基坑樁錨設(shè)計(jì)計(jì)算過(guò)程(手算)

1、FGH段地層信息：基坑深7.3m , 樁錨支護(hù)，第一排錨桿2.2m, 第二排在4.7m處，角度30°。地層天然重度粘聚力內(nèi)摩擦角土體與錨固體粘結(jié)強(qiáng)度標(biāo)準(zhǔn)值填土18.3121230粉質(zhì)粘土19.8301860全風(fēng)化礫巖20.54522100土壓力系數(shù)地層KaKaKpKp1填土0.65580.80981.52521.23502粉質(zhì)粘土0.52780.72651.89451.37643全風(fēng)化礫巖0.45500.67452.19811.4826一、)基坑示意圖：1） 基坑外側(cè)主動(dòng)土壓力計(jì)算如下：（1） 填土：填土頂部主動(dòng)土壓力強(qiáng)度：p上a1=q ka1 - 2c1ka1 =20x0.6558

2、-2x12x0.8098=-6.32Kpa填土底部的主動(dòng)土壓力強(qiáng)度：p下a1=（r1h1+q）ka1-2c1ka1 =(18.3x10.5+20)x0.6558-2x12x0.8098=119.69kpa（2） 粉質(zhì)粘土：粉質(zhì)粘土頂部的主動(dòng)土壓力強(qiáng)度：pa2上 = （r1*h1+q）ka2 -2c2ka2 = =(18.3x10.5+20)x0.5278-2x12x0.7265=94.54kpa粉質(zhì)粘土底部的主動(dòng)土壓力強(qiáng)度：pa2下 =（r1*h1 +r2*h2+q）ka2-2c2ka2 = =(18.3x10.5+19.8x1.8+20)x0.5278-2x12x0.7265=113.35k

3、pa （3） 臨界深度：Zo=2c1/ r1ka1 q/r1=2x12/18.3x0.8098-20/18.3=0.53m 2）第一層錨桿計(jì)算： 基坑開(kāi)挖到5.2m，設(shè)置第一排錨桿的水平分力為T1。1） 此時(shí)基坑開(kāi)挖深度為h=5.2m，基坑外側(cè)底部的主動(dòng)土壓力強(qiáng)度：pa1坑底 =（r1*h+q）ka1-2c1ka1 =(18.3x5.2+20)x0.6558-2x12x0.8098=56.09kpa基坑內(nèi)側(cè)的被動(dòng)土壓力強(qiáng)度：pp1坑底= 2c1kp1=2x12x1.2350=29.64kpa.pp1下=r1（h1- h）kp1+2c1kp1= 18.3x(10.5-5.2)x1.5252+2x

4、12x1.2350=177.57kpa.知：pa1下 < pp1下 , pp1坑底 < pa1坑底知鉸點(diǎn)位于坑底與填土層間：設(shè)鉸點(diǎn)為o, 距離坑底y m.ppo =paoppo= r1y kp1+2c1kp1 = y18.3x1.5252+2x12x1.2350=27.91y+29.64pao= q+r1(h+y) ka1-2c1ka1= 20+18.3(5.2+y)x0.6558-2x12x0.8098=12y+56.08解得： y=1.66m2）設(shè)置第一排錨桿的水平分力為T1，鉸點(diǎn)以上土層及錨桿力對(duì)鉸點(diǎn)起矩平衡。2.1土壓力作用位置確定：三角形分布：hai=13hi梯形分布：h

5、ai=2pai+pai3(pai+paj)hi即：2.2基坑內(nèi)側(cè)被動(dòng)土壓力作用點(diǎn)位置：（梯形分布）hp1=2pp1坑底+ppo3(pp1坑底+ppo ) h1oppo=r1y kp1+2c1kp1= 18.3x1.66x1.5252+2x12x1.2350=75.97kpa.pp1坑底= 2c1kp1=2x12x1.2350=29.64kpa.hp1=(2x29.64+75.97)/3x(29.64+75.97)x1.66=0.71m2.3基坑外側(cè)主動(dòng)土壓力作用點(diǎn)位置：（三角形分布）hao=13（h+ y-z0）已知， h=5.2m, y=1.66m, z0=0.53m即：hao=13 （5.

6、2+1.66-0.53）=2.11m2.4第一排錨桿作用點(diǎn)離起矩點(diǎn)位置：L=h+ y- d=5.2+1.66-2.2=4.66m.(d為錨桿離地面距離)2.5基坑內(nèi)側(cè)被動(dòng)土壓力合力：EP=Ppi+ppj 2 x hpi即，EP=y x (ppo+pp1坑底 )/2=1.66x (75.97+29.64)/2=87.66kpa2.6基坑外側(cè)主動(dòng)土壓力：Ea=Pai+paj 2 x haiEa=(h+y-z0）x pao/2=(5.2+1.66-0.53)x75.97/2=240.45kpa.即：T1(h + y d) + EPhp1=Eahao代入數(shù)據(jù)：4.66T1 +87.66x0.71=24

7、0.45x2.11T1=95.52kpa.三）第二排錨桿計(jì)算：此時(shí)，基坑開(kāi)挖至設(shè)計(jì)深度h坑底 =7.3m。 3.1）基坑內(nèi)側(cè)被動(dòng)土壓力強(qiáng)度：pp1坑底= 2c1kp1=2x12x1.2350=29.64kpa.pp1下=r1（h1- h坑底）kp1+2c1kp1= 18.3 x (10.5-7.3)x1.5252+2x12x1.2350=118.96kpapp2上=r1（h1- h坑底）kp2+2c2kp2=18.3x(10.5-7.3)x 1.8945+2x30x1.3764=193.53kpa.pp2下= r1（h1- h坑底）+r2 h2kp2+2c2kp2=18.3x (10.5-7.

8、3)+19.8x1.8x1.8945+2x30x1.3764=176.79kpa. 基坑外側(cè)主動(dòng)土壓力強(qiáng)度：pa1坑底=（r1*h坑底+q）ka1-2c1ka1 =(18.3x 7.3+20)x0.6558- 2x 12x0.8098=81.29kpa.pa2上=（r1*h1+q）ka2 -2c2ka2 =(18.3x10.5+20)x0.5278-2x30x0.7265=68.38kpa即：pp1下<pa1下 , pp1坑底 <pa1坑底 , pa2上 <pp2上故，假想鉸點(diǎn)為兩層土的交界處，設(shè)為M點(diǎn)，距基坑底為3.2m.3.2）設(shè)置第一排錨桿的水平分力為T2，鉸點(diǎn)以上土層

9、及錨桿力對(duì)鉸點(diǎn)起矩平衡。3.2.1土壓力作用位置確定：三角形分布：hai=13hi梯形分布：hai=2pai+pai3(pai+paj)hi基坑內(nèi)側(cè)被動(dòng)土壓力作用點(diǎn)位置：（梯形分布）hp1=2pp1坑底+pp1下3(pp1坑底+pp1下）h1坑hp1=(2x29.64+118.96)/3x(29.64+118.96)x3.2=1.28m基坑外側(cè)主動(dòng)土壓力作用點(diǎn)位置：（三角形分布）ham=13（h1-z0）ham=13（10.5-0.53）= 3.32m第一排錨桿作用點(diǎn)位置：lm1=h1-d=10.5-2.2=8.3m第二排錨桿作用點(diǎn)位置：lm2=10.5-4.7=5.8m3.2.2)土壓力合力

10、：基坑外側(cè)主動(dòng)土壓力：Ea=Pai+paj 2 x haipa1下=（r1h1+q）ka1-2c1ka1 =(18.3x10.5+20)x0.6558-2x12x0.8098=119.69kpaha1= h1-z0=10.5-0.53=9.97mEa= (119.69x9.97)/2=596.65kpa基坑內(nèi)側(cè)被動(dòng)土壓力：EP=pp1坑底+pp1下2 x hpmpp1坑底= 2c1kp1=2x12x1.2350=29.64kpa.pp1下=r1（h1- h坑底）kp1+2c1kp1= 18.3 x (10.5-7.3)x1.5252+2x12x1.2350=118.96kpahpm=3.2m.

11、EP= (29.64+118.96)x3.2/2=237.76kpa即：T2lm2+T1lm1+EPhp1=Eaham有：5.8T2+95.52x8.3+237.76x1.28=596.65x3.32得：T2=152.37kpa四）樁嵌固深度計(jì)算：4.1）基坑開(kāi)挖至設(shè)計(jì)深度時(shí)，據(jù)上結(jié)果知鉸點(diǎn)假想為土層交接點(diǎn)M點(diǎn)，則該處的剪力計(jì)算如下：根據(jù)水平方向上的平衡：即：EP1+T1+T2+vm=Ea1vm=596.65-(237.76+95.52+152.37)=111kpa設(shè)樁底端為N點(diǎn)，樁底距M點(diǎn)距離為hmn。樁MN段對(duì)樁底N起矩平衡：4.1.1）土壓力合力計(jì)算：樁內(nèi)側(cè)被動(dòng)土壓力合力：EP=pp2上

12、+pp2m下2 x hmn根據(jù)3.1有：pp2上=r1（h1- h坑底）kp2+2c2kp2=18.3x(10.5-7.3)x 1.8945+2x30x1.3764=193.53kpa.pp2m下= r1（h1- h坑底）+r2 hmnkp2+2c2kp2=18.3x (10.5-7.3)+19.8xhmnx1.8945+2x30x1.3764=110.94+37.51hmn+82.584EP=193.53hmn+18.76hmn2樁外側(cè)主動(dòng)土壓力計(jì)算：Ea=（pa2上 2+pa2m下2 ） x hmnpa2上=（r1*h1+q）ka2 -2c2ka2 =(18.3x10.5+20) x 0.

13、5278-2x30x0.7265=68.38kpapa2m下=r1 h1+r2hmn+qka2-2c2ka2=18.3x10.5+19.8xhmn+20 x 0.5278-2x30x0.7265=111.97+10.45hmn-43.59Ea=68.38hmn+5.23hmn24.1.2）土壓力作用點(diǎn)計(jì)算：樁內(nèi)側(cè)被動(dòng)土壓力作用點(diǎn)計(jì)算：hpm=2pp2上+pp2m下3(pp2上+pp2m下）hmn得，hpm=580.59+37.51hmn1161.18+112.53hmnhmn樁外側(cè)主動(dòng)土壓力作用點(diǎn)計(jì)算：ham=2pa2上+pa2m下3(pa2上+pa2m下）hmn得，ham=205.14+10

14、.45hmn410.28+31.35hmnhmn剪力vm的作用點(diǎn)位置為lm=hmn4.1.3)樁MN段對(duì)樁底N點(diǎn)起矩平衡：vm. lm+Ea. ham=EP. hpm即，vm.hmn+ 68.38hmn+5.23hmn2. 205.14+10.45hmn410.28+31.35hmnhmn=193.53hmn+18.76hmn2. 580.59+37.51hmn1161.18+112.53hmnhmn解得，hmn=1.63m則嵌固深度, t=3.2+1.63=4.83m.入土深度增大系數(shù)r0=1.20即，樁的嵌固深度，t'=r0t=1.20x4.83=5.80m五）樁身最大彎矩計(jì)算：5

15、.1）第一步開(kāi)挖 第一次開(kāi)挖到第一排錨桿下0.5m即2.7m處。pp1坑底=2c1kp1=2x12x1.2350=29.64kpapp1下=r1h'kp1+2c1kp1= 18.3x(10.5-2.7)x1.5252+2x12x1.2350=247.35kpapa1下=（r1h1+q）ka1-2c1ka1 =(18.3x10.5+20)x0.6558-2x12x0.8098=119.69kpaEP=pp1坑底+pp1下2 x h'=(29.64+247.35)x7.8/2=1080.26kpaEa1=（pa1上 2+pa1下2 ） x h1=119.69x10.5/2=628.

16、37kpa.5.2)設(shè)u點(diǎn)剪力為0，點(diǎn)u到此步開(kāi)挖基坑底的距離為hu.ppu下=r1hukp1+2c1kp1= 18.3x hux1.5252+2x12x1.2350=27.91hu+29.64EP1u=pp1坑底+ppu下2 x hu=(59.28+27.91hu) hu/2pau下=r1(hu+h坑底）+q)ka1-2c1ka1=18.3x(hu+2.7)+20x0.6558-2x12x0.8098=26.08+12huEa1u=（pa1上 2+pau下2 ）(hu+h坑底-z0)=(26.08+12hu)( hu+2.7-0.53)/2因o點(diǎn)處剪力為0，即有，EP1u=Ea1u解得，hu

17、=0.91m有，pau下=r1(hu+h坑底）+q)ka1-2c1ka1=26.08+12hu=37kpa.ppu下=r1hukp1+2c1kp1=27.91hu+29.64=55.04kpa.EP1u=Ea1u=56.98kpahau=13(hu+h坑底-z0)hpu=2pp1上+ppu下3(pp1上+ppu下）huhau= (2.7+0.91-0.53)/3=1.03hpu=0.91(2x29.64+55.04)/3(29.64+55.04)=0.41mM=Ea1uhau-EP1uhpu=56.98x(1.03-0.41)=35.33kpa.六）第二步開(kāi)挖至5.2m，可知開(kāi)挖面上下各有一個(gè)

18、剪力零點(diǎn)，設(shè)其為Q,R，分別到5.2m開(kāi)挖面的距離為x, y。6.1) pa1Q下=r1(h開(kāi)挖-x )+qka1-2c1ka1 =18.3(5.2-x)+20x0.6558-2x12x0.8098=56.09-12xEa1Q=（pa1上 2+pa1Q下2 ） x (h開(kāi)挖-x-z0)Ea1Q=(56.09-12x)(5.2-x-0.53)/2使得，Ea1Q=T1即，解得x=0.68m又，haQ=13(h開(kāi)挖-x-z0)=1.33mQ點(diǎn)彎矩可計(jì)算MQ=T1h開(kāi)挖-d1-x-Ea1QhaQ=95.52x(5.2-2.2-0.68)-1.33=94.56kpa.6.2) pp1R上=2c1kp1=

19、2x12x1.2350=29.64kpa.pp1R下=r1ykp1+2c1kp1=18.3yx1.5252+2x12x1.2350=27.91y+29.64EP=pp1R上+pp1R下2 yEP1R=(27.91y+29.64+29.64）y/2=(13.96y+29.64)ypa1R下=r1h開(kāi)挖+y+qka1-2c1ka1=18.3(5.2+y)+20x0.6558-2x12x0.8098=56.09+12yEa1R=Pa1R下2(h開(kāi)挖+y-Z0)Ea1R=(56.09+12y)(5.2+y-0.53)/2使得，Ea1R=T1+EP1R即解得，y=4.34mpp1R上=29.64kpap

20、p1R下=150.77kpaEa1R=487.31kpaEP1R=391.58kpahaR=13(h開(kāi)挖+y-z0)=(5.2+4.34-0.52)/3=3mhpR=2pp1R上+pp1R下3(pp1R上+pp1R下）hRhpR=2x29.64+150.773(29.64+150.77)x4.34=1.68mhTR=(h開(kāi)挖+y-d1)=7.34mR點(diǎn)處彎矩，MR=T1hTR+EP1Rhp1R-Ea1RhaR=95.52X7.34+391.58X1.68-487.31X3=-102.96KPA七）第三次開(kāi)挖至設(shè)計(jì)深度7.3m，知在開(kāi)挖基坑面上下各有一個(gè)剪力為0的點(diǎn)。因，p下a1坑=（r1h基底

21、+q）ka1-2c1ka1 =(18.3x7.3+20)x0.6558-2x12x0.8098=81.29kpaha坑=13(h基底-z0)=（7.3-0.53）/3=2.26mEa1坑底=Pa1坑下2(h基底-Z0)=275.17Ea1坑底>T1+T2即，在該基坑底面與第二排錨桿之間存在剪力為0 的點(diǎn)，設(shè)為U，該點(diǎn)到基坑底面的距離為x。pa1U下=r1(h基底-x )+qka1-2c1ka1 =18.3(7.3-x)+20x0.6558-2x12x0.8098=81.29-12xEa1u=pa1U上 2 x (h基底-x-z0)Ea1u=(81.29-12x)(7.3-x-0.53)/

22、2Ea1U=T1+T2解得，x=0.35mhaU=13(h基底-x-z0)haU=（7.3-0.35-0.53）/3=2.14mEa1u=247.46kpaU點(diǎn)處的彎矩，MU=247.46x2.14-95.52x4.75-152.37x2.15=251.75kpapp1坑底= 2c1kp1=2x12x1.2350=29.64kpa.pp1下=r1（h1- h坑底）kp1+2c1kp1= 18.3 x (10.5-7.3)x1.5252+2x12x1.2350=118.96kpaEP1= (29.64+118.96)x3.2/2=237.76kpap下a1=（r1h1+q）ka1-2c1ka1

23、=(18.3x10.5+20)x0.6558-2x12x0.8098=119.69kpaEa1= (119.69x9.97)/2=596.65kpaEP1+T1+T2<Ea1即在坑底與第二層土間存在一個(gè)剪力為O的點(diǎn)，設(shè)為W，該點(diǎn)到第一層底面的距離為Y。pa2w下=r1 h1+r2y+qka2-2c2ka2=18.3x10.5+19.8y+20x0.5278-2x30x0.7265=68.38+19.8ypa2上=r1h1+qka2-2c2ka2=18.3x10.5+20x0.5278-2x30x0.7265=68.38kpap下a1=（r1h1+q）ka1-2c1ka1 =(18.3x1

24、0.5+20)x0.6558-2x12x0.8098=119.69kpaEa2w=pa2w下+pa2上2yEa1=pa1下2(h1-z0)Ea1=119.69x(10.5-0.53)/2=596.65kpa.Ea2w=(68.38+68.38+19.8y)y/2pp1上=2c1kp1=29.64kpapp2上=18.3x3.2x1.8945+2x30x1.3764=193.53kpapp1下=18.3x3.2x1.5252+2x12x1.2350=118.96kpa.pp2w下=18.3x3.2+19.8yx1.8945+2x30x1.3764=193.53+37.51yEP1=pp1上+pp

25、1下2 3.2Ep2w=pp2w下+pp2上2yEP1=(29.64+118.96)x3.2/2=237.76kpa.Ep2w=(193.53+193.53+37.51y)y/2EP1+EP2w+T1+T2=Ea2w+Ea1596.65+(68.38+68.38+19.8y)y/2=95.52+152.37+237.76+(193.53+193.53+37.51y)y/2解得，y=0.83mW點(diǎn)處的彎矩，hp1=2pp1上+pp1下3(pp1上+pp1下）3.2hp2w=2pp2上+pp2w下3(pp2上+pp2w下）yhp1=(29.64x2+118.96)x3.2/3(29.64+118.

26、96)=1.28mpp2w下=224.66kpa pp2上=193.53kpa hp2w=0.40mha1=13(h1-z0)ha1=3.32mha2w=2pa2上+pa2w下3(pa2上+pa2w下）ypa2上=68.38kpa pa2w下=84.81kpa ha2w=0.4mMw=Ea2wha2w+Ea1ha1-(EP1hp1+EP2whp2w+T1l1+T2l2)=596.65x3.32+25.43-237.76x1.28-173.55x0.4-95.52x9.13-152.37x6.63=-249.76kpa八）錨桿計(jì)算：11.1）錨桿配筋：Nk=(Ricos15°) x S

27、h N=rorfNkNfpyAp Nk：錨桿軸向拉力標(biāo)準(zhǔn)值N：錨桿軸向拉力設(shè)計(jì)值Sh：錨桿間距fpy:預(yù)應(yīng)力筋拉強(qiáng)度設(shè)計(jì)值 Ap：預(yù)應(yīng)力筋的截面面積 第一排錨桿：N1=rorfNk= 1.1x1.25x(95.52/cos30°)x2=301.93kpa.Ap1N1fp=301.93/360x1000=838.69mm2<D2=x162,選用HRB400。第二排錨桿：N1=rorfNk=1.1x1.25x(152.37/cos30°)x2=481.63kpaAp2N2fp=481.63/360x1000=1337mm2<222，選用HRB400。8.2）錨桿自由

28、端長(zhǎng)度：m=12x10.5+18x1.812.3=12.88lf(1+2-dtan)sin(45°-m2)sin(45°+m2+)+d/cos+1.51:錨桿錨頭中點(diǎn)到基坑底面的距離2：基坑內(nèi)外側(cè)土壓力等值的點(diǎn)第一排錨桿的自由端長(zhǎng)度：lf1(5.1+3.2-tan30°)(sin45°-6.44)sin(45°+12.88°2+30°)+1/cos30°+1.5lf17.48mlf1=8m第二排錨桿的自由端長(zhǎng)度：lf2(2.5+3.2-tan30°)(sin45°-6.44)sin(45

29、6;+12.88°2+30°)+1/cos30°+1.5lf25.86mlf2=6m8.3 錨桿固定端長(zhǎng)度：RKKtNKKt:錨桿抗拔安全系數(shù)（1.6） NK：錨桿軸向拉力標(biāo)準(zhǔn)值 RK：極限抗拔承載力特征值RK=dqsiklid:錨固體直徑（150mm）qsik：錨固體與第i層土的極限粘結(jié)強(qiáng)度標(biāo)準(zhǔn)值。li：錨桿的錨固段在第i層中的長(zhǎng)度。11.3.1）第一排錨桿：RK1KtNK=1.6x95.52cos30°x2=351.34kpaRK1=dqsikli=0.15x30li8sin30°=4m，因，錨桿錨固段在填土中的長(zhǎng)度為ld1=8.3-8si

30、n30°sin30°=8.6mld2=1.8sin30°=3.6mRK1=0.15x(8.6x30+60x3.6+100ld3) 得ld3=2.72m所以，第一排錨桿的錨固長(zhǎng)度為8.6+3.6+2.7=14.9m113.2）第二排錨桿：RK2KtNK=1.6x152.37cos30°x2=560.44kpa6sin30°=3m,第二排錨桿錨固段在填土中的長(zhǎng)度：ld1=5.8-6sin30°sin30°=5.6m第二排錨桿錨固段在第二層土中的錨固長(zhǎng)度：ld2=1.8sin30°=3.6mRK2=0.15x(5.6x3

31、0+60x3.6+100ld3) 得ld3=8.06m所以，第一排錨桿的錨固長(zhǎng)度為5.6+3.6+8.06=17.26m第一排錨桿總長(zhǎng)度L1=14.9+8=22.9m，設(shè)計(jì)長(zhǎng)度23m第二排錨桿總長(zhǎng)度L2=6+17.26=23.26m，錨桿長(zhǎng)度取23.5m，設(shè)計(jì)長(zhǎng)度24m.九）樁身設(shè)計(jì)：已知單位寬度最大的彎矩M=251.75kpa,支護(hù)樁直徑D=1.0m，樁間距2.0m,選用C30混凝土，基坑為一級(jí)支護(hù)基坑。樁身彎矩設(shè)計(jì)值M=0rFMsh=1.1x1.25x251.75x2=692.31kpa混凝土強(qiáng)度設(shè)計(jì)值：fc=14.3N/mm2,鋼筋強(qiáng)度設(shè)計(jì)值：fy=360N/mm2支護(hù)樁的截面積：A=d2=3.14x5002=785000mm2, 混凝土面層厚度50mm2，主筋所在的半徑rs=450mm.s=M/(fc × A × r)=692310000/(14.3x785000x450)=0.137查表可得，rs=0.923,=0.148As= (× fc ×A)/ fy=(0.148x14.4x785000)/360=4614.93mm2初步設(shè)計(jì)13根直徑22mm的HRB400鋼筋。主筋面積為4941.3mm2As=十）樁錨設(shè)計(jì)驗(yàn)算：抗傾覆安全系數(shù)