| 摘要: | 本文針對不同裂隙程度之巨觀等向性岩體在不同取樣體積下，三維裂隙程度（P32）與力學性質（單壓強度與楊氏模數）之不確定性進行探討。在裂隙方面，首先於岩體模型內，隨機生成裂隙中心點，再計算每一裂隙中心點進入取樣範圍內之機率，此一機率問題為伯努利試驗，透過二項式定理，可推導得P30不確定性之解析解。透過P30 與P32之關係，轉換為P32不確定性之解析解。利用FracMan生成具有不同裂隙程度之離散裂隙網絡（discrete fracture network, DFN），建構岩體模型，再以不同體積取樣，分別計算量測P32，獲得量測P32不確定性之數值解，並解析解進行比較與驗證，當裂隙直徑與取樣邊長之比例小於0.5時，其兩者結果極為相近。
力學方面本文利用FracMan軟體在岩體模型(rock mass model)內生成不同裂隙程度離散裂隙網絡，並進行不同尺寸之取樣，再將裂隙資料導入顆粒流軟體PFC3D，套用平滑節理模型（smooth joint model, SJM）以生成具有之合成岩體（synthetic rock mass, SRM），以位移控制方式，模擬一系列岩體在單壓試驗下之力學行為，計算在不同條件下，合成岩體之單壓強度與楊氏模數之平均值及變異係數。合成岩體力學性質不確定性受到（1）裂隙排列及（2）裂隙程度之影響。Esmaieli等人(2010)利用現地裂隙岩體之P32產生合成岩體，從中取樣進行單壓之數值試驗，以探討力學性質之不確定性，雖然可獲得整體之不確定性。但因每個試體之P32非固定，故無法分離裂隙排列與裂隙程度對岩體力學性質不確定性之貢獻度。本文提出直接法與取樣微調法兩種方法，使試體之P32得以固定。在固定P32的條件下，建立裂隙排列所引致之不確定性。裂隙程度引致之不確定性則可透過力學性質(UCS及E50)與P32之趨勢線及P32變異係數之解析解以求得。本文研究結果顯示：（1）直接法與取樣微調法所求得裂隙排列引致之不確定性結果相近（2）單壓強度之變異係數裂隙程度引致之不確定性與裂隙排列之影響相近（3）楊氏模數之變異係數裂隙程度引致之不確定性皆大於裂隙排列造成之影響（4）合成岩體力學性質之變係數之平方為裂隙排列引致之變異係數與裂隙程度引致之變異係數之平方和，此一關係可由變異數分析(ANOVA)之理論加以驗證。
綜合本文對岩體裂隙程度及力學性質不確定性之研究，可發現裂隙程度之變異係數隨著P32增加而減少，而單壓強度與楊氏模數之變異係數則隨P32增加而增加，且在本文參數研究範圍內，楊氏模數之變異係數皆小於單壓強度之變異係數，岩體表徵單元體積在P32小於1.9 m-1為裂隙程度之變異係數最大，單壓強度次之，楊氏模數最小，在P32大於1.9 m-1為單壓強度之變異係數最大，裂隙程度次之，楊氏模數最小。
;This paper presents the uncertainties of geometrical and mechanical properties based on macroscopically isotropic synthetic rock mass. In the geometrical section, the analytical approach used the probability of whether each fracture center point would be sampled or not. The coefficient of variance of P30 could then be calculated by binomial theorem. According to the relation between P30 and P32, the coefficient of variance of P32 could also be yielded. To verify the analytical solution, FracMan was used to generate the rock mass model and discrete fracture network (DFN) to simulate the measurements and access the coefficient of variance of P32. The analytical solution and numerical solution were very similar when the ratio of the fracture diameter and the length of the sample volume was smaller than 0.5.
In the mechanical section, this paper adopted the concept of synthetic rock mass (SRM). FracMan was used to generate DFN in rock mass models and to execute the sampling. The SRM was generated by combining the fracture data from FracMan and the bonded particle model in PFC3D. The uniaxial compression test, which uses strain control, was conducted to investigate the mechanical behavior of SRM. The uncertainty in the mechanical behavior of SRM is derived from fracture permutation and sampled fracture intensity. In past studies, the effects of these two factors were studied at the same time, but the precise effect of each factor could not be obtained due to the methodology used in these studies. To quantify the effect of fracture permutation, the P32 of each sample must be the same. The direct-generate method and sample-modify method were therefore adopted to ensure that each sample’s P32 were the same. By using the analytical solution of P32 and the relation between P32 and the mechanical property, the effect of the sampled fracture intensity could be calculated. The results showed that the effect of fracture permutation and fracture intensity were almost the same for uniaxial compression strength, and that the effect of fracture intensity was larger than fracture permutation on Young’s modulus. The variance of the mechanical behavior of SRM was also equal to the combination of the variance affected by fracture permutation and sampled fracture intensity. This relationship could also be proven by the theory of analysis of variance.
According to this paper, as P32 increases, the coefficient of variance of fracture intensity will decrease and the coefficient of variance of both uniaxial compression strength and Young’s modulus will increase. In the range of parameters adopted in this paper, when P32 was smaller than 1.8 m-1, the coefficient of variance of fracture intensity was larger than coefficient of variance of uniaxial compression strength, and Young’s modulus was the smallest among them. When P32 was greater than 1.8 m-1, the coefficient of variance of uniaxial compression strength was larger than the coefficient of variance of fracture intensity, and Young’s modulus was the smallest among them. |
