桩基础知识练习题

1、、单桩承载力例题1条件：有一批桩，经单桩竖向静载荷试验得三根试桩的单桩竖向极限承载力分别为830kN、860kN和880kN要求：单桩竖向承载力容许值。答案:根据建筑地基与基础规范附录Q (6), (7)进行计算。其单桩竖向极限承载力平均值为:830 860 8802575 =858.3kN3350极差880-830=50kN 。 =5.82% <30% ,极差小于平均值的30%858.3858.3R =429.3kN2例题2求单桩竖向极限承载力 942条件：某工程柱下桩基础，采用振动沉管灌注桩，桩身设计直径为377mm ,桩身有效计算长度13.6m。地质资料如右图。要求：确定单桩竖向承

2、载力容许值。答案：我枇 照舔+0.02Cr i 1, Jn.Ra =彳(uZ %Lqik +%Apqrk) 2 i 1查表粉质黏土，粉土，黏性土摩阻力标准值分别为45kPa、55 kPa、53 kPa。1Ra 】=、(uZ 支Jqik +%Apq.k) 2 i 1_21 /0.3773.14 0.377(0.7 2.3 45 0.9 8.6 55 0.6 2.7 53)0.6 3.14 22002 41 ,=1.18 父(72.45 +425.7+85.86)+147.272=418.2kPa二、单排桩桩基算例设计资料：某直线桥的排架桩墩由2根1.0m钢筋混凝土钻孔桩组成，混凝土采用C20 ,

3、承台底部中心荷精品资料载：£ N =5000kN工 H =100kN ,£ M =320kN m。其他有关资料如图所示，桥下无水。2试求出桩身弯矩的分布、桩顶水平位移及转角(已知地基比例系数m=8000kPa/m ,答案:(1)桩的计算宽度b1b产 kkf(d 1)=1.0 0.9(1 1)=1.8(m)(2)桩的变形系数_2一一 _72m=8000kPa/m , b = 1.8(m), Ec = 2.7父10 kN/md4 二641.04 二64=0.049 m4= 0.4234/m5 mh=580000 1.8'0.8EcI - 0.8 2.7 107 0.04

4、9桩的换算深度h=o(h =0.4234x16 =6.76 >2.5,属弹性桩。(3)桩顶受力N 5000MiMy=2500kN320=160kN m2Qi100= 50kN(4)地面处桩的内力P0 =P =2500kNM0 MMi QJ0 =160 50 4 =360kN mQ0 =Qi -50kN(5)桩在地面处的横向位移和转角Xz弁 Bx a A二 2EI二 3EIM 0 cQo aB A :EI : EI其中无量纲系数查附表1、2、5、6A =2.44066, Ap=1.62100, Bx =1.62100 , B中=1.75058Xz/Bx：2EI-Q-Ax t360 1.62

5、100 - 50 2.44066：3EI 0.4234 2 8640000.4234 3 864000= 0.003760.00186 = 0.0056(m)咒=会叱斋A 0.423436864000 M 1.75058 + 0.4234250864000 父 621。)= (0.00172 +0.00052)=-0.00224( rad)(6)底面以下深度z处桩截面的弯矩MzMz=M°Bm Q0AM =360Bm 50-AM =360Bm 118.09am0.4234无量纲系数AM、Bm查附表3、7z =otzzAmBm118.09A m360BmMz000103603600.30

6、.70.29010.9938234.25791357.7752392.03310.61.40.529380.9586162.51448345.0996407.61410.92.10.689260.8860781.39471318.9852400.37991.22.80.761830.7741589.9645278.694368.65851.53.50.754660.6408189.1178230.6916319.80941.84.30.684880.4988980.87748179.6004260.47792.25.20.53160.3202562.77664115.29178.06662.6

7、6.10.354580.1754641.8723563.1656105.03837.10.193050.0759522.7972727.34250.139273.58.30.050810.013546.0001534.874410.8745549.40.000050.000090.0059050.03240.038305(7)桩顶水平位移及转角M x = 2Bxi二 EI3 .二 EIQ：2EIAi其中A1 =为、Ai)Bx1 = B用查附表14 16h =郎=0.4234 M16 =6.76 >2.5,取 h =4, 1。=田0 = 0.4234 M 4.0 = 1.692Ax1 =1

8、4.58671 , Bx1 = A5 =6.01938 ； Bq =3.44258EI =0.8EcI =0.8 2.7 107 0.049 = 864000 m2X1喋T Bx1鼎 Ax11600.42342 8640006.01938500.42343 86400014.58671= 0.00621 +0.01112 =0.01733 (m)二一(二 EIAqi)= -(16050 3.44258 2 6.01938 0.4234 8640000.42342 864000= 40.00151 +0.00194) =-0.00345( rad)(8)桩身最大弯矩 M max及最大弯矩位置计算

9、M M M = M0由公式(4-70)胃Cq =Q00.4234 360二 3.048550由 Cq =3.0485 及 h =oth =0.4234x16 =6.7744 查附表 13 得 ZMmax =0.658 ,故Zmmax0.6580.4234= 1.554(m)由 ZM=0.658 及 h =6.7744 查附表 13 得 KM =1.1022maxMmax = KM M 0 =1.1022 360 =396.80(kN m)(9)桩身配筋计算及桩身材料截面强度验算a)纵向钢筋面积桩内竖向钢筋按含筋率 0.2%配置：A = 1.02 0.2% =15.7 10“(m2)g 4(下面

10、还未算完)现选用10根622的HRB335级钢筋：A =37.9M104(m2), fsd =280MPa桩柱采用的C20混凝土， fcd =9.2MPa。b)计算偏心距增大系数nln 16因为长细比：-32 < 17.5i 0.5所以偏心距增大系数：c)计算截面实际偏心距e0eomaxmax720.173017.11= 0.239(m)d）根据公路桥涵地基与基础设计规范（JTG D63-2007 ）求得轴向力的偏心距 60:BfcdD：gfsdAfcdCfsd其中：r = 825mm, P =0.002 ；并设 g =0.9 则9.2B 0.002 0.9 280D9.2A 0.002

11、 280C825 =9.2B 0.504D9.2A 0.56C825以下采用试算法列表计算ABCD6060（60）/ /向0.792.09260.59821.593810418410.82.12340.58981.63811.12122422391.0125520.812.1540.5811.68111.09342342390.979079由上表可见，当£=0.80时，（e0）= 242.mm与实际的兔=239mm很接近，故去0.80为计算值。e)计算截面抗压承载力Nu =Ar2fcd C：r2fsd =2.1234 8252 9.2 1.6381 0.00

12、2 8252 280=13920.56( kN) >Nj =3017.11( kN)Mu =Br3fcd +C&r3fsd =0.5898父8253 父9.2+1.1212 父 0.002 父0.9 黑 8253 父280 满足要求 =3364.18 kN，m) >Mj =720.17(kN m)三、桩基础习题4-11某桥台为多排桩钻孔灌注桩基础，承台及桩基尺寸如图。纵桥向作用于承台底面中心处的设计荷载为：N=6400KN;H=1365kN ; M=714kN.m 。桥台处无冲刷。地基土为砂性土，土的内摩擦角§=36° 土的重322度,=19kN /m

13、；桩侧土摩阻力标准值 q =45kN/m ,地基比例系数 m=8200kPa/m ；桩底2土基本承载力容许值fao =250kN/m ；计算参数取九= 0.7,mo =0.6,k2 =4.0。试确定桩长并进行配筋设计答案:1.桩长的计算桩（直径1.5m ）自重每延米二 1.5215=26.49(kN)1 n:.Nh =Ra=u"qiklim0AP、fa0k2 2S3 -凯2 yN 1Nhqh4 26400 126.49 h=1600 13.25h42计算Ra时取以下数据：桩的设计桩径 1.5m,桩周长.2,、 A 二(1.5),2u =n黑1.5 =4.71(m) , Ap=-(-=

14、1.77m ,九=0.7, m0=0.6, k2 = 4 ,4fao =250.00kPa , % =19.00kN/m3 , qk=45kPa。所以得1 / _Ra - -(1.5 h 45)0.7 0.6 1.77 250 4.0 19 (h -3)= 105.98h 0.7434(22 76h) = Nh =1600 13.25hh=10.61m现取h =11m ,2.桩的内力计算(1)桩的计算宽度匕(P133)b1 : kkf (d 1)已知：kf =0.9 , d =1.5m ,L1 =2.4m <0.6h1 =0.6M3(d +1) = 0.6 父 7.5 = 4.5m ,则

15、系数k按照此式计算：k = b2 +1 -b20.6Lh1n = 2, b2 = 0.61 -b2 L10.6 h1= 0.60.62.43 (1.5 1)= 0.813b1=kkf(d 1)=0.813 0.9(1.5 1) =1.829 _ 2d =3(2)桩的变形系数口4二 1.547/2、I= = 0.2484m ； E =0.8Ec =0.8 2.55 10 (kN /m )64a8200 1.8290.8 2.55 107 0.2484= 0.3121(m,)其计算长则为：h =uh =0.3121父11 =3.4 >2.5,故按弹性桩计算。(3)桩顶刚度系数°pp

16、, 0hh , 0mh , 0mm值计算:PP :1l0 h . LAEC0A01 二d2二 1.522l0 =0m, h =11m, =,A= = 1.77m ,2 44C0=m0h=8200 11 =9.02 104(kN/m3)A0 -'d Wn( +htan )91.5=二(11 tan 2360)2 =19.50(m2)I ?2：:.22S = 3.9 =11.94(m )44.2故取 A0 = 11.94m佐 p =1。h . AEC0A00 - 1121.77 0.8 2.55 1079.02 104 11.94_ _5_= 9.25 105 =0.1826EIh =c(

17、h =0.3121 父11=3.4, 10 =叫=0.3120x0 = 0查附表17,18,19得xQ =1.01950,xM =0.95828, % =1.46614。由式(4-86d )得:3EIXq =0.0310EI HHQ、2mh =： EIxm =0.0933EI;mm =二 El，=0.45758EI(4)计算承台底面原点O处位移a0, C0, 00、式(4-92)、式(4-93)得：N 64008762.32C0 - T-n：pP 4 0.1826EI Eln_2(n'mm ' ;>pXi )H n; mhM_i 1a0 _nn：)H (n：，M:pp&#

18、39; x；) n272MHi=1 nn：MM:pp'x；% 0.45758EI 0.1826EI 4 1.952 -4.6077EI1 1n：MH =4 0.0933EI =0.3732EI ,n2 ：2mh -0.13928(EI )2n2 一(n #MM + #PP 匕 x ) H + n Pmh Mci 1ao =n- ，一.2 .2、2 -2n>HH (n ? MM ' : pp L, xi ) - nMH1 14.6077EI 1365 0.3732EI 71415173.24=-9 =0.1240EI M4.6077EI 0.13928 EI)2 EIn”

19、n：MHH0 n.，-.一 2、2 -、2nHH (n： MM - >PX ) n 丁 MHi 10.1240EI 714 0.3732EI 13651383.913- 0.1240EI 4.6077EI -0.13928(EI)2 一 El(5)计算作用在每根桩顶上作用力P ,Qi, M i按式(4-97)计算:竖向力水平力P = *ppG ： PP(c0 ' xi '0)=0.1826EI(8762.32EII” 1383.913、2092.77kN±1.95 父)=EI 1107.23kNQi = ：' HH a0 - ： MH '0= 0

20、.0310EI15173.24EI1383.913-0.0933EI=341.25kNEI弯矩M i = : MM -0 一MH a01383.91315173.240.45758EI0.0933EI= -782.41kN mEIEI(6)桥台处无冲刷桩身内力M0,Q0,F0与桩顶P,Qi,Mi相等。M0 = Mi = -782.41(kN.m)Q0 -341.25kNF0 =2092.77(kN)(7)深度z处桩截面的弯矩 Mz及桩身最大弯矩Mmax计算a.局部冲刷线以下深度z处桩截面的弯矩 Mz计算Mz =M°Bm +®Am =782.41Bm +闻竺Am =782.4

21、1Bm +1093.40% 无量纲系数有 0.3121由Qz =0得:CQ二 M。Q00.3121 782.41341.25= 0.7156由 Cq =0.7156 及 h= cth =0.3121 父11 =3.4331 查附表 13 得Zmax =1.135，故 Zmmax1.135=3.640.3121由 h =3.4331, Zmax =1.135查附表 13 得，Km =2.143Mmax 二KMM 0 =2.143 308.18=660.43附表3、附表7分别查得，Z =azzAmBm1093.40A m782.41B mMz00010782.41782.410.30.960.28

22、9650.99363316.70331777.4261094.1290.61.920.526030.95726575.161202748.96981324.1310.92.880.678740.87987742.134316688.41911430.5531.23.840.73880.76503807.80392598.56711406.3711.54.810.713540.62469780.184636488.76371268.9481.85.770.620920.47411678.913928370.94841049.8622.27.050.43420.28334474.75428221.

23、688696.44232.68.330.231810.13062253.461054102.1984355.659439.610.076280.0369483.40455228.90223112.30683.511.210.000010.000040.0109340.0312960.0422349.40000b.桩身最大弯矩 Mmax及最大弯矩位置A0.7464BM =0.7922, AM =0.7464,KM M BM = 0.7922 =3.440CQ0.2819MmKMM0 =3.440 308.18 =1060.14(8)桩身配筋计算及桩身材料截面强度验算按照h=13米计算三、桩基础习

24、题4-11某桥台为多排桩钻孔灌注桩基础，承台及桩基尺寸如图。纵桥向作用于承台底面中心处的设计荷载为：N=6400KN;H=1365kN ; M=714kN.m 。桥台处无冲刷。地基土为砂性土，土的内摩擦角 §=36° 土的重度尸=19kN/m3；桩侧土摩阻力标准值 q=45kN/m2,地基比例系数 m = 8200kPa/m2 ；桩底2一_ _ 一一土基本承载力容许值fa0 =250kN / m ；计算参数取九=0.7,mo = 0.6,k2 = 4.0 。试确定桩长并进行配筋设计答案:1.桩长的计算桩（直径1.5m ）自重每延米二 152_ q=-M15 = 26.49(

25、kN)(已考虑浮力)_ _1 n _一一 一 一，Nh =R =-ux qiJmoAp! fao k2 2S3 -3).，2 i4N 1Nh qh4 26400 126.49 h=1600 13.25h42计算Ra时取以下数据：桩的设计桩径1.5m,桩周长. 二(1.5)2,2CC ,u =n M1.5 =4.71(m) , Ap =1.77m ,九=0.7, m0=0.6, k2 = 4 ,4fa。 =250.00kPa , % =19.00kN/m3 , qk=45kPa。所以得1 ,、Ra=(二 1.5 h 45) 0.7 0.6 1.77 250 4.0 9 (h -3) 2= 105

26、.98h +0.7434(142 +36h) = Nh =1600 +13.25hh =12.51m现取h =13m ,2.桩的内力计算(1)桩的计算宽度匕(P133)b1 . kkf (d 1)已知：kf =0.9 , d =1.5m ,L1 =2.4m <0.6h1 =0.6父39 +1) = 0.6 父 7.5 = 4.5m ,1 'b2 L1则系数k按照此式计算：k =b2 +2 -10.6h1n = 2, b2 =0.6。k =b21sb2L1=0.6 1°24=0.8130.6h10.63 (1.5 1)b1=kkf(d 1)=0.813 0.9(1.5 1

27、) =1.829 - 2d =3(2)桩的变形系数a4:1.547/2、I= = 0.2484m ； E=0.8Ec=0.8 2.55 10 (kN /m )64mbi二58200 1.8290.8 2.55 107 0.2484= 0.3121(m)其计算长则为：h =uh =0.3121父13 = 4.05 >2.5，故按弹性桩计算。(3)桩顶刚度系数Ppp, Phh , Pmh , Pmm值计算;PP =AEC0A0，-，“1 A10 = 0m, h = 13m,= ,A =2二上二1.77m2,4C0=m0h=8200 13 =1.066 105( kN/m3)A0 =二(h t

28、an )24=311.5(13 tan23602_2)=24.776(m )22S = 3.9 =11.94(m )44故取 A =11.94m2101321.77 0.8 2.55 101.066 105 11.94AEC0A0= 1.04 106 =0.2044EIh =时=0.3121M13=4.05， l° =3。= 0.3120M 0 =0查附表17,18,19得Xq =1.06423, Xm =0.98545,中m =1.48375。由式(4-86d )得:-3EIxQ -0.0324EI二 ：2EIxM =0.0960EI:mm =旧 m =0.4631EI(4)计算承

29、台底面原点O处位移a0, Q,瓦、式(4-92)、式(4-93)得：N 64007827.79Co 二二二n：-pp 4 0.2044EI EIn ,_2、._ _ _(nrMM ,PP.二 xi )H n : mh M-i 1a0 =nn：HH (n：MM ,:PP、xi2) n2：2MH i 1n 2on：MM7PpV xi =4 0.4631EI 0.2044EI 4 1.952 = 4.9613EIi 4n 7MH =4 0.0960EI =0.3840EI ,n2 ；?2mh =0.1475(EI)2n 2、(n )mm ,> pp 二 xi ) H n : mh Ma =i-

30、a0 -nnrHH(n：MM : PP 二.xi ) - n : MH i 14.9613EI 1365 0.3840EI 71414221.1320.1296EI 4.9613EI -0.1475(EI)2 EIn :hh M n ：mh Hr nn：HH(n：MM ,:pp' x；)-n2：2MHi 10.1296EI 714 0.3840EI 13651244.63- 0.1296EI 4.9613EI -0.1475(EI)2 - EI(5)计算作用在 每根桩顶上作用力 P ,Qi, M i按式(4-97)计算:P = PppG = Ppp(c° +x 00)竖向力=

31、 0.2044EI (7827.79EI1244.632096.08kN±1 95 乂) 1*EIJ103.92kN水平力Qi - :，HH a0 1MH - 0= 0.0324EI 14221.13 0.0960EI 124463 = 341.28kNEIEI弯矩M i - ? MM P -，MH a01244.6314221.13=0.4631EI-0.0960EI=-788.84kN mEIEI(6)桥台处无冲刷桩身内力M0,Q0,P0与桩顶P,Q,Mi相等。M0 = Mi = -788.84(kN.m)Q0 =341.28kNP0 -2096.08(kN)(7)深度z处桩截面

32、的弯矩 Mz及桩身最大弯矩Mmax计算a.局部冲刷线以下深度 z处桩截面的弯矩 Mz计算Mz =M0BM +Q0-AM = 782.41 BM +34128AM =788.84BM + 1093.40AM 无量纲系数有0.3121附表3、附表7分别查得,z=azzAmBm1093.40A m788.84B mMz00010788.84788.840.30.960.289650.99363316.70331783.81511100.5180.61.920.526030.95726575.161202755.1251330.2860.92.880.678740.87987742.134316694

33、.07671436.2111.23.840.73880.76503807.80392603.48631411.291.54.810.713540.62469780.184636492.78051272.9651.85.770.620920.47411678.913928373.99691052.9112.27.050.43420.28334474.75428223.5099698.26422.68.330.231810.13062253.461054103.0383356.499339.610.076280.0369483.40455229.13975112.54433.511.210.000010.000040.0109340.0315540.04248849.40000b.桩身最大弯矩 Mmax及最大弯矩位置 C 二Mo 由 Qz = 0 得：CQ =Qo0.3121 788.84341.28= 0.72139Zmax =1.0320,故 Zmmax1.03200.3121= 3.3066由 Cq =0.72139 及 h =uh =0.3121M13 =4.057 查附表 13 得由 h =4.057, Zmax =1.0320 查附表 13 得，Km =1.9107Mmax =KMM 0 =1.9107 788.84 =1507.251.812