整合公路平面與縱斷線形幾何設計最佳化之研究

Abstract

公路之設計過程中常缺乏以符合成本最佳化設計，一般設計皆是先由踏勘、初測、定測，然後依照工程師經驗以符合設計速度之幾何設計規範設計，故需要花費大量的人工不斷的修正，以期能達到最好的設計。而在地勢起伏的丘陵與山嶺區公路幾何設計之過程複雜及需要大量數據運算，相當費時、費力、費資，且由於設計工作複雜，以人工設計能滿足規範設計已屬不易，尚無法運用有效的系統方法設計出成本最佳化設計。而一般幾何設計規範皆以平面座標觀點規定平面線型之直線、緩和曲線、圓曲線、超高、曲線半徑、設計速度與縱坡度之凸豎曲線、凹豎曲線規範，至於平面與縱斷線形立體之整合觀點，目前只有定性方面的描述，且一般也常被設計者所忽略。因此本研究以整合平面線形與縱斷線形觀點，以達到行車安全及視覺下，構建數學規劃模式，求解整合成本最佳化問題，以達到路工費用、行車與養護費成本最小化的目標。 本研究將考慮行車視距、行車速率、超高、摩擦力、平曲線半徑、緩和曲線、縱坡度、豎曲線參數為因素，納入公路平面線形與縱斷線形之限制範圍，例如最大縱坡度、曲線關係、切線轉點與縱坡度變化點關係、最短視距、豎曲線最小縱坡、最大超高、設計速率等，而整合公路平面線形與縱斷線形之成本最佳化設計，並以工程成本、行車成本及養護成本最小化為目標。最後推導出定量限制與目標式數學規劃模式，利用現有套裝程式Lingo於Pentum電腦WindowNT系統下進行修正單純法求解。並應用Surfer6套裝程式進行三度空間（3-D）繪製公路立體圖。經由本研究可建立起一套有系統的符合平面及縱斷線形之幾何設計模式，有效精簡人力、物力、財力，以達到成本最佳化的目的。本模式先以例題測試可用性後，再以公路設計實例進行實測分析。

Designing highway procedure usually lack of accomplishing optimal cost design. It always previously apply reconnaissance, preliminary survey, final location survey, then according it's designing velocity and geometry specification to design highway by engineer experience. Therefore it must consume amount of labor to revise, expecting to achieve best designation. Because of mountainous and hilly terrain contenting up and down topography, so it needs complex geometry designation and a mount of data to calculate. It wastes of time, labor and money. Due to geometry designation and specification viewing 2-dimention space concepts of horizontal alignment (line, transition curve, curve), super elevation, radius, designing velocity and vertical alignment (crest and sag curve), 3-dimention space design only qualify statement, none of quantitative analysis and guideline. In this research, on the circumstance of driving and view safety , we coordinate horizontal and vertical 3-dimention space to lay out highway earthwork designation and formulate mathematical models in order to optimizing achieve the minimum cost of earthwork、retaining wall、operation and maintain goal. In considering of sight distance, speed, super elevation, friction, curve radium, transition, grade line, crest parameters elements, we contain horizontal and vertical alignment restraints, ex., maximum grade line, curve relationship, tangent transitional point, grade line variation point relationship, minimum sight distance, vertical alignment minimum gradient, maximum super elevation etc.. Finally we formulate certain object and constraint mathematical models and make use of lingo program under window NT system by revised simplex method, 3-d graph by sufer6 program. This research can establish available coordinating horizontal and vertical alignment geometric model, efficiently condense labor, material, goods, to achieve optimal cost objection. This model firstly test by example in order to regard it's practice, then we apply practical designing highway case to practical analysis.