沉降计算例题.docx

1、沉降计算例题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（mm）；e1-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

2、时，在地基可能受荷变形的压缩层围，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Hi0.4B（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sz和附加应力z；并绘制应力分布曲线。4）确定压缩层厚度满足z=0.2sz的深度点可作为压缩层的下限；对于软土则应满足z=0.1sz；对一般建筑物可按下式计算zn=B(2.5-0.4lnB)。5）计算各分层加载前后的平均垂直应力p1

3、=sz； p2=sz+z6）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）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。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2.52.5m，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，sD=19.52=39（kPa）z=1m，sz

4、1=39+19.51=58.5（kPa）z=2m，sz1=58.5+201=78.5（kPa）z=3m，sz1=78.5+201=98.5（kPa）z=4m，sz1=98.5+(20-10)1=108.5（kPa）z=5m，sz1=108.5+(20-10)1=118.5（kPa）z=6m，sz1=118.5+18.51=137（kPa）z=7m，sz1=137+18.51=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，zi=4Ksip0，查附加应力系数表

5、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/2Ksz(kPa)sz(kPa)z/sz(%)zn(m)0123456700.81.62.43.24.04.85.60.250 00.199 90.112 30.064 20.040 10.027 00.019 30.014 8201160.790.2951.6232.2421.7115.5211.903958.578.598.8108.5118.5137155.529.7118.3211.337.6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，

6、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2 z (m) (kPa) (kPa) H (cm) 自重应力平均值(kPa) 附加应力平均值(kPa) (kPa) e1e2(kPa-1) (kPa) (cm) (cm) 0 39 201 10010010010010010010048.7568.5088.50103.5113.5127.5146.25180.85125.5070.9641.9326.9818.6213.71 229.6194159.46145.43140.48146.12159.96 0.710.640.6350.630.630.690.68 0.640.610.62

7、0.620.620.680.67 0.0003870.0002390.0002110.0002380.0003710.0005370.000729 4418686177496848439331472304 4.091.830.920.610.610.590.59 5.926.847.458.068.659.24 1 58.5 160.7 2 78.5 90.29 3 98.5 51.62 4 108.5 32.24 5 118.5 21.71 6 137 15.52 7 155.5 11.90 二、建筑地基基础设计规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（GBJ7-89）所推

8、荐的，简称规推荐法，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深度围的附加应力按等面积原则化为相同深度围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（mm）； n-地基压缩层（即受压层）围所划分的土层数； 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-分别为基础底面至第i层和第i-1层底面的距离（m）

9、； i、i-1-分别为基础底面计算点至第i层和第i-1层底面围平均附加应力系数，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/B L/B1.01.21.41.61.82.02.42.83.23.64.0 5.0 10 0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.02.12.22.32.42.52.62.72.82.93.03.13.23.33.43.53.63.73.83.94.04.14.24.34.44.54.64.74.84.95.01.0000.9970.9870.

10、9670.9360.9000.8580.8160.7750.7350.6980.6630.6310.6010.5730.5480.5240.5020.4820.4630.4460.4290.4140.4000.3870.3740.3620.3510.3410.3310.3220.3130.3050.2970.2890.2820.2760.2690.2630.2570.2510.2460.2410.2360.2310.2260.2220.2180.2140.2100.2061.0000.9980.9900.9730.9470.9150.8780.8400.8010.7640.7230.6940.

11、6630.6330.6050.5800.5560.5330.5130.4930.4750.4590.4430.4280.4140.4010.3890.3770.3660.3560.3460.3370.3280.3200.3120.3040.2970.2900.2840.2770.2710.2650.2600.2550.2500.2450.2400.2350.2310.2270.2231.0000.9980.9910.9760.9530.9240.8900.8550.8190.7840.7490.7170.6860.6570.6290.6040.5800.5580.5270.5170.4990.

12、4820.4660.4510.4360.4230.4100.3980.3870.3770.3660.3570.3480.3390.3310.3230.3150.3080.3010.2940.2880.2820.2760.2700.2650.2600.2550.2500.2450.2410.2371.0000.9980.9920.9780.9560.9290.8980.8650.8310.7970.7640.7330.7030.6740.6480.6220.5990.5770.5560.5360.5180.5000.4840.4690.4540.4410.4280.4160.4040.3930.

13、3830.3730.3640.3550.3460.3380.3300.3230.3160.3090.3020.2960.2900.2840.2780.2730.2680.2630.2580.2530.2491.0000.9980.9920.9790.9580.9330.9030.8710.8390.8060.7750.7440.7150.6880.6610.6370.6130.5910.5710.5510.5330.5150.4990.4840.4690.4550.4420.4300.4180.4070.3970.3870.3770.3680.3590.3510.3430.3350.3280.

14、3210.3140.3080.3020.2960.2900.2850.2790.2740.2690.2650.2601.0000.9980.9920.9790.9650.9350.9060.8760.8440.8130.7830.7530.7250.6980.6720.6430.6250.6030.5830.5630.5450.5280.5110.4960.4810.4680.4550.4420.4300.4190.4090.3980.3890.3790.3710.3620.3540.3460.3390.3320.3250.3180.3120.3060.3000.2940.2890.2840.

15、2790.2740.2691.0000.9980.9930.9800.9610.9370.9100.8810.8510.8210.7920.7640.7370.7110.6870.6640.6410.6200.6000.5810.5630.5460.5300.5150.5000.4860.4730.4610.4490.4380.4270.4170.4070.3970.3880.3800.3720.3640.3560.3490.3420.3350.3280.3220.3160.3100.3050.2990.2940.2890.2841.0000.9980.9930.9800.9620.9390.

16、9120.8840.8550.8260.7980.7710.7440.7190.6960.6760.6510.6310.6110.5930.5750.5590.5430.5280.5130.5000.4870.4740.4630.4510.4410.4300.4200.4110.4020.3930.3850.3770.3690.3620.3550.3480.3410.3350.3290.3230.3170.3120.3060.3010.2961.0000.9980.9930.9810.9620.9390.9130.8850.8570.8290.8010.7750.7490.7250.7010.

17、6790.6580.6380.6190.6010.5840.5670.5520.5370.5230.5090.4960.4840.4720.4610.4510.4400.4310.4210.4120.4030.3950.3870.3790.3720.3650.3680.3520.3450.3390.3330.3270.3210.3160.3110.3061.0000.9980.9930.9810.9630.9400.9140.8860.8580.8300.8030.7770.7520.7280.7050.6830.6630.6430.6240.6060.5900.5740.5580.5440.

18、5300.5160.5040.4920.4800.4690.4590.4480.4390.4290.4200.4120.4030.3950.3880.3800.3730.3660.3590.3630.3470.3410.3350.3290.3240.3190.3131.0000.9980.9930.9810.9630.9400.9140.8870.8590.8310.8040.7790.7540.7300.7080.6860.6660.6460.6290.6100.5940.5780.5630.5480.5350.5220.5090.4970.4860.4750.4650.4540.4450.

19、4360.4270.4180.4100.4020.3940.3870.3790.3720.3660.3590.3530.3470.3410.3360.3300.3250.3201.0000.9980.9930.9810.9630.9400.9150.8870.8600.8320.8060.7800.7560.7330.7110.6900.6700.6510.6330.6160.6000.5850.5700.5560.5430.5300.5180.5060.4950.4850.4740.4640.4550.4460.4370.4290.4210.4130.4050.3980.3910.3840.

20、3770.3710.3650.3590.3530.3470.3420.3370.3321.0000.9980.9930.9820.9630.9400.9150.8880.8600.8330.8070.7820.7580.7350.7140.6930.6750.6560.6380.6220.6060.5910.5770.5640.5510.5390.5280.5170.5060.4960.4870.4770.4680.4600.4520.4440.4360.4290.4220.4150.4080.4020.3960.3900.3840.3780.3730.3670.3620.3570.352（二

21、）规推荐公式由（4-12）式乘以沉降计算经验系数s，即为规推荐的沉降计算公式：式中：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=fk1.41.31.00.40.2p00.75fk1.11.00.70.40.2注：表列数值可插；当变形计算深度围有多层土时，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：式中：Sn-在

22、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4-3z取值B(m)22B44B88B1515B3030 z(m)0.3 0.6 0.8 1.0 1.2 1.5Si-在深度zn围，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：规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2.52.5m，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。试用规法计算基础中点最终沉降量。解：按建筑地基基础设计规计算，采用下式，计算结果详见下表。例题4-2 计算表格z

23、(m) L/B z/B Esi(kPa) (cm) (cm) 0 0 0.2500 0 1.0 0.8 0.2346 0.2346 0.2346 4418 4.27 4.27 2.0 1.6 0.1939 0.3878 0.1532 6861 1.80 6.07 3.0 2.4 0.1578 0.4734 0.0856 7749 0.89 6.96 4.0 3.2 0.1310 0.5240 0.0506 6848 0.59 7.55 5.0 4.0 0.1114 0.5570 0.033 4393 0.60 8.15 6.0 4.8 0.0967 0.5802 0.0232 3147 0.5

24、9 8.74 7.0 5.6 0.0852 0.5964 0.0162 2304 0.57 9.31 7.6 6.08 0.0804 0.6110 0.0146 35000 0.03 9.34 按规确定受压层下限，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。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：式中：Sd-瞬时沉降（亦称初始沉