地基沉降量計(jì)算建筑B類

1、地基沉降量計(jì)算地基變形在其表面形成的垂直變形量稱為建筑物的沉降量。在外荷載作用下地基土層被壓縮達(dá)到穩(wěn)定時(shí)基礎(chǔ)底面的沉降量稱為地基最終沉降量。一、分層總和法計(jì)算地基最終沉降量計(jì)算地基的最終沉降量，目前最常用的就是分層總和法。（一）基本原理該方法只考慮地基的垂向變形，沒有考慮側(cè)向變形，地基的變形同室內(nèi)側(cè)限壓縮試驗(yàn)中的情況基本一致，屬一維壓縮問題。地基的最終沉降量可用室內(nèi)壓縮試驗(yàn)確定的參數(shù)（ei、es、a）進(jìn)行計(jì)算，有：變換后得：或式中：s-地基最終沉降量（mm）；e1-地基受荷前（自重應(yīng)力作用下）的孔隙比；e2-地基受荷（自重與附加應(yīng)力作用下）沉降穩(wěn)定后的孔隙比；h-土層的厚度。計(jì)算沉降量時(shí)，在地

2、基可能受荷變形的壓縮層范圍內(nèi)，根據(jù)土的特性、應(yīng)力狀態(tài)以及地下水位進(jìn)行分層。然后按式（4-9）或（4-10）計(jì)算各分層的沉降量si。最后將各分層的沉降量總和起來即為地基的最終沉降量：（二）計(jì)算步驟1）劃分土層如圖4-7所示，各天然土層界面和地下水位必須作為分層界面；各分層厚度必須滿足hi0.4b（b為基底寬度）。2）計(jì)算基底附加壓力p03）計(jì)算各分層界面的自重應(yīng)力sz和附加應(yīng)力z；并繪制應(yīng)力分布曲線。4）確定壓縮層厚度滿足z=0.2sz的深度點(diǎn)可作為壓縮層的下限；對(duì)于軟土則應(yīng)滿足z=0.1sz；對(duì)一般建筑物可按下式計(jì)算zn=b(2.5-0.4lnb)。5）計(jì)算各分層加載前后的平均垂直應(yīng)力p1=s

3、z； p2=sz+z6）按各分層的p1和p2在e-p曲線上查取相應(yīng)的孔隙比或確定a、es等其它壓縮性指標(biāo)7）根據(jù)不同的壓縮性指標(biāo)，選用公式（4-9）、（4-10）計(jì)算各分層的沉降量si8）按公式（4-11）計(jì)算總沉降量s。分層總和法的具體計(jì)算過程可參例題4-1。例題41已知柱下單獨(dú)方形基礎(chǔ)，基礎(chǔ)底面尺寸為2.5×2.5m，埋深2m，作用于基礎(chǔ)上（設(shè)計(jì)地面標(biāo)高處）的軸向荷載n=1250kn，有關(guān)地基勘察資料與基礎(chǔ)剖面詳見下圖。試用單向分層總和法計(jì)算基礎(chǔ)中點(diǎn)最終沉降量。解：按單向分層總和法計(jì)算（1）計(jì)算地基土的自重應(yīng)力。z自基底標(biāo)高起算。當(dāng)z=0m，sd=19.5×2=39（k

4、pa）z=1m，sz1=39+19.5×1=58.5（kpa）z=2m，sz1=58.5+20×1=78.5（kpa）z=3m，sz1=78.5+20×1=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+18.5×1=137（kpa）z=7m，sz1=137+18.5×1=155.5（kpa）（2）基底壓力計(jì)算?；A(chǔ)底面以上，基礎(chǔ)與填土的混合容重取0=20kn/m3。（3）基底附加壓力計(jì)算

5、。（4）基礎(chǔ)中點(diǎn)下地基中豎向附加應(yīng)力計(jì)算。 用角點(diǎn)法計(jì)算，l/b=1，zi=4ksi·p0，查附加應(yīng)力系數(shù)表得ksi。（5）確定沉降計(jì)算深度zn考慮第層土壓縮性比第層土大，經(jīng)計(jì)算后確定zn=7m，見下表。例題4-1計(jì)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 8201160.790.2951.6232.2421.7115.5211.903958.578.598.810

6、8.5118.5137155.529.7118.3211.337.6按7m計(jì)（6）計(jì)算基礎(chǔ)中點(diǎn)最終沉降量。利用勘察資料中的e-p曲線，求按單向分層總和法公式計(jì)算結(jié)果見下表。例題4-1計(jì)算表格2 z   (m) (kpa) (kpa) h (cm) 自重應(yīng)力平均值 (kpa) 附加應(yīng)力平均值 (kpa) (kpa) e1 e2 (kpa-1)   (kpa)   (cm)   (cm) 0 39 201 100100100100100100100 48.7568.5088.50103.5113.5127.5146.25 180.85125.5070.964

7、1.9326.9818.6213.71 229.6194159.46145.43140.48146.12159.96 0.710.640.6350.630.630.690.68 0.640.610.620.620.620.680.67 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.

8、62 4 108.5 32.24 5 118.5 21.71 6 137 15.52 7 155.5 11.90 二、建筑地基基礎(chǔ)設(shè)計(jì)規(guī)范推薦的沉降計(jì)算法下面計(jì)算沉降量的方法是建筑地基基礎(chǔ)設(shè)計(jì)規(guī)范（gbj7-89）所推薦的，簡(jiǎn)稱規(guī)范推薦法，有時(shí)也叫應(yīng)力面積法。（一）計(jì)算原理應(yīng)力面積法一般按地基土的天然分層面劃分計(jì)算土層，引入土層平均附加應(yīng)力的概念，通過平均附加應(yīng)力系數(shù)，將基底中心以下地基中zi-1-zi深度范圍的附加應(yīng)力按等面積原則化為相同深度范圍內(nèi)矩形分布時(shí)的分布應(yīng)力大小，再按矩形分布應(yīng)力情況計(jì)算土層的壓縮量，各土層壓縮量的總和即為地基的計(jì)算沉降量。理論上基礎(chǔ)的平均沉降量可表示為式中：s-地

9、基最終沉降量（mm）； n-地基壓縮層（即受壓層）范圍內(nèi)所劃分的土層數(shù)； p0-基礎(chǔ)底面處的附加壓力（kpa）； esi-基礎(chǔ)底面下第i層土的壓縮模量（mpa）； zi、zi-1-分別為基礎(chǔ)底面至第i層和第i-1層底面的距離（m）； i、i-1-分別為基礎(chǔ)底面計(jì)算點(diǎn)至第i層和第i-1層底面范圍內(nèi)平均附加應(yīng)力系數(shù)，可查表4-1。表4-1 矩形面積上均布荷載作用下，通過中心點(diǎn)豎線上的平均附加應(yīng)力系數(shù) 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

10、.41.51.61.71.81.92.02.12.22.32.42.52.62.72.82.93.03.13.23.33.43.53.63.73.83.94.04.14.24.34.44.54.64.74.84.95.01.0000.9970.9870.9670.9360.9000.8580.8160.7750.7350.6980.6630.6310.6010.5730.5480.5240.5020.4820.4630.4460.4290.4140.4000.3870.3740.3620.3510.3410.3310.3220.3130.3050.2970.2890.2820.2760.269

11、0.2630.2570.2510.2460.2410.2360.2310.2260.2220.2180.2140.2100.2061.0000.9980.9900.9730.9470.9150.8780.8400.8010.7640.7230.6940.6630.6330.6050.5800.5560.5330.5130.4930.4750.4590.4430.4280.4140.4010.3890.3770.3660.3560.3460.3370.3280.3200.3120.3040.2970.2900.2840.2770.2710.2650.2600.2550.2500.2450.240

12、0.2350.2310.2270.2231.0000.9980.9910.9760.9530.9240.8900.8550.8190.7840.7490.7170.6860.6570.6290.6040.5800.5580.5270.5170.4990.4820.4660.4510.4360.4230.4100.3980.3870.3770.3660.3570.3480.3390.3310.3230.3150.3080.3010.2940.2880.2820.2760.2700.2650.2600.2550.2500.2450.2410.2371.0000.9980.9920.9780.956

13、0.9290.8980.8650.8310.7970.7640.7330.7030.6740.6480.6220.5990.5770.5560.5360.5180.5000.4840.4690.4540.4410.4280.4160.4040.3930.3830.3730.3640.3550.3460.3380.3300.3230.3160.3090.3020.2960.2900.2840.2780.2730.2680.2630.2580.2530.2491.0000.9980.9920.9790.9580.9330.9030.8710.8390.8060.7750.7440.7150.688

14、0.6610.6370.6130.5910.5710.5510.5330.5150.4990.4840.4690.4550.4420.4300.4180.4070.3970.3870.3770.3680.3590.3510.3430.3350.3280.3210.3140.3080.3020.2960.2900.2850.2790.2740.2690.2650.2601.0000.9980.9920.9790.9650.9350.9060.8760.8440.8130.7830.7530.7250.6980.6720.6430.6250.6030.5830.5630.5450.5280.511

15、0.4960.4810.4680.4550.4420.4300.4190.4090.3980.3890.3790.3710.3620.3540.3460.3390.3320.3250.3180.3120.3060.3000.2940.2890.2840.2790.2740.2691.0000.9980.9930.9800.9610.9370.9100.8810.8510.8210.7920.7640.7370.7110.6870.6640.6410.6200.6000.5810.5630.5460.5300.5150.5000.4860.4730.4610.4490.4380.4270.417

16、0.4070.3970.3880.3800.3720.3640.3560.3490.3420.3350.3280.3220.3160.3100.3050.2990.2940.2890.2841.0000.9980.9930.9800.9620.9390.9120.8840.8550.8260.7980.7710.7440.7190.6960.6760.6510.6310.6110.5930.5750.5590.5430.5280.5130.5000.4870.4740.4630.4510.4410.4300.4200.4110.4020.3930.3850.3770.3690.3620.355

17、0.3480.3410.3350.3290.3230.3170.3120.3060.3010.2961.0000.9980.9930.9810.9620.9390.9130.8850.8570.8290.8010.7750.7490.7250.7010.6790.6580.6380.6190.6010.5840.5670.5520.5370.5230.5090.4960.4840.4720.4610.4510.4400.4310.4210.4120.4030.3950.3870.3790.3720.3650.3680.3520.3450.3390.3330.3270.3210.3160.311

18、0.3061.0000.9980.9930.9810.9630.9400.9140.8860.8580.8300.8030.7770.7520.7280.7050.6830.6630.6430.6240.6060.5900.5740.5580.5440.5300.5160.5040.4920.4800.4690.4590.4480.4390.4290.4200.4120.4030.3950.3880.3800.3730.3660.3590.3630.3470.3410.3350.3290.3240.3190.3131.0000.9980.9930.9810.9630.9400.9140.887

19、0.8590.8310.8040.7790.7540.7300.7080.6860.6660.6460.6290.6100.5940.5780.5630.5480.5350.5220.5090.4970.4860.4750.4650.4540.4450.4360.4270.4180.4100.4020.3940.3870.3790.3720.3660.3590.3530.3470.3410.3360.3300.3250.3201.0000.9980.9930.9810.9630.9400.9150.8870.8600.8320.8060.7800.7560.7330.7110.6900.670

20、0.6510.6330.6160.6000.5850.5700.5560.5430.5300.5180.5060.4950.4850.4740.4640.4550.4460.4370.4290.4210.4130.4050.3980.3910.3840.3770.3710.3650.3590.3530.3470.3420.3370.3321.0000.9980.9930.9820.9630.9400.9150.8880.8600.8330.8070.7820.7580.7350.7140.6930.6750.6560.6380.6220.6060.5910.5770.5640.5510.539

21、0.5280.5170.5060.4960.4870.4770.4680.4600.4520.4440.4360.4290.4220.4150.4080.4020.3960.3900.3840.3780.3730.3670.3620.3570.352（二）規(guī)范推薦公式由（4-12）式乘以沉降計(jì)算經(jīng)驗(yàn)系數(shù)s，即為規(guī)范推薦的沉降計(jì)算公式：式中：s-沉降計(jì)算經(jīng)驗(yàn)系數(shù)，應(yīng)根據(jù)同類地區(qū)已有房屋和構(gòu)筑物實(shí)測(cè)最終沉降量與計(jì)算沉降量對(duì)比確定，一般采用表4-2的數(shù)值；表4-2 沉降計(jì)算經(jīng)驗(yàn)系數(shù)s基底附加壓力p0(kpa)壓縮模量es(mpa)2.54.07.015.020.0p0=fk1.41.31.00.40

22、.2p00.75fk1.11.00.70.40.2注：表列數(shù)值可內(nèi)插；當(dāng)變形計(jì)算深度范圍內(nèi)有多層土?xí)r，es可按附加應(yīng)力面積a的加權(quán)平均值采用，即（三）地基受壓層計(jì)算深度的確定計(jì)算深度zn可按下述方法確定：1）存在相鄰荷載影響的情況下，應(yīng)滿足下式要求：式中：sn-在深度zn處，向上取計(jì)算厚度為z的計(jì)算變形值；z查表4-3；表4-3   z取值b(m)22b44b88b1515b30>30 z(m)0.3 0.6 0.8 1.0 1.2 1.5si-在深度zn范圍內(nèi)，第i層土的計(jì)算變形量。2）對(duì)無(wú)相鄰荷載的獨(dú)立基礎(chǔ)，可按下列簡(jiǎn)化的經(jīng)驗(yàn)公式確定沉降計(jì)算深度zn：規(guī)

23、范法的具體計(jì)算過程可參例題4-2?！纠}42】已知柱下單獨(dú)方形基礎(chǔ)，基礎(chǔ)底面尺寸為2.5×2.5m，埋深2m，作用于基礎(chǔ)上（設(shè)計(jì)地面標(biāo)高處）的軸向荷載n=1250kn，有關(guān)地基勘察資料與基礎(chǔ)剖面詳見下圖。試用規(guī)范法計(jì)算基礎(chǔ)中點(diǎn)最終沉降量。解：按建筑地基基礎(chǔ)設(shè)計(jì)規(guī)范計(jì)算，采用下式，計(jì)算結(jié)果詳見下表。例題4-2 計(jì)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

24、 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

25、 9.34 按規(guī)范確定受壓層下限，zn=2.5(2.5-0.4ln2.5)=5.3m；由于下面土層仍軟弱，在層粘土底面以下取z厚度計(jì)算，根據(jù)表4-3的要求，取z=0.6m，則zn=7.6m，計(jì)算得厚度z的沉降量為0.03cm，滿足要求。查表4-2得沉降計(jì)算經(jīng)驗(yàn)系數(shù)s=1.17。那么，最終沉降量為： 三、按粘性土的沉降機(jī)理計(jì)算沉降根據(jù)對(duì)粘性土地基在局部（基礎(chǔ)）荷載作用下的實(shí)際變形特征的觀察和分析，粘性土地基的沉降s可以認(rèn)為是由機(jī)理不同的三部分沉降組成（圖4-8），亦即：式中：sd-瞬時(shí)沉降（亦稱初始沉降）；sc-固結(jié)沉降（亦稱主固結(jié)沉降）；ss-次固結(jié)沉降（亦稱蠕變沉降）。瞬時(shí)沉降是指加載后地基

26、瞬時(shí)發(fā)生的沉降。由于基礎(chǔ)加載面積為有限尺寸，加載后地基中會(huì)有剪應(yīng)變產(chǎn)生，剪應(yīng)變會(huì)引起側(cè)向變形而造成瞬時(shí)沉降。固結(jié)沉降是指飽和與接近飽和的粘性土在基礎(chǔ)荷載作用下，隨著超靜孔隙水壓力的消散，土骨架產(chǎn)生變形所造成的沉降（固結(jié)壓密）。固結(jié)沉降速率取決于孔隙水的排出速率。次固結(jié)沉降是指主固結(jié)過程（超靜孔隙水壓力消散過程）結(jié)束后，在有效應(yīng)力不變的情況下，土的骨架仍隨時(shí)間繼續(xù)發(fā)生變形。這種變形的速率取決于土骨架本身的蠕變性質(zhì)。（一）瞬時(shí)沉降計(jì)算瞬時(shí)沉降沒有體積變形，可認(rèn)為是彈性變形，因此一般按彈性理論計(jì)算，按式（4-17）求解。式中：-沉降系數(shù)，可從表4-4中查用；p0-基底附加應(yīng)力；-泊松比，這時(shí)是在不排水條件下沒有體積變形所產(chǎn)生的變形量，所以應(yīng)取=0.5； eu-不排水變形模量，常根據(jù)不排水抗剪強(qiáng)度cu和eu的經(jīng)驗(yàn)關(guān)系式（4-18）求得。上式中的低值適用于較