The right intersection angle between the culvert and the route is 120° (α=90°-120°=-30°), the roadbed slope m0=1.5 (i.e. 1:1.5), and the back-side slope ratio of the front section of the wall n0=4 (i.e. 4:1), the top width of the front section c0=40cm, the section height of the opening H=479cm, the height of the tail section h=70cm, the front and side lines turn to the culvert axis and the angle β=-20° (around point O Counterclockwise (negative), the flow slope of the culvert axis is i=2%.
The relevant calculations are as follows: 1. The wall calculation takes into account the flow slope i: m=m0/(1±m0i/cosα), which is positive in the upstream and negative in the downstream, m=1.5/(1+1.5*2%/cos30 °)=1.4498; 2. The length of the culvert axis: L=(H-h)m/cosα=(4.79-0.7)*1.4498/cos30°=6.847m; 3. The top width of the wall at the opening section: c=c0/cos(β -α)=0.40/cos(-20°+30°)=0.406m; 4. The back side slope ratio of the opening section wall: n=[nsignβsin(β-α)/m]cos(β-α), sign is the sign function signβ=sign(-20°)=-1,n=[4-sin(-20°+30°)/1.4498]cos(-20°+30°)=3.8213 Ignore the influence of the flow slope i ,n'=[4-sin(-20°+30°)/1.5]cos(-20°+30°)=3.82525. Bottom width of hole section: a=c+H/n=0.406+4.79/3.8213= 1.660m, (n'→1.658m); 6. Bottom width of Jiwei section: b=c+h/n=0.406+0.70/3.8213=0.589m, (n'→0.588m); 7. Wall volume calculation (arbitrarily take an ultra-thin dz segment parallel to the hole section for analysis, such as the shaded part of the elevation), its volume is: dV≈[(c+x)y/2]dz, where x=c+y/n, Substituting dz=mdy we get: dV≈[y2/2/n+cy]mdy, integrate y from h~H and sort it out: V=0.5[(H3-h3)/3/n+c(H2-h2) ]mV=0.5*[(4.793-0.73)/3/3.8213+0.406*(4.792-0.72)]*1.4498=13.536m3 (n'→V=13.529m3) Substitute (H-h)m=Lcosα to get: V= 0.5[(H2+Hh+h2)/3/n+c(H+h)]Lcosα