687 80.25 00.9028 356.5732 33.214333.390601.02 0.00 409.8947 10.6555 80.25 00.9628 452.8865 43.213739.10703.80 0.00 423.5574 0.0000 80.25 01.0029 484.9370 53.213239.710714.78 0.00 378.7757 0.0000 80.25 01.0279 479.3013 63.212738.650695.70 0.00 315.8412 0.0000 80.25 01.0451 460.8847 73.212236.540657.72 0.00 246.3862 0.0000 80.25 01.0543 436.0632 83.211736.660659.88 0.00 192.9302 0.0000 80.25 01.0555 436.7443 93.211232.530585.54 0.00 121.7406 0.0000 80.25 01.0487 398.6846 103.21826.610.17478.98 2.72 66.6611 0.0000 80.25 32.11.0375 344.6841 113.21319.130.96344.34 15.36 18.0214 0.0000 80.25 64.21.0164 279.9362 123.21011.481.15206.64 18.40 0.0000 0.0000 80.25 64.21.0000 206.1789 133.22-63.840.5269.12 8.32 -7.2250 0.0000 80.50 64.40.9590 128.6810 144675.1395152634.0623 计算可得=1.7749= 4.4% 1%故 需要重新假设计算值 （2）假设=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12345678910111213土条 编号土条宽(m)()路堤部分面积地基部分面积Wti(kN)Wdi(KN)WisinQisinCtibiCdibi=1.78=1.7813.21578.140146.52 0.00 122.8820 13.1034 80.25 0.00 0.8165 212.8684 23.215022.40403.20 0.00 308.8691 11.9687 80.25 0.00 0.8911 361.2491 33.214333.390601.02 0.00 409.8947 10.6555 80.25 0.00 0.9524 457.8334 43.213739.10703.80 0.00 423.5574 0.0000 80.25 0.00 0.9937 489.4170 53.213239.710714.78 0.00 378.7757 0.0000 80.25 0.00 1.0198 483.1005 63.212738.650695.70 0.00 315.8412 0.0000 80.25 0.00 1.0382 463.9592 73.212236.540657.72 0.00 246.3862 0.0000 80.25 0.00 1.0486 438.4396 83.211736.660659.88 0.00 192.9302 0.0000 80.25 0.00 1.0511 438.5976 93.211232.530585.54 0.00 121.7406 0.0000 80.25 0.00 1.0455 399.8939 103.21826.610.17478.98 2.72 66.6611 0.0000 80.25 32.10 1.0354 345.3909 113.21319.130.96344.34 15.36 18.0214 0.0000 80.25 64.20 1.0156 280.1563 123.21011.481.15206.64 18.40 0.0000 0.0000 80.25 64.20 1.0000 206.1789 133.22-63.840.5269.12 8.32 -7.2250 0.0000 80.50 64.40 0.9606 128.4674 144705.5521 152634.0623 计算可得=1.7864= 0.36% 1.35所以此边坡满足稳定行要求。2.2.4.4以4为圆心过坡脚做一滑动面，R=38.37m。见下图2.4 图2.4 以O4为圆心的滑动面计算简图（1）假设=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 编号土条宽(m)()路堤部分面积地基部分面积Wti(kN)Wdi(KN)WisinQisinCtibiCdibi=1.90=1.9013.586011.480206.64 0.00 178.9555 13.5308 89.50 0.00 0.7630 285.3825 23.585130.90556.20 0.00 432.2486 12.1421 89.50 0.00 0.8653 484.7211 33.584344.840807.12 0.00 550.4545 10.6555 89.50 0.00 0.9385 601.2188 43.583655.530999.54 0.00 587.5149 9.1836 89.50 0.00 0.9875 683.7846 53.583060.7301093.14 0.00 546.5700 0.0000 89.50 0.00 1.0179 707.5988 63.582458.7601057.68 0.00 430.1972 0.0000 89.50 0.00 1.0371 674.7710 73.581854.910.29988.38 4.64 305.4262 0.0000 89.50 28.20 1.0449 633.0598 83.581248.292.89869.22 46.24 180.7210 0.0000 89.50 71.60 1.0413 583.7692 93.58742.975.11773.46 81.76 94.2611 0.0000 89.50 71.60 1.0296 549.3116 103.58233.486.09602.64 97.44 21.0318 0.0000 89.50 71.60 1.0100 468.0163 113.58-423.985.87431.64 93.92 -30.1097 0.0000 89.50 71.60 0.9764 381.7603 123.58-914.474.43260.46 70.88 -40.7449 0.0000 89.50 71.60 0.9402 282.4834 133.66-154.971.7489.46 27.84 -23.1540 0.0000 91.50 73.20 0.8873 172.7123 146508.5896 153278.8842 计算可得=1.9850= 4.47% 1%故 需要重新假设计算值 （2）假设=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)()路堤部分面积地基部分面积Wti(kN)Wdi(KN)WisinQisinCtibiCdibi=1.98=1.9813.586011.480206.64 0.00 178.9555 13.5308 89.50 0.00 0.7524 289.4131 23.585130.90556.20 0.00 432.2486 12.1421 89.50 0.00 0.8558 490.1221 33.584344.840807.12 0.00 550.4545 10.6555 89.50 0.00 0.9301 606.6280 43.583655.530999.54 0.00 587.5149 9.1836 89.50 0.00 0.9803 688.8152 53.583060.7301093.14 0.00 546.5700 0.0000 89.50 0.00 1.0117 711.8896 63.582458.7601057.68 0.00 430.1972 0.0000 89.50 0.00 1.0321 678.0339 73.581854.910.29988.38 4.64 305.4262 0.0000 89.50 28.20 1.0411 635.3653 83.581248.292.89869.22 46.24 180.7210 0.0000 89.50 71.60 1.0387 585.2029 93.58742.975.11773.46 81.76 94.2611 0.0000 89.50 71.60 1.0281 550.1106 103.58233.486.09602.64 97.44 21.0318 0.0000 89.50 71.60 1.0096 468.2148 113.58-423.985.87431.64 93.92 -30.1097 0.0000 89.50 71.60 0.9772 381.4259 123.58-914.474.43260.46 70.88 -40.7449 0.0000 89.50 71.60 0.9421 281.9079 133.66-154.971.7489.46 27.84 -23.1540 0.0000 91.50 73.20 0.8905 172.0963 146539.2257 153278.8842 计算可得=1.9943= 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Omin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：2.2.5.1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=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)()路堤部分面积地基部分面积Wti(kN)Wdi(KN)WisinQisinCtibiCdibi=1.98=1.9814.425611.38 0204.80 0.00 178.9555 169.7902 110.50 0.00 0.8008 285.5593 24.424836.31 0653.51 0.00 432.2486 485.6511 110.50 0.00 0.8857 550.4998 34.424024.14 0434.50 0.00 550.4545 279.2925 110.50 0.00 0.9534 378.8778 44.423450.62 0911.23 0.00 587.5149 509.5545 110.50 0.00 0.9920 641.4159 54.422749.64 0893.50 0.00 546.5700 405.6414 110.50 0.00 1.0233 611.7924 64.422250.25 0904.43 0.51 430.1972 338.8047 110.50 8.60 1.0363 618.9926 74.421639.17 0.03 705.08 55.02 305.4262 194.3458 110.50 88.40 1.0416 603.8251 84.421024.68 3.44 444.29 128.46 180.7210 77.1508 110.50 88.40 1.0354 487.2478 94.42510.20 8.03 183.51 171.23 94.2611 15.9940 110.50 88.40 1.0216 360.7208 104.4200.30 10.70 5.42 184.53 21.0318 0.0000 110.50 88.40 1.0000 157.5403 114.42-60.00 11.53 0.00 168.69 -30.1097 0.0000 110.50 88.40 0.9641 155.3869 124.42-110.00 10.54 0.00 123.26 -40.7449 0.0000 110.50 88.40 0.9260 143.9145 134.46-160.00 7.70 0.00 46.99 -23.1540 0.0000 111.50 89.20 0.8809 120.6727 145116.4458 152500.7888 计算可得=2.0459= 3.33% 1%故 需要重新假设计算值 （2）假设=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土条 编号土条宽(m)()路堤部分面积地基部分面积Wti(kN)Wdi(KN)WisinQisinCtibiCdibi=1.98=1.9814.425611.38 0204.80 0.00 178.9555 169.7902 110.50 0.00 0.7937 288.1158 24.424836.31 0653.51 0.00 432.2486 485.6511 110.50 0.00 0.8793 554.4874 34.424024.14 0434.50 0.00 550.4545 279.2925 110.50 0.00 0.9479 381.0800 44.423450.62 0911.23 0.00 587.5149 509.5545 110.50 0.00 0.9872 644.5299 54.422749.64 0893.50 0.00 546.5700 405.6414 110.50 0.00 1.0194 614.1276 64.422250.25 0904.43 0.51 430.1972 338.8047 110.50 8.60 1.0331 620.9068 74.421639.17 0.03 705.08 55.02 305.4262 194.3458 110.50 88.40 1.0392 605.1122 84.421024.68 3.44 444.29 128.46 180.7210 77.1508 110.50 88.40 1.0339 487.8807 94.42510.20 8.03 183.51 171.23 94.2611 15.9940 110.50 88.40 1.0208 360.9451 104.4200.30 10.70 5.42 184.53 21.0318 0.0000 110.50 88.40 1.0000 157.5403 114.42-60.00 11.53 0.00 168.69 -30.1097 0.0000 110.50 88.40 0.9650 155.2426 124.42-110.00 10.54 0.00 123.26 -40.7449 0.0000 110.50 88.40 0.9277 143.6608 134.46-160.00 7.70 0.00 46.99 -23.1540 0.0000 111.50 89.20 0.8833 120.3500 145133.9794 152500.7888 计算可得=2.0529= 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=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12345678910111213土条 编号土条宽(m)()路堤部分面积地基部分面积Wti(kN)Wdi(KN)WisinQisinCtibiCdibi=1.8=1.812.53552.71 048.76 0.00 39.9435 12.7984 63.25 0.00 0.8362 120.0736 22.534910.12 0182.12 0.00 137.4507 11.7916 63.25 0.00 0.8980 197.4983 32.534513.24 0238.32 0.00 168.5177 0.0000 63.25 0.00 0.9338 214.9992 42.534014.82 0266.67 0.00 171.4122 0.0000 63.25 0.00 0.9721 223.3515 52.533615.54 0279.77 0.00 164.4470 0.0000 63.25 0.00 0.9974