1. INTRODUCTION
Initial An extensive experimental study was undertaken by Singh (1997) to investigate the strength and deformational behavior of regularly jointed blocky mass. Only a brief review of the experimental programme is prented here. Singh (1997) tested more than fifty specimens of a jointed block mass under uniaxial loading conditions. A commercially available model material, sand-lime brick was ud to simulate a weak rock material. Properties of this model material are prented in Table 1.
The bricks of the model material were cut into small elemental blocks of size 25 × 25 × 25 mm, and the blocks were asmbled carefully in a certain fashion to form the specimens of rock mass. The size of each of the specimens was 15 × 15 × 15 cm and on an average there were more than 260 cubes. Figure 1 shows the configurations of joint ts. The prepared specimen of the jointed mass consisted of three regular joint ts. Joint t-I was continuous and was inclined at an angle (θ) with the horizontal. Joint t-II was orthogonal to t-I and stepped at variable step length(s). Set-III had vertical orientation in all the specimens. Various combinations of parameters (θ) and (s) were ud to obtain rock mass specimens with different configurations. The specimens were tested under tuniaxial loading conditions by applying a uniformly distributed load through a loading platen placed at the top of specimen. Teflon sheets were placed at the top and bottom of the rock mass specimen to reduce the e
nd friction. Deformations of the specimen were measured in horizontal as well as in vertical directions. LVDTs were ud to measure deformations of the specimen (Figure 2). It was possible to calculate the changes in vertical and horizontal dimensions of the specimen during the loading process by using the obrvations from the LVDTs [5].
2.EXPRIMENTAL PROGRAMME
An extensive experimental study was undertaken by Singh (1997) to investigate the strength and deformational behaviour of regularly jointed blocky mass. Only a brief review of the experimental programme is prented here. Singh (1997) tested more than fifty specimens of a jointed block mass under uniaxial loading conditions. A commercially available model material, sand-lime brick was ud to simulate a weak rock material. Properties of this model material are prented in Table 1.
ARMA 10-510
Numerical Modeling of Mechanical Behavior of a Jointed Rock Mass
M. ASADIZADEH
Dept. of Mining Engineering, Shahid Bahonar University of Kerman, Iran
R. RAHMANNEJAD
Dept. of Mining Engineering, Shahid Bahonar University of Kerman, Iran
Copyright 2010 ARMA, American Rock Mechanics Association
This paper was prepared for prentation at the 44th US Rock Mechanics Symposium and 5th U.S.-Canada Rock Mechanics Symposium, held in
Salt Lake City, UT June 27–30, 2010.
This paper was lected for prentation at the symposium by an ARMA Technical Program Committee bad on a technical and critical review of
the paper by a minimum of two technical reviewers. The material, as prented, does not necessarily reflect any position of ARMA, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purpos without the written connt of ARMA
is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words;
illustrations may not be copied. The abstract must contain conspicuous acknowledgement of where and by whom the paper was prented.
ABSTRACT: An asssment of mechanical behavior of jointed rock mass is an esntial requirement in the site lection, design and successful execution of Civil and Mining Engineering projects. A quick estimate of the properties for preliminary evaluation of alternate sites will reduce considerable expenditures for field tests. A large number of tests on a jointed rock mass with various joint configurations had been done by Mahendra Singh and others. In this prent study, an attempt has been made to compare the results between numerical simulation of experimental modelling on strength and deformability of jointed block mass. For this purpo, numerical simulation of experimental tests for rock mass modulus and strength has been done by 3 Dimensional Distinct Element Code (3DEC). Results showed numerical simulation and experimental testes have good agreement.
The bricks of the model material were cut into small elemental blocks of size 25 × 25 × 25 mm, and the blocks were asmbled carefully in a certain fashion to form the specimens of rock mass. The size of each of the specimens was 15 × 15 × 15 cm and on an average there were more than 260 cubes. Figure 1 shows the configurations of joint ts. The prepared specimen of the jointed mass c
onsisted of three regular joint ts. Joint t-I was continuous and was inclined at an angle (θ) with the horizontal. Joint t-II was orthogonal to t-
水调歌头意思
I and stepped at variable step length(s). Set-III had vertical orientation in all the specimens. Various combinations of parameters (θ) and(s) were ud to obtain rock mass specimens with different configurations.
The specimens were tested under uniaxial loading conditions by applying a uniformly distributed load through a loading platen placed at the top of specimen. Teflon sheets were placed at the top and bottom of the rock mass specimen to reduce the end friction. Deformations of the specimen were measured in horizontal as well as in vertical directions. LVDTs were ud to measure deformations of the specimen (Figure 2). It was possible to calculate the changes in vertical and horizontal dimensions of the specimen during the loading process by using the obrvations from the LVDTs [5].
Table 1. Properties of the material [5].
Fig. 1. Configuration of joint ts [5].
Fig. 2. (a). Measurement of vertical deformations of specimen.
(b). Measurement of horizontal deformations of specimen [5].
3. RESULTS OF LABORATORY TESTS Results of axial stress vs. corresponding strains in the axial and lateral directions were obtained from the experimental programme. The peak axial stress has been taken as the rock mass strength (σcj). The strength and deformational characteristics are found to change with different combinations of inclination of joints (θ) and interlocking(s). The effect of stepping(s) on strength and tangent modulus for specimens is shown in Figure 3. The values are shown in terms of ratios as defined below:
cr cj ci
张庄中学σσσ
=
(1)
r j i
E E E
遇见的说说唯美句子
=
(2)
property value Dry density (kg/m3) 16.36
Porosity (%) 36.94
UCS, σci (MPa) 17.13
闻名中外的近义词Brazilian strengs, σti (MPa) 2.49
Tangent modulus, E i(GPa) 5.34
Poisson’s ratio ߥ0.19
Cohesion, c i (MPa) 4.67
Friction angel of intact material, ߶i33
Friction angel along the joints, ߶j37
Deere-miller classification (1966) EM
Where (σc) and (E) refer to the uniaxial compressive strength and tangent modulus respectively, the subscripts (i) and (j) refer to intact and jointed specimens
respectively.
Fig. 3(a) Effect of stepping(s) on the strength of the jointed block mass, (b) Effect of stepping(s) on the tangent modulus of the jointed block mass [5].
The variation of strength and tangent modulus for specimens with inclination is shown in Figure 4. The properties have been plotted against the angle (β) which is the orientation of continuous joints relative to the
loading direction, (90)θ°
−
[4].
Fig. 4. Anisotropic behaviour in strength and tangent
modulus [5]
4. NUMERICAL MODELLING IN 3DEC
The rock mass is reprented as an asmbly of discrete blocks with joints as interfaces between distinct bodies. Numerical model was made for orientations(θ): 0° ,10°,30°, 50°,60°, 80°, 90° and the values of (s): 0,1/8, 2/8, 3/8, 4/8, 5/8, 6/8 and 7/8 of the width of the block. The joint Set-III remained vertical. About 56 models were simulated in this modeling. The material properties
stay the same for all of them. The step by step procedure to form the 3DEC model is given below:
4.1 establishment of the model geometry
I. Commands are available to perform various tasks. For example, a combined block of rock and steel platens was first generated by giving the command ‘poly brick’ [6]. II. Interfaces can now be created through the ‘jt’ and ‘hide dip’ commands. Horizontal interfaces were generated at the top and bottom of the block formed earlier to form loading platens. The middle portion of the block forms the rock mass specimen. a view of model in 3DEC is shown in Figure 5 [6].
独船
Fig. 5. The view of model in 3DEC
4.2 assignment of material models and properties
3DEC allows the blocks to be deformable or rigid. By default, all blocks are rigid, in most analys, blocks should be made deformable. Blocks are made deformable via the command ‘gen edge v’. The GEN (or GENERATE) command invokes an automatic mesh generator that fills each block with tetrahedral-shaped finite difference zones. The command ‘gen edge v’ will work for blocks of any arbitrary shape. The value (v) defines the average edge length of the tetrahedral zones. Choices are available in the 3DEC to define the constitutive behavior of the intact rock that includes: null model, elastic isotropic model, elastic anisotropic model, Mohr–Coulomb model, Bilinear Strain-Hardening/Softening Ubiquitous Joint model. The Mohr–Coulomb model was lected in this study. Similarly, the following joint constitutive models are available to define the behavior of joints: Coulomb slip model, continuously yielding joint model; elastic joint model [6]. In the prent analysis, continuously yielding model has been employed. The continuously yielding
model is considered more ‘realistic’ than the standard Mohr-Coulomb joint model in that the continuously yielding model attempts to account for some non-linear behavior obrved in physical t
ests [6]. Various properties assigned to joints and block material in 3DEC model are prented in Tables 2 and 3 respectively. 4.3 application of axial load
In this modeling loads were applied in steps in the downward direction to the top loading platen by applying stress. The displacements in the axial and lateral directions were recorded through FISH functions. In the next step, axial stress, axial strain and lateral strain were recorded. A FISH programme was written for this purpo. FISH is a programming language, similar to C, with which the rearcher can u complex quence of commands repeatedly, perform computations and also access the internal data structure. Average vertical displacement of the top platen and lateral displacement at the mid points of the vertical sides of the 3DEC model during loading is recorded by FISH function. The FISH functions are called by 3DEC in each time step during the process of simulation. The history files were ud to record the average axial stress and strain, during the loading process. After, the stress applied to the top platen reached a peak, it decread with increasing deformation. The simulation was terminated when the axial stress have reduced considerably compared to the peak stress. A failure pattern from 3DEC model is
showed in Figure 6.
Fig. 6. A failure pattern from 3DEC model Table 2. Material properties in 3DEC model [7].
property rock Steel plates
Block constitutive model
Mohr-coulomb Linear elastic
density 1686 kg/m3 7800 kg/m3 Bulk modulus 2876 MPa 185E3 MPa
Shear modulus
2245 MPa
-
人民的名义dvd
Cohesion 4.67 MPa - Friction angel 33° - Tensile strength
2.49 MPa
-
Table 3. Joint properties in 3DEC model [7]. property Rock to rock contact Rock to steel
大学新生自我介绍contact
Steel to
steel contact Joint
constitutive model Continuously yielding model Continuously yielding model Coulob slip model joint normal stiffness k n 11190 MPa/m
11190 MPa/m
1E6 MPa/m joint shear stiffness k s 5886 MPa/m 5886 MPa/m
1e5 MPa/m Joint normal stiffness exponent e n 0.6271 0.6271 -
joint shear stiffness exponent e s 0.0 0.0 - joint initial friction angle if 37° 30° - Joint residual friction angle fric
30°
28°
-
Joint cohesion coh
- - 10 MPa
Joint tensile
strength tensile
- - 1E4 MPa
Joint friction angle fric
-
-
28°
5. RESULTS OF 3DEC MODEL
Results of 3DEC modelling are in the form of history files for axial stress, axial strain, and lateral strain
个人简历免费模版against time step numbers. Peak strength (σcj) and tangent modulus in 50% peak strength are calculated (Ej) from stress-strain curves for all testes.
Comparison between experimental and numerical modelling results by investigating the effect of stepping(s) on the strength and tangent modulus of the jointed block mass is shown in Figures 7 (a) and (b)
respectively.
Fig. 7. Comparison between experimental and numerical modelling results of the jointed block mass in the Effect of stepping (s) on the strength (a) and tangent modulus (b)
Also, comparison between experimental and numerical modelling results by investigating anisotropic behavior in strength and tangent modulus is shown in Figures 8
and 9 respectively.
Fig. 8. Comparison between experimental and numerical modelling results by investigating anisotropic behavior in strength
