某涵洞八字墙墙身计算方法

某涵洞八字墙墙身计算方法某涵洞八字墙墙身设计如下(见下图：涵洞右侧洞口前方冀墙)：涵洞与路线右交角为120°(α=90°-120°=-30°)，路基边坡m0=1.5(即1:1.5)，冀墙正截面背侧坡比n0=4(即4:1)，正截面顶宽c0=40cm，洞口截面高H=479cm，冀尾截面高h=70cm，正侧面与涵洞轴线夹角β=-20°(绕O点逆时针取负)，涵洞轴线流水坡度i=2%。相关计算如下：1.墙身计算考虑流水坡度i合成:m=m0/(1±m0i/cosα)，下游取负,m=1.5/(1+1.5*2%/cos30°)=1.4498；2.涵洞轴线冀长:L=(H-h)m/cosα=(4.79-0.7)*1.4498/cos30°=6.847m；3.洞口截面墙顶宽：c=c0/cos(β-α)=0.40/cos(-20°+30°)=0.406m；4.洞口截面墙背侧坡比:n=[n0+signβsin(β-α)/m]cos(β-α)，sign为取符号函数signβ=sign(-20°)=-1,n=[4-sin(-20°+30°)/1.4498]cos(-20°+30°)=3.8213忽略流水坡度i影响,n’=[4-sin(-20°+30°)/1.5]cos(-20°+30°)=3.82525.洞口截面底宽:a=c+H/n=0.406+4.79/3.8213=1.660m，（n’→1.658m）；6.冀尾截面底宽:b=c+h/n=0.406+0.70/3.8213=0.589m，（n’→0.588m）；7.墙身体积计算(如图中取与洞口截面平行的任一超薄dz段分析),其体积为:dV≈[(c+x)y/2]dz，其中x=c+y/n，dz=mdy代入得：dV≈[y2/2/n+cy]mdy,对y从h～H积分并整理得:V=[(H3-h3)/3/n+c(H2-h2)]m/2V=[(4.793-0.73)/3/3.8213+0.406*(4.792-0.72)]*1.4498/2=13.536m3（n’→V=13.529m3）令Lcosα=(H-h)m得:V=[(H2+Hh+h2)/3/n+c(H+h)]Lcosα/2