沉降計(jì)算例題

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：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

2、量時(shí)，在地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(lái)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Hi00.4B （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crsz和附加應(yīng)力bz;并繪制應(yīng)力分布曲線。4）確定壓縮層厚度滿足（rz=0.2 bsz的深度點(diǎn)可作為壓縮層的下限；對(duì)于軟土則應(yīng)滿足（rz=0.1 o-sz；對(duì)一般建筑物可按下式計(jì)算zn=B（2.5-0.4

3、lnB） 。5）計(jì)算各分層加載前后的平均垂直應(yīng)力p1 =（T sz;p2=（r sz+（TZ6）按各分層的pl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(guò)程可參。例題41已知柱下單獨(dú)方形基礎(chǔ)，基礎(chǔ)底面尺寸為2.5X2.5m,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

4、標(biāo)高起算。當(dāng) z=0m , b sD=19.5 X 2=39( kPa)z=, b sz1=39+19.5 x 1=58kPa)z=, b sz1=58.5+20 x 1=78kPa)z=, b sz1=78.5+20 x 1=98kPa)z=, b sz1=98.5+(2010)收108.5 (kPa)z=, b sz1=108.5+(2010) 1=118.5 (kPa)z=, b sz1=118.5+18.5 x 1=1kPa)z=, b sz1=137+18.5 x 1=155kPa)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。(4

5、)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 , bZi=4Ksi ； p0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)z B/2Kscz(kPa)csz(kPa)8 sz (%)zn (m)012345670 0.8 1.6 2.4 3.2 4.0 4.8 5.60.250 00.199 90.112 30.064 20.040 10.027 00.019 30.014 8201160.790.2951.6232.2421.7115.5211.903958.578.598.81

6、08.5118.5137155.529.7118.3211.337.6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2z(m)(kPa)(kPa)H( c m )自重應(yīng)力 平均值(kPa)附加應(yīng)力 平均值(kPa)(kPa)e1e(kPa-1)(kPa)(cm)(cm)039201100158.5160.70.278.590.29076398.551.621144108.532.240000.00035118.521.71613715.520.871660.0002048.75180.85229.6413944184.

7、09068.50125.50194000.000268611.835.92188.5070.96159.46.1177490.926.840103.541.93145.43660.000268480.617.450113.526.98140.48323843930.618.061127.518.62146.12500.000331470.598.6500.717155.511.900146.2513.71159.96.60.000523040.599.24162370300.000700.291.60620300.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（

8、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(guò)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

9、和第i-1層底面的距離（mm ;ai、a 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矩形面積上均布荷載作用下，通過(guò)中心點(diǎn)豎線上的平均附加應(yīng)力系數(shù)z/ BL/B1.01.21.41.61.82.02.42.83.23.64.05.0100.1.001.001.001.001.001.001.001.001.001.001.001.001.00000000000000000.0.990.990.990.990.990.990.990.990.990.990.990.990.99178888888888880.0.980.990.990.990.99

10、0.990.990.990.990.990.990.990.99270122233333330.0.960.970.970.970.970.970.980.980.980.980.980.980.98373689900111120.40.9360.9470.9530.9560.9580.9650.9610.9620.9620.9630.9630.9630.9630.0.900.910.920.920.930.930.930.930.930.940.940.940.94505493579900000.0.850.870.890.890.900.900.910.910.910.910.910.91

11、0.91688083602344550.0.810.840.850.860.870.870.880.880.880.880.880.880.88760551614567780.0.770.800.810.830.830.840.850.850.850.850.850.860.86851919415789000.0.730.760.780.790.800.810.820.820.820.830.830.830.83954476316901231.0.690.720.740.760.770.780.790.790.800.800.800.800.80083945328134671.0.660.69

12、0.710.730.740.750.760.770.770.770.770.780.78134734341579021.0.630.660.680.700.710.720.730.740.740.750.750.750.75213635574924681.0.600.630.650.670.680.690.710.710.720.720.730.730.73313748819580351.0.570.600.620.640.660.670.680.690.700.700.700.710.71435981276158141.0.540.580.600.620.630.640.660.670.67

13、0.680.680.690.69580427346936031.0.520.550.580.590.610.620.640.650.650.660.660.670.67646093511836051.0.500.530.550.570.590.600.620.630.630.640.640.650.65723871301836161.0.480.510.520.550.570.580.600.610.610.620.620.630.63823761301949381.0.460.490.510.530.550.560.580.590.600.600.610.610.62933761313160

14、622.0.440.470.490.510.530.540.560.570.580.590.590.600.60065983535404062.0.420.450.480.500.510.520.540.550.560.570.570.580.59199205869748512.0.410.440.460.480.490.510.530.540.550.550.560.570.57243649103283072.0.400.420.450.460.480.490.510.520.530.540.540.550.56308194658748642.40.3870.4140.4360.4540.4

15、690.4810.5000.5130.5230.5300.5350.5430.5512.0.370.400.420.440.450.460.480.500.500.510.520.530.53541315860962092.0.360.380.410.420.440.450.470.480.490.500.500.510.52629082537649882.0.350.370.390.410.430.440.460.470.480.490.490.500.51717860214427672.0.340.360.380.400.410.430.440.460.470.480.480.490.50

16、816748093206562.0.330.350.370.390.400.410.430.450.460.460.470.480.49916737981195563.0.320.340.360.380.390.400.420.440.450.450.460.470.48026637971195473.0.310.330.350.370.380.390.410.430.440.440.450.460.47137737870084473.0.300.320.340.360.370.380.400.420.430.430.440.450.46258847970195583.0.290.320.33

17、0.350.360.370.390.410.420.420.430.440.46370958971196603.0.280.310.330.340.350.370.380.400.410.420.420.430.45492169182207723.0.280.300.320.330.350.360.380.390.400.410.410.420.44524381203328943.0.270.290.310.330.340.350.370.380.390.400.410.420.43667503425530163.0.260.290.300.320.330.340.360.370.380.39

18、0.400.410.42790835647752393.0.260.280.300.310.320.330.350.360.370.380.390.400.42834168969984523.0.250.270.290.300.320.330.340.360.370.380.380.390.41977491292207854.0.250.270.280.300.310.320.340.350.360.370.370.390.40011824525539184.0.240.260.280.290.300.310.330.340.360.360.370.380.40165268858862424.

19、0.240.260.270.290.300.310.320.340.350.350.360.370.39210602281296764.0.230.250.270.280.290.300.320.330.340.360.350.370.39365046625539104.0.230.250.260.270.290.300.310.320.330.340.350.360.38410580069973544.0.220.240.260.270.280.290.310.320.330.340.340.350.37565035403317984.0.220.240.250.260.270.280.30

20、0.310.320.330.340.350.37620589957751334.0.210.230.250.260.270.280.290.310.320.320.330.340.36785034492196774.0.210.230.240.250.260.270.290.300.310.320.330.340.36841589946640224.0.210.220.240.250.260.270.280.300.310.310.320.330.35907135491195775.0.200.220.230.240.260.260.280.290.300.310.320.330.350637

21、9094663022（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) 巾s,即為規(guī)范推薦的沉降計(jì)算公 式：式中：巾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，一般采用的數(shù)值；表4-2沉降計(jì)算經(jīng)驗(yàn)系數(shù)ips基底附加壓力 p0（kPa）壓縮模里Es（MPa）2.54.07.015.020.0p0=fk1.41.31.00.40.2p0 0.75fk1.11.00.70.40.2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

22、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)算厚度為的計(jì)算變形值；Az查;表4-3 Az取值B(m)22V B44V B88V B 1515V B30 z(m)0.30.60.81.01.21.5 Si-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)范法的具體計(jì)算過(guò)程可參?！纠}42】已知柱下單獨(dú)方形基礎(chǔ)，基礎(chǔ)底面尺寸為 2.5X2.5m,埋深2nl 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)

23、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/Bz/BEsi(kP a)(cm)(cm)000.250001.00.80.23460.23460.234644184.274.272.01.60.19390.38780.153268611.806.073.02.40.15780.47340.085677490.896.964.03.20.13100.52400.050668480.597.555.04.00.11140.55700.03343930.608.156.04.80.09670.58020.023231470.598.747.05.60.08520.59640.01

24、6223040.579.317.66.080.08040.61100.0146350000.039.34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Az厚度計(jì)算，根據(jù)的要求，取Az=0.6m,則zn=7.6m,計(jì)算得厚度Az的沉降量為0.03cm,滿足要求。查得沉降計(jì)算經(jīng)驗(yàn)系數(shù)Ws=1.1%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）； S

25、c-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(guò)程（超靜孔隙水壓力消散過(guò)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)，可從中查用；p0-基底附加應(yīng)力；N-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)取產(chǎn)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軟的、高塑性有機(jī)土，高值適用于一般較硬的粘性土表4-4沉降系數(shù),值受衲圓形