| 摘要: | 本文分別提出異質性介質（heterogeneous media）及不連續岩體（discontinuous rock mass）的體積比（volumetric fraction）、裂隙程度（fracture intensity）及力學性質不確定性之解析解及數值解，並根據統計定理得知幾何及力學性質之關係。
由體積比或裂隙程度引致之不確定性可根據幾何模型量測的不確定性推導得知。針對異質性介質（併構岩、混凝土等）量測體積比之不確定性，本文利用表徵單元（representative volume element, RVE）作為統計推論模型，分別得到以一維及二維量測體積比不確定性之解析解；外方內圓的表徵單元被應用於二維等向異質性介質之形貌，而外平行四邊形內橢圓的表徵單元被應用於二維異向異質性介質之形貌，另外方內球的表徵單元應用於三維等向異質性介質之形貌。此外，本文分別撰寫二維及三維異質性介質模擬一維及二維量測體積比的不確定性，提出數值解並驗證解析解之正確性。此數值程式應用週期性邊界（periodic boundaries），可消弭邊界效應及精準控制異質性介質之體積比。針對不連續岩體（裂隙岩體）量測裂隙程度之不確定性，本文利用柏松分配（Poisson distribution）模型分別推得一維、二維及三維裂隙程度之不確定性解析解。此外，本文利用自行撰寫之離散裂隙網絡（discrete fracture network, DFN）及市售離散裂隙網絡軟體FracMan模擬一維、二維及三維裂隙程度之不確定性數值解，並驗證解析解之結果。
由體積比及裂隙程度引致力學性質之不確定性，可將體積比及裂隙程度的不確定性代入至常態隨機變數及幾何力學關係式中得知。有關異質性介質的幾何及力學性質關係式可由微觀力學模式（micro-mechanical models）或顆粒流軟體（Particle Flow Code, PFC）模擬決定，而不連續岩體的幾何及力學性質關係式則由合成岩體（synthetic rock mass, SRM = DFN + PFC）模型模擬得知。由塊體或裂隙排列引致之力學性質之不確定性係由一系列參數研究得知。根據統計推導，異質性介質或裂隙岩體力學性質的不確定性可分別由「體積比及裂隙程度引致力學性質之不確定性」及「塊體或裂隙排列引致力學性質之不確定性」計算得到，此結果業經數值驗證。另本文在每章節末，提供一至數個實例操作及案例示範如何使用本文提出之幾何及力學性質不確定性之解。;
This study proposes analytical and numerical solutions for the uncertainties of volumetric fraction (Vf), fracture intensity (FI), and mechanical properties in heterogeneous media and discontinuous rock masses, respectively. In addition, the relationship of the uncertainties of geometries estimates and mechanical properties can be also obtained via statistical theorem.
The uncertainties induced by Vf or FI can be obtained by addressing the solutions of geometric uncertainty. For a heterogeneous media (bimrock, concrete…), the representative volume element (RVE) is employed for a statistical derivation model. The circle-squared RVE is used for 2D isotropic (or randomly orientated) heterogeneous rock features, the ellipse-parallelogram RVE is used for 2D anisotropic (or preferred orientation) heterogeneous medium features, and the sphere-cubic RVE is used for 3D heterogeneous medium features. To validate the analytical solutions, this study develops numerical heterogeneous media codes in 2D and 3D to demonstrate 1D and 2D Vf measurements, respectively. These codes employ periodic boundaries to eliminate the boundary effect and to control the volumetric fraction of the model more precisely. For a discontinuous rock mass (fractured rock), the Poisson distribution model is used for a mathematical derivation model for 1D, 2D, and 3D fracture intensity (P10, P21, and P32, respectively) measurements. This study also develops a discrete fracture network (DFN) code to simulate P10 and P21 measurements. In addition, the commercial DFN code, FracMan, is employed to simulate P21 and P32 measurements. Similarly, these simulations are used to validate the analytical solutions of fractured rock.
The uncertainty of the mechanical properties induced by Vf or FI can be obtained by substituting the results for the uncertainty of Vf or FI into a normal random variable from a correlative model of that property. In the correlative model analysis, the mechanical properties of a heterogeneous rock mass can be determined using micro-mechanical models or Particle Flow Code (PFC) simulations, and the mechanical properties of a discontinuous rock mass can be determined via simulations of a synthetic rock mass (SRM, which combines DFN and PFC models). Several systematic parametric studies are carried out to investigate the mechanical properties and their uncertainties and obtain those of a heterogeneous or discontinuous rock induced by assemblages (block, fracture, or particle). According to the statistical analysis, the uncertainties of the mechanical properties of site samplings can be calculated from the uncertainties induced by the Vf or FI and the uncertainties induced by assemblages of blocks, fractures, and particles. This relation can be confirmed through numerical simulations. One or two illustrations of how to use the proposed solutions are given at the end of each chapter. |
