土方方格网计算公式图示及推导

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1、方格网土方计算公式推导：1、两点开挖工程量计算公式：如上图示：d=A*h2/(h1+h2);e=A*h3/(h3+h4);S1=d*h2/2;S2=e*h3/2S0=(d+e)/2*(h2+h3)/2/2根据拟柱体体积计算公式：V=B/6*(S1+4*S0+S2)将上面已知数代入公式可得：V=B/6*{A*h2/(h1+h2)*h2/2+4*[A*h2/(h1+h2)+A*h3/(h3+h4)]/2*(h2+h3)/2/2+h3*A*h3/(h3+h4)/2}=A*B/6*{h2*h2/(h1+h2)+h2*

2、(h2+h3)/(h1+h2)+h3*(h2+h3)/(h3+h4)+h3*h3/(h3+h4)}/2=A*B/12*{(2h2^2+h2*h3)/(h1+h2)+(2*h3^2+h2*h3)/(h3+h4)}2、三点开挖的挖方量计算公式：由图分解可得，挖方体积=v1+v2-(v3-v4),由拟柱体体积计算公式可以得出：V1={A*(h3+h4)/2+4*A/2*(h3+h2+h2+h4)/4}*B/6=A*B/12*{h3+h4+2*h2+h3+h4}=A*B*(h2+h3+h4)/6V2、V3、V4分别按

3、四棱锥、三棱锥、三棱锥体积计算公式进行计算（体积=底面积*高/3）V2=[√(A^2+B^2)]*1/2*1/3*[√(A^2+B^2)]*(h2+h4)/2=(A^2+B^2)*(h2+h4)/12V3=A*B/2/3*h1=A*B*h1/6V4=h1/3*(B*h1/(h1+h4)*A*h1/(h1+h2)/2=A*B/6*h1^3/(h1+h2)/(h1+h4)V=V1+V2-V3+V4=A*B*(h2+h3+h4)/6+(A^2+B^2)*(h2+h4)/6+A*B/6*h1^2/(h1+h2)/(h

4、1+h4)-A*B*h1/6=A*B/6*[h2+h3+h4-h1+h1^3/(h1+h2)/(h1+h4)]+(A^2+B^2)*(h2+h4)/123、不机邻两点回填方量计算公式推导：如图示：从h1和h3处将图形分成平面为两个直角三角形体：h4侧的体积公式如下：Vh4=V1+V3-V2根据锥体体积公式：底面积*高/3可得V1=(h1+h3)/2*[√(A^2+B^2)]/3*[√(A^2+B^2)]/2=(h1+h3)*(A^2+B^2)/12V2=A*B/2*h4/3=A*B*h4/6V3=h4/3*(

5、B*h4/(h4+h1)*A*h4/(h4+h3)/2=A*B/6*h4^3/(h4+h1)/(h4+h3)V=(h1+h3)*(A^2+B^2)/12-A*B*h4/6+A*B/6*h4^3/(h4+h1)/(h4+h3)=A*B/6*[h4^3/(h4+h1)/(h4+h3)-h4]+(h1+h3)*(A^2+B^2)/12h2侧的体积公式推导方法h4侧的体积公式：Vh2=A*B/6*[h2^3/(h2+h1)/(h2+h3)-h2]+(h1+h3)*(A^2+B^2)/12V=Vh2+Vh4=A*B/6

6、*[h2^3/(h2+h1)/(h2+h3)-h2]+(h1+h3)*(A^2+B^2)/12+A*B/6*[h4^3/(h4+h1)/(h4+h3)-h4]+(h1+h3)*(A^2+B^2)/12=A*B/6*[h2^3/(h2+h1)/(h2+h3)+h4^3/(h4+h1)/(h4+h3)-h2-h4]+(h1+h3)*(A^2+B^2)/6