Numerical BuiltIn Method for the Nonlinear JRC/JCS Model in Rock Joint.  
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PMID: 24693245 Owner: NLM Status: InDataReview 
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The joint surface is widely distributed in the rock, thus leading to the nonlinear characteristics of rock mass strength and limiting the effectiveness of the linear model in reflecting characteristics. The JRC/JCS model is the nonlinear failure criterion and generally believed to describe the characteristics of joints better than other models. In order to develop the numerical program for JRC/JCS model, this paper established the relationship between the parameters of the JRC/JCS and MohrCoulomb models. Thereafter, the numerical implement method and implementation process of the JRC/JCS model were discussed and the reliability of the numerical method was verified by the shear tests of jointed rock mass. Finally, the effect of the JRC/JCS model parameters on the shear strength of the joint was analyzed. 
Authors:

Qunyi Liu; Wanli Xing; Ying Li 
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Type: Journal Article Date: 20140211 
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Title: TheScientificWorldJournal Volume: 2014 ISSN: 1537744X ISO Abbreviation: ScientificWorldJournal Publication Date: 2014 
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Created Date: 20140402 Completed Date:  Revised Date:  
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Nlm Unique ID: 101131163 Medline TA: ScientificWorldJournal Country: England 
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Languages: eng Pagination: 735497 Citation Subset: IM 
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Journal Information Journal ID (nlmta): ScientificWorldJournal Journal ID (isoabbrev): ScientificWorldJournal Journal ID (publisherid): TSWJ ISSN: 1537744X Publisher: Hindawi Publishing Corporation 
Article Information Download PDF Copyright © 2014 Qunyi Liu et al. openaccess: Received Day: 15 Month: 11 Year: 2013 Accepted Day: 1 Month: 1 Year: 2014 collection publication date: Year: 2014 Electronic publication date: Day: 11 Month: 2 Year: 2014 Volume: 2014Elocation ID: 735497 PubMed Id: 24693245 ID: 3944205 DOI: 10.1155/2014/735497 
Numerical BuiltIn Method for the Nonlinear JRC/JCS Model in Rock Joint  
Qunyi LiuI1  http://orcid.org/0000000167490057 
Wanli XingI1  
Ying LiI1*  
Institute of Mineral Resources, Chinese Academy of Geological Sciences, Beijing 100037, China 

Correspondence: *Ying Li: liyingacgs@126.com [other] Academic Editors: A. Esmaeily and A. RodríguezCastellanos 
The MohrCoulomb linear model is generally used to study the characteristics of rock mass strength [^{1}–^{3}]. Lin et al. [^{1}] used numerical algorithm to simulate the mechanical behavior of a layered rock mass under true triaxial compression by MohrCoulomb linear model. Most calculation software are based on the MohrCoulomb model, which represents rock strength with cohesion c and internal friction angle ϕ [^{4}–^{7}]. However, the joint surface is widely distributed in the rock, thus leading to the nonlinear characteristics of rock mass strength and limiting the effectiveness of the linear model in reflecting characteristics [^{8}]. Therefore, scholars introduced nonlinear models, such as the HoekBrown model [^{9}, ^{10}] and JRC/JCS model [^{11}–^{13}], which can describe rock mass strength. Halakatevakis and Sofianos [^{14}] investigated the HoekBrown criterion analytically through an extended plane of weakness theory. Babanouri et al. [^{13}] developed extended Barton's shear failure criterion for rock joints to consider the effect of various paths of normal loading/unloading before shearing and overconsolidation ratio in a fracture. Park and Song [^{15}] produced a rough joint with a joint roughness coefficient (JRC) value ranging from 10 to 20 in an intact sample by defining the jointcontacts along a predefined joint surface. Studies have contributed significantly to the nonlinear description of rock mass strength. However, the JRC/JCS model, which was proposed by Barton et al. on the basis of a large number of shear tests on jointed rock mass, is generally believed to describe the characteristics of joints better than other models [^{11}, ^{16}]. The JRC/JCS model is mainly studied by theoretical and experimental approaches and not by numerical approaches. On the basis of the above considerations, this paper established the relationship between the parameters of the JRC/JCS and MohrCoulomb models. Thereafter, the numerical implement method and implementation process of the JRC/JCS model were discussed and the reliability of the numerical method was verified by the shear tests of jointed rock mass. Finally, the effect of the JRC/JCS model parameters on the shear strength of the joint was analyzed.
The JRC/JCS model was formulated as follows [^{11}]:
(1)
τ=σntan[ϕb+JRC log10(JCSσn)], 
The MohrCoulomb model was formulated as follows:
(2)
τc=σntanϕ+c. 
(3)
tanϕ=∂τ∂σn. 
(4)
tanϕ=∂τ∂σn=fa−fb, 
The triangle transformation of (4) is as follows:
(5)
ϕ=arctan(fa−fb),sinϕ=fa−fbfa2+fb2−2fafb,cosϕ=1fa2+fb2−2fafb,c=σnfb. 
(6)
σmin=10[ log (JCS)((70−ϕb)/JRC)]. 
Assuming that the rock basic friction angle was 30° and that JCS = 5 MPa to 105 MPa and JRC = 0 to 18 were changed, Figures 1 and 2 could be determined. The cohesion c and internal friction angle ϕ increase gradually with increasing JRC (Figure 1), and the slope of the relation curve of c and JRC increases gradually with increasing JRC. By contrast, the slope of the relation curve of ϕ and JRC decreases gradually with increasing JRC. The curve of the effect of JRC on the internal friction angle (Figure 1(b)) demonstrates that the internal friction angle that corresponds to the same JRC increases with increasing rock compressive strength. Furthermore, for the same increment of JCS, the increment of the internal friction angle is greater with increasing JRC. However, for the same increment of JRC, the range ability of the internal friction angle decreases with increasing JCS. This observation highlights that the effect of JRC on the internal friction angle is greater than the effect of JCS. Cohesion c increases linearly with increasing JCS, whereas the internal friction angle ϕ increases nonlinearly with increasing JCS (Figure 2). The slope of the curve of JCS and cohesion increases gradually with increasing JRC; thus, a rougher joint surface corresponds to the greater influence of JCS on cohesion (Figure 2(a)). When JRC = 0, that is, the roughness of the joint surface is high, the internal friction angle of joint surface is the basic friction angle with a value of 30° (Figure 2(b)).
To establish the numerical computation method in the JRC/JCS model, the incremental formula of stress and deformation was obtained by elastic incremental theory:
(7)
Δσ1=α1Δε1e+α2(Δε2e+Δε3e),Δσ2=α1Δε2e+α2(Δε1e+Δε3e),Δσ3=α1Δε3e+α2(Δε1e+Δε2e), 
The stress components could be calculated by elastic theory:
(8)
σiI=σi0+Δσi, (i=1,2,3), 
Thereafter, new stress components σ_{1}^{N}, σ_{2}^{N}, and σ_{3}^{N} could be deduced by the theory that incremental strain Δε_{i} is the sum of the elastic incremental strain Δε_{i}^{e} and plastic incremental strain Δε_{i}^{p} under the plastic state:
(9)
σ1N−σ10=α1(Δε1−Δε1p)+α2(Δε2+Δε3−Δε3p), 
(10)
σ2N−σ20=α1Δε2+α2(Δε1−Δε1p+Δε3−Δε3p), 
(11)
σ3N−σ30=α1(Δε3−Δε3p)+α2(Δε1+Δε2−Δε1p). 
(12)
σ1N=σ1I−α1Δε1p−α2Δε3p,σ2N=σ2I−α2(Δε1p+Δε3p),σ3N=σ3I−α1Δε3p−α2Δε1p 
(13)
σnN=12[σ1N+σ3N+(σ1N−σ3N)cos2α],τN=12[(σ1N−σ3N)sin2α], 
The VC++ language was used for the secondary development of the numerical calculation module of FLAC3D, and the corresponding program was developed [^{18}–^{20}]. During the calculation, the strain and the stress of every unit were calculated by elastic theory. Thereafter, to judge if the yield condition was achieved, the corresponding stress should be adjusted to meet the yield function by adding the JRC/JCS model. Test data that comprised the shear strength and normal stress of the joint obtained by joint shear tests in the laboratory were used to verify the correctness of the program, as shown in Table 1. The JRC = 16 is taken for calculation, and the numerical model is shown in Figure 3. As described by Lin et al. [^{21}], FLAC3D is difficult to use for building large, complex, and threedimensional mining models. Lin et al. [^{21}] combined the advantages of FLAC3D in numerical calculation and those of SURPAC in threedimensional modeling and compiled the interface program. In this paper, we used ANSYS to build the model then transformed it to FLAC3D. The comparison between the calculated and test results is shown in Table 1 and Figure 4. The joint shear strength obtained from the test increases nonlinearly with increasing normal stress. Moreover, the results from the MohrCoulomb model and JRC/JCS model are in good agreement with the test results. However, when the normal stress of the joint surface is small, the nonlinear characteristics of the shear strength are obvious and the MohrCoulomb model cannot describe the nonlinear characteristics. By contrast, the JRC/JCS model can describe the characteristics well. The correlation coefficient of the results from the JRC/JCS model and test model is 0.99315, which is higher than the correlation coefficient of the results of the MohrCoulomb model at 0.99072. Therefore, the reliability of the numerical calculation method of the JRC/JCS model is verified. The calculations show that the parameters of the JRC/JCS model are JRC = 15.42 and JCS = 57.387 MPa, whereas the parameters of the MohrCoulomb model are c = 1.926 MPa and ϕ = 33.45°.
To study further how JRC and JCS affect the shear strength of the joint surface, σ_{n} = 2.0 MPa was fixed through calculation and the relationship of JRC and JCS with the shear strength of the joint surface was obtained (Figures 5 and 6). In Figures 5 and 6 the shear strength of the joint surface increases nonlinearly with increasing JRC and JCS. The slope of the relation curve of the shear strength and JRC increases with increasing JRC, whereas the slope of the relation curve of shear strength and JCS decreases with increasing JCS. Thus, changes in JRC affect the shear strength more than changes in JCS.
(1) The cohesion c and internal friction angle ϕ increase gradually with increasing JRC. The internal friction angle that corresponds to the same JRC increases with increasing rock compressive strength. Furthermore, for the same increment of JCS, the increment of the internal friction angle is greater with increasing JRC. The effect of JRC on the internal friction angle is greater than the effect of JCS. Cohesion c increases linearly with increasing JCS, whereas the internal friction angle ϕ increases nonlinearly with increasing JCS.
(2) The results from the MohrCoulomb model and JRC/JCS model are in good agreement with the test results. However, when the normal stress of the joint surface is small, the nonlinear characteristics of the shear strength are obvious and the MohrCoulomb model cannot describe the nonlinear characteristics. By contrast, the JRC/JCS model can describe the characteristics well.
(3) The shear strength of the joint surface increases nonlinearly with increasing JRC and JCS. Changes in JRC affect the shear strength more than changes in JCS.
The research project was supported by the National Natural Science Foundation of China (41202057).
The authors declare that there is no conflict of interests regarding the publication of this paper.
References
1.  Lin H,Cao P,Wang Y. Numerical simulation of a layered rock under triaxial compressionInternational Journal of Rock Mechanics and Mining SciencesYear: 2013601218 
2.  Li LC,Tang CA,Zhu WC,Liang ZZ. Numerical analysis of slope stability based on the gravity increase methodComputers and GeotechnicsYear: 2009367124612582s2.067650979174 
3.  Unlu T,Gercek H. Effect of Poisson’s ratio on the normalized radial displacements occurring around the face of a circular tunnelTunnelling and Underground Space TechnologyYear: 20031855475532s2.00141537894 
4.  Lin H,Xiong W,Cao P. Stability of soil nailed slope using strength reduction methodEuropean Journal of Environmental and Civil EngineeringYear: 201317872885 
5.  Liu T,Cao P,Lin H. Evolution procedure of multiple rock cracks under seepage pressureMathematical Problems in EngineeringYear: 201319112 
6.  Wang SY,Sloan SW,Tang CA,Zhu WC. Numerical simulation of the failure mechanism of circular tunnels in transversely isotropic rock massesTunnelling and Underground Space TechnologyYear: 201232231244 
7.  Sun D,Yao YP,Matsuoka H. Modification of critical state models by MohrCoulomb criterionMechanics Research CommunicationsYear: 20063322172322s2.027744546810 
8.  Khani A,Baghbanan A,Norouzi S,Hashemolhosseini H. Effects of fracture geometry and stress on the strength of a fractured rock massInternational Journal of Rock Mechanics and Mining SciencesYear: 201360345352 
9.  Hoek E,CarranzaTorres C. Corkum B. HoekBrown failure criterion2002 editionProceedings of NARMSTAC2002267273 
10.  Hoek E,Brown ET. Practical estimates of rock mass strengthInternational Journal of Rock Mechanics and Mining SciencesYear: 1997348116511862s2.00031432421 
11.  Barton N,Bandis S. Review of predictive capabilities of JRCJCS model in engineering practicePublikasjonYear: 1991182182s2.00025890526 
12.  Du S,Hu Y,Hu X,Guo X. Comparison between empirical estimation by JRCJCS model and direct shear test for joint shear strengthJournal of Earth ScienceYear: 20112234114202s2.079957840678 
13.  Babanouri N,Karimi Nasab S,Baghbanan A,Mohamadi HR. Overconsolidation effect on shear behavior of rock jointsInternational Journal of Rock Mechanics and Mining SciencesYear: 2011488128312912s2.081955161956 
14.  Halakatevakis N,Sofianos AI. Correlation of the HoekBrown failure criterion for a sparsely jointed rock mass with an extended plane of weakness theoryInternational Journal of Rock Mechanics and Mining SciencesYear: 2010477116611792s2.077956651848 
15.  Park JW,Song JJ. Numerical simulation of a direct shear test on a rock joint using a bondedparticle modelInternational Journal of Rock Mechanics and Mining SciencesYear: 2009468131513282s2.070449534065 
16.  Zhao J. Joint surface matching and shear strength. Part B: JRCJMC shear strength criterionInternational Journal of Rock Mechanics and Mining Sciences & Geomechanics AbstractsYear: 19973421791852s2.00031079862 
17.  Lin H,Zhong W,Cao P,Liu T. Variational safety factors and slip surfaces of slope using threedimensional strength reduction analysisJournal of the Geological Society of IndiaYear: 201382545552 
18.  Cai M. Influence of stress path on tunnel excavation response—numerical tool selection and modeling strategyTunnelling and Underground Space TechnologyYear: 20082366186282s2.046449136036 
19.  Rutqvist J. Status of the TOUGHFLAC simulator and recent applications related to coupled fluid flow and crustal deformationsComputers and GeosciencesYear: 20113767397502s2.079957618337 
20.  Zhang Q,Jiang BS,Wu XS,Zhang HQ,Han LJ. Elastoplastic coupling analysis of circular openings in elastobrittleplastic rock massTheoretical and Applied Fracture MechanicsYear: 2012606067 
21.  Lin H,Liu T,Li J,Cao P. A simple generation technique of complex geotechnical computational modelMathematical Problems in EngineeringYear: 201320138 pages863104 
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