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ABSTRACT One of the difficulties in describing the rock mass behavior is assigning the appropriate constitutive model. This limitation may be overcome with the progress in discrete element software such as PFC, which does not need the user to prescribe a constitutive model for rock mass. In this paper, the model size of 30m × 30m was analyzed by using the fracture geometry from two tunnel sites. PFC simulations were carried out to examine the mechanical behavior of rock masses. From the numerical tests, it can be concluded that as the number of joint sets increased, the values of mechanical properties of rock masses were decreased to about 50% of those values of rock mass without joints. And the behavior of the rock mass changed from brittle to perfectly plastic with increase in the number of joints. Also the values of Young's modulus, Poisson's ratio and peak strength are almost similar from PFC model and empirical methods. As expected, the presence of joints had a pronounced effect on mechanical properties of the rock mass. More importantly, the mechanical response of the PFC model was not determined by a user specified constitutive model. So the discrete element model gives very contrasting results compared to the traditional model. 1 INTRODUCTION Although the evaluation of the mechanical properties and behavior of discontinuous rock masses is very important for the design of underground openings, it has always been considered the most difficult problem. The reason is that it is often impossible to carry out large-scale in situ tests and, although widely used, the correlations between strength parameters and quality indexes (for instance GSI or Q index) are still affected by considerable uncertainties (Ribacchi 2000). The evaluation of rock mechanical properties such as deformation and strength properties can be achieved through the application of empirical relationships or by a theoretical approach based on numerical modeling. Both methodologies imply some assumptions and uncertainties that need to be considered. Deformation properties and rock mass strength are not only dependent on the intact rock, but also on the fracture network (number and orientation of fracture sets, intensity, mineralization, and so on) and the presence of deformation zones. Therefore, characterization of both the intact rock and of the fractures is required to define the mechanical behavior of the rock mass. Discontinuous rock masses are usually weaker and more deformable and are highly anisotropic when compared with intact rocks. So constitutive modeling of discontinuous rock masses has long been a subject of interest and numerous models have been developed in attempt to simulate their mechanical responses (Staub et al. 2002). Recent developments in numerical modeling that allow study of the overall response of a synthetic material containing discrete heterogeneities and discontinuities both at the micro (particle) scale and at the larger scale of jointed rock masses can greatly aid the interpretation and application of laboratory test results on these materials (Potyondy & Fairhurst 1999). The methodology for the rock mechanical descriptive model was developed in Sweden.
ABSTRACT In this paper, the author discusses the problems encountered in modeling jointed rock reinforced by support structures such as rock bolts. It is well known that rock bolts are extremely effective for reinforcing jointed rock, particularly jointed hard rock. If the concerned rock is highly jointed, a continuum approach could be well applicable in its modeling. It should be noted, however, that in a continuum approach, mechanical properties such as Young's modulus and shear strength are properties for a continuous material mechanically equivalent to the jointed rock. Therefore, if rock bolts are installed for reinforcing equivalent material, the effect of the rock bolts in restricting the movement of the joints is not properly taken into account because all the joints have disappeared. In order to overcome this difficulty, jointed rock should not be modeled independently of the rock bolts, but should be modeled simultaneously by considering the effect of the rock bolts. For determining the mechanical parameters of equivalent material, the homogenization theory is applicable at the design stage, and a back analysis technique can be used during the excavation. 1 INTRODUCTION Numerical analysis is a powerful tool when designing rock structures like tunnels and slopes. However, the accuracy of numerical analyses entirely depends on what numerical model is used to model the rock. Since there are various uncertainties involved in the geological and the geomechanical characteristics of rock, it is not an easy task to model the rock. In the modeling of rock, there are two approaches available. One is a continuum approach and the other is a discontinuum approach. If a rock mass is highly jointed, the continuum approach could be well applicable. In the continuum approach, it should be noted that the values for the mechanical properties, such as Young's modulus and shear strength, determined by in situ tests such as plate bearing tests and direct shear tests, respectively, are values for a continuous material mechanically equivalent to the jointed rock mass. In other words, the concerned jointed rock mass is implicitly assumed to be a continuum from which all joints disappear. Therefore, it is obvious from Fig. 1 that if rock bolts are installed into such an equivalent material, the effect of the rock bolts in restricting the movement of the joints may not be properly taken into account. This means that in the continuum approach, the effect of restricting the movement of the joints should be taken into account in a suitable manner. (Figure in full paper) Fig. 1 Conventional continuum approach for the modeling procedure for a jointed rock mass reinforced by rock bolts 2 FAILURE CRITERION 2.1 Hoek-Brown criterion The Hoek-Brown criterion is one of the most popular failure criteria for rock masses. The criterion is given in the following equations:(Equation in full paper) where σ1 and σ3 are the major and the minor principal effective stresses, respectively, and σ c is the uniaxial compressive strength of the intact rock.
Estimation of Deformation Modulus In a Weathered Granite Using the Decrease In Transmissivity With Depth
Jiang, X.W. (China University of Geosciences) | Wang, X.S. (China University of Geosciences) | Wan, L. (China University of Geosciences) | Wu, X. (China University of Geosciences) | Kang, A.B. (China University of Geosciences)
ABSTRACT Both hydraulic and mechanical properties of fractured rock masses are related to the geometry of fractures. From the perspective of hydro-mechanical coupling, the nonlinear decrease in transmissivity with depth can be utilized to calculate fracture normal stiffness of large scale rock masses. In the current study, the degree of weathering and the non-linear decrease in transmissivity with depth are considered simultaneously to estimate fracture normal stiffness of a granite rock mass. The equations of transmissivity-depth correlation in each zone with different degree of weathering are employed to calculate the corresponding fracture normal stiffness; then the equivalent continuum model is utilized to calculate deformation modulus of the rock masses. In the highly weathered zone, the deformation modulus ranges between 2 and 4 GPa; in the moderately weathered zone, the deformation modulus ranges from 15 to 19 GPa; in the slightly weathered zone, the deformation modulus ranges between 24 to 26 GPa. Compared with the values of deformation modulus obtained from measurements or engineering analogy method, which were determined by others, the results in the present study are reasonable. 1 INTRODUCTION The deformation modulus is the most representative parameter describing the pre-failure mechanical behavior of a rock mass. Numerous researchers had reported that deformation modulus, or compressibility, which is defined as the reciprocal of deformation modulus, of rocks is stress dependent (Adams and Williamson, 1923; Fatt, 1958; Zimmerman, 1991). Unfortunately, in situ measurements of the deformation modulus involve difficult test procedures, and are expensive and time-consuming. Moreover, even such in situ tests are still not able to obtain parameters that can represent large scale rock masses. Both hydraulic and mechanical properties of rock masses are related to the geometry of fractures (Chen, 1990), which suggests a new way to estimate mechanical properties from hydraulic information. Rutqvist (1995) utilized hydraulic jacking test to determine normal stiffness of fractures in hard rocks. Jiang et al. (2008) estimated the stress-dependent fracture normal stiffness of large scale rock masses using the permeability data from packer test in a wide range of depths. In Jiang et al. (2008), the most important and sensitive parameter for calculation of normal stiffness is the permeability-depth correlation. It was assumed that the depth dependency of permeability was caused by the nonlinear normal stress-aperture relationship of fractures (Goodman, 1976), which had been observed by Snow (1968) using field permeability measurements. However, the depth-dependent permeability is also influenced by weathering of the rock mass (Rutqvist and Stephansson, 2003). Moreover, it is well known that the mechanical properties, including deformability, differ greatly in rock masses with different intensity of weathering. Therefore, the degree of weathering should be considered while estimating the deformation modulus of large scale rock masses. In this paper, the theory for estimation of deformation modulus using permeability data is presented. This method is then applied to a study area which is composed of weathered granite. 2 THEORY 2.1 The relationship among fracture normal stiffness, transmissivity and stress.
- Asia > China (0.29)
- North America > United States (0.28)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Rock Type > Igneous Rock > Granite (0.82)