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。、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)（e、E、a）進(jìn)行計(jì)算，有：出二外-。+光）百a變換后得：s二口出1+句或1+4式中：S-地基最終沉降量（mm；e-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

2、層的厚度。計(jì)算沉降量時(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S。最后將各分層的沉降量總和起來即為地基的最終沉降量：(4-11)S=2-1（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H00.4B（B為基底寬度）。2）計(jì)算基底附加壓力po3）計(jì)算各分層界面的自重應(yīng)力cz和附加應(yīng)力門；并繪制應(yīng)力分布曲線。4）確定壓縮層厚度滿足=0.2nz的深度點(diǎn)可作為壓縮層的下限；對(duì)于軟土則應(yīng)滿足CTz=0.1（Tsz；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Pl=（Tsz；P2=（Tsz+（Tz6）按各分層的Pi和P2在e-p曲線上查取相應(yīng)的孔隙比或確定a、E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S8）按公式（4-11）計(jì)算總沉降量S士層土層自重應(yīng)為分布曲線沉降計(jì)算深扇附加應(yīng)力分布曲姓土層包圖4-T分層總和法計(jì)算地基沉降量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)

4、算基礎(chǔ)中點(diǎn)最終沉降量。崎質(zhì)黏土產(chǎn)aokN,加蜂黏土7-18.5kK4n'卵石-720SkNin1f=20.5kN/m'沿IROkN個(gè)"yW#F土E卡IfSkNM°我一解：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=19.52=39(kPa)z=1m,初=39+19.51=58.5(kPa)z=2m,m=58.5+201=78.5(kPa)z=3m,血=78.5+201=98.5(kPa)z=4m,物=98.5+(20-10)1=108.5(kPa)z=5m,血=108.5+(20-10)1=118.5(kPa)z=6m

5、,(sz1=118.5+18.5竹137(kPa)z=7m,血=137+18.51=155.5(kPa)N+G1250+25x25x2x20240kp或(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。25x25(3)基底附加壓力計(jì)算。p-p-yD-240-19,5x2,0=201kp置(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,(rzi=4Ksip0,查附加應(yīng)力系數(shù)表得Ksio(5)確定沉降計(jì)算深度zn例題4-1計(jì)算表格1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。z(m)zB/2Kscz(kPa)(Sz(kPa)d/sz(%)

6、zn(m)000.25002013910.80.1999160.758.521.60.112390.2978.532.40.064251.6298.843.20.040132.24108.529.7154.00.027021.71118.518.3264.80.019315.5213711.337L5.6J:0.0148J11.90155.57.6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)心(kPa)H(cm自重應(yīng)力平均值附加應(yīng)力平均值hiz+Kg(kPa)ee2r%ELM為5=包(cm)(kPa

7、)(kPa)(kPa-1)(kPa)(cm)0392010.6158.5160.229.6471940.6278.590.2910048.7568.5088.50180.85159.46145.40.710.640.6310.620.00038744184.09398.551.62100100125.500.0002390.000211686177491.830.925.926.844108.532.24100103.5113.570.963140.450.630.620.00023868480.617.455118.521.71100100127.5146.2541.9326.988146.

8、120.630.690.680.620.60.0003710.000537439331470.610.598.068.65613715.5210018.6213.710.00072923040.599.24159.987155.511.9060.67建筑地基基礎(chǔ)設(shè)計(jì)規(guī)范推薦的沉降計(jì)算法GBJ7-8吩所推薦的,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（簡稱規(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-i-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

9、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s,二£卻倡&-（4-12）ilN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）；日-基礎(chǔ)底面下第i層土的壓縮模量（MPa;Zi、Zi-i-分別為基礎(chǔ)底面至第i層和第i-1層底面的距離（nj）；ai、ai-i-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)az/BL/B1.01.21.41

10、.61.82.02.42.83.23.64.05.0>100.1.001.001.001.001.001.001.001.001.001.001.001.001.00000000000000000.0.990.990.990.990.990.990.990.990.990.990.990.990.99178888888888880.0.980.990.990.990.990.990.990.990.990.990.990.990.99270122233333330.0.960.970.970.970.970.970.980.980.980.980.980.980.983736899001

11、11120.0.930.940.950.950.950.960.960.960.960.960.960.960.96467368512233330.0.900.910.920.920.930.930.930.930.930.940.940.940.94505493579900000.0.850.870.890.890.900.900.910.910.910.910.910.910.91688083602344550.0.810.840.850.860.870.870.880.880.880.880.880.880.88760551614567780.0.770.800.810.830.830.

12、840.850.850.850.850.850.860.86851919415789000.0.730.760.780.790.800.810.820.820.820.830.830.830.83954476316901231.0.690.720.740.760.770.780.790.790.800.800.800.800.80083945328134671.0.660.690.710.730.740.750.760.770.770.770.770.780.78134734341579021.0.630.660.680.700.710.720.730.740.740.750.750.750.

13、75213635574924681.0.600.630.650.670.680.690.710.710.720.720.730.730.73313748819580351.0.570.600.620.640.660.670.680.690.700.700.700.710.71435981276158141.0.540.580.600.620.630.640.660.670.670.680.680.690.69580427346936031.0.520.550.580.590.610.620.640.650.650.660.660.670.67646093511836051.0.500.530.

14、550.570.590.600.620.630.630.640.640.650.65723871301836161.0.480.510.520.550.570.580.600.610.610.620.620.630.63823761301949381.0.460.490.510.530.550.560.580.590.600.600.610.610.62933761313160622.0.440.470.490.510.530.540.560.570.580.590.590.600.60065983535404062.0.420.450.480.500.510.520.540.550.560.

15、570.570.580.59199205869748512.0.410.440.460.480.490.510.530.540.550.550.560.570.57243649103283072.0.400.420.450.460.480.490.510.520.530.540.540.550.56308194658748642.0.380.410.430.450.460.480.500.510.520.530.530.540.55474649103305312.0.370.400.420.440.450.460.480.500.500.510.520.530.5354131586096209

16、2.0.360.380.410.420.440.450.470.480.490.500.500.510.52629082537649882.0.350.370.390.410.430.440.460.470.480.490.490.500.51717860214427672.0.340.360.380.400.410.430.440.460.470.480.480.490.50816748093206562.0.330.350.370.390.400.410.430.450.460.460.470.480.49916737981195563.0.320.340.360.380.390.400.

17、420.440.450.450.460.470.48026637971195473.0.310.330.350.370.380.390.410.430.440.440.450.460.47137737870084473.0.300.320.340.360.370.380.400.420.430.430.440.450.46258847970195583.0.290.320.330.350.360.370.390.410.420.420.430.440.46370958971196603.0.280.310.330.340.350.370.380.400.410.420.420.430.4549

18、2169182207723.0.280.300.320.330.350.360.380.390.400.410.410.420.44524381203328943.0.270.290.310.330.340.350.370.380.390.400.410.420.43667503425530163.0.260.290.300.320.330.340.360.370.380.390.400.410.42790835647752393.0.260.280.300.310.320.330.350.360.370.380.390.400.42834168969984523.0.250.270.290.

19、300.320.330.340.360.370.380.380.390.41977491292207854.0.250.270.280.300.310.320.340.350.360.370.370.390.40011824525539184.0.240.260.280.290.300.310.330.340.360.360.370.380.40165268858862424.0.240.260.270.290.300.310.320.340.350.350.360.370.39210602281296764.0.230.250.270.280.290.300.320.330.340.360.

20、350.370.39365046625539104.0.230.250.260.270.290.300.310.320.330.340.350.360.38410580069973544.0.220.240.260.270.280.290.310.320.330.340.340.350.37565035403317984.0.220.240.250.260.270.280.300.310.320.330.340.350.37620589957751334.0.210.230.250.260.270.280.290.310.320.320.330.340.36785034492196774.0.

21、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（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S二W二%2普（馬酸-舁1%-0（4-13）紇i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

22、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)如基底附加壓力p0（kPa）壓縮模里Es（MPa）2.54.07.015.020.0p0=fk1.41.31.00.40.2po<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y.4（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：故;£002宅?。?-14）式中：&'-在深度Zn處，向上取計(jì)算厚度為z的計(jì)算變形值；Az查表4-3;表4-3Az

23、取值B(m)<22VB<44VB<88VB<1515<B<30>30z(m)0.30.60.81.01.21.5S'-在深度Zn范圍內(nèi)，第i層土的計(jì)算變形量2）對(duì)無相鄰荷載的獨(dú)立基礎(chǔ)，可按下列簡化的經(jīng)驗(yàn)公式確定沉降計(jì)算深度Zn：朝土產(chǎn)KSkNjiu'NM250kN=5(2.5-0,41115)(4-15)規(guī)范法的具體計(jì)算過程可參例題4-20【例題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

24、終沉降量。黏土產(chǎn)l&MNAn'成1石720SkN4n,f=20.SkN/m'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/Bz/Ba日(kPa)AuS*(丐為一叼Ta-1)(cm)(cm)0=12.500.250001.00.80.23460.23460.234644184.274.272.01.60.19390.38780.153268611.806.073.02.40.15780.47340.085677490.896.964.03.20.13100.52400.050668480.597.555.04.00.11140.

25、55700.03343930.608.156.04.80.09670.58020.023231470.598.747.05.60.08520.59640.016223040.579.317.66.080.08040.61100.0146350000.039.34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)表4-3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。并假這=如查表4-2得沉降計(jì)算經(jīng)驗(yàn)系數(shù)巾s=1.17。那么，最終沉降量為:.sr=117x9.34=10.9

26、8cm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:(4-16)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。壬=吟1-）（4-17）式中：-沉降系數(shù)，可從表4-4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)取尸0.5;Eu-不排水變形模量，常根據(jù)不排水抗剪強(qiáng)度G和Eu的經(jīng)驗(yàn)關(guān)系式（4-18）求得。=（300-1250）0,（4-18）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