research article 3d multiscale integrated modeling approach of...

Research Article3D Multiscale Integrated Modeling Approach of Complex RockMass Structures

Mingchao Li12 Yanqing Han2 Gang Wang3 and Fugen Yan2

1 State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin UniversityTianjin 300072 China

2 School of Civil Engineering Tianjin University Tianjin 300072 China3 Chengdu Design amp Research Institute Chengdu 410014 China

Correspondence should be addressed to Mingchao Li lmctjueducn

Received 19 April 2014 Revised 21 June 2014 Accepted 1 July 2014 Published 10 July 2014

Academic Editor Changchun Hua

Copyright copy 2014 Mingchao Li et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Based on abundant geological data of different regions and different scales in hydraulic engineering a new approach of 3Dengineering-scale and statistical-scale integrated modeling was put forward considering the complex relationships amonggeological structures and discontinuities and hydraulic structures For engineering-scale geological structures the 3D rock massmodel of the study region was built by the exact match modeling method and the reliability analysis technique For statistical-scalejointed rockmass the randomnetwork simulationmodelingmethodwas realized including Baecher structure planemodelMonteCarlo simulation and dynamic check of random discontinuities and the corresponding software program was developed Finallythe refined model was reconstructed integrating with the engineering-scale model of rock structures the statistical-scale model ofdiscontinuities network and the hydraulic structures model It has been applied to the practical hydraulic project and offers themodel basis for the analysis of hydraulic rock mass structures

1 Introduction

At present a reconstructed 3D geological model in a largeregional tectonic range has been applied to analyze rockmass structures for engineering structures widely [1ndash3]based on abundant initial data such as topographic con-tours geological observation points drills adits and remote-sensing images However there are many other minor-scalerandom structures such as discontinuities in rock masses Acomplicated system of rockmass structures is combined withtheseminor-scale structures and somemajor-scale geologicalstructures such as strata faults and weak layers Theycontrol and influence the stability of foundation engineeringunderground engineering and slope engineering [4]

Then the rock mass environment in the engineeringregion can be represented together by multiscale data fromdeterminate geological structures by exploration and sta-tistical data of discontinuities by field investigation It isimportant to solve practical problems of engineering geology

that two kinds of data should be integrated into awholemodeleffectively There are several relevant modeling approachesabout the problem Zhang [5] built different scale models toanalyze rock quality evaluation and slope stability Aitken andBetts [6] simulated the geological structures of an actual areausing the multiscale structural and aeromagnetic analysismethod Jones et al [7] developed a 3D geospatial system tocombine all kinds of geological and geophysical data sourcesfromoutcrop to regional scale into a singlemodel Xu [8] builta hierarchical rock mass structure model (RSM) to deal withthe problemThese results are pertinent for various geologicaldata from different sources

This paper presents a new 3D modeling approach inte-grating major engineering-scale geological structures withminor statistical-scale data of discontinuities The recon-structed refined geoengineering model can describe discon-tinuous structures into rock masses in depth and actualgeological environment objectively

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 867542 6 pageshttpdxdoiorg1011552014867542

2 Mathematical Problems in Engineering

2 Multiscale Classification of Complex RockMass Structures

Geological boundaries with a certain direction and extensionare collectively referred to as structural surfaces includ-ing substance differentiation surfaces (such as horizonsschistosities weak intercalated layers and intrusions) anddiscontinuous fractured planes (such as faults joints andweathering or relief fissures) Then corresponding rockmasses are constrained by these different combined structuralsurfaces which are dominant

In the field of geotechnical engineering structural sur-faces are classified into five levels that is I II III IV and V[5 9] They can be divided into four spatial scales

(1) Regional-scale structures corresponding to levels Iand II such as regional faults they may affect theregion stability with hundreds of kilometers exten-sion

(2) Engineering-scale structures corresponding to levelIII such as horizons weak layers and faults theyextend from hundreds to thousands of meters withgood continuity and a certain thickness And theymay destruct the continuity and stability of rockmasses

(3) Statistical-scale structures corresponding to level IVsuch as horizons weak layers and faults they extendfrom several to tens of meters with random discretedistributions and statistical-advantaged directionsAnd they may affect the deformation mode of rockmasses and result in anisotropic rock mechanicalproperties Due to lack of determined spatial infor-mation they may be described by statistical modelswith certain probability distribution and are calledstatistical-scale geological data

(4) Sample-scale structures corresponding to level Vsuch as hiddenmicrocracks their length level is aboutmillimeter or centimeter They are short and closewith random discrete distributions And they maydecrease the rock strength

Among the four structures engineering-scale and statisti-cal-scale data are emphases in hydraulic engineering geologyas shown in Figure 1 Generally major engineering-scaledata are acquired by geological exploration of drills andadits and interpreted to different cross-sections while minorstatistical-scale data are drawn to geolograph charts fromfield discontinuities Then according to their data featureswe will use different methods to build two kinds of modelsand realize their integration effectively

3 3D Modeling of MajorEngineering-Scale Structures

The regional engineering-scale geological data of hydraulicprojects mainly include topographic contours geologicalpoints remote sensing images drills adits and geophysical

informationThey can be interpreted to a variety of 2D cross-sections by geological engineers All these data are the basisof reconstructing 3D models

The general structure of 3D modeling of major engi-neering-scale rock mass structures is shown in Figure 2Firstly based onmultisource geological data and engineeringdesign data geological objects are classified into terrainhorizons and faults while engineering objects are dividedinto dam structure underground tunnels and drills and aditsby the object-oriented technique Secondly corresponding3D models of geological and engineering structures arebuilt by enhanced NURBS (Nonuniform Rational B-Spline)modeling method [1] During the process the models mustbe verified and revised using the original exploration dataThe verification includes checks of topological geometrystructural rationality and accuracy tests on raw data [1]Finally the integrated geoengineering model is completedthrough a series of complex 3D Boolean operations

4 3D Stochastic Modeling of MinorStatistical-Scale Jointed Rock Mass Network

All kinds of stochastic discontinuities are distributed inrock masses widely And they may control the strength anddeformation of rockmasses and are named jointed rockmassnetwork system It is defined by International Society forRock Mechanics [10] that a variety of mechanical jointedsurfaces or zones grow in rock structures such as minorfaults weak belts and joints

According to many results from field survey disconti-nuities are so numerous that it is difficult to discover thegeometric and mechanical properties of each individualHowever due to their randomness and irregularity theircritical parameters can be assumed to stochastic variablesand described by probability and stochastic models basedon plenty of measured data Then 3D stochastic simulationtechnique of structural plane network was put forward toanalyse their distribution rules

Priest and Samaniego [11] built the 2D model of discon-tinuous rock structures using the random statistical methodKulatilake et al [12] estimated joint geometry parameters andcompleted the 3D joint network model based on statisticalhomogeneity investigation sample correction and stereolog-ical method Zhou et al [13] put forward a self-coordinatedapproach to generate the 3D fracture network model by themeasured 2D data Li et al [14] developed the generation andvisualization system of 3D stochastic structural planes usingthe Poisson random process Turanboy et al [15] realizedthe 3D visualization of landslide discontinuities based on theacquired exploration data Dowd et al [16] cut the actualgranite into layers and obtained true three-dimensionalfracture network data sets through direct measurement andanalysis Pan et al [17] built the 3D fracture model withcrack permeability tensor to analyze the flow and transportin fractured rock

Therefore the jointed network simulation approach anal-yses actual measured data to obtain their statistical param-eters of the occurrence interval and density and thengenerate geometric models based on the probability model

Mathematical Problems in Engineering 3

(a) (b)

Figure 1 Two critical types of rock mass structures in hydraulic engineering (a) Major engineering-scale geological structures (b) Minorstatistical-scale discontinuities

2D cross-sections

Exploration data

Geometricmodeling

Further geological excavation

NURBS technique

Horizons

Dam structures Underground structures

Object-orientedmethod

Faults

Geological objects

Engineering objects

Drills

Terrain

Majorgeological models

Engineering models

3D geoengineeringmodel

Supplement andverification

Engineering data

middot middot middot


Figure 2 3D geological modeling general framework of engineering-scale structures

and certain simulation method We adopted Baecherrsquos diskmodel [18] and Monte Carlo simulation technique to realizethe stochastic simulation modeling of jointed rock massnetwork while the above engineering-scale geological modeprovides the reliable boundary

41 Baecherrsquos Disk Model This model was developed byBaecher et al [18] and the fractures are defined as ldquoboundedplanar features of random size and orientation randomlypositioned in three-dimensional spacerdquo [19] The fundamen-tal assumptions of the model are listed as followsAS1 joints are circular 2D disksAS2 the center points of joints are randomly and indepen-

dently distributed in space forming a Poisson fieldAS3 the radii of joints are lognormally distributedAS4 joint radius and dip are uncorrelated (statistically

independent)AS5 joint radius and spatial location are uncorrelated

(statistically independent)Then the size and location of a circular fracture can

be defined by three critical parameters that is the centralpoint 119874 (119909

0 1199100 1199110) the radius 119877 and the occurrence 119881(120572 120573)

Baecherrsquos disk model has been most extensively used forrock mechanics studies for it is conceptually simple andapplicable and the corresponding numerical analysis will berelatively easy

42 3D Simulation of Stochastic Jointed Network Based onBaecherrsquos model and the corresponding assumptions 3Dsimulation of stochastic jointed network can be realized bythe following steps

(1) Define valid simulated subregions Its size is deter-mined by homogeneous sampling subregions andengineering requirements Due to inhomogeneity ofstochastic discontinuities there are multiple homo-geneous subregions in the engineering region Forexample there are 119899 subregions in the whole engi-neering region Ω and one subregion is Ω

119894(119894 =

1 2 119899) The corresponding simulated subregion119872119894to Ω119894is defined by the minimum bounding box

algorithm

119872119894=

119883min le 119909 le 119883max119884min le 119910 le 119884max119885min le 119911 le 119885max

(1)

where (119883min 119884min 119885min) and (119883max 119884max 119885max) aretheminimumandmaximum coordinates ofΩ

119894Then

Ω119894may be irregular while 119872

119894must be a rectangular

solid and Ω119894sube 119872119894

(2) Simulate structural plane parameters of jointed net-work This process is opposite to the field mea-surement and statistics Here the Monte Carlo sim-ulation method is adopted According to obtained


distribution functions of different stochastic vari-ables random numbers with uniform distributionare generated by algorithm Then structural planeparameters can be simulated to satisfy measureddistribution functions by random sampling fromgenerated random numbers

(3) Generate jointed structural planes Based on theassumption of random uniform distribution forstructure planes three stochastic values of theircentral points (119909

1198940 1199101198940 1199111198940) are independent and

uniformly distributed If 1199031119894 1199032119894 1199033119894are independent

random numbers of standard uniform distributionthen the central point 119874

119894(1199091198940 1199101198940 1199111198940) of the structure

plane 119863119894can be calculated

1199091198940

= 119883min + (119883max minus 119883min) 1199031119894

1199101198940

= 119884min + (119884max minus 119884min) 1199032119894

1199111198940

= 119885min + (119885max minus 119885min) 1199033119894

(2)

Although (2) can ensure that the plane 119863119894= 119891(119874

119894 119881119894 119877119894)

locates in the region119872119894Ω119894sube 119872119894 andweneed to compute the

spatial relationship between 119874119894and Ω

119894to decide its validity

43 Verification of Simulated Results The simulated resultscan be in accordance with the measured data statisticallybut there are some differences with the sampling region Toimprove the accuracy the model should be checked verifiedand revised We set up three verification principles based onthe measured discontinuities from statistics (1) Verify thatthe measured and simulated discontinuities belong to thesame group to ensure that their occurrences are similar (2)Verify the nearest measured and simulated discontinuitiesfrom center points to ensure their consistent distributionfeatures (3) Verify all outcropped discontinuities in thesampling region

5 Multiscale Model Integrationand Application

51 Integrated Modeling Process Considering geologicalstructures discontinuities hydraulic structures and theircomplicated relationship the multiscale integrated mathe-matical model is set up based on NURBS modeling [20] asfollows

119872Ω

=

1198991

⋃

119894=1

119872119888119894

oplus

1198992

⋃

119895=1

119872119889119895

oplus

119898

⋃

119896=1

119872119890119896

119872119888119894

= 1198781198941

cup 1198781198942

cup (

119902119894

⋃

119897=1

119878119897119894119897) 119894 = 1 2 119899

1

119872119889119895

= 119891 (119874119895 119881119895 119877119895) 119895 = 1 2 119899

2

119872119890119896

= 119865 (1198891199011

1198891199012

) 119896 = 1 2 119898

Table 1 Characteristic parameters of simulated random structuralplanes

Parameters GroupNE NWW NW

AVG 119877 140 196 148STDEV 119877 102 57 64AVG Dip direction 803 2945 3441AVG Dip angle 659 675 883

119878119894119909

= 119904 (P119894119909

) 119894 = 1 2 1198991 119909 = 1 2

119878119897119894119897

= 1199041015840(V119894119897) V

119894119897isin 1205971198781198941

cup 1205971198781198942

119894 = 1 2 1198991 119897 = 1 2 119902

119894

(3)

whereΩ is thewhole study region119872Ωis thewhole geological

model of Ω 1198991 1198992 and 119898 are the total number of rock

structures simulated jointed planes andhydraulic structures119872119888119894is the 119894th rock structure body which is built by twomajor

structural surfaces of 1198781198941 1198781198942 and 119902

119894peripheral surfaces 119878119897

119894119897

connecting 1198781198941and 119878

1198942 1198781198941and 119878

1198942are the NURBS surfaces

fitted by their point sets P119894119909 P1198942 1205971198781198941and 120597119878

1198942are the set of all

bounding vertexes of 1198781198941and 1198781198942 119872119889119895is the 119895th jointed plane

which is simulated through parametric modeling methodwith its center point 119874

119895 occurrence 119881

119895 and radius 119877

119895 119872119890119896

is the 119896th hydraulic structure submodel by some designparameters

According to the principle of spatial subdivision anyobject with complex geometry may be reconstructed by (3)Each geological body is enclosed by six boundary surfacesof top and bottom front and back and left and rightWhen all kinds of geological structures are simulated usingthe proposed approach the whole geological model canbe reconstructed by geometric operations For example ahorizon body is formed by 3D Boolean operations amongNURBS surfaces of top bottom and topographic body

52 Case Analysis The proposed approach was applied to ahydropower project with complicated geological conditionsThe project is a pumped storage power station includingupper and lower reservoirs main and auxiliary dams watertransport tunnels and the underground powerhouse Thegeological structures of this area are complex due to greatvariability in lithology intensive tectonic deformation andabundant fractures In the current study the proposedapproach was used to model the projectrsquos geological informa-tion with a primary focus on the underground powerhousearea

Based on the multisource data from the geological explo-ration and interpretation the actual geoengineeringmodel ofthe project region was reconstructed as shown in Figure 3The models contain several rock units (S3m

3-1 S3m3-2 and

S3m3-3 are different quartz sandstones) Quaternary overbur-

den (Qs) some faults related with the project and mainhydraulic structures such as the dams the upper reservoirand the underground tunnels group


Auxiliary dam

Upperreservoir

Main damS3m

3-1

S3m3-2

S3m3-3

Qs

(a)

S3m3-1

S3m3-1

S3m3-2

S3m3-2

S3m3-3

Fault

Undergroundpowerhouse

(b)

Figure 3 Practical 3D geoengineering models with major geological structures and hydraulic engineering structures (a) Model in the damregion (b) Model in the underground powerhouse region

(a) (b)

Figure 4 3D models of the studied powerhouse region (a) Geological model of the main powerhouse (b) Geological section along the axisof the main powerhouse

(a) (b)

Figure 5 3D integrated mode with minor discontinuities (a) 1557 simulated discontinuities in the powerhouse region (b) 3D multiscalemodel of rock mass structures with the powerhouse

The length width and height of the underground powerstation are 2199m 235m and 553m respectively as shownin Figure 4 The rock formation of this area includes S3m

3-1

rocks a few faults and many discontinuitiesThe dominant occurrences of the discontinuities in the

studied region were divided into three groups as shownin Table 1 Totally 1557 planes were simulated as shown inFigure 5(a) Integrating these discontinuities with the majorgeological structures and the main powerhouse the multi-scale model could be obtained by 3D Boolean operations

as shown in Figure 5(b) which described the distributionof complex rock mass and discontinuities They would offeruseful supports for rock mass structure analysis of civil engi-neering such as rock mass quality classification landslidestability assessment and critical blocks identification

6 Conclusions

According to the multiscale data of rock mass structuresfrom different regions this paper put forward different 3D


modeling and integrated modeling methods cohering withgeologic accuracy structural continuity and data storage

(1) For major engineering-scale geological structuressome techniques including hybrid data structurebased on NURBS classified objects modeling meth-od and exactmatching algorithmwere used to recon-struct the 3D geoengineering model of the wholeregionThe model could also offer the boundaries fordiscontinuities

(2) For minor statistical-scale discontinuities the 3Dstochastic modeling approach of discontinuities net-work was proposed based on measured data andrelated statistical analysis The approach consists ofBaecherrsquos disk model Monte Carlo simulation ofdiscontinuities network and model verification andthe realized program module has been developed

(3) Considering the complicated relationship among geo-logical structures stochastic discontinuities andhydraulic structures the integrated mathematicalmodel was built with major engineering-scale andminor statistical-scale structures And it was appliedto an actual hydraulic project and the multiscalemodel of the powerhouse region was completed

Then next emphasis is that the model should be appliedto engineering practices such as rock mass classificationstability analysis and seepage analysis while it would berevised and improved in practice

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grant nos 51379006 51021004) theNational Basic Research Program of China (973 Program)(Grant no 2013CB035903) and the Program for New Cen-tury Excellent Talents in University of Ministry of Educationof China (Grant no NCET-12-0404)

References

[1] D-H Zhong M-C Li L-G Song and G Wang ldquoEnhancedNURBS modeling and visualization for large 3D geoengi-neering applications an example from the Jinping first-levelhydropower engineering project Chinardquo Computers amp Geo-sciences vol 32 no 9 pp 1270ndash1282 2006

[2] R Hack B Orlic S Ozmutlu S Zhu and N Rengers ldquoThreeand more dimensional modelling in geo-engineeringrdquo Bulletinof Engineering Geology and the Environment vol 65 no 2 pp143ndash153 2006

[3] S R Sun Y X Lu Y Y Xu J Liu and J H Wei ldquoStudyon analog theory of rock mass simulation and its engineeringapplicationrdquo Mathematical Problems in Engineering vol 2013Article ID 491069 11 pages 2013

[4] R E Goodman Introduction to Rock Mechanics John Wiley ampSons New York NY USA 2nd edition 1989

[5] F M Zhang Multi-Scale Geometric Simulation of GeologicalStructures and Applications Science Press Beijing China 2007

[6] A R A Aitken and P G Betts ldquoMulti-scale integratedstructural and aeromagnetic analysis to guide tectonic modelsan example from the eastern Musgrave Province CentralAustraliardquo Tectonophysics vol 476 no 3-4 pp 418ndash435 2009

[7] R R Jones K J W McCaffrey P Clegg et al ldquoIntegration ofregional to outcrop digital data 3D visualisation of multi-scalegeological modelsrdquo Computers amp Geosciences vol 35 no 1 pp4ndash18 2009

[8] N X Xu ldquoIdentifying rock blocks based on hierarchical rock-mass structure modelrdquo Science in China D Earth Sciences vol52 no 10 pp 1612ndash1623 2009

[9] D Z GuGeological Mechanics Foundation of Rock EngineeringScience Press Beijing China 1979

[10] ISRM Rock Characterization Testing and Monitoring ISRMSuggested Methods Pergamon Press Oxford UK 1981

[11] S D Priest and A Samaniego ldquoA model for the analysis ofdiscontinuity characteristics in two dimensionsrdquo in Proceedingsof the 5th International Congress onRockMechanics pp 199ndash207Melbourne Australia 1983

[12] P H S W Kulatilake D N Wathugala and O StephanssonldquoJoint network modelling with a validation exercise in Stripamine Swedenrdquo International Journal of Rock Mechanics andMining Sciences amp Geomechanics Abstracts vol 30 no 5 pp503ndash526 1993

[13] W Y Zhou R G Yang J M Yin and Z R Wang ldquoThreedimensional joint network in rockmass using self-adjustedmethod and engineering applicationrdquo Chinese Journal of RockMechanics and Engineering vol 16 no 1 pp 29ndash35 1997

[14] X Li S Yang and X Wang ldquoGeneration and visualiza-tion technologies of three-dimensional network of rockmassstochastic structural planerdquo Chinese Journal of Rock Mechanicsand Engineering vol 26 no 12 pp 2564ndash2569 2007

[15] A Turanboy M K Gokay and E Ulker ldquoAn approach togeometrical modelling of slope curves and discontinuitiesrdquoSimulationModelling Practice andTheory vol 16 no 4 pp 445ndash461 2008

[16] P A Dowd J A Martin C Xu R J Fowell and K V MardialdquoA three-dimensional fracture network data set for a block ofgraniterdquo International Journal of Rock Mechanics and MiningSciences vol 46 no 5 pp 811ndash818 2009

[17] J Pan C Lee C LeeH Yeh andH Lin ldquoApplication of fracturenetwork model with crack permeability tensor on flow andtransport in fractured rockrdquo Engineering Geology vol 116 no1-2 pp 166ndash177 2010

[18] G B Baecher N A Lanney and H H Einstein ldquoStatisticaldescription of rock properties and samplingrdquo in Proceeding ofthe 18th US Symposium on Rock Mechanics (USRMS 77) pp501ndash508 Golden Colo USA 1977

[19] G B Baecher ldquoStatistical analysis of rockmass fracturingrdquo Jour-nal of the International Association for Mathematical Geologyvol 15 no 2 pp 329ndash348 1983

[20] D H Zhong and M C Li Theories and Applications of 3DEngineering-Geological Modeling and Analysis to Hydraulic andHydroelectric Projects ChinaWater Power Press Beijing China2006

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Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


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2 Multiscale Classification of Complex RockMass Structures

Geological boundaries with a certain direction and extensionare collectively referred to as structural surfaces includ-ing substance differentiation surfaces (such as horizonsschistosities weak intercalated layers and intrusions) anddiscontinuous fractured planes (such as faults joints andweathering or relief fissures) Then corresponding rockmasses are constrained by these different combined structuralsurfaces which are dominant

In the field of geotechnical engineering structural sur-faces are classified into five levels that is I II III IV and V[5 9] They can be divided into four spatial scales

(1) Regional-scale structures corresponding to levels Iand II such as regional faults they may affect theregion stability with hundreds of kilometers exten-sion

(2) Engineering-scale structures corresponding to levelIII such as horizons weak layers and faults theyextend from hundreds to thousands of meters withgood continuity and a certain thickness And theymay destruct the continuity and stability of rockmasses

(3) Statistical-scale structures corresponding to level IVsuch as horizons weak layers and faults they extendfrom several to tens of meters with random discretedistributions and statistical-advantaged directionsAnd they may affect the deformation mode of rockmasses and result in anisotropic rock mechanicalproperties Due to lack of determined spatial infor-mation they may be described by statistical modelswith certain probability distribution and are calledstatistical-scale geological data

(4) Sample-scale structures corresponding to level Vsuch as hiddenmicrocracks their length level is aboutmillimeter or centimeter They are short and closewith random discrete distributions And they maydecrease the rock strength

Among the four structures engineering-scale and statisti-cal-scale data are emphases in hydraulic engineering geologyas shown in Figure 1 Generally major engineering-scaledata are acquired by geological exploration of drills andadits and interpreted to different cross-sections while minorstatistical-scale data are drawn to geolograph charts fromfield discontinuities Then according to their data featureswe will use different methods to build two kinds of modelsand realize their integration effectively

3 3D Modeling of MajorEngineering-Scale Structures

The regional engineering-scale geological data of hydraulicprojects mainly include topographic contours geologicalpoints remote sensing images drills adits and geophysical

informationThey can be interpreted to a variety of 2D cross-sections by geological engineers All these data are the basisof reconstructing 3D models

The general structure of 3D modeling of major engi-neering-scale rock mass structures is shown in Figure 2Firstly based onmultisource geological data and engineeringdesign data geological objects are classified into terrainhorizons and faults while engineering objects are dividedinto dam structure underground tunnels and drills and aditsby the object-oriented technique Secondly corresponding3D models of geological and engineering structures arebuilt by enhanced NURBS (Nonuniform Rational B-Spline)modeling method [1] During the process the models mustbe verified and revised using the original exploration dataThe verification includes checks of topological geometrystructural rationality and accuracy tests on raw data [1]Finally the integrated geoengineering model is completedthrough a series of complex 3D Boolean operations

4 3D Stochastic Modeling of MinorStatistical-Scale Jointed Rock Mass Network

All kinds of stochastic discontinuities are distributed inrock masses widely And they may control the strength anddeformation of rockmasses and are named jointed rockmassnetwork system It is defined by International Society forRock Mechanics [10] that a variety of mechanical jointedsurfaces or zones grow in rock structures such as minorfaults weak belts and joints

According to many results from field survey disconti-nuities are so numerous that it is difficult to discover thegeometric and mechanical properties of each individualHowever due to their randomness and irregularity theircritical parameters can be assumed to stochastic variablesand described by probability and stochastic models basedon plenty of measured data Then 3D stochastic simulationtechnique of structural plane network was put forward toanalyse their distribution rules

Priest and Samaniego [11] built the 2D model of discon-tinuous rock structures using the random statistical methodKulatilake et al [12] estimated joint geometry parameters andcompleted the 3D joint network model based on statisticalhomogeneity investigation sample correction and stereolog-ical method Zhou et al [13] put forward a self-coordinatedapproach to generate the 3D fracture network model by themeasured 2D data Li et al [14] developed the generation andvisualization system of 3D stochastic structural planes usingthe Poisson random process Turanboy et al [15] realizedthe 3D visualization of landslide discontinuities based on theacquired exploration data Dowd et al [16] cut the actualgranite into layers and obtained true three-dimensionalfracture network data sets through direct measurement andanalysis Pan et al [17] built the 3D fracture model withcrack permeability tensor to analyze the flow and transportin fractured rock

Therefore the jointed network simulation approach anal-yses actual measured data to obtain their statistical param-eters of the occurrence interval and density and thengenerate geometric models based on the probability model


(a) (b)


2D cross-sections

Exploration data

Geometricmodeling


NURBS technique

Horizons



Faults

Geological objects

Engineering objects

Drills

Terrain


Engineering models



Engineering data














119894(119894 =


algorithm

119872119894=


(1)


119894Then



solid and Ω119894sube 119872119894








119894(1199091198940 1199101198940 1199111198940) of the structure


1199091198940

= 119883min + (119883max minus 119883min) 1199031119894

1199101198940

= 119884min + (119884max minus 119884min) 1199032119894

1199111198940

= 119885min + (119885max minus 119885min) 1199033119894

(2)


119894 119881119894 119877119894)







119872Ω

=

1198991

⋃

119894=1

119872119888119894

oplus

1198992

⋃

119895=1

119872119889119895

oplus

119898

⋃

119896=1

119872119890119896

119872119888119894

= 1198781198941

cup 1198781198942

cup (

119902119894

⋃

119897=1

119878119897119894119897) 119894 = 1 2 119899

1

119872119889119895

= 119891 (119874119895 119881119895 119877119895) 119895 = 1 2 119899

2

119872119890119896

= 119865 (1198891199011

1198891199012

) 119896 = 1 2 119898




119878119894119909

= 119904 (P119894119909

) 119894 = 1 2 1198991 119909 = 1 2

119878119897119894119897

= 1199041015840(V119894119897) V

119894119897isin 1205971198781198941

cup 1205971198781198942

119894 = 1 2 1198991 119897 = 1 2 119902

119894

(3)






119894119897

connecting 1198781198941and 119878

1198942 1198781198941and 119878







119895 and radius 119877

119895 119872119890119896





3-1 S3m3-2 and




Auxiliary dam

Upperreservoir

Main damS3m

3-1

S3m3-2

S3m3-3

Qs

(a)

S3m3-1

S3m3-1

S3m3-2

S3m3-2

S3m3-3

Fault


(b)


(a) (b)


(a) (b)



3-1




6 Conclusions










Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b)


2D cross-sections

Exploration data

Geometricmodeling


NURBS technique

Horizons



Faults

Geological objects

Engineering objects

Drills

Terrain


Engineering models



Engineering data














119894(119894 =


algorithm

119872119894=


(1)


119894Then



solid and Ω119894sube 119872119894








119894(1199091198940 1199101198940 1199111198940) of the structure


1199091198940

= 119883min + (119883max minus 119883min) 1199031119894

1199101198940

= 119884min + (119884max minus 119884min) 1199032119894

1199111198940

= 119885min + (119885max minus 119885min) 1199033119894

(2)


119894 119881119894 119877119894)







119872Ω

=

1198991

⋃

119894=1

119872119888119894

oplus

1198992

⋃

119895=1

119872119889119895

oplus

119898

⋃

119896=1

119872119890119896

119872119888119894

= 1198781198941

cup 1198781198942

cup (

119902119894

⋃

119897=1

119878119897119894119897) 119894 = 1 2 119899

1

119872119889119895

= 119891 (119874119895 119881119895 119877119895) 119895 = 1 2 119899

2

119872119890119896

= 119865 (1198891199011

1198891199012

) 119896 = 1 2 119898




119878119894119909

= 119904 (P119894119909

) 119894 = 1 2 1198991 119909 = 1 2

119878119897119894119897

= 1199041015840(V119894119897) V

119894119897isin 1205971198781198941

cup 1205971198781198942

119894 = 1 2 1198991 119897 = 1 2 119902

119894

(3)






119894119897

connecting 1198781198941and 119878

1198942 1198781198941and 119878







119895 and radius 119877

119895 119872119890119896





3-1 S3m3-2 and




Auxiliary dam

Upperreservoir

Main damS3m

3-1

S3m3-2

S3m3-3

Qs

(a)

S3m3-1

S3m3-1

S3m3-2

S3m3-2

S3m3-3

Fault


(b)


(a) (b)


(a) (b)



3-1




6 Conclusions










Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra















119894(1199091198940 1199101198940 1199111198940) of the structure


1199091198940

= 119883min + (119883max minus 119883min) 1199031119894

1199101198940

= 119884min + (119884max minus 119884min) 1199032119894

1199111198940

= 119885min + (119885max minus 119885min) 1199033119894

(2)


119894 119881119894 119877119894)







119872Ω

=

1198991

⋃

119894=1

119872119888119894

oplus

1198992

⋃

119895=1

119872119889119895

oplus

119898

⋃

119896=1

119872119890119896

119872119888119894

= 1198781198941

cup 1198781198942

cup (

119902119894

⋃

119897=1

119878119897119894119897) 119894 = 1 2 119899

1

119872119889119895

= 119891 (119874119895 119881119895 119877119895) 119895 = 1 2 119899

2

119872119890119896

= 119865 (1198891199011

1198891199012

) 119896 = 1 2 119898




119878119894119909

= 119904 (P119894119909

) 119894 = 1 2 1198991 119909 = 1 2

119878119897119894119897

= 1199041015840(V119894119897) V

119894119897isin 1205971198781198941

cup 1205971198781198942

119894 = 1 2 1198991 119897 = 1 2 119902

119894

(3)






119894119897

connecting 1198781198941and 119878

1198942 1198781198941and 119878







119895 and radius 119877

119895 119872119890119896





3-1 S3m3-2 and




Auxiliary dam

Upperreservoir

Main damS3m

3-1

S3m3-2

S3m3-3

Qs

(a)

S3m3-1

S3m3-1

S3m3-2

S3m3-2

S3m3-3

Fault


(b)


(a) (b)


(a) (b)



3-1




6 Conclusions










Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Auxiliary dam

Upperreservoir

Main damS3m

3-1

S3m3-2

S3m3-3

Qs

(a)

S3m3-1

S3m3-1

S3m3-2

S3m3-2

S3m3-3

Fault


(b)


(a) (b)


(a) (b)



3-1




6 Conclusions










Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article 3d multiscale integrated modeling approach of...

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