沉降計算例題

1、地基沉降量計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到穩(wěn)定時基礎底面的沉降量稱為地基最終沉降量。、分層總和法計算地基最終沉降量計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)壓縮試驗確定的參數(shù)（e、E、a）進行計算，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（自重應力作用下）的孔隙比；e2-地基受荷（自重與附加應力作用下）沉降穩(wěn)定后的孔隙比；H-土

2、層的厚度。計算沉降量時，在地基可能受荷變形的壓縮層范圍內(nèi)，根據(jù)土的特性、應力狀態(tài)以及地下水位進行分層。然后按式（4-9）或（4-10）計算各分層的沉降量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）計算基底附加壓力po3）計算各分層界面的自重應力cz和附加應力門；并繪制應力分布曲線。4）確定壓縮層厚度滿足=0.2nz的深度點可作為壓縮層的下限；對于軟土則應滿足CTz=0.1（Tsz；對一般建筑物可按下式計算zn=B（2.5-0.4

3、lnB）。5）計算各分層加載前后的平均垂直應力Pl=（Tsz；P2=（Tsz+（Tz6）按各分層的Pi和P2在e-p曲線上查取相應的孔隙比或確定a、E等其它壓縮性指標7）根據(jù)不同的壓縮性指標，選用公式（4-9）、（4-10）計算各分層的沉降量S8）按公式（4-11）計算總沉降量S士層土層自重應為分布曲線沉降計算深扇附加應力分布曲姓土層包圖4-T分層總和法計算地基沉降量分層總和法的具體計算過程可參例題4-1例題41已知柱下單獨方形基礎，基礎底面尺寸為2.5>2.5m,埋深2m,作用于基礎上（設計地面標高處）的軸向荷載N=1250kN,有關地基勘察資料與基礎剖面詳見下圖。試用單向分層總和法計

4、算基礎中點最終沉降量。崎質(zhì)黏土產(chǎn)aokN,加蜂黏土7-18.5kK4n'卵石-720SkNin1f=20.5kN/m'沿IROkN個"yW#F土E卡IfSkNM°我一解：按單向分層總和法計算(1)計算地基土的自重應力。Z自基底標高起算當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)基底壓力計算。基礎底面以上，基礎與填土的混合容重取0=20kN/m3。25x25(3)基底附加壓力計算。p-p-yD-240-19,5x2,0=201kp置(4)基礎中點下地基中豎向附加應力計算。用角點法計算，L/B=1,(rzi=4Ksip0,查附加應力系數(shù)表得Ksio(5)確定沉降計算深度zn例題4-1計算表格1考慮第層土壓縮性比第層土大，經(jīng)計算后確定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(6)計算基礎中點最終沉降量。利用勘察資料中的e-p曲線，求按單向分層總和法公式計算結果見下表。例題4-1計算表格2Z(m(kPa)心(kPa)H(cm自重應力平均值附加應力平均值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建筑地基基礎設計規(guī)范推薦的沉降計算法GBJ7-8吩所推薦的,下面計算沉降量的方法是建筑地基基礎設計規(guī)范（簡稱規(guī)范推薦法，有時也叫應力面積法。（一）計算原理應力面積法一般按地基土的天然分層面劃分計算土層，引入土層平均附加應力的概念，通過平均附加應力系數(shù)，將基底中心以下地基中Zi-i-Zi深度范圍的附加應力按等面積原則化為相同深度范圍內(nèi)矩形分布時的分布

9、應力大小，再按矩形分布應力情況計算土層的壓縮量，各土層壓縮量的總和即為地基的計算沉降量。理論上基礎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-基礎底面處的附加壓力（kPa）；日-基礎底面下第i層土的壓縮模量（MPa;Zi、Zi-i-分別為基礎底面至第i層和第i-1層底面的距離（nj）；ai、ai-i-分別為基礎底面計算點至第i層和第i-1層底面范圍內(nèi)平均附加應力系數(shù)，可查表4-1。表4-1矩形面積上均布荷載作用下，通過中心點豎線上的平均附加應力系數(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）式乘以沉降計算經(jīng)驗系數(shù)巾s,即為規(guī)范推薦的沉降計算公S二W二%2普（馬酸-舁1%-0（4-13）紇i式中：巾S-沉降計算經(jīng)驗系數(shù)，應根據(jù)同類地區(qū)已有房屋和構筑物實測最終

22、沉降量與計算沉降量對比確定，一般采用表4-2的數(shù)值；表4-2沉降計算經(jīng)驗系數(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;當變形計算深度范圍內(nèi)有多層土時,Es可按附加應力面積A的加權平均值采用，即y.4（三）地基受壓層計算深度的確定計算深度Zn可按下述方法確定：1）存在相鄰荷載影響的情況下，應滿足下式要求：故;£002宅?。?-14）式中：&'-在深度Zn處，向上取計算厚度為z的計算變形值；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層土的計算變形量2）對無相鄰荷載的獨立基礎，可按下列簡化的經(jīng)驗公式確定沉降計算深度Zn：朝土產(chǎn)KSkNjiu'NM250kN=5(2.5-0,41115)(4-15)規(guī)范法的具體計算過程可參例題4-20【例題42】已知柱下單獨方形基礎，基礎底面尺寸為2.5>2.5m,埋深2m,作用于基礎上（設計地面標高處）的軸向荷載N=1250kN,有關地基勘察資料與基礎剖面詳見下圖。試用規(guī)范法計算基礎中點最

24、終沉降量。黏土產(chǎn)l&MNAn'成1石720SkN4n,f=20.SkN/m'解：按建筑地基基礎設計規(guī)范計算，采用下式，計算結果詳見下表。例題4-2計算表格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厚度計算，根據(jù)表4-3的要求，取Az=0.6m,則Zn=7.6m,計算得厚度Az的沉降量為0.03cm,滿足要求。并假這=如查表4-2得沉降計算經(jīng)驗系數(shù)巾s=1.17。那么，最終沉降量為:.sr=117x9.34=10.9

26、8cm三、按粘性土的沉降機理計算沉降根據(jù)對粘性土地基在局部（基礎）荷載作用下的實際變形特征的觀察和分析，粘性土地基的沉降S可以認為是由機理不同的三部分沉降組成（圖4-8）,亦即:(4-16)式中：Sd-瞬時沉降（亦稱初始沉降）；Sc-固結沉降（亦稱主固結沉降）；Ss-次固結沉降（亦稱蠕變沉降）。瞬時沉降是指加載后地基瞬時發(fā)生的沉降。由于基礎加載面積為有限尺寸，加載后地基中會有剪應變產(chǎn)生，剪應變會引起側(cè)向變形而造成瞬時沉降。固結沉降是指飽和與接近飽和的粘性土在基礎荷載作用下，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（固結壓密）。固結沉降速率取決于孔隙水的排出速率。次固結沉降是指主固結過程（超靜孔隙水壓力消散過程）結束后，在有效應力不變的情況下，土的骨架仍隨時間繼續(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）瞬時沉降計算瞬時沉降沒有體積變形，可認為是彈性變形，因此一般按彈性理論計算，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-基底附加應力；N-泊松比，這時是在不排水條件下沒有體積變形所產(chǎn)生的變形量，所以應取尸0.5;Eu-不排水變形模量，常根據(jù)不排水抗剪強度G和Eu的經(jīng)驗關系式（4-18）求得。=（300-1250）0,（4-18）上式中的低值適用于較軟的、高塑性有機土，高值適用于一般較硬的粘性土。表4-4沉降