Characterization on jointed rock masses based on PFC2D

Abstract

Geometrical parameters of discontinuities, such as spacing, length, dip and fault throw between joints have a great influence on the mechanical behavior of jointed rock masses. Accurate characterization for discontinuities is important for investigate the stability of rock masses. In this paper, the PFC2D is combined with joint network generation method to examine the mechanical behaviors of jointed mass. Taking Miaogou Open-pit Mine as an example, the information and statistical distributions of discontinuities of the slope rock masses are measured by ShapeMetriX3D measuring tool. Then, the automatic generation algorithm of random joints network based on the Monte-Carlo method is proposed using the programming language (FISH) embedded within PFC2D. This algorithm could represent the discontinuities compared with the geological surveys. In simulating the compression test of a jointed rock sample, the mechanical behavior and crack propagation were investigated. The results reveal that the failure mode and crack propagation of the jointed rock are dominated by the distribution of joints in addition to the intact rock properties. The simulation result shows the feasibility of the joints generating method in application to jointed rock mass.

Keywords

jointed rock masses / shape metrix3D / monte-carlo stochastic simulation method / PFC2D

Introduction

Rock mass is a geologic body composing by the discontinuities which have a critical influence on deformational behavior of blocky rock systems [1]. In jointed rocks, the strength and deformational behavior of rock mass depend principally on the state of intact rock whose obtaining method for the mechanical properties is relatively systematic and existing discontinuities whose strength and distributions are both the key influencers. Therefore, accurate description of joints is an important topic for estimating and evaluating the deformability of rock masses.

In practice the mechanical properties of jointed rock massed can be determined by using both continuum and discontinuum numerical methods. The discontinuum approaches, and in particular Particle Flow Code developed by the ITASCA Consulting Group based on DEM theory [2] could simulate the discontinuous deformation behaviors of rock masses such as slippage and fracture, and thus have broad prospect in the filed of mechanical behavior investigation for jointed rock mass. Therefore, obtaining accurate intact rock properties, reliable discontinuity properties and employing powerful numerical approaches such as Particle Flow Code can provide an optimum solution to heavily jointed rock mass stability. These fracture defects can be large scale geological structures, such as faults which could easily be captured by geological survey or medium scale fractures, such as joints which present objective statistical laws of the randomicity. Geometric parameters of discontinuities compose of mean spacing, trace length, dip angle and fault throw, etc. The probability distribution model for these parameters may be negative exponential distribution, normal distribution, logarithmic normal distribution or uniform distribution [3]. The PFC’s builtin joint generating function (JSET) [4], however, could only get normal or uniform distribution and thus an improved function for generating stochastic joints is requisite.

The improved processes of the stochastic generation of a discontinuous rock mass model with PFC2D are presented in this paper, using the data handled directly in the open-pit slope of Miaogou Iron Mine, located in Hebei province, China. The orientation data of the discontinuities is acquired using ShapeMetrix3D which is an approach for rock face characterization using scaled three-dimensional images. Then, the automatic generation algorithm of random joints network based on the Monte-Carlo method is proposed using the programming language (FISH) embedded within PFC2D. This algorithm could represent the discontinuities compared with the geological surveys. In simulating the compression test of a jointed rock sample, the mechanical behavior and crack propagation were investigated in this paper.

Generation of a fracture system model by ShapeMetriX3D

ShapeMetriX3D is a powerful tool for the geological and geotechnical data collection and assessment for rock masses [5]. During measuring process, two digital photos taken by a calibrated camera serve for a 3D reconstruction of the rock face geometry which is represented on the computer by a photorealistic spatial characterization. From it, measurements are taken by marking visible rock mass features, such as spatial orientations of joint surfaces and traces, as well as areas, lengths, or positions. Finally, the probability statistical models of discontinuities are established. It is generally applied in the following typical situations such as long rock faces at small height, rock slopes with complex geometries [6]. Almost any rock face can be reconstructed at its optimum resolution by using this equipment and its matching software.

Collection of structure data

Stereoscopic photogrammetry deals with the measurement of three-dimensional information from two images showing the same object or surface but taken from two different angles, just as shown in Fig. 1. By automatic identification of corresponding points within the image pair, the result of the acquisition is a metric 3D image that covers the geometry of the rock surface together with a real photo. Once the image of a rock wall is ready, geometric measurements can be taken shown in Fig. 2. There are total three groups of discontinuities in this bench face.

The measured orientation in a hemispherical plot could also be captured as Fig. 3. Figure 4 shows the results of the distribution of joints. The determination of the joint density and spacing as well as trance length can be acquired.

Characteristics of the discontinuities

The probability statistical models of joint traces, as well as dip angle, lengths, or spacing are listed in Table 1. Type 1 of the probability statistical model in Table 1 stands for negative exponential distribution, type 2 for normal distribution, type 3 for logarithmic normal distribution and type 4 for uniform distribution. Although ShapeMetriX3D could give a detailed geological data of the structures, it cannot be directly used by the mechanical simulation model in PFC2D. In the ensuring, the fundamental of stochastic modeling on fracture networks based on the geological data will be discussed in detail.

Fracture system modeling for PFC2D

Fundamental principles of Monte-Carlo

Using the Monte-Carlo Stochastic Simulation Method (MCSSM), a random-sampling technique, discontinuities network model is established. Namely through the stochastic simulation, the implement course how to obtain the discontinuities network submitting to the geometry parameter probability model which is established according to the actual statistical is introduced as is shown in Fig.5.

The establishment of discontinuities network using MCSSM is the reverse process of geological date collection. The MCSSM could give the basic random data such as dip angles or trace length for the network simulation of rock mass discontinuities based on the acquired probability distribution model of the discontinuities geometric parameters that are measured in situ [7]. Network geometric graphics are simulated with the data from MCSSM by a second development of PFC2D using the FISH programming language. Randomness of the data such as dip angel is the core of MCSSM and it will be generated by using urand, a build-in FISH function uniformly distributed on the interval from 0 to 1 in PFC2D. In the program, area-ratio is defined by trace length and fault throw of one certain set of joints. The process of realizing the basic random data are presented based on the normal distribution function from Eq. (1).

(1)F\left(x\right)={\displaystyle \frac{\mathrm{1}}{\sqrt{\mathrm{2}\mathrm{\pi }}{\sigma }_x}}{\displaystyle \underset{\mathrm{\infty }}{\overset{x}{\int }}\exp \left[-{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\left({\displaystyle \frac{x-{\mu }_x}{{\sigma }_x}}\right)}^{\mathrm{2}}\right]}\mathrm{d}x,

where \mu is the average value of particular geological parameter such as dip angle, length or spacing of joints, \sigma is the standard deviation of this parameter. As Eq. (1) is a function whose definite integral is hard to obtain, random number n_i is solved based on the center limit theorem of mathematical statistical theory [8,9] implied by Eq. (2).

(2)n_i=\sigma {\displaystyle \sum _{i=\mathrm{1}}^{\mathrm{12}}\left(r_i-\mathrm{6}\right)+\mu }.

Fracture system generation and validation

In the following section, the impact of joints on the macroscale response is to be examined by performing several compression tests. Figure 6 shows the numerical model built in PFC2D, whose size is 5.0 m× 10.0 m and is made up of approximately 5092 randomly placed particles with the radius of 5.0 cm.

The behavior of granular sample is concerned with the movement and interactions of particles. This can be modeled correctly in PFC simply by defining micro properties of particles and contacts. No quantitative relation has been established between macro-mechanical properties of a particle assemblage and micro parameters of particles and contacts. Generally, the macro mechanical properties are determined in an additional step by performing a series of calibration tests within a uniaxial/biaxial compression and Brazilian tensile strength test implemented in PFC [10–12]. To summarize, the bonded-particle model [13] is used in this simulation and the properties of particles and contacts are listed in Table 2 referring to those in Itasca, Consulting Group Inc (2004) [14]. To simulate a decrease of joint strength, the bond strength between particles involved in the joint contacts was reduced by up to 70%. The shear behavior and failure progress at a given stress corresponded well to those observed in laboratory tests [15].

The model was loaded by applying a constant strain rate to the top and fixing the bottom wall. The visualized contact force chains were also analyzed (yellow for tensile type, red for shear type). At the initial stage of compression, the contact normal force chains spread in the whole model. Stresses concentrating in the particles, accompanied with bond breakages occurred with the compression. In the end, 5 main inclined macro fractures localized by the bond breakages formed in the model as is shown in Fig. 7(f).

After a bond of one joint breaks, a microcrack is considered to be occurred in PFC. After the breakage the stress is redistributed and, hence, more cracks may form nearby. In the fracture process, crack orientation and propagation are also monitored in Fig. 8, where black lines represent tensile cracks and red ones indicate shear cracks. According to the simulation, microcracks are distributed and extend along strike direction of joints. Therefore rock mass failures are controlled by properties of the dominant joints. The deformation behavior is mainly controlled by shear cracks and the result agrees well with that analyzed by scanning electron microscope (SEM) [16] and tests from DIC analyses [17].

The stress-strain behaviors as well as progressive cracks number of intact rock model and jointed rock model under uniaxial compression are displayed in Fig. 9, respectively.

Crack-initiation stress levels (Fig. 9) of two different models differ from each other. In intact rock sample, little cracks occurred at the beginning until the uniaxial stress was approximate 4.15 MPa. However, the initial generation progress of cracks was a sharp development and the initial stress level was only 0.45 MPa in jointed rock model. Strength of the intact rock was about 5.4 MPa and only 4.5 MPa of jointed rock model. And at the same time, the elastic modulus of intact rock was larger than that of jointed rock model through comparison.

Conclusions

An automatic generation algorithm of random joints network based on the Monte-Carlo method is proposed using the programming language (FISH) embedded within PFC2D. The discontinuities compared with the geological surveys were characterized. The influence on the rock fracture apart from the mechanical behavior in an intact rock model and a jointed rock model was investigated through numerical analyses in this paper.

According to the simulation, microcracks are distributed and extend along strike direction of joints. Rock mass failures are controlled by properties of the dominant joints and the deformation behavior is mainly controlled by shear cracks. From the numerical analyses, a joint geometry dependent failure process has been observed. Based upon the result, it can be argued that the joint network has a large influence on the behavior of rock deformation and the method proposed in this paper is feasible.

This study presents limited views of the phenomenon. Further study is required to identify the surface roughness which plays an important role in the deformation behavior of rock mass [18,19].

References

[1] Pariseau W G, Puri S, Schmelter S C. A new model for effects of impersistent joint sets on rock slope stability. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(2): 122–131

[2] Cundall P A. A computer model for simulating progressive large-scale movements in block systems. In: Proceedings of the Symposium of the International Society of Rock Mechanics. Rotterdam: A.A Balkema, 1971, 1: 8–12

[3] Huang Y F, Feng J. Theory, Programs and Examples of Computing Engineering Geology. Beijing: Weapon Industry Press, 1992 (in Chinese)

[4] Itasca Consulting Group, Inc. Particle Flow Code in 2-Dimensions: Command Reference version 3.1. Minneapolis, 2004

[5] Austrian Startup Company. ShapeMetriX3D model merger user manual. Shenyang: Earth Products China Ltd, 2008

[6] Yang T H, Yu Q L, Chen S K. Rock mass structure digital recognition and hydro-mechanical parameters characterization of sandstone in Fangezhuang coal mine. Chinese Journal of Rock Mechanics and Engineering, 2009, 28(12): 2482–2488 (in Chinese)

[7] Shen H Y, Zhang P, Wang K. Improved linear congruential random number generators. Journal of Tsinghua University (Science & Technology), 2009, 49(2): 191–193

[8] Su J M, Zhang L H, Liu B. Applications of MATLAB toolboxes. Beijing: Publishing House of Electronics Industry, 2004

[9] Jiao Y Y, Zhang X L, Li T C. DDARF Method for Simulating the Whole Process of Rock Failure. Beijing: Science Publishing House, 2010

[10] Bäckström A, Antikainen J, Backers T, Feng X, Jing L, Kobayashi A, Koyama T, Pan P, Rinne M, Shen B, Hudson J A. Numerical modelling of uniaxial compressive failure of granite with and without saline porewater. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(7): 1126–1142

[11] Potyondy D O. Simulating stress corrosion with a bonded-particle model for rock. International Journal of Rock Mechanics and Mining Sciences, 2007, 44(5): 677–691

[12] Wang Y N, Fulvio T. Modeling Lac du Bonnet granite using a discrete element model. International Journal of Rock Mechanics and Mining Sciences, 2009, 46(7): 1124–1135

[13] Hazzard J F, Young P P. Simulation acoustic emissions in bonded-particle models of rock. International Journal of Rock Mechanics and Mining Sciences, 2000, 37(5): 867–872

[14] Itasca, Consulting Group Inc. Particle Flow Code in 2-Dimensions: FISH in PFC2D version 3.1. Minneapolis, 2004

[15] Park J W, Song J J. Numerical simulation of a direct shear test on a rock joint using a bonded-particle model. International Journal of Rock Mechanics and Mining Sciences, 2009, 46(8): 1315–1328

[16] Fu Z L. Experiment course on rock mechanics. Beijing: Chemical Industry Press, 2011 (in Chinese)

[17] Hall S A, Muir Wood D, Ibraim E, Viggiani G. Localised deformation patterning in 2D granular materials revealed by digital image correlation. Granular Matter, 2010, 12(1): 1–14

[18] Jiang Y J, Li B, Yosihiko T. Estimating the relation between surface roughness and mechanical properties of rock joints. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(6): 837–846

[19] Fardin N, Stephansson O, Jing L R. The scale dependence of rock joint surface roughness. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(5): 659–669

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg