沉降计算例题

1、时间：二0二一年七月二十九日地基沉降量计算之樊仲川亿创作时间：二0二一年七月二十九日地基变形在其概略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，目前最经常使用的就是分层总和法.（一）基来源根底理该办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（ei、Es、a）进行计算,有：变换后得：或式中：S-地基最终沉降量（mrj）；e1-地基受荷前（自重应力作用下）的孔隙比；时间：二o二

2、一年七月二十九日时间：二O二一年七月二十九日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,在地基可能受荷变形的压缩层规模内,按照土的特性、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Si.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）计算步调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Hi<0.4B（B为基底宽度）.2）计算基底附加压力p03）计算各分层界面的自重应力（Tsz和附加应力（Tz;并绘制应力散布曲线.4）确定压缩层厚度满足（7z=0.2（7sz的

3、深度点可作为压缩层的下限；对于软土则应满足7z=0.17Sz；对一般建筑物可按下式计算zn=B（2.5-0.4lnB）.时间：二O二一年七月二十九日时间：二O二一年七月二十九日5）计算各分层加载前后的平均垂直应力p1=csz;p2=csz+cz6）按各分层的p1和p2在e-p曲线上查取相应的孔隙比或确定a、Es等其它压缩性指标7）按照不合的压缩性指标,选用公式（4-9）、（4-10）计算各分层的沉降量Si8）按公式（4-11）计算总沉降量S.分层总和法的具体计算过程可参例题4-1.例题41已知柱下单独方形基础，基础底面尺寸为2.5x2.5m,埋深2m,作用于基础上（设计地面标高处）的轴向荷载N

4、=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,csD=19.5x2=39（kPa）z=1m,csz1=39+19.5x1=58.5（kPa）z=2m,csz1=58.5+20x1=78.5（kPa）z=3m,csz1=78.5+20x1=98.5（kPa）z=4m,csz仁98.5+(20-10)X1=108.5(kPa)z=5m,csz仁108.5+(20-10)X仁118.5(kPa)z=6m,csz1二118.5+18.5X仁137(kPa)z=7m,csz1

5、二137+18.5X仁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丫0=20kN/m3.(3) 基底附加压力计算.(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,czi=4Ksip0,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二7m,见下表.例题4-1计算表格1z(m)zB/2Kscz(kPa)csz(kPa)cz/csz(%)zn(m)000.25002013910.80.1999160.758.521.60.112390.2978.529.7132.40.064251.6298.8

6、18.32按7m计43.20.040132.24108.511.3354.00.027021.71118.57.664.80.019315.5213775.60.014811.90155.5(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计算结果见下表.例题4-1计算表格2z(m)(kPa)升(kPa)H(cm)自重应力平均值恥(kPa)附加应力平均值吕(kPa)(kPa)e1e2£(cm)S=Safj(cm)5a(kPa)r示(kPa-1)0392010.60.00038160.229.647158.5171940.60.0002390.2180.

7、8278.5148.75159.40.71199100544184.0968.5060.640.60.00021398551.6100125.568611.835.92398.5288.50145.40.6321100077490.926.84108.32.2103.5350.60.00023410070.9668480.617.4554113.5140.40.632811821710041.9343930.618.065118.21.7127.580.630.60.0003751100146.226.98146.10.69231470.598.65115.510018.6223040.599

8、.246137c520.680.60.00053213.71159.987155.11.9760.60.000725079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办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-1-zi深度规模的附加应力按等面积原则化为相同深度规模内矩形散布时的散布应力大小，再按矩形散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暗示为式中：S

9、-地基最终沉降量（mm；n-地基压缩层（即受压层）规模内所划分的土层数；p0-基础底面处的附加压力（kPa）；Esi-基础底面下第i层土的压缩模量（MPa;zi、zi-1-辨别为基础底面至第i层和第i-1层底面的距离（m；ai、ai-1-辨别为基础底面计算点至第i层和第i-1层底面规模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/BL/B1.01.21.41.61.82.02.42.83.23.64.05.0>100.1.001.001.001.001.001.001.001.001.001.001.001.001.000000

10、00000000000.0.990.990.990.990.990.990.990.990.990.990.990.990.99178888888888880.0.980.990.990.990.990.990.990.990.990.990.990.990.99270122233333330.0.960.970.970.970.970.970.980.980.980.980.980.980.98373689900111120.0.930.940.950.950.950.960.960.960.960.960.960.960.96467368512233330.0.900.910.920.92

11、0.930.930.930.930.930.940.940.940.94505493579900000.0.850.870.890.890.900.900.910.910.910.910.910.910.91688083602344550.0.810.840.850.860.870.870.880.880.880.880.880.880.88760551614567780.0.770.800.810.830.830.840.850.850.850.850.850.860.86851919415789000.0.730.760.780.790.800.810.820.820.820.830.83

12、0.830.83954476316901231.0.690.720.740.760.770.780.790.790.800.800.800.800.80083945328134671.0.660.690.710.730.740.750.760.770.770.770.770.780.78134734341579021.0.630.660.680.700.710.720.730.740.740.750.750.750.75213635574924681.0.600.630.650.670.680.690.710.710.720.720.730.730.73313748819580351.0.57

13、0.600.620.640.660.670.680.690.700.700.700.710.71435981276158141.0.540.580.600.620.630.640.660.670.670.680.680.690.69580427346936031.0.520.550.580.590.610.620.640.650.650.660.660.670.67646093511836051.0.500.530.550.570.590.600.620.630.630.640.640.650.65723871301836161.0.480.510.520.550.570.580.600.61

14、0.610.620.620.630.63823761301949381.0.460.490.510.530.550.560.580.590.600.600.610.610.62933761313160622.0.440.470.490.510.530.540.560.570.580.590.590.600.60065983535404062.0.420.450.480.500.510.520.540.550.560.570.570.580.59199205869748512.0.410.440.460.480.490.510.530.540.550.550.560.570.5724364910

15、3283072.0.400.420.450.460.480.490.510.520.530.540.540.550.56308194658748642.0.380.410.430.450.460.480.500.510.520.530.530.540.55474649103305312.0.370.400.420.440.450.460.480.500.500.510.520.530.53541315860962092.0.360.380.410.420.440.450.470.480.490.500.500.510.52629082537649882.0.350.370.390.410.43

16、0.440.460.470.480.490.490.500.51717860214427672.0.340.360.380.400.410.430.440.460.470.480.480.490.50816748093206562.0.330.350.370.390.400.410.430.450.460.460.470.480.49916737981195563.0.320.340.360.380.390.400.420.440.450.450.460.470.48026637971195473.0.310.330.350.370.380.390.410.430.440.440.450.46

17、0.47137737870084473.0.300.320.340.360.370.380.400.420.430.430.440.450.46258847970195583.0.290.320.330.350.360.370.390.410.420.420.430.440.46370958971196603.0.280.310.330.340.350.370.380.400.410.420.420.430.45492169182207723.0.280.300.320.330.350.360.380.390.400.410.410.420.44524381203328943.0.270.29

18、0.310.330.340.350.370.380.390.400.410.420.43667503425530163.0.260.290.300.320.330.340.360.370.380.390.400.410.42790835647752393.0.260.280.300.310.320.330.350.360.370.380.390.400.42834168969984523.0.250.270.290.300.320.330.340.360.370.380.380.390.41977491292207854.0.250.270.280.300.310.320.340.350.36

19、0.370.370.390.40011824525539184.0.240.260.280.290.300.310.330.340.360.360.370.380.40165268858862424.0.240.260.270.290.300.310.320.340.350.350.360.370.39210602281296764.0.230.250.270.280.290.300.320.330.340.360.350.370.39365046625539104.0.230.250.260.270.290.300.310.320.330.340.350.360.38410580069973

20、544.0.220.240.260.270.280.290.310.320.330.340.340.350.37565035403317984.0.220.240.250.260.270.280.300.310.320.330.340.350.37620589957751334.0.210.230.250.260.270.280.290.310.320.320.330.340.36785034492196774.0.210.230.240.250.260.270.290.300.310.320.330.340.36841589946640224.0.210.220.240.250.260.27

21、0.280.300.310.310.320.330.35907135491195775.0.200.220.230.240.260.260.280.290.300.310.320.330.3506379094663022(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：®s-沉降计算经验系数，应按照同类地区已有衡宇和修建物实测最终沉降量与计算沉降量对比确定，一般采取表4-2的数值；表4-2沉降计算经验系数"s基底附加压力p0(kPa)压缩模量Es(MPa)2.54.07.015.020.0p0=fk1.41.31.00

22、.40.2p0v0.75fk1.11.00.70.40.2注：表列数值可内插;当变形计算深度规模内有多层土时,Es可按附加应力面积A的加权平均值采取，即时间：二0二一年七月二十九日（三）地基受压层计算深度的确定计算深度zn可按下述办法确定：1）存在相邻荷载影响的情况下，应满足下式要求：式中：Sn-在深度zn处,向上取计算厚度为Az的计算变形值;z查表4-3;表4-3z取值Si'-在深度zn规模内，第i层土的计算变形量B(m)W22vBW44VBW88vBW1515VBW30>30z(m)0.30.60.81.01.21.52）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

23、计算深度zn: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2.5x2.5m,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，采取下式，计算结果详见下表.例题4-2计算表格z(m)L/Bz/B邑函叼Esi(kPa)(cm)(cm)000.250001.00.80.23460.23460.234644184.274.272.01.60.19390.38780.153268611.806.073.0耳“252.40.15780.47340.

24、085677490.896.964.03.20.13100.52400.050668480.597.555.04.00.11140.55700.03343930.608.156.04.80.09670.58020.023231470.598.747.05.60.08520.59640.016223040.579.317.66.080.08040.61100.0146350000.039.34按规范确定受压层下限工n=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Az厚度计算，按照表4-3的要求，取z=0.6m,则zn=7.6m,计算得厚度Az的沉降量为0.

25、03cm,满足要求.查表4-2得沉降计算经验系数®s=1.17.那么，最终沉降量为：三、按粘性土的沉降机理计算沉降按照对粘性土地基在局部（基础）荷载作用下的实际变形特征的不雅察和阐发，粘性土地基的沉降S可以认为是由机理不合的三部分沉降组成（图4-8）,亦即：式中：Sd-瞬时沉降（亦称初始沉降）；Sc-凝结沉降（亦称主凝结沉降）；Ss-次凝结沉降（亦称蠕变沉降）.时间：二O二一年七月二十九日瞬时沉降是指加载后地基瞬时产生的沉降.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.凝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

26、力的消散,土骨架产生变形所造成的沉降（凝结压密）.凝结沉降速率取决于孔隙水的排出速率.次凝结沉降是指主凝结过程（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产生变形.这种变形的速率取决于土骨架自己的蠕变性质.（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.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，常按照不排水抗剪强度Cu和Eu的经验关系式（4-18）求得.上式中的低值适用于较软的、高塑性有机土，高值适用于