沉降计算例题(试题学习)

1、页丿门页脚町咆删除仅供借鉴页丿门页脚町咆删除仅供借鉴高等教育高等教育#1高等教育高等教育#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、E、a）进行计算，有：is3=珀一门+芒J令变换后得：式中：S-地基最终沉降量（mm）；e-地基受荷前（自重应力作用

2、下）的孔隙比；e1-地基受荷（自重与附加应力作用下）沉降稳定后的孔隙比H2-土层的厚度。计算沉降量时，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：i=(4-11)i-l1）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HW0.4B（B为基底宽度）。i2）计算基底附加压力p03）计算各分层界面的自重应力。和附加应力。；并绘制应力分布曲线。szz4）确定压缩层厚度满足。=0.2。的深度点可作为压缩层的下限；zsz对于软土则应

3、满足。=0.1。；zsz对一般建筑物可按下式计算z=B（2.5-0.4lnB）。n5）计算各分层加载前后的平均垂直应力p=。；p=。+。1sz2szz6）按各分层的p和p在e-p曲线上查取相应的孔隙比或确定a、E等其它压12s缩性指标7）根据不同的压缩性指标，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。页丿门贝脚町咆删除仅供借鑒页丿门贝脚町咆删除仅供借鑒页丿门贝脚町咆删除仅供借鑒页丿门贝脚町咆删除仅供借鑒贝眉页脚可i贝眉页脚可i键删除仅供借鉴高等教育高等教育#1高等教育高等教育#1高等教育高等教育#1土层I沉降计算探鳳自重应为分布曲线分常番线受压

4、层4-7廿层总和法计算地基沉降童土层I沉降计算探鳳自重应为分布曲线分常番线受压层4-7廿层总和法计算地基沉降童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(设计地面标咼处)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,jD=19.5x2=39(kPa)z=1m,o1=39+19.5x1=58.5(kPa)sz1z=2m，o1=58.5+20 x1=78.5(kPa)sz1z=

5、3m，o1=78.5+20 x1=98.5(kPa)sz1z=4m,冬1=98.5+(20-10)x1=108.5(kPa)z=5m,；Z=108.5+(20-10)x1=118.5(kPa)z=6m,o：=118.5+18.5x1=137(kPa)sz1z=7m,o=137+18.5x1=155.5(kPa)sz1（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。=240kPa=240kPa2.5x2.53）基底附加压力计算。pyU24019.52.020lU?a4）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,。尸4札p0，查附加应力系数表得K.oz

6、isisi5）确定沉降计算深度zn按单向分层总和法公式按单向分层总和法公式考虑第层土压缩性比第层土大，经计算后确定z=7m,见下表。n例题4-1计算表格1z(m)zB/2Ksoz(kPa)osz(kPa)叽(%)zn(m)000.25002013910.80.1999160.758.521.60.112390.2978.532.40.064251.6298.843.20.040132.24108.529.7154.00.027021.71118.518.3264.80.019315.5213711.3375.60.014811.90155.57.6按7m计6）计算基础中点最终沉降量。利用勘察资

7、料中的e-p曲线，求贝丿廿贝脚町键删除仅供借鉴贝丿廿贝脚町键删除仅供借鉴贝丿廿贝脚町键删除仅供借鉴贝丿廿贝脚町键删除仅供借鉴高等教育高等教育#1高等教育高等教育#1计算结果见下表。例题4-1计算表格2b血by(kPa(kPa)(cm)自重应力平均值阳（kPa）附加应力平均(kPa)b當+(kPa)(kPa-1)(kPa)(cm)(cm)039201158.5160.7278.590.29398.551.624108.532.245118.521.7115.50.6b血by(kPa(kPa)(cm)自重应力平均值阳（kPa）附加应力平均(kPa)b當+(kPa)(kPa-1)(kPa)(cm)(

8、cm)039201158.5160.7278.590.29398.551.624108.532.245118.521.7115.50.60.000386137210010010010010010010048.7568.5088.50103.5113.5127.5146.25180.85125.5070.9641.9326.9818.6213.71155.11.950229.6194159.46145.43140.48146.12159.960.710.640.6350.630.630.690.680.60.60.60.60.60.60.000230.000210.000230.000370.0

9、00530.0007244186861774968484393314723044.091.830.920.610.610.590.595.926.847.458.068.659.24二、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z._-z.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

10、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贝m贝m脚町咆删除仅供借鉴贝m贝m脚町咆删除仅供借鉴高等教育高等教育#1高等教育高等教育#1芒工g；=倘-习_l)(4-12)i-li-1E.式中：S-地基最终沉降量（mm）；n-地基压缩层（即受压层）范围内所划分的土层数；p基础底面处的附加压力（kPa）；E-基础底面下第i层土的压缩模量（MPa）；siz、z分别为基础底面至第i层和第i-1层底面的距离（m）；ii-1a、a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ii-1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az/B1

11、.01.21.41.61.82.00.1.001.001.001.001.001.0000000000.0.990.990.990.990.990.9917888880.0.980.990.990.990.990.9927012220.0.960.970.970.970.970.9737368990.0.930.940.950.950.950.9646736850.0.900.910.920.920.930.9350549350.0.850.870.890.890.900.9068808360.0.810.840.850.860.870.8776055160.0.770.800.810.830

12、.830.8485191940.0.730.760.780.790.800.8195447631.0.690.720.740.760.770.7808394531.0.660.690.710.730.740.7513473431.0.630.660.680.700.710.722136355L/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.

13、9800111120.960.960.960.960.960.960.9612233330.930.930.930.940.940.940.9479900000.910.910.910.910.910.910.9102344550.880.880.880.880.880.880.8814567780.850.850.850.850.850.860.8615789000.820.820.820.830.830.830.8316901230.790.790.800.800.800.800.8028134670.760.770.770.770.770.780.7841579020.730.740.7

14、40.750.750.750.757492468页丿门贝脚町咆删除仅供借鉴页丿门贝脚町咆删除仅供借鉴页丿门贝脚町咆删除仅供借鉴页丿门贝脚町咆删除仅供借鉴高等教育高等教育#1高等教育高等教育#11.0.600.630.650.670.680.690.710.710.720.720.730.730.73313748819580351.0.570.600.620.640.660.670.680.690.700.700.700.710.71435981276158141.0.540.580.600.620.630.640.660.670.670.680.680.690.6958042734693603

15、1.0.520.550.580.590.610.620.640.650.650.660.660.670.67646093511836051.0.500.530.550.570.590.600.620.630.630.640.640.650.65723871301836161.0.480.510.520.550.570.580.600.610.610.620.620.630.63823761301949381.0.460.490.510.530.550.560.580.590.600.600.610.610.62933761313160622.0.440.470.490.510.530.540.

16、560.570.580.590.590.600.60065983535404062.0.420.450.480.500.510.520.540.550.560.570.570.580.59199205869748512.0.410.440.460.480.490.510.530.540.550.550.560.570.57243649103283072.0.400.420.450.460.480.490.510.520.530.540.540.550.56308194658748642.0.380.410.430.450.460.480.500.510.520.530.530.540.5547

17、4649103305312.0.370.400.420.440.450.460.480.500.500.510.520.530.53541315860962092.0.360.380.410.420.440.450.470.480.490.500.500.510.52629082537649882.0.350.370.390.410.430.440.460.470.480.490.490.500.51717860214427672.0.340.360.380.400.410.430.440.460.470.480.480.490.50816748093206562.0.330.350.370.

18、390.400.410.430.450.460.460.470.480.49916737981195563.0.320.340.360.380.390.400.420.440.450.450.460.470.48026637971195473.0.310.330.350.370.380.390.410.430.440.440.450.460.47137737870084473.0.300.320.340.360.370.380.400.420.430.430.440.450.46258847970195583.0.290.320.330.350.360.370.390.410.420.420.

19、430.440.46370958971196603.0.280.310.330.340.350.370.380.400.410.420.420.430.45492169182207723.0.280.300.320.330.350.360.380.390.400.410.410.420.44524381203328943.0.270.290.310.330.340.350.370.380.390.400.410.420.43667503425530163.0.260.290.300.320.330.340.360.370.380.390.400.410.42790835647752393.0.

20、260.280.300.310.320.330.350.360.370.380.390.400.42834168969984523.0.250.270.290.300.320.330.340.360.370.380.380.390.41977491292207854.0.250.270.280.300.310.320.340.350.360.370.370.390.40011824525539184.0.240.260.280.290.300.310.330.340.360.360.370.380.40165268858862424.0.240.260.270.290.300.310.320.

21、340.350.350.360.370.39210602281296764.0.230.250.270.280.290.300.320.330.340.360.350.370.39365046625539104.0.230.250.260.270.290.300.310.320.330.340.350.360.38410580069973544.0.220.240.260.270.280.290.310.320.330.340.340.350.37565035403317984.0.220.240.250.260.270.280.300.310.320.330.340.350.37620589

22、957751334.0.210.230.250.260.270.280.290.310.320.320.330.340.36785034492196774.0.210.230.240.250.260.270.290.300.310.320.330.340.36841589946640224.0.210.220.240.250.260.270.280.300.310.310.320.330.35907135491195775.0.200.220.230.240.260.260.280.290.300.310.320.330.3506379094663022页丿门页脚町咆删除仅供借鑒页丿门页脚町咆

23、删除仅供借鑒页丿门页脚町咆删除仅供借鑒页丿门页脚町咆删除仅供借鑒页眉页脚可一键删除仅供借鉴页眉页脚可一键删除仅供借鉴咼等教育咼等教育#1咼等教育咼等教育#1高等教育高等教育#1由(4-12)式乘以沉降计算经验系数V，即为规范推荐的沉降计算公s式中：V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s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沉降计算经验系数次基底附加压力p0(kPa)压缩模量Es(MPa)2.54.07.015.020.0Po=k1.41.31.00.40.2PoV075f1.11.00.70.40.2注：表列数值可内插;当变形计算深度范围内有多层土时

24、，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z可按下述方法确定：n1)存在相邻荷载影响的情况下，应满足下式要求：朋；兰0Q25土丘冕(4-14)i-i式中:Sz-在深度z处，向上取计算厚度为Az的计算变形值；z查表4-3；nn表4-3z取值B(m)22VB44VB88VB1515VB30z(m)0.30.60.81.01.21.5S-在深度z范围内，第i层土的计算变形量。in2)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z：n玉=5(2.5-0.4n)(4-15)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

25、面尺寸为2.5x2.5m,埋深2m,作用于基础上(设计地面标咼处)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。例题4-2计算表格z/B(m)001.00.82.01.62.43.04.03.24.05.04.86.07.05.67.66.080.25000.23460.19390.15780.13100.11140.09670.08520.08040.23460.38780.47340.52400.55700.58020.59640.61100.23460.15320.08560.

26、05060.0330.02320.01620.0146Esi(kPa)(cm)(cm)4418686177496848439331472304350004.271.800.890.590.600.590.570.034.276.076.967.558.158.749.319.34z/B(m)001.00.82.01.62.43.04.03.24.05.04.86.07.05.67.66.080.25000.23460.19390.15780.13100.11140.09670.08520.08040.23460.38780.47340.52400.55700.58020.59640.61100

27、.23460.15320.08560.05060.0330.02320.01620.0146Esi(kPa)(cm)(cm)4418686177496848439331472304350004.271.800.890.590.600.590.570.034.276.076.967.558.158.749.319.34页眉贾脚可一页眉贾脚可一键删除仅供借鉴页丿门贝脚町咆删除仅供借鉴页丿门贝脚町咆删除仅供借鉴高等教育高等教育#1高等教育高等教育#1按规范确定受压层下限，zn=2.5（2.5-0.41n2.5）=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，根据表4-3的要求，取Az

28、=0.6m,则z=7.6m,计算得厚度Az的沉降量为0.03cm，满足要求。n由&=弓-=5淤kPa,并假定/；=朋查表4-2得沉降计算经验系数2=1.17。那么，最终沉降量为:s=忆=1.17x9.34=10.98cm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*+迅+$(4-16)式中：S-瞬时沉降（亦称初始沉降）；dS-次固结沉降（亦称蠕变沉降）。S-固结沉降（亦称主固结沉降）；cS-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有限尺寸，加载后地基中会有

29、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，按式(4-17)求解。亀乂筈A1-/)(4-17)式中：s沉降系数，可从表4-4中查用；p0-基底附加应力；卩一泊松比，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；E不排水变形模量，常根据不排水抗剪强度C和E的经验关系式(4-18)uuu氏-(300-1250)(7,(4-1S)上式中的低