坡面回彈係數及粗糙性於單粒落石運動軌跡之影響

The Influence of Slope Restitution Coefficient and Roughness on Moving Paths of A Single Falling Rock

林育玄(Yu-Hsuan Lin)

指導教授 ： 葛德治

中原大學/工學院/土木工程研究所/碩士(2002年)

https://doi.org/10.6840/cycu200200041

摘要

台灣是多高山及豪雨、地震頻繁之地區，尤其是在921集集大地震後，山區道路旁盡是大範圍裸落破碎之岩坡，落石 (rockfall)往往瞬間造成其運動路徑上人、車及房舍等結構物之重大損失和破壞，為了能有效經濟地解決落石問題，必需精確地推估現地落石的運動軌跡。由於現地邊坡的幾何、落石與邊坡的接觸特性及落石初始狀態皆具有變異性，使得落石運動軌跡充滿隨機性，因此使用「ROCKPATH」程式來模擬落石之運動軌跡。
本文使用以質點模式撰寫且具有Monte Carlo 模擬之能力之「ROCKPATH」程式做為主要研究工具，其可模擬單粒落石之單次和多次運動軌跡。至於參數之離散性部分，先前只能處理邊坡之接觸特性，由於地形起伏會量測不準及時空之變異性，將此視為坡面粗糙性，並將此參數功能納入『ROCKPATH』程式中，以期能使此程式有更強大模擬現地狀況之功能。
於單一斜坡落石彈跳之敏感性分析中，針對一簡單幾何之邊坡進行敏感性分析，分析回彈係數（en , et）、粗糙角i與坡角β的影響。而二階削坡落石彈跳之敏感性分析方面，針對一簡單二階削坡進行敏感性分析，分析回彈係數（en , et）、粗糙角i與削坡長度W的影響。對於單一斜坡和二階削坡之落石彈跳敏感性分析，所得結果顯示：1) 不論傾角 β 和 D 為多少，回彈係數en愈高，則所需之設計高度 h95 也較高；2) 不論回彈係數et和 D 為多少，設計高度 h95會隨著傾角 β增加而增加；3) 當粗糙角i增加，落石運動軌跡與彈跳高度會變大。至於案例分析結果可知，單粒落石之多次軌跡模擬能修正落石外形之忽略及邊坡幾何不準確的差異部分。
在落石模擬問題之未來發展方向上，除了葛德治博士已發展的「ROCKPATH」程式剛體版外，並需考慮起伏坡形、多邊形落石之模擬及落石群之效應探討，才能瞭解真實之落石行為。

關鍵字

回彈係數 ； 落石 ； 運動軌跡 ； 粗糙性 ； 接觸特性

並列摘要

Taiwan is a mountainous island of frequent rainfalls and earthquakes, and particularly after the 921 Chi-Chi Earthquake, numerous disturbed rock slopes of high potential of landslides have been left along many hillside roads. Among various modes of landslides, rockfall is a great threat to any structure on its moving path. In order to select the most adequate measure, it requires precisely predicting the movement paths of in-situ falling rocks. However, because of inheritable variability of slope profile, contact property between falling rocks and slope, and rock initial state, the modified ROCKPATH code is used to simulate the motion of a falling rock.
In this thesis, the above code which is based on the particle mode and with the capability of Monte Carlo simulation is the main research tool. It can simulate the single and multiple movement paths of a single falling rock. The previous version only dealt with the randomness of contact property, excluding that of surface roughness on the rock surface, which really exists due to measurement error and time variation. The modified code includes this feature to more suitably match the site condition.
In the sensitivity study of a rock bouncing on a straight slope, the influences of restitution coefficients (en, et), roughness angle i and slope angle β on its movement path were investigated. Besides, for a straight slope with a bench, the influences of restitution coefficients (en, et), roughness angle i and bench width W were examined. The analysis results of both sensitivity studies indicated that: 1) with a larger value of en, design height of a rock-trap wall h95 increases; 2) h95 also increases with β. On the other hand, the results of two case studies showed that the Monte Carlo simulations would take into account the effects of rock shape and measurement error in determining slope profile.

並列關鍵字

roughness. ； contact property ； movement path ； restitution coefficient ； rockfall

參考文獻

[4] 紀宗吉、陳宏宇, 1997, 落石運動軌跡之現地調查與模擬分析案例介紹, 地工技術, 第六十四期：59-68.

[2] Irwin R. Miller, John E. Freund, and Richard Johnson, 1990, "Probability and Statistics for Engineers," 4th Edition, Prentice Hall.

[7] Giani, G. P., 1992, "Rock slope stability analysis," Balkema, Rotterdam：361.

[13] Fookes, P. G., and Sweeney, M., 1976, "Stabilization and contral of local rock falls and degrading rock slope," Quarterly J. Engrg. Geology, Vol. 9：37-55.

[15] Chan, Y. C., Chan, C. F., and Au, W. C., 1986, "Design of a boulder fence in Hong Kong," Proc. Conf. Rock Engrg. In an Urban Environment, Inst. Min.& Metallur., Hong Kong：87-96.