砂岩力學行為之微觀機制-以個別元素法探討

The microscopic mechanism associated with mechanical behavior of sandstone – using distinct element method

李宏輝(Hung-Hui Li)

指導教授 ： 黃燦輝

共同指導教授 ： 鄭富書(Fu-Shu Jeng)

國立臺灣大學/工學院/土木工程學研究所/博士(2008年)

https://doi.org/10.6342/NTU.2008.03101

摘要

本研究透過數值模擬探討砂岩與互層岩體在單軸壓縮試驗條件下之力學行為，並針對其微觀機制與微觀性質之可能範圍進行討論。採用之數值工具，係以個別元素法為理論基礎所發展之二維顆粒流分析軟體，以建立一具鍵結特性之二維圓盤數值模型(a bonded-particle model,簡稱BPM)。
在砂岩微觀組構因子與力學行為之研究部份，根據砂岩的薄片影像觀察，提出BPM數值模型內應具有不同的顆粒種類，以分別代表礦物顆粒(GP)、基質顆粒(MP)與孔隙基質顆粒(PP)。其中基質顆粒與孔隙基質顆粒主要用以反映顆粒面積比(GAR)與孔隙率(n)在數值模型中的變化。由顆粒種類及顆粒間的接觸關係，模型內可區分G-G、M-G、M-M與P-P四種接觸型態。本文研究結果顯示，在低孔隙率與高顆粒面積比條件下，砂岩力學行為由M-M與M-G接觸主控；在高孔隙率與低顆粒面積比條件下，砂岩力學行為則轉由P-P接觸主控。
在互層岩體力學行為部分，本研究提出之互層岩體數值模型係由岩層A與岩層B所組成，岩層A與岩層B所需之參數，係根據完整岩材單壓試驗模擬結果予以驗證。其次，互層介面A-B接觸之BPM參數，係根據互層岩體單壓試驗模擬過程決定之。根據本研究之模擬與分析結果，無論是強度與變形性二者與互層傾角之關係，或是互層岩體在不同傾角條件下之破壞模態，結果均符合實驗觀察。其次，透過斷鍵的發展與分佈，本研究進一步討論互層岩體在傾角改變時，導致其強度與變形性變化之微觀機制。
綜合以上所述，本研究提出之BPM數值模型，不僅能反映岩材的宏觀力學行為，同時亦提供了良好的途徑，得以窺探組成材料之微觀性質，及影響力學行為之微觀機制。

關鍵字

台灣西部麓山帶砂岩 ； 砂頁岩互層 ； 個別元素法 ； 微觀組構因子

並列摘要

Macroscopic mechanical properties of, such as uniaxial compressive strength and Young’s modulus were found to be significantly affected by their petrographic properties, e.g. the porosity n and the grain area ration GAR. The intricate relationship between the macroscopic properties of sandstones and their petrographic or microscopic properties necessitates further study in exploring how the microscopic properties influence the macroscopic mechanical behavior.
In this research, numerical analyses based on the bonded-particle model (BPM), the microscopic properties of which originated from the bonded strength and stiffness, were thus conducted as a systematic study aiming at unraveling these microscopic mechanisms. A series of tests was conducted, and the results were compared with the actual behavior of sandstone. A numerical model comprised of three types of particles, grain particles GP, matrix particles MP and porous matrix particles PP, was accordingly proposed to represent the sandstone.
The results of analyses demonstrated how the petrographic parameter GAR and porosity n determined the proportions and the numbers of GP, MP and PP. The strength and stiffness of these bonds were estimated based on back-analyses. Accordingly, the results of parametric study indicate that matrix particles tend to have stronger bonding strength yet softer stiffness, when compared to the grain particles.
On the other hand, since a conventional petrographic analysis does not allow a systematic and detailed study on how the microscopic factors affect the macroscopic behavior of inter-layered rocks, this research adopted the bonded particle model to explore the micro-mechanisms associated with the strength and stiffness of inter-layered rocks. The model was first calibrated by comparing the simulations to the actual behavior until they tally with each other. Following, the microscopic factors, including the bond strength, the bond stiffness, type of bonds and friction of particles and type of bond stiffness, are varied to study their influences. As expected, the bond strength and the bond stiffness are found to have a direct and significant influence on the macroscopic uniaxial compressive strength and stiffness, respectively. Furthermore, close observations on the breaking of bonds during the loading process reveal interesting phenomena, including the transition of shear/normal bond breaking, the type of internal fracture and the factors controlling internal failure, etc. These phenomena enlighten the interpretations about the micro-mechanisms accounting for the macroscopic strength and stiffness of inter-layered rocks.

並列關鍵字

sandstones ； inter-layered rocks ； distinct element method ； petrographic parameters ； strength ； deformational behavior

參考文獻

[18] 陳正旺 (2005)：車籠埔斷層周圍岩石力學特性之初探，國立台灣大學土木工程研究所碩士論文。

[20] 蔡立盛 (2006)：砂岩依時性力學特性研究及應用，國立台灣大學土木工程學研究所博士論文。

[11] 林銘郎、鄭富書、翁作新、洪如江 (2000)：台灣斷層泥之特性及斷層泥力學評估新發展，地工技術雜誌，第79 期，第91-106 頁。

[23] 鄭富書、黃燦輝、林銘郎 (2000)：台灣隧道工程老問題之新探討－軟岩之力學特性，地工技術，第79期，第81-90頁

[8] 林子平 (1985)：南港砂岩工程性質之影響因素研究，國立台灣大學地質學研究所碩士論文。