地基沉降量计算

1、地基沉降量计算地基变形在其表面形成的垂直变形量称为建筑物的 沉降量在外荷载作用下地基土层被压缩达到稳定时基础底面的沉降量称为地基最终沉降量。一、分层总和法计算地基最终沉降量计算地基的最终沉降量，目前最常用的就是 分层总和法（一）基本原理该方法只考虑地基的垂向变形，没有考虑侧向变形，地基的变形同室内侧限 压缩试验中的情况基本一致，属一维压缩问题。地基的最终沉降量可用室内压缩 试验确定的参数（e、巳、a）进行计算，有：变换后得:式中：S-地基最终沉降量（mr）i；ei-地基受荷前（自重应力作用下）的孔隙比；e2-地基受荷（自重与附加应力作用下）沉降稳定后的孔隙比; H- 土层的厚度。计算沉降量时，

2、在地基可能受荷变形的压缩层范围内，根据土的特性、应力 状态以及地下水位进行分层。然后按式（4-9 ）或（4-10）计算各分层的沉降量 S。最后将各分层的沉降量总和起来即为地基的最终沉降量：（二）计算步骤1）划分土层如图4-7所示，各天然土层界面和地下水位必须作为分层界面；各分层厚度 必须满足H 2.5m,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。试用单向分层总和法计算基础中点最终沉降量。解：按单向分层总和法计算(1) 计算地基土的自重应力。z自基底标高起算当 z=0m, 肌=19.5 忽=39 (kPa)z=1m, cszi=

3、39+19.5 1=58.5 (kPa)z=2m, zi=58.5+20 =78.5 (kPa)z=3m, (?zi=78.5+20 =98.5 (kPa)z=4m, (?zi=98.5+(20-10) 1 108.5 (kPa)z=5m, (?zi=108.5+(20-10) 1=118.5 (kPa)z=6m, (?zi=118.5+18.5 1=137 (kPa)z=7m, 宓=137+18.5 X=155.5 (kPa)(2) 基底压力计算。基础底面以上，基础与填土的混合容重取 Y=20kN/m3=240kPa1250+2 5x2 5x2x202.5x2.5(3) 基底附加压力计算 =

4、 -=20-19 5x2.0= 201kPa(4) 基础中点下地基中竖向附加应力计算用角点法计算，L/B=1, (7 zi=4Ksi po，查附加应力系数表得 Ksi(5) 确定沉降计算深度zn考虑第层土压缩性比第层土大，经计算后确定zn=7m，见下表。例题4-1计算表格1z(m)zB/2Ks7(kPa)csz(kPa)7/ sz(%)zn(m)000.250 02013910.80.199 9160.758.521.60.112 390.2978.532.40.064 251.6298.843.20.040 132.24108.529.7154.00.027 021.71118.518.32

5、64.80.019 315.5213711.337 5.6 J0.014 811.90155.57.6按7m计(6)计算基础中点最终沉降量。利用勘察资料中的e-p曲线，求按单向分层总和法公式* ff为耆比i-L %计算结果见下表。例题4-1计算表格2Z(kPa(kPaH自重应力平均附加应力平均e1e2耳5aS = Ssj(m(cm值b坦值9(kPa)(cm)(kPa 1)(kPa)(cm)(kPa)(kPa)0392010.60.00038160.229.647158.571940.60.0002390.2180.8278.548.75159.40.71199100544184.0968.50

6、60.640.60.00021c o u51.6100125.568611.835.92398.5288.50145.40.6321100077490.926.84108.32.2103.5350.60.00023410070.9668480.617.4554113.5140.40.632811821 710041.9343930.618.065118.2 1.7127.580.630.60.000375110026.9831470.598.65146.2146.10.692115.510018.6223040.599.246137520.680.60.00053213.71159.98715

7、5.11.9760.60.000725079建筑地基基础设计规范推荐的沉降计算法下面计算沉降量的方法是建筑地基基础设计规范（GBJ7-89）所推荐的，简称规范推荐法，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划分计算土层，引入土层平均附加应力的概念，通过平均附加应力系数，将基底中心以下地基中Zi-i-Zi深度范围的附 加应力按等面积原则化为相同深度范围内矩形分布时的分布应力大小，再按矩形分布应力情况计算土层的压缩量，各土层压缩量的总和即为地基的计算沉降量。 理论上基础的平均沉降量可表示为式中：S-地基最终沉降量（mr）i；n-地基压缩层（即受压层）范围内所划分的土层

8、数；Po-基础底面处的附加压力（kPa）；Es-基础底面下第i层土的压缩模量（MPa ;乙、Zi-i -分别为基础底面至第i层和第i-1层底面的距离（m ;ai、a i-1-分别为基础底面计算点至第i层和第i-1层底面范围内平均附 加应力系数，可查表4-1。表4-1矩形面积上均布荷载作用下，通过中心点竖线上的平均附加应力系数Z/B1.01.21.41.61.82.00.1.001.001.001.001.001.0000000000.0.990.990.990.990.990.9917888880.0.980.990.990.990.990.9927012220.0.960.970.970.9

9、70.970.9737368990.0.930.940.950.950.950.9646736850.0.900.910.920.920.930.9350549350.0.850.870.890.890.900.9068808360.0.810.840.850.860.870.8776055160.0.770.800.810.830.830.8485191940.0.730.760.780.790.800.8195447631.0.690.720.740.760.770.7808394531.0.660.690.710.730.740.7513473431.0.630.660.680.700.

10、710.7221363551.0.600.630.650.670.680.69L/B2.42.83.23.64.05.0101.001.001.001.001.001.001.0000000000.990.990.990.990.990.990.9988888880.990.990.990.990.990.990.9933333330.980.980.980.980.980.980.9800111120.960.960.960.960.960.960.9612233330.930.930.930.940.940.940.9479900000.910.910.910.910.910.910.91

11、02344550.880.880.880.880.880.880.8814567780.850.850.850.850.850.860.8615789000.820.820.820.830.830.830.8316901230.790.790.800.800.800.800.8028134670.760.770.770.770.770.780.7841579020.730.740.740.750.750.750.7574924680.710.710.720.720.730.730.73313748819580351.0.570.600.620.640.660.670.680.690.700.7

12、00.700.710.71435981276158141.0.540.580.600.620.630.640.660.670.670.680.680.690.69580427346936031.0.520.550.580.590.610.620.640.650.650.660.660.670.67646093511836051.0.500.530.550.570.590.600.620.630.630.640.640.650.65723871301836161.0.480.510.520.550.570.580.600.610.610.620.620.630.63823761301949381

13、.0.460.490.510.530.550.560.580.590.600.600.610.610.62933761313160622.0.440.470.490.510.530.540.560.570.580.590.590.600.60065983535404062.0.420.450.480.500.510.520.540.550.560.570.570.580.59199205869748512.0.410.440.460.480.490.510.530.540.550.550.560.570.57243649103283072.0.400.420.450.460.480.490.5

14、10.520.530.540.540.550.56308194658748642.0.380.410.430.450.460.480.500.510.520.530.530.540.55474649103305312.0.370.400.420.440.450.460.480.500.500.510.520.530.53541315860962092.0.360.380.410.420.440.450.470.480.490.500.500.510.52629082537649882.0.350.370.390.410.430.440.460.470.480.490.490.500.51717

15、860214427672.0.340.360.380.400.410.430.440.460.470.480.480.490.50816748093206562.0.330.350.370.390.400.410.430.450.460.460.470.480.49916737981195563.0.320.340.360.380.390.400.420.440.450.450.460.470.48026637971195473.0.310.330.350.370.380.390.410.430.440.440.450.460.47137737870084473.0.300.320.340.3

16、60.370.380.400.420.430.430.440.450.46258847970195583.0.290.320.330.350.360.370.390.410.420.420.430.440.46370958971196603.0.280.310.330.340.350.370.380.400.410.420.420.430.45492169182207723.0.280.300.320.330.350.360.380.390.400.410.410.420.44524381203328943.0.270.290.310.330.340.350.370.380.390.400.4

17、10.420.43667503425530163.0.260.290.300.320.330.340.360.370.380.390.400.410.42790835647752393.0.260.280.300.310.320.330.350.360.370.380.390.400.42834168969984523.0.250.270.290.300.320.330.340.360.370.380.380.390.41977491292207854.0.250.270.280.300.310.320.340.350.360.370.370.390.40011824525539184.0.2

18、40.260.280.290.300.310.330.340.360.360.370.380.40165268858862424.0.240.260.270.290.300.310.320.340.350.350.360.370.39210602281296764.0.230.250.270.280.290.300.320.330.340.360.350.370.39365046625539104.0.230.250.260.270.290.300.310.320.330.340.350.360.38410580069973544.0.220.240.260.270.280.290.310.3

19、20.330.340.340.350.37565035403317984.0.220.240.250.260.270.280.300.310.320.330.340.350.37620589957751334.0.210.230.250.260.270.280.290.310.320.320.330.340.36785034492196774.0.210.230.240.250.260.270.290.300.310.320.330.340.36841589946640224.0.210.220.240.250.260.270.280.300.310.310.320.330.359071354

20、91195775.0.200.220.230.240.260.260.280.290.300.310.320.330.3506379094663022（二）规范推荐公式由(4-12 )式乘以沉降计算经验系数 s,即为规范推荐的沉降计算公 式：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沉降计算经验系数此基底附加压力 po(kPa)压缩模量Es(MPa)2.54.07.015.020.0po=fk1.41.31.00.40.2pov 0.75fk1.11.00.70.40.2注：表列数值可内插;当变形计算深度

21、范围内有多层土时，Es可按附加应力面积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：亞匹QQ2疣隅(4 - M)i-l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 ;表4-3 z取值B(m)22v B44 v B88v B 1515v B30 z(m)0.30.60.81.01.21.5 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：(4-15)规范法的具体计算过程可参例题4-2【例题4 2】已知柱下单独方形基

22、础，基础底面尺寸为 2.5 2.5m，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。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。i-l例题4-2计算表格Z(m)L/Bz/B命Esi(kPa)(cm)(cm)000.250001.00.80.23460.23460.234644184.274.272.01.60.19390.38780.153268611.806.073.02 52.40.15780.47340.085677490.896.964.03.20.13100.52400.

23、050668480.597.555.04.00.11140.55700.03343930.608.156.04.80.09670.58020.023231470.598.747.05.60.08520.59640.016223040.579.317.66.080.08040.61100.0146350000.039.34按规范确定受压层下限，Zn=2.5（2.5-0.4l n2.5）=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X =并假定加zA&查表4-2得沉降计算

24、经验系数 书s=1.17。那么，最终沉降量为：s = V = L17x 9.34 = 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:E = H卫0-16)式中：Sd-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）。U4-8地基沅降英型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

25、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，按 式（ 4-17）求解。=（4-17）迟式中：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所产生的变形量，所以应取卩=0.5 ;Eu-不排水变形模量，常根据不排水抗剪强度 C和Eu的经验关系式（4-18 ） 求得。巴=（300 -1250）（4-1E）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。表4-4沉降系数3值受何面形 状L/B中占1八、矩形角点，圆形周边平均值刚性基础圆形1.000.640.85