Journal of Engineering Geology

---

Hoek and Brown suggested a method to estimate the strength and deformation modulus parameters of rock masses. The method was then widely used in rock engineering designs. In such designs, the mean values of Hoek and Brown parameters are often used which are not proper values due to the variability of rock mass properties within a great range of values. In such cases, probability analysis of rock mass properties is highly important. The geological strength index is one of the most important parameters in Hoek and Brown equations. Determination of this parameter includes greater uncertainties than determining other parameters. In this paper, based on the results of rock mechanical tests carried out on rock samples of Gol-Gohar iron ore mine, and the required field surveys, the sensitivity of rock mass geomechanical properties on the type of the statistical distribution function of the geological strength index in statistical analysis of these parameters using Monte Carlo simulation method was investigated. The results showed that the sensitivity of Hoek and Brown equations to determine different rock mass geomechanical parameters varies as the type of the statistical distribution function of the geological strength index changes. The sensitivity of geomechanical parameters such as internal friction angle, cohesion, total strength and rock mass modulus on the type of the statistical distribution function of the geological strength index is much less than parameters such as uniaxial compressive strength and tension strength of rock mass. The greatest variations based on changes of the type of the statistical distribution function of the geological strength index are less than 5% for the internal friction angle, cohesion and total strength, less than 10% for the modulus, and less than 25% for the uniaxial compressive strength and tension strength.

---

Introduction
The rock block volumes are formed due to the intersection of discontinuities in the jointed rock mass. The block dimensions affected by joint spacing, joint orientation, joint sets, are taken to be the most important parameters determining the rock mass behavior, strength parameters, and deformations. In the numerical modeling using distinct element method, the creation of the discontinuities can affect the final results very much. Using 3DEC software, it is possible to create joint sets in four conditions: regular and persistent, regular and non-persistent, non-regular and persistent, irregular and non-persistent. As an important point to consider, the major effect of block dimensions on rock mass behavior, strength parameters and deformation modulus can help to decide which one is most suitable to indicate the real conditions of rock mass. As explained in the previous studies, the use of persistent joints leads to the block dimensions being considered as small ones. In this way, due to the high strength of intact rock compared to the joints, the possibility of instability increases.
Material and methods
In this research, from quantitative point of view, Geological Strength Index (GSI) is calculated, based on block dimensions as an influential parameter, to consider the most appropriate case for creating joints in the numerical method. In this regard, according to valuable studies in Bakhtiari dam structure, the characteristics of discontinuities system and GSI of rock mass are utilized to come up with real conditions. Then, the modeling is done with different conditions of joints, block volume distribution, GSI for each case, and the results are compared with quantitative ones. And then the most suitable case for creation of joints in numerical modeling is suggested by using 3 DEC software, regarding the blocks volumes, type of distribution function, and GSI value. Also, the accuracy of this finding is investigated for other structures, independently of input parameters, by making changes in spacing, and joints persistence as two effective parameters in rock blocks dimensions. Owing to the difficulty in the accurate definition of joints persistence, which is related to dimensions of the location, the numerical models for joint persistence are done in an acceptable level in order to create blocks with high conformity in terms of the dimensions. Then, the comparison is made between block dimensions from perspectives of numerical models and GSI values, to choose the best ones showing high conformity with real conditions.
Results and discussion
The comparison of the modeling results using creation of joints in different cases with quantitative results obtained according to geological strength shows that the created block volumes are not properly distributed due to the creation of joints as irregular ones in the two cases of persistent and non-persistent. In this case, the blocks volume changes from a few centimeter to cubic meter, and as the block dimensions increase, the created blocks become bigger. Thus, according to the created blocks volume and the obtained GSI range, the creation of joints is not a suitable method as an irregular one. The creation of regular and persistent joints is not an appropriate method either, as the most created blocks are small, and blocks volume distributions do not comply with quantitative distribution. But with creation of joints as regular and persistent ones, the distribution function of blocks volume in numerical method and quantitative method is log normal. Therefore, according to the created blocks dimensions and GSI range using 3DEC software, the most suitable case is the creation of joints as regular and non-persistent ones. 
Conclusion
According to the obtained results in the four cases, when the joints are considered only as regular and non-persistent ones, the blocks volume range is more compatible with real conditions and follows log normal distribution. Thus it can be concluded that the suggested method for creation of joints in the numerical modeling using 3DEC software is more suitable than others considering the rock blocks dimensions and their distributions. This method can be utilized in any structure to accurately define the persistence of joints regarding created blocks dimension.