以PFC2D模擬砂土直剪實驗中之剪動帶及應用之研究

Abstract

過去的工程師習慣使用連續體的分析方法來模擬砂土問題，但是常常碰到模擬過程中無法解決破裂及翻滾的情形，為了解析真實土壤所受到的應力應變情形，使用非連續體分析方法來模擬各種實驗及現地狀況的研究是越來越多。但是儘管如此，剪動帶的位置該如何定義仍舊是一個尚待深入了解的課題。 有鑑於此，本研究使用非續體力學的商用軟體PFC2D針對土壤力學實驗中最基本的直剪實驗做模擬，目標是提出一個可以在非連續體分析中圈繪剪動帶的方法學。首先定義如何計算試體中受到的剪力應變量：定義方式參照Ramsay and Huber(1983)提出之構造地質學的解析方法，將均質應變的剪力應變量用橢圓率(ellipticity, R)來表示，橢圓率R為剪應變γ之關係式。接著再定義節點網格，就是將試體劃分成許多矩形區塊，每個矩形區域可視為一個計算剪力應變量的最小單元，稱之為節點網格，當節點網格的大小很小的時候，其應變可視為均質應變，也就可以使用R代表該節點網格的剪力應變量。根據以上兩項定義可以求得各個節點網格的剪力應變量，再依照各節點網格受到的剪力應變量的大小給予不同的代表顏色，如此一來即可看到剪動帶的分佈。最後再將這個圈繪剪動帶的方法學應用在斷層砂箱模擬及邊坡滑動模擬，並將斷層砂箱的模擬結果與鐘春富(2007)的研究進行比對。 由於PFC2D本身無法直接計算一堆顆粒的應變量，因此本研究使用矩陣運算軟體Matlab，自行編寫計算應變量的程式來計算應變量。 由本研究的模擬結果可以看到剪動帶在直剪實驗中呈現水平的帶狀，並且外型就像一個凸透鏡一樣，並且在剪動帶的內部會有許多顆粒翻滾的現象。在斷層砂箱的模擬中可以看到剪動帶在土層中的發展，及三角剪切帶之破裂尖端的位置。而在邊坡滑動的模擬結果當中可以看到弧型滑動的位置及其發展過程，還有張裂縫的出現。

Engineers are accustomed to using finite element method (FEM) to simulate the failure problem in sand. In this way, however, they are unable to solve the case with rapture and rolling. In order to analyse the real stress and strain situation in soil, more and more researchers choose to use distinct element method (DEM) to simulate the physics experiment and field problem. Nevertheless, the shear zone localization is still a significant issue to be further studied. In order to localize the shear zone, this research simulates the most basic soil experiment, direct shear test, by using a DEM software PFC2D, trying to propose a method which can point out the shear zone location. According to a structural geologic analysis method recommended by Ramsay and Huber (1983), this study defines the homogeneous strain in the soil by ellipticity R. R is a relative physical quantity to shear strain γ which is more familiar to engineers. Then this study set many grid points in the direct shear test simulation, separating the simulating soil into several squares with same area size. Every square is a shear strain calculating unit named grid square. The shear strain can be regarded as homogeneous if the grid square is small enough, and then the shear strain of the grid square can be represented by the ellipticity R. Combining two definition mentioned above, we can calculate the shear strain of every single grid square. Then, it is clear to localize the shear zone by giving every square different color related to its shear strain. Finally, this study also localize the shear zone in the fault sand box simulation and land slide simulation, and compare the result in the fault sand box in this study with the research studied by Chung (2007). No program can calculate the ellipticity in PFC2D, so in this study matrix calculating software MatLab is used to develop a program that can solve this problem. The simulation results indicate that the shear zone in the direct shear test is horizontal and its shape looks like lens. Also, particle rolling inside the shear zone can be observed. In the fault sand box simulation, the result demonstrates the development of the shear zone and the fault tip of tri-shear zone. In the land slide simulation, the result demonstrates the development of sliding surface and the appearance of tension crack.