悬臂式挡土墙工程实例——成都市三环路与铁路立交工程设计路段为K23+385.728—K23+486.726右幅快车道；已知，填方最大高度5米，地基承载力设计值=150kpa,墙身设计高度H=4m；填土标准重度=18KN/m3，填土表面均布荷载q=10KN/m2,填土内摩擦角Φ=35。,底板与地基摩擦系数f=0.3,墙身采用C20混凝土，HRB335钢筋。一、截面选择选择悬臂式挡土墙。尺寸按悬臂式挡土墙规定初步拟定，如图所示根据规范要求H1=110H=400mm,H2=H-H1=3600mm,H0=810mm,b=250mm,B=0.8H=3200mm；地面活荷载q的作用，采用换算立柱高：01050.55189qHrB3的初步估算：22250(810)0.05=470mmBH3201.4348.78=22300.3(40.55)1.0518rcKmExBBHmf—0.47（H+）B1=B-B3-B2=3200-2230-470=500mmA2.71KpaB20.27kpac22.22kpaq=10KpaBCDAEabc2503200223047050081040003600400图1悬臂式支挡结构计算图（单位：mm)min=71.54kpa1=97.45kpa2=102.91kpamax=108.72kpa1:0.05二、荷载计算1.土压力计算由于地面水平，墙背竖直且光滑，土压力计算选用朗金理论公式计算：2tan450.2712K地面处水平压力：A=H。*Ka=18590.271=2.71kpa悬臂底B点水平压力：B=(H。+H2)Ka=18(59+3.6)0.271=20.27kpa底板c点水平压力：c=(H。+H2+H1)Ka=18(59+3.6+0.4)0.271=22.22kpa土压力及合力作用点位置：Ea1=AH2=2.713.6=9.76KN/m；Za1=22H+H1=2.2mEa2=12(B-A)H=12（20.27-2.71）3.6=31.61KN/m；Za2=13H2+H1=1.6mEa3=12(c-A)H=12(22.22-2.71)4=39.02KN/m；Za3=13（H1+H2）=1.333m2．竖向荷载计算（1）立臂自重力钢筋混凝土标准容重γk＝25kN/m3，其自重力G1k=0.2502.47(3.6+0.81)25=39.69KN/mX1=0.5+0.224.410.50.22230.254.41(0.22+0.125)(0.50.224.41+0.254.41)=0.7844m（2）底板自重力G2k=(0.5+0.47+2.23)0.425=32KN/mX2=3.22=1.6m（3）地面均布活载及填土的自重力G3k=(q+γH2)B1=(10+183.6)2.23=166.81KN/mX3=0.5+0.47+2.232=2.085m三、抗倾覆稳定验算稳定力矩112233xkkkkMGxGxGx=39.690.7844+321.6+166.812.085=430.13KN*m/m倾覆力矩Mqk=Ea1*Za1+Ea3*Za3=9.672.2+39.021.333=73.49KN*m/m0430.135.8573.9.541xkqkMKM故稳定四、抗滑稳定验算竖向力之和Gk=Gik=39.69+32+166.81=238.50KN/m抗滑力Ff=Gk*f=238.500.3=71.55KN/m滑移力E=Ea1+Ea3=9.76+39.02=48.78KN/m71.5548.781.471.3kcGfKE故稳定五、地基承载力验算地基承载力采用设计荷载，分项系数：地面活荷载r1＝1.30；土荷载r2＝1.20；自重r3＝1.20。基础底面偏心距e0，先计算总竖向力到墙趾的距离：0VHkMMeGMH=1.3Ea1*Za1+1.Ea3*Za3=1.39.762.2+1.239.021.333e0=90.33KN/mGk=1.2(39.69+32+183.62.232.085)=288.42KN/mMv=1.2(39.690.7844+321.6+183.62.232.085)+1.3（102.232.085）=520.79KN*m/m偏心距e=520.7990.33288.42=1.49m=2B-e=3.22-1.49=0.11m<6B=0.53m地基压力max=6e(1+)GkBB=288.423.2(1+60.113.2)=108.72kpamin=6e(1)GkBB=288.423.2(1-60.113.2)=71.54kpamax=108.72<=150kpa故地基承载力满足要求.六、结构设计立臂与底板均采用C20混凝土和HRB335级钢筋，查表得fcd＝9.2Mpa，ftd＝1.06Mpa，ftk=1.54Mpa,Ec=2.55104Mpa,fsd＝280Mpa，f1sd=280Mpa,Es＝2×105Mpa（1）立臂设计底截面设计弯矩M=1.39.763.62+1.231.613.63=68.36KN*m/m标准弯矩Mk=9.763.62+31.613.63=55.50KN*m/m有效高度h0=250-30=220mm由fcd*b*X=fsd*As得X=2809.0(200)1As=0.03As其中混凝土保护层厚度C=30mmM=fsd*As*(250-30-2X)代入化简得：0.0152A2s-220As+244143=0即As=13257mm2（舍），As=1217mm2取16@165钢筋，As=1219mm2裂缝验算ststsAA=12190.0098,=0.010.51000250stststsAA取6055.50102380.870.872201219ksksMMpahA0.650.651.541.101.100.680.01238tktsskf最大裂缝宽度2.10,30,16crcqacmmdmmmaxmax51.90.08238162.10.681.9300.080.310.202100.01cqskcrstsdwacEwmmmm不满足，改用16@125钢筋，As=1609mm216090.0130.5100250ts655.50101800.872201609skMpa0.651.541.100.670.013180max5180162.10.671.9300.080.190.202100.013wmmmm故裂缝宽度满足要求墙踵板根部D点设计弯矩：2.232.232.232.230.4251.2182.233.61.2102.231.302222.2312....
