挡墙受力计算Word文件下载.docx
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挡墙受力计算Word文件下载.docx
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黏聚力c(kpa)
内摩擦角φ(°
)
饱和土重度γsat(kN/m3)
水土合算
1
碎石土
18
10
15
否
2
粘性土
19
8
21
是
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
/
条形局部荷载
4、计算系数
结构重要性系数γ0
综合分项系数γF
1.25
圆弧滑动稳定安全系数Ks
1.3
抗滑移安全系数Ksl
1.2
抗倾覆安全系数Kov
抗隆起安全系数Kb
1.4
经验系数ηb
0.8
突涌稳定安全系数Kh
墙体材料的抗剪断系数μ
0.5
二、土压力计算
1、主动土压力计算
1)主动土压力系数
Ka1=tan2(45°
-φ1/2)=tan2(45-15/2)=0.589;
Ka2=tan2(45°
-φ2/2)=tan2(45-15/2)=0.589;
Ka3=tan2(45°
-φ3/2)=tan2(45-20/2)=0.49;
2)土压力、地下水产生的水平荷载
第1层土:
0-3.5m
H1'
=[∑γ0h0+∑q1]/γ1=[0+3]/18=0.167m
Pak1上=γ1H1'
Ka1-2c1Ka10.5=18×
0.167×
0.589-2×
10×
0.5890.5=-13.579kN/m2
Pak1下=γ1(h1+H1'
)Ka1-2c1Ka10.5=18×
(3.5+0.167)×
0.5890.5=23.528kN/m2
第2层土:
3.5-4m
H2'
=[∑γ1h1+∑q1]/γsat2=[63+3]/20=3.3m
Pak2上=γsat2H2'
Ka2-2c2Ka20.5=20×
3.3×
0.5890.5=23.525kN/m2
Pak2下=γsat2(h2+H2'
)Ka2-2c2Ka20.5=20×
(0.5+3.3)×
0.5890.5=29.415kN/m2
第3层土:
4-9.9m
H3'
=[∑γ2h2+∑q1+∑q1b1/(b1+2a1)]/γsat3=[73+3+1.167]/21=3.675m
Pak3上=[γsat3H3'
-γw(∑h2-ha)]Ka3-2c3Ka30.5+γw(∑h2-ha)=[21×
3.675-10×
(4-3.5)]×
0.49-2×
8×
0.490.5+10×
(4-3.5)=29.166kN/m2
Pak3下=[γsat3(H3'
+h3)-γw(∑h3-ha)]Ka3-2c3Ka30.5+γw(∑h2-ha)=[21×
(3.675+5.9)-10×
(9.9-3.5)]×
(9.9-3.5)=119.967kN/m2
3)水平荷载
临界深度:
Z0=Pak1下h1/(Pak1上+Pak1下)=23.528×
3.5/(13.579+23.528)=2.219m;
第1层土
Eak1=0.5Pak1下Z0×
1=0.5×
23.528×
2.219×
1=26.104kN;
aa1=Z0/3+∑h2=2.219/3+6.4=7.14m;
第2层土
Eak2=h2(Pa2上+Pa2下)×
1/2=0.5×
(23.525+29.415)×
1/2=13.235kN;
aa2=h2(2Pa2上+Pa2下)/(3Pa2上+3Pa2下)+∑h3=0.5×
(2×
23.525+29.415)/(3×
23.525+3×
29.415)+5.9=6.141m;
第3层土
Eak3=h3(Pa3上+Pa3下)×
1/2=5.9×
(29.166+119.967)×
1/2=439.942kN;
aa3=h3(2Pa3上+Pa3下)/(3Pa3上+3Pa3下)=5.9×
29.166+119.967)/(3×
29.166+3×
119.967)=2.351m;
土压力合力:
Eak=ΣEaki=26.104+13.235+439.942=479.281kN;
合力作用点:
aa=Σ(aaiEaki)/Eak=(7.14×
26.104+6.141×
13.235+2.351×
439.942)/479.281=2.716m;
2、被动土压力计算
1)被动土压力系数
Kp1=tan2(45°
+φ1/2)=tan2(45+15/2)=1.698;
Kp2=tan2(45°
+φ2/2)=tan2(45+20/2)=2.04;
Kp3=tan2(45°
+φ3/2)=tan2(45+20/2)=2.04;
3.9-4m
=[∑γ0h0]/γ1=[0]/18=0m
Ppk1上=γ1H1'
Kp1+2c1Kp10.5=18×
0×
1.698+2×
1.6980.5=26.061kN/m2
Ppk1下=γ1(hi+H1'
)Kp1+2c1Kp10.5=18×
(0.1+0)×
1.6980.5=29.118kN/m2
4-6.9m
=[∑γ1h1]/γ2=[1.8]/19=0.095m
Ppk2上=γ2H2'
Kp2+2c2Kp20.5=19×
0.095×
2.04+2×
2.040.5=26.535kN/m2
Ppk2下=γ2(hi+H2'
)Kp2+2c2Kp20.5=19×
(2.9+0.095)×
2.040.5=138.939kN/m2
6.9-9.9m
=[∑γ2h2]/γsat3=[56.9]/21=2.71m
Ppk3上=[γsat3H3'
-γw(∑h2-hp)]Kp3+2c3Kp30.5+γw(∑h2-hp)=[21×
2.71-10×
(3-3)]×
2.040.5+10×
(3-3)=138.949kN/m2
Ppk3下=[γsat3(H3'
+h3)-γw(∑h3-hp)]Kp3+2c3Kp30.5+γw(∑h2-hp)=[21×
(2.71+3)-10×
(6-3)]×
(6-3)=236.269kN/m2
Epk1=1×
h1(Pp1上+Pp1下)/2=1×
0.1×
(26.061+29.118)/2=2.759kN;
ap1=h1(2Pp1上+Pp1下)/(3Pp1上+3Pp1下)+∑h2=0.1×
26.061+29.118)/(3×
26.061+3×
29.118)+5.9=5.949m;
Epk2=1×
h2(Pp2上+Pp2下)/2=1×
2.9×
(26.535+138.939)/2=239.937kN;
ap2=h2(2Pp2上+Pp2下)/(3Pp2上+3Pp2下)+∑h3=2.9×
26.535+138.939)/(3×
26.535+3×
138.939)+3=4.122m;
Epk3=1×
h3(Pp3上+Pp3下)/2=1×
3×
(138.949+236.269)/2=562.827kN;
ap3=h3(2Pp3上+Pp3下)/(3Pp3上+3Pp3下)=3×
138.949+236.269)/(3×
138.949+3×
236.269)=1.37m;
Epk=ΣEpki=2.759+239.937+562.827=805.523kN;
ap=Σ(apiEpki)/Epk=(5.949×
2.759+4.122×
239.937+1.37×
562.827)/805.523=2.205m;
3、基坑内侧土反力计算
Psk1上=(0.2φ12-φ1+c1)∑h0(1-∑h0/ld)υ/υb+γ1H1'
Ka1=(0.2×
152-15+10)×
(1-0/6)×
0.012/0.012+18×
1.698=0kN/m2
Psk1下=(0.2φ12-φ1+c1)∑h1(1-∑h1/ld)υ/υb+γ1(h1+H1'
)Ka1=(0.2×
(1-0.1/6)×
(0+0.1)×
1.698=6.99kN/m2
Psk2上=(0.2φ22-φ2+c2)∑h1(1-∑h1/ld)υ/υb+γ2H2'
Ka2=(0.2×
202-20+8)×
0.012/0.012+19×
2.04=10.369kN/m2
Psk2下=(0.2φ22-φ2+c2)∑h2(1-∑h2/ld)υ/υb+γ2(h2+H2'
)Ka2=(0.2×
(1-3/6)×
(0.095+2.9)×
2.04=218.086kN/m2
Psk3上=(0.2φ32-φ3+c3)∑h2(1-∑h2/ld)υ/υb+[γsat3H3'
-γw(∑h2-hp)]Kp3+γw(∑h2-hp)=(0.2×
12/12+[21×
2.04+10×
(3-3)=218.096kN/m2
Psk3下=(0.2φ32-φ3+c3)∑h3(1-∑h3/ld)υ/υb+[γsat3(H3'
+h3)-γw(∑h3-hp)]Kp3+γw(∑h3-hp)=(0.2×
6×
(1-6/6)×
(6-3)=213.416kN/m2
Psk1=b0h1(Ps1上+Ps1下)/2=1×
(0+6.99)/2=0.35kN;
as1=h1(2Ps1上+Ps1下)/(3Ps1上+3Ps1下)+∑h2=0.1×
0+6.99)/(3×
0+3×
6.99)+5.9=5.933m;
Psk2=b0h2(Ps2上+Ps2下)/2=1×
(10.369+218.086)/2=331.26kN;
as2=h2(2Ps2上+Ps2下)/(3Ps2上+3Ps2下)+∑h3=2.9×
10.369+218.086)/(3×
10.369+3×
218.086)+3=4.011m;
Psk3=b0h3(Ps3上+Ps3下)/2=1×
(218.096+213.416)/2=647.268kN;
as3=h3(2Ps3上+Ps3下)/(3Ps3上+3Ps3下)=3×
218.096+213.416)/(3×
218.096+3×
213.416)=1.505m;
Ppk=ΣPpki=0.35+331.26+647.268=978.878kN;
as=Σ(asiPski)/Ppk=(5.933×
0.35+4.011×
331.26+1.505×
647.268)/978.878=2.355m;
三、稳定性验算
1、滑移稳定性验算
滑移稳定性验算示意图
如上图所示,水泥土墙的滑移稳定性应按下式验算:
(Epk+(G-μmB)tanφ+cB)/Eak=(805.523+(653.4-47×
3.3)×
tan(20°
)+8×
3.3)/479.281=2.114≥Ksl=1.2
满足要求!
2、倾覆稳定性验算
倾覆稳定性验算示意图
如上图所示,水泥土墙的倾覆稳定性应按下式验算:
(Epkap+(G-μmB)aG)/(Eakaa)=(805.523×
2.205+(653.4-47×
1.65)/(479.281×
2.716)=1.996≥Kov=1.3
3、整体滑动稳定性验算
整体滑动稳定性验算示意图
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,……}=1.879≥Ks=1.3
4、抗隆起稳定性验算
1)水泥土墙底面处的抗隆起验算
水泥土墙底面处的抗隆起验算示意图
如上图所示,抗隆起稳定性按下式计算:
γm1=Σγihi/(h+ld)=196.9/(3.9+6)=19.889kN/m
γm2=Σγihi/ld=119.9/6=19.983kN/m
Nq=tan2(45°
+φ/2)eπtanφ=tan2(45°
+20/2)eπtan20=6.399
Nc=(Nq-1)/tanφ=(6.399-1)/tan(20)=14.834
(γm2ldNq+cNc)/(γm1(h+ld)+q0)=(19.983×
6.399+8×
14.834)/(19.889×
(3.9+6)+3.707)=4.416≥Kb=1.4
2)软弱层土的抗隆起验算
软弱层土的抗隆起验算示意图
γm1=Σγihi/(h+D0)=196.9/(3.9+6)=19.889kN/m
γm2=Σγihi/D0=119.9/6=19.983kN/m
(γm2D0Nq+cNc)/(γm1(h+D0)+q0)=(19.983×
5、渗透稳定性验算
承压水作用下的坑底突涌稳定性验算:
Dγ/(hwγw)=∑hiγi/(hwγw)=(0.1×
18+3.4×
19)/(4×
10)=1.66
Dγ/(hwγw)=1.66≥Kh=1.2
四、正截面承载力验算
取单位长度水泥土墙进行计算
1、截面弯矩计算
计算简图(kN)
弯矩图(kN·
m)
Mk=995.315kN.m
M=γ0γFMk=1×
1.25×
995.315=1244.144kN.m
剪力图(kN)
Vk=499.61kN
2、正截面应力计算
1)拉应力
6M/B2-γcsz=6×
1244.144/3.32-20×
9.9=0.487N/mm2≤0.15fcs=1.673N/mm2
2)压应力
6M/B2+γ0γFγcsz=6×
1244.144/3.32+1×
20×
9.9=0.933N/mm2≤fcs=11.15N/mm2
3)剪应力
(Eaki-μGi-Epki)/B=(479.281-0.5×
653.4-805.523)/3.3=-0.198N/mm2≤fcs/6=1.858N/mm2
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