| 摘要: | 在裂隙岩體中進行岩石工程，如隧道、岩坡和基礎建設，不連續面的存在是影響工程行為的重要因素，不僅與不連續面的方位相關，還與隧道開挖方向、岩坡傾向以及基礎配置方向等因素有密切關聯。儘管先前的工程師早已確認岩石工程中存在異向性行為，並廣泛應用經驗法則於實際工程中，但由於岩石工程中異向性行為的複雜性，這一問題長期以來一直缺乏嚴謹且全面的物理模型試驗、解析分析或數值分析的結果，以驗證經驗法則的正確性。
本文旨在探討岩石隧道異向性行為，驗證Rock Mass Rating及Rock Structure Rating在探討方位評分調整的合理性外，更著重於三維合成岩體隧道模型數值分析之數據處理與詮釋。二維數值模擬工具無法探討不同開挖方向的效應，故本文利用三維數值模擬程式PFC3D及RS3探討隧道開挖方向對裂隙岩體穩定性之影響。本文利用Kirsch equations做隧道開挖的驗證，驗證結果均符合，PFC3D與RS3兩者均適合用來模擬裂隙岩體隧道開挖。利用PFC3D生成鍵結顆粒模型（Bonded Particle Model, BPM）配合離散裂隙網絡（Discrete Fracture Network, DFN）建構具有一組不連續面之合成岩體隧道模型，傾角（??j）變因為：??j＝0?、15?、30?、45?、60?、75?及90?等七種，裂隙間距為2m之離散裂隙網絡，針對三種隧道開挖情境進行模擬：情境一（γ＝90?）：裂隙走向平行開挖方向；情境二（γ＝0?）：裂隙走向垂直開挖方向且傾向與開挖方向相同；情境三（γ＝180?）：裂隙走向垂直開挖方向且傾向與開挖方向相反。RS3也進行與上述相同變因及情境之模擬。透過數值模擬結果，探討各變因下隧道開挖後穩定性的影響，並透過位移場、徑向位移、應變不變量、應變能及位能等量化指標描述隧道的穩定性，藉由模擬結果與前人文獻相比，統整出一套裂隙對於開挖方向的評分調整系統，以及歸納出各開挖情況下隧道挖掘後變形形式及分布。
數值結果分析顯示：（1）低傾角裂隙岩體β_j＝0?～20?時，三種開挖情境皆有相同的結果，代表隧道穩定性與隧道開挖方向無關，可佐證（Bieniawski，1979）所提出之方位評分調整合理性。（2）理論上不連續面傾角β_j=90?之岩體，在γ＝0?及γ＝180?時穩定性應該一致。然而，RSR或RMR在開挖γ＝0?、180?的評價卻分別為「極有利」及「尚可」，存在悖離理論的缺陷。本文在γ＝90?、180?下，β_j=45?與β_j=90?之分析出之數據結果差距甚大，隧道行為截然不同，不宜歸納為同一傾角分群。因此針對傾角分群由原本的三群加以細分為六群，可獲致更細緻的評分且可解決RSR及RMR悖離理論的缺陷。（3）利用PFC3D模擬結果輸出之數據，以不同的採計範圍，分別針對應變不變量、徑向位移、應變能、位能等建立指標，與Bieniawski（1979）不連續面方位評分調整進行最佳化擬合。徑向位移及位能與Bieniawski（1979）吻合度最高；在18種組合中，有10種完全相同。（4）高傾角（β_j=60?~90?）之岩盤，當開挖方向與不連續面走向平行時（γ=90?），本文分別以有限元素法RS3及離散元素法PFC3D分析結果提出之方位評分調整與Bieniawski（1979）差異最大。彙整前人研究成果，可分為三類：有限元素法（含本文RS3分析結果）、離散元素法及模型試驗。其中有限元素法之結果與Bieniawski（1979）相似，離散元素法及模型試驗結果與本文結果相似。（5）PFC3D及RS3開挖模擬的結果顯示，RS3隧道周圍位移量遠小於PFC3D的位移量。尤其在開挖方向γ=0?及γ=180?時，RS3模擬所得之隧道周圍位移量極小，只有在γ=90?、β_j=60?～90?位移量略大，其位移量約為PFC3D的十分之一至六十分之一。究其原因可能在於RS3是基於連續體的有限元素法進行分析，在分析非線性、不連續性或離散性問題時，較無法精確呈現變形結果。（6）探討隧道穩定性時，數據採計範圍亦至關重要，本文分別以固定的採計半徑為隧道壁外rm＝1r及不同的採計長度（即未支撐段）lx＝2m、6m、18m，探討在不同採計範圍下之徑向位移的特性及適用性。結果顯示採計範圍lx＝18m較能完整地代表隧道開挖穩定性。（7）相對於徑向位移及位能，應變不變量、應變偏量不變量及應變能等，僅適用於小變位，當濾除大位移數據，等同忽略坍落至隧道洞內之岩塊，未必適合作為隧道穩定性指標。然而，這些不同的指標在數學上具有明確的定義，部分具有物理意義，例如：第一應變不變量（I1）代表隧道周圍岩體的體積應變；第二應變不變量（I2）及第二應變偏量不變量（J2）相當適合用以描述因不連續面滑動發生的剪切破壞；應變能（U0）代表應力及應變之積，則適合作為標記破壞位置之用。
;In the engineering of rock masses, such as tunnels, rock slopes, and foundation construction within fractured rock formations, discontinuity is a crucial factor influencing the behavior of the engineering structures. This influence is not only related to the orientation of the discontinuities but also closely tied to factors such as the excavation direction of tunnels, the slope of rock, and the orientation of foundation configurations. Despite the acknowledgment by previous engineers of the anisotropic behavior in rock engineering and the widespread application of empirical rules in practical projects, the lack of rigorous and comprehensive results from physical model tests, analytical analyses, or numerical analyses regarding anisotropic behavior in rock engineering has led to a long-standing deficiency in verifying the accuracy of empirical rules.
This paper aims to explore the anisotropic behavior of rock tunnels, focusing not only on validating the rationality of adjusting orientation scores in Rock Mass Rating (RMR) and Rock Structure Rating (RSR) but also emphasizing the data processing and interpretation of numerical analyses of three-dimensional synthetic rock mass tunnel models. Two-dimensional numerical simulation tools can not address the effects of different excavation directions, so this paper utilizes three-dimensional numerical simulation programs PFC3D and RS3 to investigate the influence of tunnel excavation direction on the stability of fractured rock masses. The verification of tunnel excavation using the Kirsch equations confirms that both PFC3D and RS3 are suitable for simulating tunnel excavation in fractured rock masses. A Bonded Particle Model (BPM) combined with a Discrete Fracture Network (DFN) is generated using PFC3D to construct synthetic rock mass tunnel models with a set of discontinuities. The dip angle (??j) variables include: ??j=0?, 15?, 30?, 45?, 60?, 75?, and 90?. Three tunnel excavation scenarios are simulated: Scenario 1 (γ=90?): Strike parallel to the excavation direction; Scenario 2 (γ=0?): Strike perpendicular to the tunnel axis and direction of drive with dip; Scenario 3 (γ=180?): Strike perpendicular to the tunnel axis and direction of drive against dip. RS3 also performs simulations with the same variables and scenarios. Through numerical simulation results, the paper investigates the influence of various variables on tunnel stability, and quantitative indicators such as displacement fields, radial displacements, strain invariants, strain energy, and potential energy are used to describe tunnel stability. By comparing simulation results with existing literature, the paper consolidates a scoring adjustment system for discontinuities concerning excavation direction and summarizes deformation patterns and distributions after tunnel excavation under various conditions.
The analysis of numerical results reveals that: (1) Displacement values around tunnels in RS3 are much smaller than those in PFC3D, especially when γ=0? and 180?. RS3 shows extremely small displacement values around tunnels, with only slightly larger values when γ=90? and ??j=60? to 90?, approximately 1/10 to 1/60 of the displacement values in PFC3D. (2) Theoretically, rock masses with a dip angle βj=90? should exhibit consistent stability when excavated in γ=0? and γ=180?. However, RSR and RMR evaluations for excavations in γ=0? and 180? are "very favorable" and "fair," respectively, deviating from theoretical expectations. The analysis results for βj=45? and βj=90? in γ=90? and 180? show significant differences, indicating distinct tunnel behaviors, and suggesting that these should not be grouped under the same dip angle. Therefore, the dip angle grouping is refined from three groups to six groups, providing a more detailed scoring system and addressing the discrepancies in RSR and RMR evaluations. (3) Using strain invariants, strain deviator invariants, strain energy, radial displacement, and potential energy, the paper performs optimization fitting with RMR discontinuity orientation score adjustments. Radial displacement and potential energy show the highest correlation with RMR; out of 18 combinations, 10 are identical, while the remaining 4 differ by one grade and 4 differ by two to three grades. Strain invariants, strain deviator invariants, and strain energy are based on the assumption of small strains and must filter out particles with large displacements, making them unsuitable as indicators for tunnel stability. (4) Rock masses with high dip angles (βj=60?~90?), when excavated parallel to the discontinuity orientation (γ=90?), exhibit significant differences in orientation score adjustments proposed by RS3 (finite element method) and PFC3D (discrete element method) compared to RMR. Reviewing previous research results, three main approaches are identified: finite element methods, discrete element methods, and model tests. Finite element methods (including RS3 in this paper) show similarities to RMR, while discrete element methods and model tests show similarities to PFC3D results. Finite element methods based on continuum mechanics may underestimate deformation significantly due to their inability to simulate large displacements associated with discontinuity sliding. This indicates that different numerical methods can lead to variations in analysis results. (5) Relative to radial displacement and potential energy, strain invariants, strain deviator invariants, and strain energy are not suitable as indicators of tunnel stability. However, each of these invariants and strain energy has different physical meanings. The first strain invariant (I1) represents volume strain in the rock mass around the tunnel; the second strain invariant (I2) and the second strain deviator invariant (J2) are suitable for describing shear failure due to discontinuity sliding; strain energy (U0) represents the product of stress and strain and is useful for marking the location of failure.(6) The investigation of tunnel stability requires careful consideration of data collection range, and this study adopts radial displacement measurements taken one and a half times the tunnel radius outward. The suitability of this approach is examined at distances of 2m, 6m, and 18m from the excavation face. When collecting data 2m ahead of the excavation face, the region near the excavation face exhibits greater stability when γ=90?, while the region with lower inclination angles (γ=180?) appears less stable. As the data collection range increases, the results show instability for γ=90?, while the radial displacement for γ=0? and 180? tends to converge. This convergence suggests that the stability of these two angles should be similar after the tunnel is completely penetrated. Therefore, the study recommends analyzing the data up to half of the model′s excavation as a more suitable approach to distinguish and examine the stability behavior for γ=0? and 180?. |
