分離元素法於擬脆性岩材微觀破裂機制之初探

Distinct Element Approach on Mesoscopic Fracture Mechanism in Quasi-brittle Rock

張家銓(Chia-Chuan Chang)

指導教授 ： 陳立憲

國立臺北科技大學/工程學院/土木與防災研究所/碩士(2007年)

https://doi.org/10.6841/NTUT.2007.00072

摘要

土木結構物受不同應力場，引致受力材料雖未達尖峰荷載水準但卻於內部產生微裂之叢聚，可能造成往後突然失穩而脆性破壞之情事，因此微觀尺度之裂縫監測對於整體結構穩定行為之研究日趨重要。
本研究以分離元素法（Distinct Element Method）之三維數值軟體PFC3D模擬圓形顆粒元素間之微觀非連體力學行為，嘗試建立顆粒微觀參數與整體材料巨觀參數相互關聯性之敏感分析。再以三軸試驗（含單壓）及巴西試驗為例，作為微、巨觀參數之核驗；進而探討擬脆性岩材受到剪力或拉力等不同應力路徑之微觀行為。模擬受載過程中，輒以顆粒元素間產生微裂之破壞型態，與聲射實驗文獻之結果作定性比較。由此局部式微觀開裂機制與傳統全面式巨觀材料破壞行為之校核探討，應有助於預測相關擬脆性材料結構之破壞演化（時間特徵）；並提供另一種研判局部至全面破壞區域之定位方法（空間特徵）。
透過幾何參數（顆粒元素粒徑與數量）之設定，進行PFC3D模擬結果發現，顆粒元素粒徑大小對於巨觀材料參數（彈性模數、柏松比、單壓強度）之影響甚鉅；又由電腦合理運算範圍內之參數敏感分析顯示，元素顆粒數量約在7000顆後，巨觀材料參數方較穩定而趨於定值。而就材料微、巨觀參數校核之關聯性探討，得知顆粒元素之微觀彈性模數與粒間鍵結強度；分別與材料巨觀彈性模數和單壓強度約成正比關係；觀顆粒元素之正/切向勁度比則與另一材料巨觀參數柏松比成正相關；微觀之粒間摩擦係數亦與巨觀摩擦角呈正面影響，但會因試驗方式或受試材料之不同而有所差異。
依巨、微觀參數之敏感度分析結果，選擇三軸（含單壓）試驗與數值模型調準（model fitting）作比對而推估具物理意義之諸微觀材料參數。經求算顯示出PFC3D模擬三軸（含單壓）試驗所輸入之微觀材料參數；確可適切反應出實驗過程之巨觀彈、塑性參數。另就其局部微觀破裂演化之觀察得知，稍早於尖峰強度的粒間剪/張微裂增量比之變化趨勢；暨不同加載歷程之粒間微裂位置，可定性判知單壓破壞時主要為局部之粒間剪裂所控制。再以相同之微觀參數代表相同岩材進行巴西試驗之模擬，仍可由其峰前之剪/張微裂增量比的變化趨勢；暨不同加載歷程之粒間微裂位置，來判知破壞乃為局部之粒間拉裂所控制；惟所求之巨觀間接張力強度較文獻之實驗值有高估現象。最後就數值求算之粒間微裂位置與試驗文獻之聲射微裂的叢聚位置與發生時機作比較，二者於單壓試驗所生成之微裂叢聚分別發生於加載比為61％及51％時；而巴西試驗則各發生於加載比為65％及61％時，二者之比較，顯示PFC3D可定性預測微裂叢聚現象之發生位置與時機。

關鍵字

分離元素法 ； 擬脆性 ； 微裂 ； 叢聚 ； 正/切向勁度比 ； 粒間剪/張微裂增量比 ； 加載比

並列摘要

Due to the growth of microcracks leading to localization within quasi-brittle materials, the engineering structure subjected to different stress paths would be caused an unexpected damage prior to peak load. Therefore, it is more important to understand the evolution of microcracks for the stability of structural materials.
This study presents a numerical simulation of displacement discontinuity behavior by using Particle Flow Code in three dimensions（PFC3D）which bases on the principle of distinct element method（DEM）. First of all, we proceed the sensitivity of parametric studies to calibrate the consistency of micro-to-macro material properties during both triaxial including unconfinement case and Brazilian test, and discuss mesoscopic behavior of quasi-brittle rock under different stress paths. Secondly, the numerical results in terms of the development of micro crack as well as the failure type of cracks between particles were compared with experimental data of acoustic emission qualitatively. It evolves the failure characteristic of quasi-brittle materials by viewing mesoscopic fracture behavior and conventional global failure criterion, and provides an option to identify the location of damage zone under certain stress level.
This numerical simulation shows that, by setting proper micro-geometrical parameters, a significant influence of particle radius on some macroscopic material parameters such as E, υ, qu. In this study, 7000 balls of particle numbers were used to conduct a series of parametric studies. Furthermore, the relation between micro- and macro- material properties: micro elastic modulus versus macroscopic elastic modulus, and bond strength versus confinement strength are found the existence of linear relation. In addition, there is a fair correlation between the normal/ shear stiffness and Poisson’s ratio. Macroscopic friction angle is also controlled by micro friction coefficient in spite of the upper bound of friction angle may not be controlled well with respect to different material and stress path.
According to analysis of sensitivity parametric, numerical model fitting is able to match through triaxial test including unconfing case. It shows that the micro-properties of PFC3D indeed response a good agreement with laboratory results in terms of both elastic and plastic parameters. By monitoring shear/ tensile cracks increment ratio and localization of particle cracks corresponding different load level, local shear cracking somehow dominated the damage around peak in uniaxial compression test. On the other hand, by simulating Brazilian test with same micro-properties, relatively tensile crack in element which dominates damage was found. However the estimation of tensile strength is higher than laboratory experiment value about 3 times. Finally, appearance of localization are obtained about 61% and 51% for numerical simulation and experimental AE data under uniaxial test respectively, and about 65% and 61% under Brazilian test. It shows that PFC3D could be used to verify the growth of micro cracks as well as its localization qualitively.

並列關鍵字

distinct element method ； quasi-brittle ； micro-crack ； localization ； normal/shear stiffness ratio ； shear/tensile cracks increment ratio ； loading level

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