| 摘要: | 岩體因微觀組構優選方位或不連續面在力學、水力傳導等性質受方向所控制，稱之為岩體之異向性（anisotropy）。順向坡（dip slope）與逆向坡（anti-dip slope）穩定性分析中，常以極限平衡法或二維數值方法，忽略坡面走向邊界之邊界效應（end effect）進行二向度分析，然而斜交坡（oblique slope）穩定性分析實屬三維問題，坡面走向之邊界條件將顯著影響岩坡崩塌行為。
本文利用PFC3D生成BPM配合DFN建構具有一組不連續面之合成岩坡模型，探討在不同邊界條件下，不同斜交角（|α_j-α_s |）之岩坡崩塌行為。本文以坡高50公尺，坡角60˚，坡長200公尺之三維岩坡模型為例，採用的邊界條件包括：fixed、periodic、roller及free並給定不同的斜交角（0˚、10˚、15˚、20˚），透過數值模擬的結果，探討各種變因下岩坡之崩塌過程，並透過波及範圍、位移方向及崩塌能量等量化指標描述岩坡崩塌規模，藉由模擬結果統整如何降低邊界效應，並決定臨界斜交角，以及歸納各邊界條件的適用情境。
數值分析結果顯示：（1）PFC3D可合理地模擬岩坡於不同斜交角及邊界條件下之崩塌行為，崩塌過程中會出現幾個巨觀滑動面（failure surface），初始的滑動面於坡頂附近產生，深度較淺，後繼的滑動面逐漸遠離坡頂，深度較深，形成漸進式破壞（progressive failure），先前掉落的崩塌體堆積於坡趾附近，使得坡度變緩，後方不連續面不再見光，岩坡逐漸趨於穩定。（2）PFC3D模型係由不同大小的球顆粒組成，為了合理地反映球顆粒尺寸的影響，在處理球顆粒位移向量的數據時，本文提出重量加權位移法（weighted displacement），將每一顆粒的位移向量乘以該球顆粒的重量加總，再除以所有顆粒總重量。重量加權位移法可有效降低微小位移（trivial displacement）及微小球顆粒之影響，可更合理地呈現岩坡整體位移狀況。本文以重量加權位移法為基礎，探討不同斜交角下崩塌體之水平位移方向（δ）。分析結果表明，崩塌體之位移和向量方向皆介於坡面傾向α_s與不連續面傾向α_j之間，且與坡面傾向α_s較為一致。此外，若將每一顆粒的位移垂直分量乘以該球顆粒的重量加總，即為崩塌能量。（3）本文將不同斜交角及不同邊界條件下之岩坡模型分段（left, middle, right，長度比為1:2:1），數據表明，不同斜交角岩坡中段，其位移方向、崩塌能量、崩塌體積等崩塌行為均相當接近且與週期性邊界的崩塌行為接近。可印證透過去除左、右分段，保留中段可降低邊界效應的影響。此外，週期性邊界受邊界效應的影響最小，是最適合用於探討斜交角對岩坡崩塌行為影響的邊界條件。（4）隨著斜交角的增加，崩塌體積及崩塌能量亦急遽下降，當岩坡趨於穩定（或只有零星崩塌量體）所對應的斜交角本文稱為臨界斜交角（critical oblique angle）。以岩坡於週期性邊界為例，其臨界斜交角為20˚，此結果與一般工程經驗或技術規範相符。（5）週期性邊界可有效降低邊界效應、球顆粒數及運算時間，提供一個適合模擬無限邊坡（infinite slope）行為的方法。當坡長比L/H>6時，可視為無限邊坡，邊界效應的影響已不明顯，但球顆粒數會過多，造成運算時程過長，建議採用週期性邊界條件，以週期性地延伸模型，提升運算效率。當坡長比L/H≦6時，可視為有限邊坡（finite slope），根據現場岩坡兩側面（side surface）完全無支撐、有擋土牆且牆面粗糙及有擋土牆且牆面光滑的情境，分別對應free、fixed、roller三種邊界條件。
;The properties of rock mass such as mechanical behavior and hydraulic conductivity are controlled by the direction because of the orientation of discontinuities. In the stability analyses of the dip slope and the anti-dip slope, the limit equilibrium method and two-dimensional numerical methods ignoring the end effect of the slope strike boundary are often used. However, the stability analyses of oblique slope are three-dimensional problems. The boundary condition of the slope strike plays an important role of the collapse behavior of the rock slope.
PFC3D is adopted in this study to generate BPM and DFN to be a synthetic rock slope model with a set of discontinuity. Resreach the collapse behavior of rock slope with different |α_j-α_s | by using different boundary conditions. This study takes a 3D slope model with slope height 50 meters, slope angle 60°, and slope length 200 meters as an example. The boundary conditions used include fixed, periodic, roller, and free, and different |α_j-α_s | are 0˚、10˚、15˚、20˚. Based on the results of numerical simulation, we can discuss the collapse process of rock slopes in different variables, and describe the collapse behavior of rock slope by using quantitative indicators such as the impact area, the direction of displacement, and the energy release of landslide. Base on the results, introduce how to reduce the end effect, determine the critical oblique angle, and summarize the applicable scenarios of each boundary condition.
Numerical analysis results show that：(1) PFC3D can reasonably simulate the collapse behavior of rock slopes at different |α_j-α_s |. There will be several macroscopic failure surfaces in the process. The progressive failure happens with the initial failure surface generating near the top of the slope, and the depth of the failure surface is relatively shallow. The subsequent failure surface gradually retrogresses from the top of the slope, and the failure surface is deeper. (2) The synthetic rock slope model is composed of particles of different radius. When dealing with the data of the particle displacement vector, this study proposes the weighted displacement method in order to reasonably reflect the influence of the size of particles. The displacement vector of each particle is multiplied by the weight of the particle and divided by the sum weight of particles. The weighted displacement method can effectively reduce the influence of trivial displacement and tiny particles, and can more reasonably present the overall displacement of rock slopes. Based on the weighted displacement method, this study discusses the horizontal displacement direction of the collapsed body in at different |α_j-α_s |. The results show that the horizontal displacement direction of the collapsed body in each boundary condition is between α_s and α_j, and is relatively consistent with α_s. Besides, the energy release of landslide is sum of the vertical displacement multiplied by the weight of the particles. (3) In this study, the rock slope model at different |α_j-α_s | and in each boundary condition is segmented to left, middle, right, and the length ratio is 1:2:1. The serults show that the collapse behavior such as direction ofdisplacement, energy release of landslide, and collapse volume are quite close to those of periodic boundary condition. It can be confirmed that the influence of end effect can be reduced by removing the left and right segments. In addition, periodic boundary conditions are effected by the minimal end effect, and are the most suitable boundary conditions to research the collapse behavior of rock slope at different oblique angles. (4) As |α_j-α_s | increases, the collapse volume and the energy release of landslide are also decreases sharply.In this study, |α_j-α_s | corresponding to when the rock slope tends to be stable (or only thimbleful collapse volume) is called critical oblique angle. Taking a rock slope in periodic boundary as an example, the critical oblique angle is 20°, which is consistent with general engineering experience or technical regulations. (5) Periodic boundary conditions can effectively reduce the end effect, the number of particles and the calculate time, and provide a method suitable for simulating the behavior of infinite slopes. When the slope length ratio L/H>6, it can be regarded as an infinite slope, but the number of particles will be too many, resulting in a long calculation time. It is recommended to use periodic boundary conditions to periodically extend the model to improve computing efficiency. When the slope length ratio L/H≦6, it can be regarded as a finite slope. According to the site, the side surface of the rock slope is completely unsupported, with a retaining wall and a rough wall, and with a retaining wall and a wall. The situation with a smooth surface corresponds to three boundary conditions: free, fixed, and roller. |
