engineeringclassificationofjointedrockmassbasedon...

Research ArticleEngineering Classification of Jointed Rock Mass Based onConnectional Expectation A Case Study for Songta DamSite China

Shengyuan Song12 Qiang Xu 2 Jianping Chen1 Wen Zhang1 Chen Cao1

and Yongchao Li1

1College of Construction Engineering Jilin University Changchun 130026 China2State Key Laboratory of Geohazard Prevention and Geoenvironment Protection Chengdu University of TechnologyChengdu 610059 China

Correspondence should be addressed to Qiang Xu xqcduteducn

Received 26 September 2019 Accepted 27 April 2020 Published 20 May 2020

Academic Editor Yinshan Tang

Copyright copy 2020 Shengyuan Song et al is 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

Engineering classification of complex jointed rock mass is influenced and controlled by many factors with random nonlinear andunascertained characteristics which is an extremely complicated problem is paper introduces a comprehensive method toclassify the rock mass with complex joints Firstly evaluation indexes are described by the interval number theory Secondly theweight values of the evaluation indexes are determined by the analytic hierarchy process (AHP) irdly the connectionalexpectation between interval numbers is analyzed and the classification grade of jointed rock mass quality is identified by the setpair analysis theory e new method can not only describe the dynamic evolution trend of various influencing factors but alsosimplify the analysis process of the relationship between interval numbers e Songta dam abutment rock mass is selected as astudy case to verify the rationality of the new method e classification results of rock mass quality obtained by the new methodare in accordance with the actual situation and are consistent with the results provided by the RMR classification

1 Introduction

Jointed rock mass quality is mainly affected by its ownstructural characteristics (integrity rock strength weath-ering degree etc) and its surrounding environment (in situstress and groundwater) which can generally reflect theengineering geological properties of rock mass within acertain spatial extent [1ndash3] erefore the classification ofrock mass quality should be based on the above influencingfactors and specific indexes should be used to evaluate rockmass properties by qualitative or quantitative methods Inlarge-scale water conservancy and hydropower projectsreasonable and accurate determination of rock mass clas-sification is not only conducive to the correct selection ofmechanical parameters of various rock masses but alsobenefit to the optimization of the engineering design and thedetermination of a reasonable foundation surface [4 5]

e classification of rock mass quality started fromunderground engineering at first and then gradually ex-panded to dam foundation engineering Early methodsmostly focused on qualitative or quantitative evaluation of asingle index such as [6] former Soviet UnionVNSaerfoslj classification (1937) H ONasmp clas-sification (1941) Terzaghi classification [7] the dam foun-dation rock mass classification proposed by the formerSoviet Union concrete gravity dam design specification andthe RQD classification introduced by Deere in the UnitedStates [8]

In the 1970s the engineering classification of rock massgradually developed from the single index to multiindexqualitative to quantitative evaluation methods e typicalrock mass classification methods for underground engi-neering are as follows RSR classification proposed byWickham et al [9] the American scholars RMR

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 3581963 15 pageshttpsdoiorg10115520203581963

classification proposed by Bieniawski [10 11] a Dutchscholar from South Africa and Q system classificationproposed by Barton et al [12] the Norwegian scholarsese methods are relatively perfect and widely applied topractical engineering

Compared with underground engineering rock massquality classification for dam foundation engineering is notperfect and is still in exploration e representative rockmass quality classification methods for dam foundationengineering abroad are as follows [6] R P Millerrsquos classi-fication scheme the classification scheme for inhomoge-neous rock mass proposed by the Spanish scholars Kikuchiet al [13] and the dam foundation rock mass classificationsystem introduced by a Japanese scholar Kikuhiro

In China the research on rock mass classification of damfoundation engineering started relatively late e repre-sentative classification methods are as follows rock massquality coefficient Z classification proposed by Gu andHuang [14] rock mass quality index M classification pro-posed by Yang [15] the YZP classification of the reeGorges Project proposed by the Yangtze River Commission[16] standard for engineering classification of rock masses(GB50218-94) [17] and code for water resources and hy-dropower engineering geological investigation (GB50287-99) [18] are proposed respectively

Generally speaking the rock mass classification isgradually developing from qualitative to quantitative on thebasis of engineering practice GB50287-99 is successfullyapplied to the Laxiwa Hydropower Station and the damfoundation rock mass is reasonably divided into 5 majorgrades and 7 subgrades [19 20] Due to the particularity ofcolumnar jointed basalt developed in the Baihetan Hydro-power Station RMR Q GB50218-94 and GB50287-99 aresynthetically used for rock mass quality classificationHowever the results obtained by the above four methods arenot exactly consistent Finally the quality grade of the rockmass is determined through comprehensive analysis andcomparison [21 22] With the increase for the scale ofengineering rock mass and the complexity of its occurrenceenvironment the practicability of the traditional rock massclassification method is limited

Since the 1990s researchers at home and abroad havegradually realized that the influencing factors of rock massquality have the characteristics of fuzziness Habibagahi andKatebi adopt the fuzzy set theory to classify rockmass quality[23] Yuan et al proposed a multiindex rock mass qualityevaluation method based on extension theory [24] Cao andZhang introduced the idea of variable weight processing intorock mass quality evaluation and established a fuzzy eval-uation method of rock mass quality based on variable weight[25] In the engineering classification of jointed rock massthe aforementioned method fully considers the fuzziness ofinfluencing factors However rockmass quality evaluation isto evaluate the engineering geological properties of rockmass in a certain space which contains a large number ofstochastic joints e geometric mechanical and hydraulicproperties of these joints often change in a certain rangeat is to say the factors affecting rock mass quality clas-sification have the characteristics of interval numbers

erefore this paper attempts to use interval numbers toexpress the influencing factors of rock mass quality and thenapplies set pair analysis theory to analyze the connectionalexpectation between interval numbers and determine thequality grade of rock mass

2 Theory for the Connectional Expectation

21 Interval Number eory Objectively speaking the de-velopment of the fractures in complex rock mass is due toanisotropy and randomness In addition limited fieldoutcrop and incomplete survey information will lead to thelack of data Hence the original data indicating the engi-neering geological properties of complex fractured rockmass are often not a certain number but some intervalnumbers Subjectively speaking engineers have a deeperunderstanding for fractured rock mass and will not stay at asingle point erefore engineers need to use intervalnumbers to quantify the engineering geological properties ofthe fractured rock mass

Usually an interval number can be used to represent acertain attribute of the research object which is defined asfollows [26ndash28]

Assume that any xminus and x+ belong to the set R of realnumbers and xminus lex+en a standard interval number canbe expressed as [X] [xminus x+] where xminus is the minimumvalue of the interval number and x+ is the maximum value ofthe interval number If xminus gt 0 then [X] is called a positiveinterval number If x+ lt 0 then [X] is called a negativeinterval number If xminus lt 0 and x+ gt 0 then [X] is called adifference interval number If xminus x+ then the intervalnumber [X] degenerates to an ordinary real number X eexpectation of interval numbers can be expressed as

E[(X)] x1p1 + x2p2 + middot middot middot + xtpt (1)

where x1 x2 xt are the measured values describing acertain attribute of the research object x1 x2 xt isin [X]and p1 p2 pt are the probability values of the measuredvalue x1 x2 xt

e study of interval number theory is not perfect andits application is not very mature Especially the problem ofcomparison and connection between two or more intervalnumbers is very difficult to solveis study will try to use setpair analysis theory to analyze the connection problembetween interval numbers

22 Set Pair Analysis eory In nature the same thing hasboth certainty and uncertainty From a philosophical pointof view they are a pair of contradictions both oppositionand same at is to say certainty and uncertainty of thingscan be transformed into each other under certain conditionsSet pair analysis theory is precisely the mathematical theoryused to deal with the interaction between certainty anduncertainty is theory was proposed by Zhao a mathe-matician in China Set pair and connection degree are themain concepts of the set pair analysis theory If the knownsets [X] and [Y] have a certain connection then the two setscan be integrated into a pair which is expressed as a set pair

2 Advances in Civil Engineering

1113954H (X Y) [29] e same difference and opposition be-tween the two sets can be expressed by the connection degreeμ(XY) e specific formula is as follows [30]

μ(XY) a + bi + cj (2)

where i is the coefficient of difference minus1le ile 1 j is the co-efficient of opposition generally j minus1 a b and c separaterepresent the same degree difference degree and oppositiondegree between the evaluation indexXpj of sampleXp and rockmass quality grade k and a + b + c 1 (Figure 1)

In the uncertain evaluation of things the intervalnumber form of the nth index value of the evaluation samplem is [Xmn] [xminus

mn x+mn] and the corresponding expectation

can be calculated according to formula (1) Similarly thegrading standard of evaluation index can also be expressedby the interval number e interval number form of the kthgrade of the nth index is [Ynk] [yminus

nk y+nk] and the cor-

responding expectation is E[Ynk] e measured data andgrade interval of the evaluation index can form a set paire

evaluation criteria for the same difference and opposition ofthe set pair is as follows if the measured data [Xmn] arecompletely within the grade interval [Ynk] ie xminus

mn gtyminusnk

and x+mn lty+

nk then the sample [Xmn] and the grade [Ynk]

are in the same relationship If the measured data [Xmn] arecompletely outside the grade interval [Ynk] ie xminus

mn gty+nk

or x+mn ltyminus

nk then the sample [Xmn] and the grade [Ynk] arein opposition relationship (Figure 2) In addition to theabove two relationships the sample [Xmn] and the grade[Ynk] are in difference relationship [31]

Usually the evaluation indexes of the sample are dividedinto two types namely cost-type and benefit-type ebenefit-type index refers to the index whose value increasesin the same direction as the grade increases However thecost-type index is just the opposite Regarding the con-nectional expectation the cost-type index can be calculatedaccording to formula (3) and the benefit-type index can becalculated according to formula (4) [32]

μ Xmn1113858 1113859 Ynk1113960 11139611113872 1113873

E Xmn1113858 1113859( 1113857 minus yminusnk

yminusnk minus yminus

nk+1 yminus

nk+1 leE Xmn1113858 1113859( 1113857ltyminusnk1113872 1113873


E Ynk1113960 11139611113872 1113873 minus yminusnk

yminusnk leE Xmn1113858 1113859( 1113857ltE Ynk1113960 11139611113872 11138731113872 1113873

E Xmn1113858 1113859( 1113857 minus y+nk

E Ynk1113960 11139611113872 1113873 minus y+nk

E Ynk1113960 11139611113872 1113873leE Xmn1113858 1113859( 1113857lty+nk1113872 1113873

y+nk minus E Xmn1113858 1113859( 1113857

y+nkminus1 minus y+

nk

y+nk leE Xmn1113858 1113859( 1113857lty+

nkminus11113872 1113873

minus1 (other)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

μ Xmn1113858 1113859 Ynk1113960 11139611113872 1113873



nkminus1 yminus

nkminus1 leE Xmn1113858 1113859( 1113857ltyminusnk1113872 1113873




E Xmn1113858 1113859( 1113857 minus y+nk

E Ynk1113960 11139611113872 1113873 minus y+nk


y+nk minus E Xmn1113858 1113859( 1113857

y+nk+1 minus y+

nk

y+nk leE Xmn1113858 1113859( 1113857lty+

nk+11113872 1113873

minus1 (other)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)

Advances in Civil Engineering 3

where μ([Xmn] [Ynk]) is the connectional expectation of thenth index of the mth sample with respect to the evaluationgrade k When the weight value of the nth index isWn thenthe integrated connectional expectation of the mth samplewith respect to the evaluation grade k is

μmk 1113944N

n1Wnμ Xmn1113858 1113859 Ynk1113960 11139611113872 1113873 (5)

If

μmk0 max μmk | k 1 2 k11139671113966 (6)

en the evaluation grade of this sample is k0

3 The Case Study

31 Study Area e Songta Hydropower Station will bebuilt on the main stream of the Nu River which is the firstcascade hydropower station in the hydropower developmentscheme for the Nu River e dam site is located in SongtaVillage Chayu County Tibet in China about 7 km distancefrom the boundary between Yunnan and Tibet along themain stream of the Nu River e flow direction of the NuRiver at the dam site is 188deg SW (Figure 3)

e upstream basin of the dam site is vast and the waterflow is largee area of the basin reaches 1035000 km2 andthe annual runoff reaches 391 billionm3 e concretedouble-curved arch dam with a design height of 318m is

planned to be built e total storage capacity is 4547 bil-lionm3 and the installed capacity is 3600MW

e dam site is a typical mountain-canyon geomor-phology and the valley exhibits an asymmetric ldquoVrdquo shapee overall slope of the river bank is approximately 50deg(Figure 4(a)) e river bank at the dam site is composed bytwo types of lithology biotite monzonitic granite and pla-gioclase amphibolite from the Yanshanian (Cretaceous)period e biotite monzonitic granite is the predominantlithology which is primarily comprised of quartz plagio-clase potassium feldspar and biotite e plagioclase am-phibolite is intruded as dykes with a width 005ndash5m into thebiotite monzonitic granite Under the action of extrusionsome stochastic joints are formed within the above rockmasses (Figure 4(b))

32 Data Acquisition and Analysis In order to ascertain theengineering geological condition of the rockmass at the damsite some adits are excavated at different elevations of thedam abutment e strike of these adits is basically per-pendicular to the flow direction of the Nu River ecommonly used window sampling method is adopted toinvestigate the joint information outcropped within the aditJoint information collected includes orientation rockstrength spacing RQD roughness aperture weatheringand groundwater

In the study the adits PDS1 PD222 PD224 and PD226located at the right dam abutment are chosen as the study

Same OppositionOpposition

Diff

eren

ces

Diff

eren

ces

Set [X] Set [Y]

Figure 1 Same difference and opposition relationships of a set pair

Xmnndash Xmn

+

E([Xmn]) E([Xmn])E([Yn k])

Xmnndash Xmn

+Yn kndash Yn k

+

Same relationship of connectional expectation

Xmnndash Xmn

+

E([Xmn]) E([Yn k]) Yn k+Yn k

ndash

Yn k+1ndash Adjacent grade

k+1Adjacent grade

kndash1Yn kndash1

+

Opposition relationship of connectional expectation

Figure 2 Diagram for same and opposition relationships of connectional expectation


case for the rock mass classification e adits PDS1 PD222PD224 and PD226 are located at elevations of 17167m17659m 18149m and 18639m respectively e lengthsof adits PDS1 PD222 PD224 and PD226 are 200m 200m150m and 150m respectively e distribution map of theabove adits is shown in Figure 5(a)

e adit outcrops display that the properties of jointsdeveloped within the rock mass varied with the horizontaldistance from the valley slope According to the engineeringgeological condition of the outcrop surface within adits andthe joint formation mechanism of the unloading zone in the

high slope of the river valley [33] the rock mass around theadits is divided into three sections from the slope surface tothe slope interior (Figure 5(b))

(i) Section 1 this area is located on the surface sectionof the valley slope In the section in situ stress issignificantly reduced and the rock mass is highlyweathered Joints are abundantly developed withinthe rock mass Joints inclined to the slope surface atgentle dip angles have a dominant advantage andthese joints are filled with clay mud

Songta dam

Flow direction

N

Nu River

96deg0prime0PrimeE 97deg0prime0PrimeE 98deg0prime0PrimeE 99deg0prime0PrimeE 100deg0prime0PrimeE

96deg0prime0PrimeE

30deg0prime0Prime

N29

deg0prime0Prime

N28

deg0prime0Prime

N27

deg0prime0Prime

N26

deg0prime0Prime

N25

deg0prime0Prime

N

30deg0prime0Prime

N29

deg0prime0Prime

N28

deg0prime0Prime

N27

deg0prime0Prime

N26

deg0prime0Prime

N25

deg0prime0Prime

N

97deg0prime0PrimeE 98deg0prime0PrimeE 99deg0prime0PrimeE 100deg0prime0PrimeE

Figure 3 Topographic and location map of the study case

(a) (b)

Nu River

Songta dam sitePlagioclaseamphibolite

Biotite monzoniticgranite

Joint

Joint

Figure 4 Geological conditions of the Songta dam site


(ii) Section 2 in situ stress increases gradually and rockmass is moderately and slightly weathered Jointsdevelop randomly within the rock mass and jointdensity decreases gradually Only a small amount ofjoints with gentle dip angles are filled with clay

(iii) Section 3 in situ stress is basically stable and rockmass is fresh Joints seldom develop within the rockmass

To ascertain the dominant orientation of the jointswithin each section of each adit the joint sets within eachsection are identified according to an improved FCMmethod proposed by Song et al [34]e dominant joint setsof each section in each adit are shown in Figure 6 e figureexhibits that the joints in each section are divided into threegroups Set 1 is the joint dipping towards the slope surface ata gentle dip angle Set 2 and Set 3 are joints with a steep dipangle In section 1 of each adit the number of joints in Set 1is much larger than that in Set 2 and Set 3 In section 3 ofeach adit the number of joints in each group is basicallyequal

33 Rock Mass Quality Evaluation Model Based on Connec-tional Expectation In this paper engineering classificationof jointed rock mass based on connectional expectation isthe comprehensive method e new method combinesthree mathematical methods to solve complex decision-making problems affected by various uncertainties Firstlyinterval number theory is adopted to represent the evalu-ation indexes of rock mass quality Secondly AHP is utilizedto determine the weight values of evaluation indexesirdly set pair analysis theory is used to analyze theconnectional expectation between interval numbers anddetermine the quality grade of rock mass e flowchart ofthe new method is shown in Figure 7

34 Selection of Evaluation Index In order to obtain morereasonable and accurate results for rock mass quality

evaluation it should be as comprehensive and scientific aspossible when selecting the evaluation index Table 1 lists themain indexes considered in the 7 typical methods for rockmass quality evaluation at home and abroad It can be seenfrom the table that the indexes considered by the 7 typicalmethods are not identical e indexes considered six ormore times are rock strength (7 times) joint spacing (6times) joint state (6 times) and groundwater (6 times) isindirectly indicates that the above indexes are the mainindexes affecting the engineering geological characteristicsof jointed rock mass

Referring to the main influencing factors of rock massquality evaluation commonly used by experts at home andabroad and combining with the rock mass structure char-acteristics of the Songta dam site this paper syntheticallyselected eight indexes to classify the quality of dam abutmentrock mass ese eight indexes include rock strength jointspacing RQD roughness aperture weathering ground-water and dip difference e dip difference refers to thedifference between the dominant dip angle of the joint setdipping towards the slope surface and the dip angle of theslope surface

When collecting joint information roughness apertureweathering and groundwater are qualitatively describedese qualitative indexes are inconvenient to participate inthe calculation of rock mass classification grade Henceroughness aperture weathering and groundwater arequantified according to qualitative description e quan-titative values of the above indexes are shown in Table 2 Onthis basis evaluation indexes of rock mass in adits PDS1PD222 PD224 and PD226 are expressed by the intervalnumber and are shown in Table 3

341 Determination of Evaluation Grade Criteria Beforedetermining the quality grade of rock mass it is necessary toestablish a single index evaluation system for influencingfactors of rock mass quality is paper mainly refers to theclassification criteria commonly used at home and abroad

Section 2Section 1 Section 3

Section 1 Section 2 Section 3



PDS12

PD222

PD224

PD226

25 50 75 100(b)(a)

125 150 175 200m002

02

02

02

25 50 75 100 125 150 175 200m0

25 50 75 100 125 150m0

25 50 75 100 125 150m0

Figure 5 e distribution map of the adits (a) and the sectional map of the rock mass around the adits (b)


such as RQD classification RMR classification Chinarsquosnational code for water resources and hydropower engi-neering geological investigation (GB50287-99) [8 10 18]

and comprehensively considers the development charac-teristics of joints in the study area In addition combiningthe quantitative values of each index in Table 2 a single


N

S

N

S

N

S


N

S

N

S

N

S


N

S

N

S

N

S

Section 1 Section 2

(a)

(b)

(c)

(d)

Section 3

N

S

E

E

E

E

W

W

W

W

N

S

E

E

E

E

W

W

W

W

N

S

E

E

E

E

W

W

W

W

Set 1Set 2Set 3

Figure 6 e dominant joint sets of each section in each adit (a) PDS1 (b) PD222 (c) PD224 (d) PD226


index evaluation system for rock mass quality is establishedas given in Table 4

342 Calculation for Weight of Evaluation Indexrough the analysis of eight evaluation indexes it can beseen that each evaluation index has a very important impacton rock mass quality but the impact degree of each eval-uation index is different at is to say the weight value ofeach evaluation index is different Only when the impactdegree (weight value) of the index is taken into account inthe evaluation of rock mass quality can a reasonableevaluation result be obtained In this section analytic hi-erarchy process (AHP) will be used to consider the impact ofeach evaluation index on rock mass quality and to calculateits weight value

AHP is one of the most commonly used methods ofweight assignment It is a multiobjective decision analysismethod that combines qualitative and quantitative researchas proposed by an American scholar Saaty [35] e basicidea of this method is to hierarchize and quantify complexdecision problems according to human thinking process andthen make multicriteria decision-making on this basis Itscharacteristic is that less quantitative information is used tomathematize the decision-making process under thepremise of fully excavating the essence of complex decisionproblemse major steps of the AHPmethod are as follows[36 37]

(1) According to the factors involved in a complexdecision problem and its membership relations thedecision problem is divided into the component

factors and a hierarchical structural model isestablishede hierarchical structural model of rockmass classification established in this paper is shownin Figure 8

(2) Assigning numerical values to each factor based onthe subjective judgment for the relative importanceof each factor a pairwise comparison matrix ofdecision factors is constructed e constructionstandard of the comparison matrix is based on the1ndash9 scale method which is shown in Table 5 Whenthe factor on the vertical axis is more important thanthe factor on the horizontal axis the value variesbetween 1 and 9 Conversely the value varies be-tween the reciprocals 12 and 19 e pairwisecomparison matrix for evaluation indexes of rockmass quality is constructed as shown in Table 6

(3) e maximum eigenvalue of the comparison matrixand its corresponding eigenvector are calculated andthe eigenvector is normalized to be the weight vectorAfter calculation the maximum eigenvalue of thecomparison matrix consisting of the evaluation in-dexes is 8125 and the corresponding eigenvectorsare [0205 0161 0164 0070 0069 0073 0088 and0179] us the corresponding weight values for theevaluation indexes of rock mass quality are shown inTable 7

(4) Determining whether the comparison matrix sat-isfies the consistence test If it does not go back andredo the pairwise comparison matrix Usually theconsistency ratio CR is used to measure the quality of

Dividing a decision problem into the component factors

Constructing a pairwise comparison matrix of decision factors

Calculating the maximum eigenvalue and its eigenvector of the comparison matrix

Determining whether the comparison matrix satisfies the consistence test

Satisfying consistency test the eigenvector is normalized to be the weight vector

Calculating the integrated connectional expectation of sample to be evaluated with respect to each evaluation grade

The grade corresponding to the maximum value of integrated connectional expectation is determined as quality grade of rock mass

Selection of evaluation indexes for rock mass classification

Evaluation indexes of sample represented by interval number

Establishing the classification criteria of each evaluation index

Each index of sample and classification criteria integrateinto a set pair

Calculating the connectional expectation for each index of sample with respect to each evaluation grade

Figure 7 Flowchart for the rock mass quality evaluation model based on connectional expectation


Table 1 A list of influencing factors considered in typical rock mass classification methods

Method RSR RMR Q Z YZP ET China nationalstandard

Number offactors

Proposed age 1972 1973 1974 1979 1985 1985 1994Number of jointsets radic 1

Joint spacing radic radic radic radic radic radic 6Joint state radic radic radic radic radic radic 6RQD radic radic radic radic radic 5Rock massstructure radic 1

Integrity radic radic radic radic radic 5Weathering radic radic radic 3In situ stress radic radic radic 3Groundwater radic radic radic radic radic radic 6Geologicalstructure radic 1

Rock strength radic radic radic radic radic radic radic 7Joint shearstrength radic radic radic 3

Rock massdeformationmodulus

radic radic 2

Rockdeformationmodel

radic 1

Rock mass elasticwave velocity radic radic radic 3

Rock wavevelocity radic radic radic radic radic 5

Joint orientation radic radic radic radic radic 5Constructionmethod radic 1

Classificationgrade 5 grades 5 grades 9 grades 5 grades 5 grades 5 grades 5 grades

Engineeringapplication

Tunnelsupport

Tunnelmining

Tunnelcavern

Dam foundation ofundergroundengineering

Rock mass ofdam

foundation

Rock mass ofdam

foundation

Undergroundand ground slope

Table 2 Quantitative table for the evaluation index of rock mass quality

Roughness Quantitativevalue Aperture Quantitative

value Weathering Quantitativevalue Groundwater Quantitative

valueToothed rough 1 Tightly close 1 Fresh 1 Dry 1Toothed slightlyrough 2 Close 2 Slightly

weathered 2 Moist 2

Toothed smooth 3 Microopen 3 Moderatelyweathered 3 Wet 3

Wavy rough 4 Open 4 Highlyweathered 4 Soaking water 4

Wavy slightlyrough 5 Medium

open 5 Completelyweathered 5 Dripping 5

Wavy smooth 6 Wide open 6 Linear drip 6

Flat rough 7 Flowingwater 7

Flat slightlyrough 8

Flat smooth 9


Tabl

e3

Evaluatio

nindexesof

rock

massin

each

aditareexpressedby

theinterval

number

Evaluatin

gindex

Interval

number

PDS1

PD222

PD224

PD226

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Rock

streng

th(M

Pa)

Minim

um474

257

739

348

673

513

626

602

878

493

1299

1170

Maxim

um1636

2415

1389

830

1316

994

1453

1891

1920

1301

2341

2397

Expectation

1022

968

1060

569

1161

940

1144

1119

1481

850

1710

1957

Jointspacing(m

)Minim

um0007

0006

1311

0003

0003

0112

0020

0033

0277

0044

0032

4153

Maxim

um4573

7349

7311

8016

5233

18781

11155

7524

33844

4699

8838

8333

Expectation

0802

1164

4046

0791

0999

4294

0981

0875

7097

0846

2006

6481

RQD

()

Minim

um54

3594

1478

7254

4592

343

868

818

Maxim

um85

100

100

9898

100

98100

100

970

1000

1000

Expectation

7484

9868

9196

7492

9866

9698

Roughn

ess

Minim

um1

14

44

44

44

44

4Maxim

um9

77

88

98

99

78

5Ex

pectation

570

489

467

549

518

525

632

678

454

457

479

406

Aperture

Minim

um1

11

11

11

11

11

1Maxim

um6

63

64

36

55

64

5Ex

pectation

243

179

133

183

142

115

200

201

173

207

114

163

Weathering

Minim

um2

21

22

11

11

21

1Maxim

um4

44

43

24

43

42

2Ex

pectation

246

267

194

251

218

197

296

172

177

285

192

194

Groun

dwater

Minim

um1

11

11

11

11

11

1Maxim

um4

44

32

45

52

44

4Ex

pectation

158

192

172

149

125

113

192

207

150

128

171

213

Dip

difference(deg )

Minim

umminus44

minus45

minus23

minus44

minus27

minus39

minus32

minus42

minus34

minus36

minus30

minus12

Maxim

um6

1710

1915

611

33minus5

1416

25Ex

pectation

minus3331

minus1994

minus250

minus1170

minus690

minus1247

minus1616

minus936

minus2462

minus1610

minus588

820


judgment made by decision makers When CRlt 01the logical consistency of judgment thinking is verygood and the weight value determined by its

comparison matrix is reasonable When CRgt 01there are contradictions in logical thinking and it isnecessary to readjust the quantitative value of the

Table 4 Classification standard for the evaluation index of rock mass quality [8 10 18]

Evaluating indexClassification grade of rock mass

1 2 3 4 5Rock strength (MPa) 250sim1000 100sim250 50sim100 25sim50 0sim25Joint spacing (m) 3sim100 1sim3 03sim1 005sim03 0sim005RQD () 90sim100 75sim90 50sim75 25sim50 0sim25Roughness 1sim3 3sim5 5sim7 7sim8 8sim9Aperture 1sim2 2sim3 3sim4 4sim5 5sim6Weathering 1sim15 15sim20 20sim25 25sim30 30sim40Groundwater 1sim2 2sim3 3sim4 4sim5 5sim7Dip difference (deg) 20sim35 5sim20 minus5sim5 minus20simminus5 minus35simminus20

Rock strength

Joint spacing

RQD

Roughness

Aperture

Weathering

Groundwater

Dip difference

Evaluation indexes of rock

mass quality

Figure 8 e hierarchical structural model of rock mass classification

Table 5 e fundamental scale of AHP (Saaty [36])

Intensity ofimportance Definition Explanation

1 Equal importance Two activities contribute equally to the objective2 Weak mdash

3 Moderate prevalence of one over another Experience and judgment slightly favor oneactivity over another

4 Moderate plus mdash

5 Strong or essential prevalence Experience and judgment strongly favor oneactivity over another

6 Strong plus mdash

7 Very strong or demonstrated prevalence An activity is favored very strongly over anotherits dominance demonstrated in practice

8 Very very strong mdash

9 Extremely high prevalence e evidence favoring one activity over another isof the highest possible order of affirmation

Reciprocals ofabove

If activity i has one of the above nonzero numbers assigned to itwhen compared with activity j then j has the reciprocal value when

compared with iA reasonable assumption

Rational Ratios arising from the scale If consistency were to be forced by obtaining nnumerical values to span the matrix


relative importance of each factor in the comparisonmatrix e consistency ratio CR can be calculatedaccording to the following formula

CR CIRI

(7)

where RI is a random consistency index which was given bySaaty as shown in Table 8 and CI is a consistency index andcan be calculated according to the following formula

CI λmax minus N

N minus 1 (8)

where λmax is the maximum eigenvalue of the comparisonmatrix and N is the order of the comparison matrix

After calculation the consistency ratio CR of the com-parison matrix is 00127 which is obviously less than 01 Itshows that the logical consistency of the comparison matrix

is good and the weight value calculated by the comparisonmatrix is reasonable

35 Determination of Rock Mass Quality Grade Firstly theinterval number expectation of each index in the sample tobe evaluated and the evaluation criteria are calculatedaccording to formula (1) Secondly each index of the sampleto be evaluated and the evaluation classification criteria areintegrated into a set pair and the connectional expectationfor each index is calculated Since rock strength jointspacing RQD and dip difference belong to cost-type in-dexes the corresponding connectional expectation is cal-culated according to formula (3) e other indexes arebenefit-type indexes and the connectional expectation canbe calculated according to formula (4)en combined withthe weight value of each index the integrated connectionalexpectation of each sample to be evaluated with respect to

Table 6 e pairwise comparison matrix for the evaluation index of rock mass quality

Evaluation index Rock strength Joint spacing RQD Roughness Aperture Weathering Groundwater Dip differenceRock strength 1 1 2 3 3 3 2 1Joint spacing 1 1 1 2 2 2 2 1RQD 12 1 1 2 3 3 2 1Roughness 13 12 12 1 1 1 12 12Aperture 13 12 13 1 1 1 1 13Weathering 13 12 13 1 1 1 1 12Groundwater 12 12 12 2 1 1 1 12Dip difference 1 1 1 2 3 2 2 1

Table 7 Weight values for the evaluation index of rock mass quality

Evaluation index Rock strength Joint spacing RQD Roughness Aperture Weathering Groundwater Dip differenceWeight value 0205 0161 0164 0070 0069 0073 0088 0179

Table 8 e random consistency index (Saaty [36])

N 1 2 3 4 5 6 7 8 9 10RI 0 0 058 090 112 124 132 141 145 149

Table 9 e results of rock mass classification

Adit μm1 μm2 μm3 μm4 μm5 e new method RMR

PDS1Section 1 minus06274 minus02493 minus01340 minus07609 minus07917 3 3Section 2 minus05128 minus01044 minus03711 minus06929 minus08059 2 2Section 3 minus01627 minus01954 minus04255 minus08725 minus10000 1 1

PD222Section 1 minus07333 minus04018 00750 minus03143 minus09226 3 3Section 2 minus03733 minus02808 minus02873 minus07541 minus09785 2 2Section 3 minus03369 minus04101 minus04705 minus06273 minus09153 1 1

PD224Section 1 minus06548 minus02621 minus02503 minus06012 minus08064 3 3Section 2 minus04100 minus01616 minus03240 minus06396 minus09506 2 2Section 3 minus00830 minus01375 minus07674 minus08562 minus07253 1 1

PD226Section 1 minus07835 minus03276 00173 minus04693 minus08231 3 3Section 2 minus01145 00437 minus05225 minus08101 minus09900 2 2Section 3 minus00648 01669 minus06793 minus10000 minus10000 2 2


the evaluation grade k is calculated according to formula (5)Finally the evaluation grade of each sample to be evaluatedis determined according to formula (6) that is the gradecorresponding to the maximum value of integrated con-nectional expectation is the classification grade of rock mass

e integrated connectional expectations of the section 1in adit PDS1 with respect to the evaluation grades 1 2 3 4and 5 are minus06274 minus02493 minus01340 minus07609 and minus07917respectively It is shown that the integrated connectionalexpectation of the section 1 in adit PDS1 with respect to thegrade 3 of rockmass quality is the largesterefore the rockmass quality of the section 1 in adit PDS1 is classified asgrade 3 Similarly the classification results of the newmethod in other homogeneous regions are shown in Table 9

To verify the reliability of the new method the RMRmethod is selected as the benchmark e classificationresults of rock mass quality obtained by the new method arein accordance with the actual situation and are consistentwith the results provided by the RMR classification ecomparison results show that the new method is reliable andcan easily deal with the evaluation indexes of rock massclassification expressed by the interval number In order tomore intuitively display the classification results of the

Songta dam abutment rock mass a spatial division map ofrock mass quality is drawn as shown in Figure 9

4 Conclusions

e stochastic joints developed within the rock mass are thekey factors affecting rock mass quality Besides the geo-metric mechanical and hydraulic properties of stochasticjoints usually change in a certain range Hence using in-terval numbers to represent the influencing factors of rockmass quality can not only reduce uncertainty but also makethe evaluation results more reasonable

is paper introduces a comprehensive method toclassify the rock mass with complex joints Firstly intervalnumber theory is adopted to represent the evaluation in-dexes of rock mass quality Secondly analytic hierarchyprocess is utilized to determine the weight values of eval-uation indexes irdly set pair analysis theory is used toanalyze the connectional expectation between intervalnumbers and determine the quality grade of rock mass enew method combines three mathematical methods to solvecomplex decision-making problems affected by variousuncertainties which can not only describe the dynamic

PDS1

PD222

PD224

PD226

0 50 100 150

1

2

3 3

4567




Section 1 Section 2 Section 3Nu River

Right bank of dam site

Quality grade of rock mass123

45

100 150500

10050 150m0

10050

200m

200m

150m0

Figure 9 Spatial division of rock mass quality in the Songta dam site


evolution trend of various influencing factors but alsosimplify the analysis process of the relationship betweeninterval numbers

e new method is applied to evaluate the quality gradeof Songta dam abutment rock masse classification resultsof rock mass quality obtained by the new method are inaccordance with the actual situation and are consistent withthe results provided by the RMR classification e qualitygrade of the section 1 in adits PDS1 PD222 PD224 andPD226 is grade 3 e quality grade of the section 2 in aditsPDS1 PD222 PD224 and PD226 and the section 3 in aditPD226 is grade 2 e quality grade of the section 3 in aditsPDS1 PD222 and PD224 is grade 1

Data Availability

e data used to support this research article are availablefrom the first author on request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

is work was supported by the National Natural Science ofChina (Grant no 41702301) Opening fund of State KeyLaboratory of Geohazard Prevention and GeoenvironmentProtection (Chengdu University of Technology) (Grant noSKLGP2018K017) and Key Project of NSFC-Yunnan JointFund (Grant no U1702241)

References

[1] T Ramamurthy ldquoA geo-engineering classification for rocksand rock massesrdquo International Journal of Rock Mechanicsand Mining Sciences vol 41 no 1 pp 89ndash101 2004

[2] X Zhou J P Chen Y K Ruan et al ldquoDemarcation ofstructural domains in fractured rock masses using a three-parameter simultaneous analysis methodrdquo Advances in CivilEngineering vol 2018 no 6 Article ID 9358098 13 pages2018

[3] Y Liu Q Wang J P Chen et al ldquoDetermination of geo-metrical REVs based on volumetric fracture intensity andstatistical testsrdquo Applied Sciences vol 8 no 5 Article ID8050800 800 pages 2018

[4] L Zhang ldquoEstimating the strength of jointed rock massesrdquoRock Mechanics and Rock Engineering vol 43 no 4pp 391ndash402 2010

[5] Q Jiang B Yang F Yan et al ldquoNew method for charac-terizing the shear damage of natural rock joint based on 3Dengraving and 3D scanningrdquo International Journal of Geo-mechanics vol 2020 no 2 Article ID 06019022 2020

[6] X W Hu and R Q Huang ldquoA simple discussion on qualityclassification of the rock mass in a water conservancy andhydroelectric projectrdquo Journal of Chengdu University ofTechnology vol 23 no 3 pp 64ndash68 1996

[7] K Terzaghi ldquoRock defects and loads on tunnel supportsrdquo inRock Tunneling with Steel Supports pp 15ndash99 CommercialShearing and Stamping Company Youngstown OH USA1946

[8] D U Deere ldquoTechnical description of rock cores for engi-neering purposesrdquo Rock Mechanics and Engineering Geologyvol 1 no 1 pp 16ndash22 1964

[9] G EWickham H R Tiedemann and E H Skinner ldquoSupportdetermination based on geologic predictionsrdquo in Proceedingsof conference on rapid excavation and tunneling pp 43ndash64Chicago IL USA June 1972

[10] Z T Bieniawski ldquoEngineering classification of jointed rockmassesrdquo Siviele Ingenieurswese vol 15 no 12 pp 335ndash3431973

[11] Z T Bieniawski ldquoGeomechanics classification of rock massesand its application in tunnelingrdquo in Proceedings of the 3rdInternational Congress on Rock Mechanics ISRM DenverColorado pp 27ndash32 September 1974

[12] N Barton R Lien and J Lunde ldquoEngineering classification ofrock masses for the design of tunnel supportrdquo RockMechanicsFelsmechanik Mecanique des Roches vol 6 no 4 pp 189ndash2361974

[13] K Kikuchi K Saito and K I Kusonoki ldquoGeotechnicallyintegrated evaluation on the stability of dam foundationrocksrdquo in Proceedings of the 14th international congress onlarge dams pp 49ndash74 Rio de Janerio Brazil May 1982

[14] D Z Gu and D C Huang ldquoClassification of rock massstructure and determination of its quality coefficientrdquoHydrogeology amp Engineering Geology vol 2 pp 10ndash15 1979

[15] Z W Yang Engineering Classification of Rock Massmdasheoryand Practice of Rock Mechanics China Water Power PressBeijing China 1981

[16] Z M Ren Research on Dam Foundation Rock Mass Engi-neering of ree Gorges Project China University of Geo-sciences Press Beijing China 1998

[17] China Planning Press ldquoNational Standards CompilationGroup of Peoplersquos Republic of China GB 50218ndash94rdquo inStandard for Engineering Classification of Rock Masses ChinaPlanning Press Beijing China 1994

[18] China Planning PressNational Standards Compilation Groupof Peoplersquos Republic of China GB 50287ndash99 Code for WaterResources and Hydropower Engineering Geological Investiga-tion China Planning Press Beijing China 1999

[19] L Y He Discussion of General Research Route to Value theRock Mass Mechanical Parameters of Dam FoundationLanzhou University Lanzhou China 2009

[20] Q Jiang G Su X-t Feng G Chen M-z Zhang and C LiuldquoExcavation optimization and stability analysis for largeunderground caverns under high geostress a case study of theChinese Laxiwa projectrdquo Rock Mechanics and Rock Engi-neering vol 52 no 3 pp 895ndash915 2018

[21] Y J Wei Study on Characteristics of Rock Mass Structure andEngineering Application of Emeishan Basalts in Project Site ofHydroelectric Power Station in Southwestern China ChengduUniversity of Technology Chengdu China 2007

[22] S G Zhang Engineering Geological Feasibility Study of HighArch Dam Construction at Baihetan Hydropower StationJinsha River Chengdu University of Technology ChengduChina 2007

[23] G Habibagahi and S Katebi ldquoRock mass classification usingfuzzy set theoryrdquo Iranian Journal of Science and Technologyvol 20 no 3 pp 273ndash284 1996

[24] G H Yuan J P Chen and L Ma ldquoApplication of extenics inevaluating of engineering quality of rock massrdquo ChineseJournal of Rock Mechanics and Engineering vol 24 no 9pp 1539ndash1544 2005

[25] W G Cao and Y J Zhang ldquoStudy on two-stage fuzzy syn-thetic judgment method with changing weight value for rock


quality classification in underground structuresrdquo ChineseJournal of Rock Mechanics and Engineering vol 25 no 8pp 1612ndash1618 2006

[26] Q Z Hu and W H Zhang Research and Application ofInterval Number eory Science Press Beijing China 2010

[27] A Sengupta and T K Pal ldquoOn comparing interval numbersrdquoEuropean Journal of Operational Research vol 127 no 1pp 28ndash43 2000

[28] M X SongW Jiang C H Xie et al ldquoA new interval numberspower average operator in multiple attribute decision mak-ingrdquo International Journal of Intelligent Systems vol 32pp 631ndash644 2016

[29] K Q Zhao Set Pair Analysis and its Preliminary ApplicationZhejiang Science and Technology Press Hangzhou China2000

[30] M-W Wang P Xu J Li and K-Y Zhao ldquoA novel set pairanalysis method based on variable weights for liquefactionevaluationrdquo Natural Hazards vol 70 no 2 pp 1527ndash15342014

[31] J Hu and L Yang ldquoDynamic stochastic multi-criteria deci-sionmakingmethod based on cumulative prospect theory andset pair analysisrdquo Systems Engineering Procedia vol 1 no 1pp 432ndash439 2011

[32] MWWang K Y Zhao and L B Zhang ldquoA novel evaluationmodel based on connectional expectation for swelling-shrinkage grade of untreated and treated expansive clayrdquoChinese Journal of Rock Mechanics and Engineering vol 36no 8 pp 1553ndash1557 2014

[33] R Q Huang F Lin D J Chen et al ldquoFormation mechanismof unloading fracture zone of high slopes and its engineeringbehaviorsrdquo Journal of Engineering Geology vol 9 no 3pp 227ndash232 2001

[34] S Song Q Wang J Chen Y Li W Zhang and Y RuanldquoFuzzy C-means clustering analysis based on quantum par-ticle swarm optimization algorithm for the grouping of rockdiscontinuity setsrdquo KSCE Journal of Civil Engineering vol 21no 4 pp 1115ndash1122 2017

[35] T L Saaty ldquoA scaling method for priorities in hierarchicalstructuresrdquo Journal of Mathematical Psychology vol 15 no 3pp 234ndash281 1977

[36] T L Saaty e Analytic Hierarchy Process McGraw-HillInternational Book Company New York NY USA 1980

[37] Y-C Liu and C-S Chen ldquoA new approach for application ofrock mass classification on rock slope stability assessmentrdquoEngineering Geology vol 89 no 2 pp 129ndash143 2007


classification proposed by Bieniawski [10 11] a Dutchscholar from South Africa and Q system classificationproposed by Barton et al [12] the Norwegian scholarsese methods are relatively perfect and widely applied topractical engineering

Compared with underground engineering rock massquality classification for dam foundation engineering is notperfect and is still in exploration e representative rockmass quality classification methods for dam foundationengineering abroad are as follows [6] R P Millerrsquos classi-fication scheme the classification scheme for inhomoge-neous rock mass proposed by the Spanish scholars Kikuchiet al [13] and the dam foundation rock mass classificationsystem introduced by a Japanese scholar Kikuhiro

In China the research on rock mass classification of damfoundation engineering started relatively late e repre-sentative classification methods are as follows rock massquality coefficient Z classification proposed by Gu andHuang [14] rock mass quality index M classification pro-posed by Yang [15] the YZP classification of the reeGorges Project proposed by the Yangtze River Commission[16] standard for engineering classification of rock masses(GB50218-94) [17] and code for water resources and hy-dropower engineering geological investigation (GB50287-99) [18] are proposed respectively

Generally speaking the rock mass classification isgradually developing from qualitative to quantitative on thebasis of engineering practice GB50287-99 is successfullyapplied to the Laxiwa Hydropower Station and the damfoundation rock mass is reasonably divided into 5 majorgrades and 7 subgrades [19 20] Due to the particularity ofcolumnar jointed basalt developed in the Baihetan Hydro-power Station RMR Q GB50218-94 and GB50287-99 aresynthetically used for rock mass quality classificationHowever the results obtained by the above four methods arenot exactly consistent Finally the quality grade of the rockmass is determined through comprehensive analysis andcomparison [21 22] With the increase for the scale ofengineering rock mass and the complexity of its occurrenceenvironment the practicability of the traditional rock massclassification method is limited

Since the 1990s researchers at home and abroad havegradually realized that the influencing factors of rock massquality have the characteristics of fuzziness Habibagahi andKatebi adopt the fuzzy set theory to classify rockmass quality[23] Yuan et al proposed a multiindex rock mass qualityevaluation method based on extension theory [24] Cao andZhang introduced the idea of variable weight processing intorock mass quality evaluation and established a fuzzy eval-uation method of rock mass quality based on variable weight[25] In the engineering classification of jointed rock massthe aforementioned method fully considers the fuzziness ofinfluencing factors However rockmass quality evaluation isto evaluate the engineering geological properties of rockmass in a certain space which contains a large number ofstochastic joints e geometric mechanical and hydraulicproperties of these joints often change in a certain rangeat is to say the factors affecting rock mass quality clas-sification have the characteristics of interval numbers

erefore this paper attempts to use interval numbers toexpress the influencing factors of rock mass quality and thenapplies set pair analysis theory to analyze the connectionalexpectation between interval numbers and determine thequality grade of rock mass

2 Theory for the Connectional Expectation

21 Interval Number eory Objectively speaking the de-velopment of the fractures in complex rock mass is due toanisotropy and randomness In addition limited fieldoutcrop and incomplete survey information will lead to thelack of data Hence the original data indicating the engi-neering geological properties of complex fractured rockmass are often not a certain number but some intervalnumbers Subjectively speaking engineers have a deeperunderstanding for fractured rock mass and will not stay at asingle point erefore engineers need to use intervalnumbers to quantify the engineering geological properties ofthe fractured rock mass

Usually an interval number can be used to represent acertain attribute of the research object which is defined asfollows [26ndash28]

Assume that any xminus and x+ belong to the set R of realnumbers and xminus lex+en a standard interval number canbe expressed as [X] [xminus x+] where xminus is the minimumvalue of the interval number and x+ is the maximum value ofthe interval number If xminus gt 0 then [X] is called a positiveinterval number If x+ lt 0 then [X] is called a negativeinterval number If xminus lt 0 and x+ gt 0 then [X] is called adifference interval number If xminus x+ then the intervalnumber [X] degenerates to an ordinary real number X eexpectation of interval numbers can be expressed as

E[(X)] x1p1 + x2p2 + middot middot middot + xtpt (1)

where x1 x2 xt are the measured values describing acertain attribute of the research object x1 x2 xt isin [X]and p1 p2 pt are the probability values of the measuredvalue x1 x2 xt

e study of interval number theory is not perfect andits application is not very mature Especially the problem ofcomparison and connection between two or more intervalnumbers is very difficult to solveis study will try to use setpair analysis theory to analyze the connection problembetween interval numbers

22 Set Pair Analysis eory In nature the same thing hasboth certainty and uncertainty From a philosophical pointof view they are a pair of contradictions both oppositionand same at is to say certainty and uncertainty of thingscan be transformed into each other under certain conditionsSet pair analysis theory is precisely the mathematical theoryused to deal with the interaction between certainty anduncertainty is theory was proposed by Zhao a mathe-matician in China Set pair and connection degree are themain concepts of the set pair analysis theory If the knownsets [X] and [Y] have a certain connection then the two setscan be integrated into a pair which is expressed as a set pair



μ(XY) a + bi + cj (2)








mn gtyminusnk

and x+mn lty+



mn gty+nk

or x+mn ltyminus



μ Xmn1113858 1113859 Ynk1113960 11139611113872 1113873



nk+1 yminus





E Xmn1113858 1113859( 1113857 minus y+nk

E Ynk1113960 11139611113872 1113873 minus y+nk


y+nk minus E Xmn1113858 1113859( 1113857

y+nkminus1 minus y+

nk

y+nk leE Xmn1113858 1113859( 1113857lty+

nkminus11113872 1113873

minus1 (other)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

μ Xmn1113858 1113859 Ynk1113960 11139611113872 1113873



nkminus1 yminus





E Xmn1113858 1113859( 1113857 minus y+nk

E Ynk1113960 11139611113872 1113873 minus y+nk


y+nk minus E Xmn1113858 1113859( 1113857

y+nk+1 minus y+

nk

y+nk leE Xmn1113858 1113859( 1113857lty+

nk+11113872 1113873

minus1 (other)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)



μmk 1113944N

n1Wnμ Xmn1113858 1113859 Ynk1113960 11139611113872 1113873 (5)

If

μmk0 max μmk | k 1 2 k11139671113966 (6)


3 The Case Study








Diff

eren

ces

Diff

eren

ces

Set [X] Set [Y]


Xmnndash Xmn

+


Xmnndash Xmn

+Yn kndash Yn k

+


Xmnndash Xmn

+


ndash


k+1Adjacent grade

kndash1Yn kndash1

+








Songta dam

Flow direction

N

Nu River


96deg0prime0PrimeE

30deg0prime0Prime

N29

deg0prime0Prime

N28

deg0prime0Prime

N27

deg0prime0Prime

N26

deg0prime0Prime

N25

deg0prime0Prime

N

30deg0prime0Prime

N29

deg0prime0Prime

N28

deg0prime0Prime

N27

deg0prime0Prime

N26

deg0prime0Prime

N25

deg0prime0Prime

N



(a) (b)

Nu River



Joint

Joint
















PDS12

PD222

PD224

PD226

25 50 75 100(b)(a)

125 150 175 200m002

02

02

02

25 50 75 100 125 150 175 200m0

25 50 75 100 125 150m0

25 50 75 100 125 150m0






N

S

N

S

N

S


N

S

N

S

N

S


N

S

N

S

N

S

Section 1 Section 2

(a)

(b)

(c)

(d)

Section 3

N

S

E

E

E

E

W

W

W

W

N

S

E

E

E

E

W

W

W

W

N

S

E

E

E

E

W

W

W

W

Set 1Set 2Set 3



























Number offactors






radic radic 2


radic 1






Tunnelsupport

Tunnelmining

Tunnelcavern


Rock mass ofdam

foundation

Rock mass ofdam

foundation






weathered 2 Moist 2








Flat smooth 9


Tabl

e3

Evaluatio

nindexesof

rock

massin

each

aditareexpressedby

theinterval

number

Evaluatin

gindex

Interval

number

PDS1

PD222

PD224

PD226

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Rock

streng

th(M

Pa)

Minim

um474

257

739

348

673

513

626

602

878

493

1299

1170

Maxim

um1636

2415

1389

830

1316

994

1453

1891

1920

1301

2341

2397

Expectation

1022

968

1060

569

1161

940

1144

1119

1481

850

1710

1957

Jointspacing(m

)Minim

um0007

0006

1311

0003

0003

0112

0020

0033

0277

0044

0032

4153

Maxim

um4573

7349

7311

8016

5233

18781

11155

7524

33844

4699

8838

8333

Expectation

0802

1164

4046

0791

0999

4294

0981

0875

7097

0846

2006

6481

RQD

()

Minim

um54

3594

1478

7254

4592

343

868

818

Maxim

um85

100

100

9898

100

98100

100

970

1000

1000

Expectation

7484

9868

9196

7492

9866

9698

Roughn

ess

Minim

um1

14

44

44

44

44

4Maxim

um9

77

88

98

99

78

5Ex

pectation

570

489

467

549

518

525

632

678

454

457

479

406

Aperture

Minim

um1

11

11

11

11

11

1Maxim

um6

63

64

36

55

64

5Ex

pectation

243

179

133

183

142

115

200

201

173

207

114

163

Weathering

Minim

um2

21

22

11

11

21

1Maxim

um4

44

43

24

43

42

2Ex

pectation

246

267

194

251

218

197

296

172

177

285

192

194

Groun

dwater

Minim

um1

11

11

11

11

11

1Maxim

um4

44

32

45

52

44

4Ex

pectation

158

192

172

149

125

113

192

207

150

128

171

213

Dip

difference(deg )

Minim

umminus44

minus45

minus23

minus44

minus27

minus39

minus32

minus42

minus34

minus36

minus30

minus12

Maxim

um6

1710

1915

611

33minus5

1416

25Ex

pectation

minus3331

minus1994

minus250

minus1170

minus690

minus1247

minus1616

minus936

minus2462

minus1610

minus588

820







Rock strength

Joint spacing

RQD

Roughness

Aperture

Weathering

Groundwater

Dip difference


mass quality








6 Strong plus mdash




Reciprocals ofabove






CR CIRI

(7)


CI λmax minus N

N minus 1 (8)










N 1 2 3 4 5 6 7 8 9 10RI 0 0 058 090 112 124 132 141 145 149












4 Conclusions



PDS1

PD222

PD224

PD226

0 50 100 150

1

2

3 3

4567







45

100 150500

10050 150m0

10050

200m

200m

150m0





Data Availability




Acknowledgments


References










































μ(XY) a + bi + cj (2)








mn gtyminusnk

and x+mn lty+



mn gty+nk

or x+mn ltyminus



μ Xmn1113858 1113859 Ynk1113960 11139611113872 1113873



nk+1 yminus





E Xmn1113858 1113859( 1113857 minus y+nk

E Ynk1113960 11139611113872 1113873 minus y+nk


y+nk minus E Xmn1113858 1113859( 1113857

y+nkminus1 minus y+

nk

y+nk leE Xmn1113858 1113859( 1113857lty+

nkminus11113872 1113873

minus1 (other)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

μ Xmn1113858 1113859 Ynk1113960 11139611113872 1113873



nkminus1 yminus





E Xmn1113858 1113859( 1113857 minus y+nk

E Ynk1113960 11139611113872 1113873 minus y+nk


y+nk minus E Xmn1113858 1113859( 1113857

y+nk+1 minus y+

nk

y+nk leE Xmn1113858 1113859( 1113857lty+

nk+11113872 1113873

minus1 (other)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)



μmk 1113944N

n1Wnμ Xmn1113858 1113859 Ynk1113960 11139611113872 1113873 (5)

If

μmk0 max μmk | k 1 2 k11139671113966 (6)


3 The Case Study








Diff

eren

ces

Diff

eren

ces

Set [X] Set [Y]


Xmnndash Xmn

+


Xmnndash Xmn

+Yn kndash Yn k

+


Xmnndash Xmn

+


ndash


k+1Adjacent grade

kndash1Yn kndash1

+








Songta dam

Flow direction

N

Nu River


96deg0prime0PrimeE

30deg0prime0Prime

N29

deg0prime0Prime

N28

deg0prime0Prime

N27

deg0prime0Prime

N26

deg0prime0Prime

N25

deg0prime0Prime

N

30deg0prime0Prime

N29

deg0prime0Prime

N28

deg0prime0Prime

N27

deg0prime0Prime

N26

deg0prime0Prime

N25

deg0prime0Prime

N



(a) (b)

Nu River



Joint

Joint
















PDS12

PD222

PD224

PD226

25 50 75 100(b)(a)

125 150 175 200m002

02

02

02

25 50 75 100 125 150 175 200m0

25 50 75 100 125 150m0

25 50 75 100 125 150m0






N

S

N

S

N

S


N

S

N

S

N

S


N

S

N

S

N

S

Section 1 Section 2

(a)

(b)

(c)

(d)

Section 3

N

S

E

E

E

E

W

W

W

W

N

S

E

E

E

E

W

W

W

W

N

S

E

E

E

E

W

W

W

W

Set 1Set 2Set 3



























Number offactors






radic radic 2


radic 1






Tunnelsupport

Tunnelmining

Tunnelcavern


Rock mass ofdam

foundation

Rock mass ofdam

foundation






weathered 2 Moist 2








Flat smooth 9


Tabl

e3

Evaluatio

nindexesof

rock

massin

each

aditareexpressedby

theinterval

number

Evaluatin

gindex

Interval

number

PDS1

PD222

PD224

PD226

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Rock

streng

th(M

Pa)

Minim

um474

257

739

348

673

513

626

602

878

493

1299

1170

Maxim

um1636

2415

1389

830

1316

994

1453

1891

1920

1301

2341

2397

Expectation

1022

968

1060

569

1161

940

1144

1119

1481

850

1710

1957

Jointspacing(m

)Minim

um0007

0006

1311

0003

0003

0112

0020

0033

0277

0044

0032

4153

Maxim

um4573

7349

7311

8016

5233

18781

11155

7524

33844

4699

8838

8333

Expectation

0802

1164

4046

0791

0999

4294

0981

0875

7097

0846

2006

6481

RQD

()

Minim

um54

3594

1478

7254

4592

343

868

818

Maxim

um85

100

100

9898

100

98100

100

970

1000

1000

Expectation

7484

9868

9196

7492

9866

9698

Roughn

ess

Minim

um1

14

44

44

44

44

4Maxim

um9

77

88

98

99

78

5Ex

pectation

570

489

467

549

518

525

632

678

454

457

479

406

Aperture

Minim

um1

11

11

11

11

11

1Maxim

um6

63

64

36

55

64

5Ex

pectation

243

179

133

183

142

115

200

201

173

207

114

163

Weathering

Minim

um2

21

22

11

11

21

1Maxim

um4

44

43

24

43

42

2Ex

pectation

246

267

194

251

218

197

296

172

177

285

192

194

Groun

dwater

Minim

um1

11

11

11

11

11

1Maxim

um4

44

32

45

52

44

4Ex

pectation

158

192

172

149

125

113

192

207

150

128

171

213

Dip

difference(deg )

Minim

umminus44

minus45

minus23

minus44

minus27

minus39

minus32

minus42

minus34

minus36

minus30

minus12

Maxim

um6

1710

1915

611

33minus5

1416

25Ex

pectation

minus3331

minus1994

minus250

minus1170

minus690

minus1247

minus1616

minus936

minus2462

minus1610

minus588

820







Rock strength

Joint spacing

RQD

Roughness

Aperture

Weathering

Groundwater

Dip difference


mass quality








6 Strong plus mdash




Reciprocals ofabove






CR CIRI

(7)


CI λmax minus N

N minus 1 (8)










N 1 2 3 4 5 6 7 8 9 10RI 0 0 058 090 112 124 132 141 145 149












4 Conclusions



PDS1

PD222

PD224

PD226

0 50 100 150

1

2

3 3

4567







45

100 150500

10050 150m0

10050

200m

200m

150m0





Data Availability




Acknowledgments


References










































μmk 1113944N

n1Wnμ Xmn1113858 1113859 Ynk1113960 11139611113872 1113873 (5)

If

μmk0 max μmk | k 1 2 k11139671113966 (6)


3 The Case Study








Diff

eren

ces

Diff

eren

ces

Set [X] Set [Y]


Xmnndash Xmn

+


Xmnndash Xmn

+Yn kndash Yn k

+


Xmnndash Xmn

+


ndash


k+1Adjacent grade

kndash1Yn kndash1

+








Songta dam

Flow direction

N

Nu River


96deg0prime0PrimeE

30deg0prime0Prime

N29

deg0prime0Prime

N28

deg0prime0Prime

N27

deg0prime0Prime

N26

deg0prime0Prime

N25

deg0prime0Prime

N

30deg0prime0Prime

N29

deg0prime0Prime

N28

deg0prime0Prime

N27

deg0prime0Prime

N26

deg0prime0Prime

N25

deg0prime0Prime

N



(a) (b)

Nu River



Joint

Joint
















PDS12

PD222

PD224

PD226

25 50 75 100(b)(a)

125 150 175 200m002

02

02

02

25 50 75 100 125 150 175 200m0

25 50 75 100 125 150m0

25 50 75 100 125 150m0






N

S

N

S

N

S


N

S

N

S

N

S


N

S

N

S

N

S

Section 1 Section 2

(a)

(b)

(c)

(d)

Section 3

N

S

E

E

E

E

W

W

W

W

N

S

E

E

E

E

W

W

W

W

N

S

E

E

E

E

W

W

W

W

Set 1Set 2Set 3



























Number offactors






radic radic 2


radic 1






Tunnelsupport

Tunnelmining

Tunnelcavern


Rock mass ofdam

foundation

Rock mass ofdam

foundation






weathered 2 Moist 2








Flat smooth 9


Tabl

e3

Evaluatio

nindexesof

rock

massin

each

aditareexpressedby

theinterval

number

Evaluatin

gindex

Interval

number

PDS1

PD222

PD224

PD226

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Rock

streng

th(M

Pa)

Minim

um474

257

739

348

673

513

626

602

878

493

1299

1170

Maxim

um1636

2415

1389

830

1316

994

1453

1891

1920

1301

2341

2397

Expectation

1022

968

1060

569

1161

940

1144

1119

1481

850

1710

1957

Jointspacing(m

)Minim

um0007

0006

1311

0003

0003

0112

0020

0033

0277

0044

0032

4153

Maxim

um4573

7349

7311

8016

5233

18781

11155

7524

33844

4699

8838

8333

Expectation

0802

1164

4046

0791

0999

4294

0981

0875

7097

0846

2006

6481

RQD

()

Minim

um54

3594

1478

7254

4592

343

868

818

Maxim

um85

100

100

9898

100

98100

100

970

1000

1000

Expectation

7484

9868

9196

7492

9866

9698

Roughn

ess

Minim

um1

14

44

44

44

44

4Maxim

um9

77

88

98

99

78

5Ex

pectation

570

489

467

549

518

525

632

678

454

457

479

406

Aperture

Minim

um1

11

11

11

11

11

1Maxim

um6

63

64

36

55

64

5Ex

pectation

243

179

133

183

142

115

200

201

173

207

114

163

Weathering

Minim

um2

21

22

11

11

21

1Maxim

um4

44

43

24

43

42

2Ex

pectation

246

267

194

251

218

197

296

172

177

285

192

194

Groun

dwater

Minim

um1

11

11

11

11

11

1Maxim

um4

44

32

45

52

44

4Ex

pectation

158

192

172

149

125

113

192

207

150

128

171

213

Dip

difference(deg )

Minim

umminus44

minus45

minus23

minus44

minus27

minus39

minus32

minus42

minus34

minus36

minus30

minus12

Maxim

um6

1710

1915

611

33minus5

1416

25Ex

pectation

minus3331

minus1994

minus250

minus1170

minus690

minus1247

minus1616

minus936

minus2462

minus1610

minus588

820







Rock strength

Joint spacing

RQD

Roughness

Aperture

Weathering

Groundwater

Dip difference


mass quality








6 Strong plus mdash




Reciprocals ofabove






CR CIRI

(7)


CI λmax minus N

N minus 1 (8)










N 1 2 3 4 5 6 7 8 9 10RI 0 0 058 090 112 124 132 141 145 149












4 Conclusions



PDS1

PD222

PD224

PD226

0 50 100 150

1

2

3 3

4567







45

100 150500

10050 150m0

10050

200m

200m

150m0





Data Availability




Acknowledgments


References













































Songta dam

Flow direction

N

Nu River


96deg0prime0PrimeE

30deg0prime0Prime

N29

deg0prime0Prime

N28

deg0prime0Prime

N27

deg0prime0Prime

N26

deg0prime0Prime

N25

deg0prime0Prime

N

30deg0prime0Prime

N29

deg0prime0Prime

N28

deg0prime0Prime

N27

deg0prime0Prime

N26

deg0prime0Prime

N25

deg0prime0Prime

N



(a) (b)

Nu River



Joint

Joint
















PDS12

PD222

PD224

PD226

25 50 75 100(b)(a)

125 150 175 200m002

02

02

02

25 50 75 100 125 150 175 200m0

25 50 75 100 125 150m0

25 50 75 100 125 150m0






N

S

N

S

N

S


N

S

N

S

N

S


N

S

N

S

N

S

Section 1 Section 2

(a)

(b)

(c)

(d)

Section 3

N

S

E

E

E

E

W

W

W

W

N

S

E

E

E

E

W

W

W

W

N

S

E

E

E

E

W

W

W

W

Set 1Set 2Set 3



























Number offactors






radic radic 2


radic 1






Tunnelsupport

Tunnelmining

Tunnelcavern


Rock mass ofdam

foundation

Rock mass ofdam

foundation






weathered 2 Moist 2








Flat smooth 9


Tabl

e3

Evaluatio

nindexesof

rock

massin

each

aditareexpressedby

theinterval

number

Evaluatin

gindex

Interval

number

PDS1

PD222

PD224

PD226

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Rock

streng

th(M

Pa)

Minim

um474

257

739

348

673

513

626

602

878

493

1299

1170

Maxim

um1636

2415

1389

830

1316

994

1453

1891

1920

1301

2341

2397

Expectation

1022

968

1060

569

1161

940

1144

1119

1481

850

1710

1957

Jointspacing(m

)Minim

um0007

0006

1311

0003

0003

0112

0020

0033

0277

0044

0032

4153

Maxim

um4573

7349

7311

8016

5233

18781

11155

7524

33844

4699

8838

8333

Expectation

0802

1164

4046

0791

0999

4294

0981

0875

7097

0846

2006

6481

RQD

()

Minim

um54

3594

1478

7254

4592

343

868

818

Maxim

um85

100

100

9898

100

98100

100

970

1000

1000

Expectation

7484

9868

9196

7492

9866

9698

Roughn

ess

Minim

um1

14

44

44

44

44

4Maxim

um9

77

88

98

99

78

5Ex

pectation

570

489

467

549

518

525

632

678

454

457

479

406

Aperture

Minim

um1

11

11

11

11

11

1Maxim

um6

63

64

36

55

64

5Ex

pectation

243

179

133

183

142

115

200

201

173

207

114

163

Weathering

Minim

um2

21

22

11

11

21

1Maxim

um4

44

43

24

43

42

2Ex

pectation

246

267

194

251

218

197

296

172

177

285

192

194

Groun

dwater

Minim

um1

11

11

11

11

11

1Maxim

um4

44

32

45

52

44

4Ex

pectation

158

192

172

149

125

113

192

207

150

128

171

213

Dip

difference(deg )

Minim

umminus44

minus45

minus23

minus44

minus27

minus39

minus32

minus42

minus34

minus36

minus30

minus12

Maxim

um6

1710

1915

611

33minus5

1416

25Ex

pectation

minus3331

minus1994

minus250

minus1170

minus690

minus1247

minus1616

minus936

minus2462

minus1610

minus588

820







Rock strength

Joint spacing

RQD

Roughness

Aperture

Weathering

Groundwater

Dip difference


mass quality








6 Strong plus mdash




Reciprocals ofabove






CR CIRI

(7)


CI λmax minus N

N minus 1 (8)










N 1 2 3 4 5 6 7 8 9 10RI 0 0 058 090 112 124 132 141 145 149












4 Conclusions



PDS1

PD222

PD224

PD226

0 50 100 150

1

2

3 3

4567







45

100 150500

10050 150m0

10050

200m

200m

150m0





Data Availability




Acknowledgments


References






















































PDS12

PD222

PD224

PD226

25 50 75 100(b)(a)

125 150 175 200m002

02

02

02

25 50 75 100 125 150 175 200m0

25 50 75 100 125 150m0

25 50 75 100 125 150m0






N

S

N

S

N

S


N

S

N

S

N

S


N

S

N

S

N

S

Section 1 Section 2

(a)

(b)

(c)

(d)

Section 3

N

S

E

E

E

E

W

W

W

W

N

S

E

E

E

E

W

W

W

W

N

S

E

E

E

E

W

W

W

W

Set 1Set 2Set 3



























Number offactors






radic radic 2


radic 1






Tunnelsupport

Tunnelmining

Tunnelcavern


Rock mass ofdam

foundation

Rock mass ofdam

foundation






weathered 2 Moist 2








Flat smooth 9


Tabl

e3

Evaluatio

nindexesof

rock

massin

each

aditareexpressedby

theinterval

number

Evaluatin

gindex

Interval

number

PDS1

PD222

PD224

PD226

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Rock

streng

th(M

Pa)

Minim

um474

257

739

348

673

513

626

602

878

493

1299

1170

Maxim

um1636

2415

1389

830

1316

994

1453

1891

1920

1301

2341

2397

Expectation

1022

968

1060

569

1161

940

1144

1119

1481

850

1710

1957

Jointspacing(m

)Minim

um0007

0006

1311

0003

0003

0112

0020

0033

0277

0044

0032

4153

Maxim

um4573

7349

7311

8016

5233

18781

11155

7524

33844

4699

8838

8333

Expectation

0802

1164

4046

0791

0999

4294

0981

0875

7097

0846

2006

6481

RQD

()

Minim

um54

3594

1478

7254

4592

343

868

818

Maxim

um85

100

100

9898

100

98100

100

970

1000

1000

Expectation

7484

9868

9196

7492

9866

9698

Roughn

ess

Minim

um1

14

44

44

44

44

4Maxim

um9

77

88

98

99

78

5Ex

pectation

570

489

467

549

518

525

632

678

454

457

479

406

Aperture

Minim

um1

11

11

11

11

11

1Maxim

um6

63

64

36

55

64

5Ex

pectation

243

179

133

183

142

115

200

201

173

207

114

163

Weathering

Minim

um2

21

22

11

11

21

1Maxim

um4

44

43

24

43

42

2Ex

pectation

246

267

194

251

218

197

296

172

177

285

192

194

Groun

dwater

Minim

um1

11

11

11

11

11

1Maxim

um4

44

32

45

52

44

4Ex

pectation

158

192

172

149

125

113

192

207

150

128

171

213

Dip

difference(deg )

Minim

umminus44

minus45

minus23

minus44

minus27

minus39

minus32

minus42

minus34

minus36

minus30

minus12

Maxim

um6

1710

1915

611

33minus5

1416

25Ex

pectation

minus3331

minus1994

minus250

minus1170

minus690

minus1247

minus1616

minus936

minus2462

minus1610

minus588

820







Rock strength

Joint spacing

RQD

Roughness

Aperture

Weathering

Groundwater

Dip difference


mass quality








6 Strong plus mdash




Reciprocals ofabove






CR CIRI

(7)


CI λmax minus N

N minus 1 (8)










N 1 2 3 4 5 6 7 8 9 10RI 0 0 058 090 112 124 132 141 145 149












4 Conclusions



PDS1

PD222

PD224

PD226

0 50 100 150

1

2

3 3

4567







45

100 150500

10050 150m0

10050

200m

200m

150m0





Data Availability




Acknowledgments


References












































N

S

N

S

N

S


N

S

N

S

N

S


N

S

N

S

N

S

Section 1 Section 2

(a)

(b)

(c)

(d)

Section 3

N

S

E

E

E

E

W

W

W

W

N

S

E

E

E

E

W

W

W

W

N

S

E

E

E

E

W

W

W

W

Set 1Set 2Set 3



























Number offactors






radic radic 2


radic 1






Tunnelsupport

Tunnelmining

Tunnelcavern


Rock mass ofdam

foundation

Rock mass ofdam

foundation






weathered 2 Moist 2








Flat smooth 9


Tabl

e3

Evaluatio

nindexesof

rock

massin

each

aditareexpressedby

theinterval

number

Evaluatin

gindex

Interval

number

PDS1

PD222

PD224

PD226

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Rock

streng

th(M

Pa)

Minim

um474

257

739

348

673

513

626

602

878

493

1299

1170

Maxim

um1636

2415

1389

830

1316

994

1453

1891

1920

1301

2341

2397

Expectation

1022

968

1060

569

1161

940

1144

1119

1481

850

1710

1957

Jointspacing(m

)Minim

um0007

0006

1311

0003

0003

0112

0020

0033

0277

0044

0032

4153

Maxim

um4573

7349

7311

8016

5233

18781

11155

7524

33844

4699

8838

8333

Expectation

0802

1164

4046

0791

0999

4294

0981

0875

7097

0846

2006

6481

RQD

()

Minim

um54

3594

1478

7254

4592

343

868

818

Maxim

um85

100

100

9898

100

98100

100

970

1000

1000

Expectation

7484

9868

9196

7492

9866

9698

Roughn

ess

Minim

um1

14

44

44

44

44

4Maxim

um9

77

88

98

99

78

5Ex

pectation

570

489

467

549

518

525

632

678

454

457

479

406

Aperture

Minim

um1

11

11

11

11

11

1Maxim

um6

63

64

36

55

64

5Ex

pectation

243

179

133

183

142

115

200

201

173

207

114

163

Weathering

Minim

um2

21

22

11

11

21

1Maxim

um4

44

43

24

43

42

2Ex

pectation

246

267

194

251

218

197

296

172

177

285

192

194

Groun

dwater

Minim

um1

11

11

11

11

11

1Maxim

um4

44

32

45

52

44

4Ex

pectation

158

192

172

149

125

113

192

207

150

128

171

213

Dip

difference(deg )

Minim

umminus44

minus45

minus23

minus44

minus27

minus39

minus32

minus42

minus34

minus36

minus30

minus12

Maxim

um6

1710

1915

611

33minus5

1416

25Ex

pectation

minus3331

minus1994

minus250

minus1170

minus690

minus1247

minus1616

minus936

minus2462

minus1610

minus588

820







Rock strength

Joint spacing

RQD

Roughness

Aperture

Weathering

Groundwater

Dip difference


mass quality








6 Strong plus mdash




Reciprocals ofabove






CR CIRI

(7)


CI λmax minus N

N minus 1 (8)










N 1 2 3 4 5 6 7 8 9 10RI 0 0 058 090 112 124 132 141 145 149












4 Conclusions



PDS1

PD222

PD224

PD226

0 50 100 150

1

2

3 3

4567







45

100 150500

10050 150m0

10050

200m

200m

150m0





Data Availability




Acknowledgments


References

































































Number offactors






radic radic 2


radic 1






Tunnelsupport

Tunnelmining

Tunnelcavern


Rock mass ofdam

foundation

Rock mass ofdam

foundation






weathered 2 Moist 2








Flat smooth 9


Tabl

e3

Evaluatio

nindexesof

rock

massin

each

aditareexpressedby

theinterval

number

Evaluatin

gindex

Interval

number

PDS1

PD222

PD224

PD226

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Rock

streng

th(M

Pa)

Minim

um474

257

739

348

673

513

626

602

878

493

1299

1170

Maxim

um1636

2415

1389

830

1316

994

1453

1891

1920

1301

2341

2397

Expectation

1022

968

1060

569

1161

940

1144

1119

1481

850

1710

1957

Jointspacing(m

)Minim

um0007

0006

1311

0003

0003

0112

0020

0033

0277

0044

0032

4153

Maxim

um4573

7349

7311

8016

5233

18781

11155

7524

33844

4699

8838

8333

Expectation

0802

1164

4046

0791

0999

4294

0981

0875

7097

0846

2006

6481

RQD

()

Minim

um54

3594

1478

7254

4592

343

868

818

Maxim

um85

100

100

9898

100

98100

100

970

1000

1000

Expectation

7484

9868

9196

7492

9866

9698

Roughn

ess

Minim

um1

14

44

44

44

44

4Maxim

um9

77

88

98

99

78

5Ex

pectation

570

489

467

549

518

525

632

678

454

457

479

406

Aperture

Minim

um1

11

11

11

11

11

1Maxim

um6

63

64

36

55

64

5Ex

pectation

243

179

133

183

142

115

200

201

173

207

114

163

Weathering

Minim

um2

21

22

11

11

21

1Maxim

um4

44

43

24

43

42

2Ex

pectation

246

267

194

251

218

197

296

172

177

285

192

194

Groun

dwater

Minim

um1

11

11

11

11

11

1Maxim

um4

44

32

45

52

44

4Ex

pectation

158

192

172

149

125

113

192

207

150

128

171

213

Dip

difference(deg )

Minim

umminus44

minus45

minus23

minus44

minus27

minus39

minus32

minus42

minus34

minus36

minus30

minus12

Maxim

um6

1710

1915

611

33minus5

1416

25Ex

pectation

minus3331

minus1994

minus250

minus1170

minus690

minus1247

minus1616

minus936

minus2462

minus1610

minus588

820







Rock strength

Joint spacing

RQD

Roughness

Aperture

Weathering

Groundwater

Dip difference


mass quality








6 Strong plus mdash




Reciprocals ofabove






CR CIRI

(7)


CI λmax minus N

N minus 1 (8)










N 1 2 3 4 5 6 7 8 9 10RI 0 0 058 090 112 124 132 141 145 149












4 Conclusions



PDS1

PD222

PD224

PD226

0 50 100 150

1

2

3 3

4567







45

100 150500

10050 150m0

10050

200m

200m

150m0





Data Availability




Acknowledgments


References









































Tabl

e3

Evaluatio

nindexesof

rock

massin

each

aditareexpressedby

theinterval

number

Evaluatin

gindex

Interval

number

PDS1

PD222

PD224

PD226

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Section1

Section2

Section3

Rock

streng

th(M

Pa)

Minim

um474

257

739

348

673

513

626

602

878

493

1299

1170

Maxim

um1636

2415

1389

830

1316

994

1453

1891

1920

1301

2341

2397

Expectation

1022

968

1060

569

1161

940

1144

1119

1481

850

1710

1957

Jointspacing(m

)Minim

um0007

0006

1311

0003

0003

0112

0020

0033

0277

0044

0032

4153

Maxim

um4573

7349

7311

8016

5233

18781

11155

7524

33844

4699

8838

8333

Expectation

0802

1164

4046

0791

0999

4294

0981

0875

7097

0846

2006

6481

RQD

()

Minim

um54

3594

1478

7254

4592

343

868

818

Maxim

um85

100

100

9898

100

98100

100

970

1000

1000

Expectation

7484

9868

9196

7492

9866

9698

Roughn

ess

Minim

um1

14

44

44

44

44

4Maxim

um9

77

88

98

99

78

5Ex

pectation

570

489

467

549

518

525

632

678

454

457

479

406

Aperture

Minim

um1

11

11

11

11

11

1Maxim

um6

63

64

36

55

64

5Ex

pectation

243

179

133

183

142

115

200

201

173

207

114

163

Weathering

Minim

um2

21

22

11

11

21

1Maxim

um4

44

43

24

43

42

2Ex

pectation

246

267

194

251

218

197

296

172

177

285

192

194

Groun

dwater

Minim

um1

11

11

11

11

11

1Maxim

um4

44

32

45

52

44

4Ex

pectation

158

192

172

149

125

113

192

207

150

128

171

213

Dip

difference(deg )

Minim

umminus44

minus45

minus23

minus44

minus27

minus39

minus32

minus42

minus34

minus36

minus30

minus12

Maxim

um6

1710

1915

611

33minus5

1416

25Ex

pectation

minus3331

minus1994

minus250

minus1170

minus690

minus1247

minus1616

minus936

minus2462

minus1610

minus588

820







Rock strength

Joint spacing

RQD

Roughness

Aperture

Weathering

Groundwater

Dip difference


mass quality








6 Strong plus mdash




Reciprocals ofabove






CR CIRI

(7)


CI λmax minus N

N minus 1 (8)










N 1 2 3 4 5 6 7 8 9 10RI 0 0 058 090 112 124 132 141 145 149












4 Conclusions



PDS1

PD222

PD224

PD226

0 50 100 150

1

2

3 3

4567







45

100 150500

10050 150m0

10050

200m

200m

150m0





Data Availability




Acknowledgments


References














































Rock strength

Joint spacing

RQD

Roughness

Aperture

Weathering

Groundwater

Dip difference


mass quality








6 Strong plus mdash




Reciprocals ofabove






CR CIRI

(7)


CI λmax minus N

N minus 1 (8)










N 1 2 3 4 5 6 7 8 9 10RI 0 0 058 090 112 124 132 141 145 149












4 Conclusions



PDS1

PD222

PD224

PD226

0 50 100 150

1

2

3 3

4567







45

100 150500

10050 150m0

10050

200m

200m

150m0





Data Availability




Acknowledgments


References










































CR CIRI

(7)


CI λmax minus N

N minus 1 (8)










N 1 2 3 4 5 6 7 8 9 10RI 0 0 058 090 112 124 132 141 145 149












4 Conclusions



PDS1

PD222

PD224

PD226

0 50 100 150

1

2

3 3

4567







45

100 150500

10050 150m0

10050

200m

200m

150m0





Data Availability




Acknowledgments


References













































4 Conclusions



PDS1

PD222

PD224

PD226

0 50 100 150

1

2

3 3

4567







45

100 150500

10050 150m0

10050

200m

200m

150m0





Data Availability




Acknowledgments


References











































Data Availability




Acknowledgments


References









































engineeringclassificationofjointedrockmassbasedon...

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