沉降量计算方法

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1、下面计算沉降量的方法是建筑地基基础设计规范推荐法，有时也叫应力面积法。（一）计算原理应力面积法一般按地基土的天然分层面力的概念，通过平均附加应力系数,将基加应力按等面积原则化为相同深度范围内矩分布应力情况计算土层的压缩量，各土层压理论上基础的平均沉降量可表示为弘】2电i式中:S-地基最终沉降量（mr)7n-地基压缩层（即受压层）范围内Po-基础底面处的附加压力kPaEsi基础底面下第i层土的压缩模乙、Zi-1-分别为基础底面至第i丿ai、ai-1-分别为基础底面计算点一加应力系数,可查表4-1o表4-1矩形面积上均布荷载作用下,通过中Z/B1.01.21.41.61.82.00.1.001.0

2、01.001.001.001.0000000000.0.990.990.990.990.990.9917888880.0.980.990.990.990.990.9927012220.0.960.970.970.970.970.9737368990.0.930.940.950.950.950.9646736850.0.900.910.920.920.930.93（GBJ7-89）所推荐的，简称规范至划分计算土层，引入土层平均附加应裘底中心以下地基中Zi-1-Zi深度范围的附也形分布时的分布应力大小，再按矩形玉缩量的总和即为地基的计算沉降量。3-%却）(4-12)勺所划分的土层数；真量（MPa；

3、层和第1-1层底面的距离（m；至第i层和第i-1层底面范围内平均附|心点竖线上的平均附加应力系数aL/B2.42.83.23.64.05.0101.001.001.001.001.001.001.0000000000.990.990.990.990.990.990.9988888880.990.990.990.990.990.990.9933333330.980.980.980.980.980.980.9800111120.960.960.960.960.960.960.9612233330.930.930.930.940.940.940.94505493579900000.0.850.870

4、.890.890.900.900.910.910.910.910.910.910.91688083602344550.0.810.840.850.860.870.870.880.880.880.880.880.880.88760551614567780.0.770.800.810.830.830.840.850.850.850.850.850.860.86851919415789000.0.730.760.780.790.800.810.820.820.820.830.830.830.83954476316901231.0.690.720.740.760.770.780.790.790.800

5、.800.800.800.80083945328134671.0.660.690.710.730.740.750.760.770.770.770.770.780.78134734341579021.0.630.660.680.700.710.720.730.740.740.750.750.750.75213635574924681.0.600.630.650.670.680.690.710.710.720.720.730.730.73313748819580351.0.570.600.620.640.660.670.680.690.700.700.700.710.714359812761581

6、41.0.540.580.600.620.630.640.660.670.670.680.680.690.69580427346936031.0.520.550.580.590.610.620.640.650.650.660.660.670.67646093511836051.0.500.530.550.570.590.600.620.630.630.640.640.650.65723871301836161.0.480.510.520.550.570.580.600.610.610.620.620.630.63823761301949381.0.460.490.510.530.550.560

7、.580.590.600.600.610.610.62933761313160622.0.440.470.490.510.530.540.560.570.580.590.590.600.60065983535404062.0.420.450.480.500.510.520.540.550.560.570.570.580.59199205869748512.0.410.440.460.480.490.510.530.540.550.550.560.570.57243649103283072.0.400.420.450.460.480.490.510.520.530.540.540.550.563

8、08194658748642.0.380.410.430.450.460.480.500.510.520.530.530.540.55474649103305312.0.370.400.420.440.450.460.480.500.500.510.520.530.53541315860962092.0.360.380.410.420.440.450.470.480.490.500.500.510.52629082537649882.0.350.370.390.410.430.440.460.470.480.490.490.500.51717860214427672.0.340.360.380

9、.400.410.430.440.460.470.480.480.490.50816748093206562.0.330.350.370.390.400.410.430.450.460.460.470.480.49916737981195563.0.320.340.360.380.390.400.420.440.450.450.460.470.48026637971195473.0.310.330.350.370.380.390.410.430.440.440.450.460.47137737870084473.0.300.320.340.360.370.380.400.420.430.430

10、.440.450.46258847970195583.0.290.320.330.350.360.370.390.410.420.420.430.440.46370958971196603.0.280.310.330.340.350.370.380.400.410.420.420.430.45492169182207723.0.280.300.320.330.350.360.380.390.400.410.410.420.44524381203328943.0.270.290.310.330.340.350.370.380.390.400.410.420.43667503425530163.0

11、.260.290.300.320.330.340.360.370.380.390.400.410.42790835647752393.0.260.280.300.310.320.330.350.360.370.380.390.400.42834168969984523.0.250.270.290.300.320.330.340.360.370.380.380.390.41977491292207854.0.250.270.280.300.310.320.340.350.360.370.370.390.40011824525539184.0.240.260.280.290.300.310.330

12、.340.360.360.370.380.40165268858862424.0.240.260.270.290.300.310.320.340.350.350.360.370.39210602281296764.0.230.250.270.280.290.300.320.330.340.360.350.370.39365046625539104.0.230.250.260.270.290.300.310.320.330.340.350.360.3841110(580069973544.0.220.240.260.270.280.290.310.320.330.340.340.350.3756

13、5035403317984.0.220.240.250.260.270.280.300.310.320.330.340.350.37620589957751334.0.210.230.250.260.270.280.290.310.320.320.330.340.36785034492196774.0.210.230.240.250.260.270.290.300.310.320.330.340.36841589946640224.0.210.220.240.250.260.270.280.300.310.310.320.330.35907135491195775.0.200.220.230.

14、240.260.260.280.290.300.310.320.330.3506379094663022(二)规范推荐公式由(4-12)式乘以沉降计算经验系数书s,即为规范推荐的沉降计算公式：A叽心串$牛匕云-片(4-13)式中：书S-沉降计算经验系数，应根据同类地区已有房屋和构筑物实测最终沉降量与计算沉降量对比确定，一般采用表4-2的数值；表4-2沉降计算经验系数帕基底附加压丨压缩模量Es(MPa)力po(kPa)2.54.07.015.020.0p0=fk1.41.31.00.40.2po0.75fk1.11.00.70.40.2注：表列数值可内插；当变形计算深度范围内有多层土时，Es可按

15、附加应力面积A的加权平均值采用，即(三)地基受压层计算深度的确定计算深度Zn可按下述方法确定：1) 存在相邻荷载影响的情况下，应满足下式要求：n0.025(4-14)!-1式中：S-在深度Zn处，向上取计算厚度为Z的计算变形值；z查表4-3;S-在深度Zn范围内，第i层土的计算变形量。2) 对无相邻荷载的独立基础，可按下列简化的经验公式确定沉降计算深度Zn：=5(2.5-0.41115)(4-15)表4-3z取值B(m)22vB44vB88vB1515vB30z(m)0.30.60.81.01.21.5规范法的具体计算过程可参例题4-2。【例题42】已知柱下单独方形基础，基础底面尺寸为2.52

16、.5m，埋深2m，作用于基础上(设计地面标高处)的轴向荷载N=1250kN，有关地基勘察资料与基础剖面详见下图。试用规范法计算基础中点最终沉降量。3.24.00.13100.52400.11140.55700.05060.033684843930.590.607.558.15z(m)L/Bz/BM=雷ESi(kPa)(cm)(cm)例题4-2计算表格输质黏土FiQQiB/m33.0m应计tid&i4J.0mV5EZ3?Om帖土瓦=205kN就O.50100150200250OPS尸如.SkM枷i3710m35.J0IUO.S解：按建筑地基基础设计规范计算，采用下式，计算结果详见下表。000.2

17、50001.00.80.23460.23460.234644184.274.272.01.60.19390.38780.153268611.806.073.02.40.15780.47340.085677490.896.964.02.5.=15.07.56.04.80.09670.58020.023231470.598.747.05.60.08520.59640.016223040.579.317.66.080.08040.61100.0146350000.039.34按规范确定受压层下限，Zn=2.5(2.5-0.4ln2.5)=5.3m;由于下面土层仍软弱，在层粘土底面以下取z厚度计算，根

18、据表4-3的要求，取z=0.6m,则Zn=7.6m,计算得厚度z的沉降量为0.03cm,满足要求。由唱=5258kPa,芥假定p於瓦查表4-2得沉降计算经验系数书s=1.17。那么，最终沉降量为:s二忆-sf=1.17x9.34=10.98cm三、按粘性土的沉降机理计算沉降根据对粘性土地基在局部（基础）荷载作用下的实际变形特征的观察和分析，粘性土地基的沉降S可以认为是由机理不同的三部分沉降组成（图4-8），亦即:S詢+&+&(4-16)式中：S-瞬时沉降（亦称初始沉降）；Sc-固结沉降（亦称主固结沉降）；Ss-次固结沉降（亦称蠕变沉降）。瞬时沉降是指加载后地基瞬时发生的沉降。由于基础加载面积为

19、有限尺寸，加载后地基中会有剪应变产生，剪应变会引起侧向变形而造成瞬时沉降。固结沉降是指饱和与接近饱和的粘性土在基础荷载作用下，随着超静孔隙水压力的消散，土骨架产生变形所造成的沉降（固结压密）。固结沉降速率取决于孔隙水的排出速率。次固结沉降是指主固结过程（超静孔隙水压力消散过程）结束后，在有效应力不变的情况下，土的骨架仍随时间继续发生变形。这种变形的速率取决于土骨架本身的蠕变性质。（一）瞬时沉降计算瞬时沉降没有体积变形，可认为是弹性变形，因此一般按弹性理论计算,式（4-17）求解。(4-17)式中：3-沉降系数，可从表4-4中查用；P0-基底附加应力；卩-泊松比，这时是在不排水条件下没有体积变形

20、所产生的变形量，应取卩=0.5;Eu-不排水变形模量，常根据不排水抗剪强度C和吕的经验关系式求得=(300-1250)(?,(4-18)所以(4-18)上式中的低值适用于较软的、高塑性有机土，高值适用于一般较硬的粘性土。受何面形状L/B中占1八、矩形角点，圆形周边平均值刚性基础圆形1.000.640.850.79正方形1.001.120.560.950.881.51.360.681.151.082.01.520.761.301.223.01.780.891.521.444.01.960.981.701.61矩形6.02.231.121.968.02.421.212.1210.02.531.27

21、2.252.1230.03.231.622.8850.03.541.773.22100.04.002.003.70表4-4沉降系数3值*平均值指柔性基础面积范围内各点瞬时沉降系数的平均值（二）固结沉降计算固结沉降是粘性土地基沉降的最主要的组成部分，可用分层总和法计算。但是分层总和法采用的是一维课题(有侧限)的假设，这与一般基础荷载(有限分布面积)作用下的地基实际性状不尽相符。司开普敦(Skempton,AW.)和贝伦(Birrum,L.)建议根据有侧向变形条件下产生的超静孔隙水压力计算固结沉降S。以轴对称课题为例，分层总和法计算的沉降量为S，Sc可用下式求解：$=卅(4-19)其中，au为SC

22、与S之间的比例系数，有邱二(4-20)i-Lau与土的性质密切相关，另外，还与基础形状及土层厚度H与基础宽度B之比有关。(三)次固结沉降的计算对一般粘性土来说，次固结沉降数值S不大，但如果是塑性指数较大的、正常固结的软粘土，尤其是有机土，SS值有可能较大，不能不予考虑。目前在生产中主要使用下述半经验方法估算土层的次固结沉降。m*VS0.11.010100100010000逊辻时问HiWiOEh-9土的Eg姙线图4-9为室内压缩试验得出的变形S与时间对数Igt的关系曲线，取曲线反弯点前后两段曲线的切线的交点m作为主固结段与次固结段的分界点；设相当于的斜率反映土的次固结变形C也就可以按下式计算土层分界点的时间为tl，次固结段（基本上是一条直线）速率，一般用Cs表示，称为土的次固结指数。知道的次固结沉降Ss:(4-21)式中：H和巴分别为土层的厚度和初始孔隙比;11对应于主固结完成的时间；t2为欲求次固结沉降量的那个时间。