以PFC2D模擬併構岩單壓強度及變形性

程泓皓(Hung-Hao Cheng)

指導教授 ： 田永銘

國立中央大學/工學院/土木工程學系/碩士(2014年)

摘要

本文以PFC2D（Particle Flow Code in 2 Dimension）模擬不同尺寸、不同體積比併構岩（Bimrock）在單壓試驗（Unconfined Compressive Test）下單壓強度、楊氏模數及柏松比等力學性質及變異性。研究顯示，單壓強度、楊氏模數、柏松比均隨體積比增加而增加。但在體積比20%以下，其增加幅度並不明顯，與純基質試體差異不大。當體積比超過20%以上，增加幅度才較為明顯。本文以微分力學模式驗證PFC2D的模擬結果，發現兩者相當吻合，說明了模擬之可行性。利用不同應變規長度量測所得之彈性係數平均值並無明顯差異，但其變異性隨長度增加而降低，並與體積比呈先升後降之趨勢。在不同尺寸下獲得之模擬結果亦有相同的趨勢。本文以中央極限定理進行回歸處理：「應變規長度、體積比與彈性係數變異性三者之關係」以及「尺寸、體積比與單壓強度、楊氏模數、柏松比變異性之關係」。在模擬過程中，觀察裂隙發展之情形，發現在尖峰強度前（單壓強度85%左右）才開始有少量的微裂隙生成，這些微裂隙發生在較為軟弱的基質或岩塊-基質介面間，且隨機分布在試體內；當過尖峰強度後，微裂隙才開始迅速延伸、發展成巨觀裂隙。本文經由統計各種變因之試體承受單壓下，三種鍵結（基質、岩塊及岩塊-基質鍵結）之斷裂數量於不同受力下所佔比例，以了解併構岩受單壓之破壞機制。

關鍵字

併構岩 ； 體積比 ； 中央極限定理

並列摘要

This paper uses PFC2D (Particle Flow Code in 2 Dimension) to simulate Bimrock to discuss volumetric fraction, sample sizes for uniaxial compression strength(UCS), Young's modulus(E), Poisson's ratio(ν) and theirs variability by Unconfined Compressive Test. Base on the numerical simulation results, the UCS, E, and ν increase with the increase of the volumetric fraction. However, in volumetric fraction for 20% or less, the UCS increase rate is not obvious. In this paper, we use differential scheme and Hashin and Shtrikman bounds to verify the simulation results and then find the good agreement. The means of Young’s modulus and Poisson’s ratio have no correlation with gauge length, but theirs coefficient of variation decrease with the gauge length, and first increased and then decreased with the volumetric fraction. The results of different sizes also have the same trend. The Central Limit Theorem has been used for statistical regression to find the relationship for "gauge length, volumetric fraction, and coefficient of variation for elastic modulus" and "sample sizes, volumetric fraction, and bimrock mechanical behavior".
During the simulation, the developing of the crack was observed that the models have a small amount of micro-cracks before peak state (about 85% of the uniaxial compressive strength). These micro-cracks randomly distributed in the relatively weak matrix or interface of blocks. After the peak state, the micro-cracks begin to extend rapidly and develop into macroscopic fractures. The article count the proportion of fracturing of three type bonds (matrix-matrix bonds, block-block bonds, and block-matrix bonds) by Unconfined Compressive Test, in order to understand bimrock’s failure mechanism under uniaxial compression.

並列關鍵字

Bimrock ； volumetric fraction ； Central Limit Theorem

參考文獻

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