方位角的相关性对隧道贯通横向误差预计中的应用

Correlation of Azimuth Angle of Plane Control Network Outside the Hole Study on the Influence of Tunnel Transversal Error Prediction

首先利用洞外平面控制网方位角相关性,建立隧道贯通横向误差预计公式。其次利用二次函数极大极小值原理推导出该公式计算结果是绝对误差预计公式计算结果的0~1.732倍,在不考虑洞内测量误差的情况下,洞外两边起测边方位角如果正相关则扩大隧道贯通横向误差,负相关则降低甚至可能完全相互抵消。最后通过该误差预计公式可以计算出使得横向中误差取得最小值的两端掘进距离即最佳贯通位置。结果表明,在建立洞外平面控制网后,选择组合起始方位边,能更科学准确地进行误差预计和获取最佳贯通位置。

Firstly,the prediction formula of tunnel transversal error considering the correlation of azimuth angles of the two initial sides of the control network outside the tunnel is established.By using the principle of maximum and minimum value of quadratic function,it is deduced that the calculation result of this formula is 0 to 1.732 times of the calculation result of the absolute error prediction formula.If the initial azimuth angle is positively correlated,the transverse error of tunnel penetration will be enlarged,while the negative correlation will decrease or even cancel each other completely.Secondly,the error prediction formula can be used to calculate the minimum value of the transverse median error.Finally,an example is given to show that the prediction error and the optimum through-through position can be more scientifically and accurately determined by selecting the initial azimuth of the combination after the control network is established.