基本型平曲线“两点法”设计计算原理

Design and Calculation Principles of the “Two-Point Method” for Basic Horizontal Curves

摘要:

为改善传统导线法存在导线与平曲线偏离较大等不足，提出“两点法”基本型平曲线形设计方法。仅需利用导线法中的直缓点与缓直点两个端点即可获得由缓和曲线及圆曲线共3段线元组成的基本型平曲线形，其平曲线总偏转角α、总切线长T为已知值。先采用迭代法确定缓和曲线长度L_S （对称基本型）或采用夹逼法获得圆曲线半径R（非对称基本型）的理论最小值、最大值，并结合平面线形技术要求确定L_S或R的设计取值范围；然后基于L_S或R进行遍历循环，通过迭代法获得缓和曲线偏转角β，进而获得各线元其余参数。研究结果表明，“两点法”设计可获得系列“平曲线族”，线形分布规律，互不交叉重叠，且全部曲线位于两端细窄、中间宽厚的“特定设计区域”；L_S、R、圆曲线长L_C及平曲线总长L_H等参数呈规律性变化，其中L_S与R、L_C的增减趋势相反，L_H平均值近似固定，非对称基本型的总切线长度之比须在（0.5，2.0）范围内方可有解。“两点法”突显坐标位置点的控制作用，线形布设高效，设计成果为特定区域内的系列平曲线族而非单条曲线，有益于结合实际地形及设计意图进行线形比选、优选和路线智能化设计。

关键词:道路工程;基本型平曲线;两点法;迭代法;平曲线族;特定设计区域;线形优选

Abstract:

To address the shortcomings of traditional traverse method such as significant deviation between the traverse and the horizontal curve， this paper proposes a “two-point method” for basic horizontal alignment design. It is only necessary to use the two endpoints named “point of tangent to spiral” and “point of spiral to tangent” to obtain the basic type horizontal curve family consisting of three elements including the transition curves and the circular curve. The total deflection angle （α） and total tangent length （T） of the horizontal curve family are known fixed parameters. First， the theoretical minimum and maximum values of the transition curve length （L_S） or the radius of circular curve （R） are calculated using the iterative method （for symmetric type） or squeeze theorem analysis method （for asymmetric type）， respectively. Then， the design value range of L_S or R is determined based on the technical requirements of horizontal alignment. Afterwards， the traversal cycle is performed based on L_S or R， and the corresponding deflection angle of the transition curve （β） is calculated using an iterative calculation method. Finally， the remaining parameters of each element is determined. The results indicate that， the “horizontal curve family” obtained through the “two-point method” has a regular distribution and does not overlap with each other， and all of the curves are located in “a specific design area” with narrow ends and wide-thick middle. The variation of parameters such as L_S， R， circular curve length （L_C）， and total horizontal curve length （L_H） is very regular. The increasing and decreasing of LS are opposite to those of R and L_C， while the average of L_H is approximately fixed. Furthermore， the ratio of the total tangent lengths is only solvable within the range from 0.5 to 2.0. The “two-point method” highlights the controlling role of coordinate location points， making the alignment layout efficient. The design outcome presents a series of horizontal curve families within a specific area， rather than a single curve. This is beneficial for comparing and selecting alignments based on actual topography and design intentions， thereby contributing to the advancement of intelligent route design.

Key words:road engineering;basic horizontal curve;two-point method;iterative calculation;horizontal curve family;specific design area;horizontal alignment optimization