悬臂支护结构设计计算书钢板桩Word文件下载.docx
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是
粉砂
12.3
18.5
3
28
22
3.6
21
6
3、荷载参数
类型
荷载q(kpa)
距支护边缘的水平距离a(m)
垂直基坑边的分布宽度b(m)
平行基坑边的分布长度l(m)
作用深度d(m)
满布荷载
1.5
/
条形局部荷载
0.75
矩形局部荷载
4、计算系数
结构重要性系数γ0
0.9
综合分项系数γF
嵌固稳定安全系数Ke
1.2
圆弧滑动稳定安全系数Ks
1.25
流土稳定性安全系数Kf
1.4
二、土压力计算
土压力分布示意图
附加荷载布置图
1、主动土压力计算
1)主动土压力系数
Ka1=tan2(45°
-φ1/2)=tan2(45-20/2)=0.49;
Ka2=tan2(45°
-φ2/2)=tan2(45-20/2)=0.49;
Ka3=tan2(45°
-φ3/2)=tan2(45-20/2)=0.49;
Ka4=tan2(45°
-φ4/2)=tan2(45-28/2)=0.361;
Ka5=tan2(45°
-φ5/2)=tan2(45-28/2)=0.361;
Ka6=tan2(45°
-φ6/2)=tan2(45-28/2)=0.361;
2)土压力、地下水产生的水平荷载
第1层土:
0-0.7m
H1'
=[∑γ0h0+∑q1]/γi=[0+1.5]/18=0.083m
Pak1上=γ1H1'
Ka1-2c1Ka10.5=18×
0.083×
0.49-2×
2×
0.490.5=-2.068kN/m2
Pak1下=γ1(h1+H1'
)Ka1-2c1Ka10.5=18×
(0.7+0.083)×
0.490.5=4.106kN/m2
第2层土:
0.7-2m
H2'
=[∑γ1h1+∑q1]/γsati=[12.6+1.5]/20=0.705m
Pak2上=[γsat2H2'
-γw(∑h1-ha)]Ka2-2c2Ka20.5+γw(∑h1-ha)=[20×
0.705-10×
(0.7-0.7)]×
0.490.5+10×
(0.7-0.7)=4.109kN/m2
Pak2下=[γsat2(H2'
+h2)-γw(∑h1-ha)]Ka2-2c2Ka20.5+γw(∑h1-ha)=[20×
(0.705+1.3)-10×
(2-0.7)]×
(2-0.7)=23.479kN/m2
第3层土:
2-3.1m
H3'
=[∑γ2h2+∑q1+∑q1b1/(b1+2a1)]/γsati=[38.6+1.5+0]/20=2.005m
Pak3上=[γsat3H3'
-γw(∑h2-ha)]Ka3-2c3Ka30.5+γw(∑h2-ha)=[20×
2.005-10×
Pak3下=[γsat3(H3'
+h3)-γw(∑h2-ha)]Ka3-2c3Ka30.5+γw(∑h2-ha)=[20×
(2.005+1.1)-10×
(3.1-0.7)]×
(3.1-0.7)=39.869kN/m2
第4层土:
3.1-5m
H4'
=[∑γ3h3+∑q1+∑q1b1/(b1+2a1)]/γsati=[60.6+1.5+0]/22=2.823m
Pak4上=[γsat4H4'
-γw(∑h3-ha)]Ka4-2c4Ka40.5+γw(∑h3-ha)=[22×
2.823-10×
0.361-2×
3×
0.3610.5+10×
(3.1-0.7)=34.151kN/m2
Pak4下=[γsat4(H4'
+h4)-γw(∑h3-ha)]Ka4-2c4Ka40.5+γw(∑h3-ha)=[22×
(2.823+1.9)-10×
(5-0.7)]×
(5-0.7)=61.382kN/m2
第5层土:
5-6m
H5'
=[∑γ4h4+∑q1+∑q1b1/(b1+2a1)+∑q1b1l1/((b1+2a1)(l1+2a1)]/γsati=[102.4+1.5+0+0]/22=4.723m
Pak5上=[γsat5H5'
-γw(∑h4-ha)]Ka5-2c5Ka50.5+γw(∑h4-ha)=[22×
4.723-10×
Pak5下=[γsat5(H5'
+h5)-γw(∑h4-ha)]Ka5-2c5Ka50.5+γw(∑h4-ha)=[22×
(4.723+1)-10×
(6-0.7)]×
(6-0.7)=75.714kN/m2
第6层土:
6-13m
H6'
=[∑γ5h5+∑q1+∑q1b1l1/((b1+2a1)(l1+2a1)]/γsati=[124.4+1.5+0]/22=5.723m
Pak6上=[γsat6H6'
-γw(∑h5-ha)]Ka6-2c6Ka60.5+γw(∑h5-ha)=[22×
5.723-10×
Pak6下=[γsat6(H6'
+h6)-γw(∑h5-ha)]Ka6-2c6Ka60.5+γw(∑h5-ha)=[22×
(5.723+7)-10×
(13-0.7)]×
(13-0.7)=176.038kN/m2
3)水平荷载
临界深度:
Z0=Pak1下h1/(Pak1上+Pak1下)=4.106×
0.7/(2.068+4.106)=0.466m;
第1层土
Eak1=0.5Pak1下Z0ba=0.5×
4.106×
0.466×
0.001=0.001kN;
aa1=Z0/3+∑h2=0.466/3+12.3=12.455m;
第2层土
Eak2=h2(Pa2上+Pa2下)ba/2=1.3×
(4.109+23.479)×
0.001/2=0.018kN;
aa2=h2(2Pa2上+Pa2下)/(3Pa2上+3Pa2下)+∑h3=1.3×
(2×
4.109+23.479)/(3×
4.109+3×
23.479)+11=11.498m;
第3层土
Eak3=h3(Pa3上+Pa3下)ba/2=1.1×
(23.479+39.869)×
0.001/2=0.035kN;
aa3=h3(2Pa3上+Pa3下)/(3Pa3上+3Pa3下)+∑h4=1.1×
23.479+39.869)/(3×
23.479+3×
39.869)+9.9=10.403m;
第4层土
Eak4=h4(Pa4上+Pa4下)ba/2=1.9×
(34.151+61.382)×
0.001/2=0.091kN;
aa4=h4(2Pa4上+Pa4下)/(3Pa4上+3Pa4下)+∑h5=1.9×
34.151+61.382)/(3×
34.151+3×
61.382)+8=8.86m;
第5层土
Eak5=h5(Pa5上+Pa5下)ba/2=1×
(61.382+75.714)×
0.001/2=0.069kN;
aa5=h5(2Pa5上+Pa5下)/(3Pa5上+3Pa5下)+∑h6=1×
61.382+75.714)/(3×
61.382+3×
75.714)+7=7.483m;
第6层土
Eak6=h6(Pa6上+Pa6下)ba/2=7×
(75.714+176.038)×
0.001/2=0.881kN;
aa6=h6(2Pa6上+Pa6下)/(3Pa6上+3Pa6下)=7×
75.714+176.038)/(3×
75.714+3×
176.038)=3.035m;
土压力合力:
Eak=ΣEaki=0.001+0.018+0.035+0.091+0.069+0.881=1.095kN;
合力作用点:
aa=Σ(aaiEaki)/Eak=(12.455×
0.001+11.498×
0.018+10.403×
0.035+8.86×
0.091+7.483×
0.069+3.035×
0.881)/1.095=4.183m;
2、被动土压力计算
1)被动土压力系数
Kp1=tan2(45°
+φ1/2)=tan2(45+28/2)=2.77;
Kp2=tan2(45°
+φ2/2)=tan2(45+28/2)=2.77;
4.5-11.3m
=[∑γ0h0]/γi=[0]/18.5=0m
Ppk1上=γ1H1'
Kp1+2c1Kp10.5=18.5×
0×
2.77+2×
2.770.5=9.986kN/m2
Ppk1下=γ1(h1+H1'
)Kp1+2c1Kp10.5=18.5×
(6.8+0)×
2.770.5=358.452kN/m2
11.3-13m
=[∑γ1h1]/γsati=[125.8]/22=5.718m
Ppk2上=[γsat2H2'
-γw(∑h1-hp)]Kp2+2c2Kp20.5+γw(∑h1-hp)=[22×
5.718-10×
(6.8-6.8)]×
2.770.5+10×
(6.8-6.8)=358.441kN/m2
Ppk2下=[γsat2(H2'
+h2)-γw(∑h1-hp)]Kp2+2c2Kp20.5+γw(∑h1-hp)=[22×
(5.718+1.7)-10×
(8.5-6.8)]×
(8.5-6.8)=431.949kN/m2
Epk1=bah1(Pp1上+Pp1下)/2=0.001×
6.8×
(9.986+358.452)/2=1.253kN;
ap1=h1(2Pp1上+Pp1下)/(3Pp1上+3Pp1下)+∑h2=6.8×
9.986+358.452)/(3×
9.986+3×
358.452)+1.7=4.028m;
Epk2=bah2(Pp2上+Pp2下)/2=0.001×
1.7×
(358.441+431.949)/2=0.672kN;
ap2=h2(2Pp2上+Pp2下)/(3Pp2上+3Pp2下)=1.7×
358.441+431.949)/(3×
358.441+3×
431.949)=0.824m;
Epk=ΣEpki=1.253+0.672=1.925kN;
ap=Σ(apiEpki)/Epk=(4.028×
1.253+0.824×
0.672)/1.925=2.91m;
3、基坑内侧土反力计算
-φ1/2)=tan2(45-28/2)=0.361;
-φ2/2)=tan2(45-28/2)=0.361;
Psk1上=(0.2φ12-φ1+c1)∑h0(1-∑h0/ld)υ/υb+γ1H1'
Ka1=(0.2×
282-28+3)×
(1-0/8.5)×
0.005/0.01+18.5×
0.361=0kN/m2
Psk1下=(0.2φ12-φ1+c1)∑h1(1-∑h1/ld)υ/υb+γ1(h1+H1'
)Ka1=(0.2×
(1-6.8/8.5)×
(0+6.8)×
0.361=135.038kN/m2
Psk2上=(0.2φ22-φ2+c2)∑h1(1-∑h1/ld)υ/υb+[γsat2H2'
-γw(∑h1-hp)]Kp2+γw(∑h1-hp)=(0.2×
5/10+[22×
0.361+10×
(6.8-6.8)=135.036kN/m2
Psk2下=(0.2φ22-φ2+c2)∑h2(1-∑h2/ld)υ/υb+[γsat2(H2'
+h2)-γw(∑h2-hp)]Kp2+γw(∑h2-hp)=(0.2×
8.5×
(1-8.5/8.5)×
(8.5-6.8)=69.777kN/m2
Psk1=b0h1(Ps1上+Ps1下)/2=0.001×
(0+135.038)/2=0.459kN;
as1=h1(2Ps1上+Ps1下)/(3Ps1上+3Ps1下)+∑h2=6.8×
0+135.038)/(3×
0+3×
135.038)+1.7=3.967m;
Psk2=b0h2(Ps2上+Ps2下)/2=0.001×
(135.036+69.777)/2=0.174kN;
as2=h2(2Ps2上+Ps2下)/(3Ps2上+3Ps2下)=1.7×
135.036+69.777)/(3×
135.036+3×
69.777)=0.94m;
Ppk=ΣPpki=0.459+0.174=0.633kN;
as=Σ(asiPski)/Ppk=(3.967×
0.459+0.94×
0.174)/0.633=3.135m;
Psk=0.633kN≤Ep=1.925kN
满足要求!
三、稳定性验算
1、嵌固稳定性验算
Epkapl/(Eakaal)=1.925×
2.91/(1.095×
4.183)=1.223≥Ke=1.2
2、整体滑动稳定性验算
圆弧滑动条分法示意图
Ksi=∑{cjlj+[(qjbj+ΔGj)cosθj-μjlj]tanφj}/∑(qjbj+ΔGj)sinθ
cj、φj──第j土条滑弧面处土的粘聚力(kPa)、内摩擦角(°
);
bj──第j土条的宽度(m);
θj──第j土条滑弧面中点处的法线与垂直面的夹角(°
lj──第j土条的滑弧段长度(m),取lj=bj/cosθj;
qj──作用在第j土条上的附加分布荷载标准值(kPa);
ΔGj──第j土条的自重(kN),按天然重度计算;
uj──第j土条在滑弧面上的孔隙水压力(kPa),采用落底式截水帷幕时,对地下水位以下的砂土、碎石土、粉土,在基坑外侧,可取uj=γwhwaj,在基坑内侧,可取uj=γwhwpj;
滑弧面在地下水位以上或对地下水位以下的粘性土,取uj=0;
γw──地下水重度(kN/m3);
hwaj──基坑外侧第j土条滑弧面中点的压力水头(m);
hwpj──基坑内侧第j土条滑弧面中点的压力水头(m);
min{Ks1,Ks2,……,Ksi,……}=-0.389<
Ks=1.25
不满足要求,增加支挡构件的嵌固深度或选用其它支挡形式!
3、渗透稳定性验算
渗透稳定性简图
匀质含水层中,地下水渗流的稳定性验算:
∑γ'
=∑(γsati-γw)hi/H=[(18-10)×
0.7+(18-10)×
2.4+(22-10)×
1.4]/4.5=9.244
(2ld+0.8D1)∑γ`/(Δhγw)=(2×
8.5+0.8×
0.5)×
9.244/(5×
10)=3.217
(2ld+0.8D1)∑γ`/(Δhγw)=3.217≥Kf=1.4
四、结构计算
1、材料参数
钢桩类型
钢板
钢桩型号
400×
170×
15.5
钢材的惯性矩I(cm4)
4670
钢材的截面抵抗矩W(cm3)
362
钢材的弹性模量E(N/mm2)
20600
钢材的抗弯强度设计值f(N/mm2)
205
钢材的抗剪强度设计值τ(N/mm2)
125
材料截面塑性发展系数γ
1.05
2、支护桩的受力简图
计算简图
弯矩图(kN·
m)
Mk=2.591kN.m
剪力图(kN)
Vk=0.64kN
3、强度设计值确定
M=γ0γFMk=0.9×
0.9×
2.591=2.099kN·
m
V=γ0γFVk=0.9×
0.64=0.518kN
4、材料的强度计算
σmax=M/(γW)=2.099×
106/(1.05×
362×
103)=5.522N/mm2≤[f]=205N/mm2
H`=(WH2-(H-t)2(W-2t))/(2(WH-(H-t)(W-2t))=(400×
1702-(170-15.5)2(400-2×
15.5))/(2(400×
170-(170-15.5)(400-2×
15.5))=125mm
S=t(H-H`)2=15.5×
(170-125)2=31388mm3,
τmax=VS/It=0.518×
31388×
103/(4670×
104×
15.5)=0.022N/mm2≤[f]=125N/mm2
结论和建议:
1.不满足要求,增加支挡构件的嵌固深度或选用其它支挡形式!