沉降量计算方法.doc

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-1-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（mm）； n-地基压缩层（即受压层）范围内所划分的土层数； 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-分别为基础底面至第i层和第i-1层底面的距离（m）； i、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/B L/B1.01.21.41.61.82.02.42.83.23.64.0 5.0 10 0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.02.12.22.32.42.52.62.72.82.93.03.13.23.33.43.53.63.73.83.94.04.14.24.34.44.54.64.74.84.95.01.0000.9970.9870.9670.9360.9000.8580.8160.7750.7350.6980.6630.6310.6010.5730.5480.5240.5020.4820.4630.4460.4290.4140.4000.3870.3740.3620.3510.3410.3310.3220.3130.3050.2970.2890.2820.2760.2690.2630.2570.2510.2460.2410.2360.2310.2260.2220.2180.2140.2100.2061.0000.9980.9900.9730.9470.9150.8780.8400.8010.7640.7230.6940.6630.6330.6050.5800.5560.5330.5130.4930.4750.4590.4430.4280.4140.4010.3890.3770.3660.3560.3460.3370.3280.3200.3120.3040.2970.2900.2840.2770.2710.2650.2600.2550.2500.2450.2400.2350.2310.2270.2231.0000.9980.9910.9760.9530.9240.8900.8550.8190.7840.7490.7170.6860.6570.6290.6040.5800.5580.5270.5170.4990.4820.4660.4510.4360.4230.4100.3980.3870.3770.3660.3570.3480.3390.3310.3230.3150.3080.3010.2940.2880.2820.2760.2700.2650.2600.2550.2500.2450.2410.2371.0000.9980.9920.9780.9560.9290.8980.8650.8310.7970.7640.7330.7030.6740.6480.6220.5990.5770.5560.5360.5180.5000.4840.4690.4540.4410.4280.4160.4040.3930.3830.3730.3640.3550.3460.3380.3300.3230.3160.3090.3020.2960.2900.2840.2780.2730.2680.2630.2580.2530.2491.0000.9980.9920.9790.9580.9330.9030.8710.8390.8060.7750.7440.7150.6880.6610.6370.6130.5910.5710.5510.5330.5150.4990.4840.4690.4550.4420.4300.4180.4070.3970.3870.3770.3680.3590.3510.3430.3350.3280.3210.3140.3080.3020.2960.2900.2850.2790.2740.2690.2650.2601.0000.9980.9920.9790.9650.9350.9060.8760.8440.8130.7830.7530.7250.6980.6720.6430.6250.6030.5830.5630.5450.5280.5110.4960.4810.4680.4550.4420.4300.4190.4090.3980.3890.3790.3710.3620.3540.3460.3390.3320.3250.3180.3120.3060.3000.2940.2890.2840.2790.2740.2691.0000.9980.9930.9800.9610.9370.9100.8810.8510.8210.7920.7640.7370.7110.6870.6640.6410.6200.6000.5810.5630.5460.5300.5150.5000.4860.4730.4610.4490.4380.4270.4170.4070.3970.3880.3800.3720.3640.3560.3490.3420.3350.3280.3220.3160.3100.3050.2990.2940.2890.2841.0000.9980.9930.9800.9620.9390.9120.8840.8550.8260.7980.7710.7440.7190.6960.6760.6510.6310.6110.5930.5750.5590.5430.5280.5130.5000.4870.4740.4630.4510.4410.4300.4200.4110.4020.3930.3850.3770.3690.3620.3550.3480.3410.3350.3290.3230.3170.3120.3060.3010.2961.0000.9980.9930.9810.9620.9390.9130.8850.8570.8290.8010.7750.7490.7250.7010.6790.6580.6380.6190.6010.5840.5670.5520.5370.5230.5090.4960.4840.4720.4610.4510.4400.4310.4210.4120.4030.3950.3870.3790.3720.3650.3680.3520.3450.3390.3330.3270.3210.3160.3110.3061.0000.9980.9930.9810.9630.9400.9140.8860.8580.8300.8030.7770.7520.7280.7050.6830.6630.6430.6240.6060.5900.5740.5580.5440.5300.5160.5040.4920.4800.4690.4590.4480.4390.4290.4200.4120.4030.3950.3880.3800.3730.3660.3590.3630.3470.3410.3350.3290.3240.3190.3131.0000.9980.9930.9810.9630.9400.9140.8870.8590.8310.8040.7790.7540.7300.7080.6860.6660.6460.6290.6100.5940.5780.5630.5480.5350.5220.5090.4970.4860.4750.4650.4540.4450.4360.4270.4180.4100.4020.3940.3870.3790.3720.3660.3590.3530.3470.3410.3360.3300.3250.3201.0000.9980.9930.9810.9630.9400.9150.8870.8600.8320.8060.7800.7560.7330.7110.6900.6700.6510.6330.6160.6000.5850.5700.5560.5430.5300.5180.5060.4950.4850.4740.4640.4550.4460.4370.4290.4210.4130.4050.3980.3910.3840.3770.3710.3650.3590.3530.3470.3420.3370.3321.0000.9980.9930.9820.9630.9400.9150.8880.8600.8330.8070.7820.7580.7350.7140.6930.6750.6560.6380.6220.6060.5910.5770.5640.5510.5390.5280.5170.5060.4960.4870.4770.4680.4600.4520.4440.4360.4290.4220.4150.4080.4020.3960.3900.3840.3780.3730.3670.3620.3570.352（二）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：表列数值可内插；当变形计算深度范围内有多层土时，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：式中：Sn-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；Si-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：表4-3z取值B(m)22B44B88B1515B3030 z(m)0.3 0.6 0.8 1.0 1.2 1.5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2.52.5m，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。例题4-2 计算表格z (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 0.59 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，按式（4-17）求解。式中：-沉降系数，可从表4-4中查用；p0-基底附加应力；-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=0.5；Eu-不排水变形模量，常根据不排水抗剪强度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，高值适用于一般较硬的粘性土。表4-4 沉降系数值受荷面形状L/B中 点矩形角点，圆形周边平均值刚性基础圆 形1.000.640.850.79正 方 形1.001.120.560.950.88矩 形1.52.03.04.06.08.010.030.050.0100.01.361.521.781.962.232.422.533.233.544.000.680.760.890.981.121.211.271.62