| dc.description.abstract | 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. | en_US |