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Int. J. Struct. & Civil Engg. Res. 2015 Huang Mingkui and Quan Jian, 2015

STUDY ON DISTRIBUTION RANGE OFSURROUNDING ROCK RESISTANCE IN TUNNEL

Huang Mingkui1* and Quan Jian1

1 No.66 Xuefu Road Nan'an District Chongqing China.

*Corresponding author: Huang Mingkui hmksmile@163.com

ISSN 2319 – 6009 www.ijscer.comVol. 4, No. 1, February 2015

© 2015 IJSCER. All Rights Reserved

Int. J. Struct. & Civil Engg. Res. 2015

Research Paper

INTRODUCTIONThe design of underground cavity generallyrefer to Code for Design of Road Tunnel (JTGD70–2004) in China. Accordingly, “the loadingstructure method is applied to the designs ofintegrated lining structure tunnel, integrated orcomposite lining in shallow-buried tunnel, liningin open cut tunnel and Song et al., (2013). Thedetermination of lining loads is important forloading structure method, which includespressure and resistance of surrounding rock.The surrounding rock resistance refers to thecapacity of surrounding rock to share the load

The surrounding rock resistance is one of the principal loads of structural design for tunnel. Thedetermination of the distribution of resisting force will influence the calculation results of thestructure, and the determination of the range of resisting force in tunnel will also influence internalforce calculation and structure design. Accordingly, based on elastic-plastic theory, the range ofresisting force of surrounding rock of all levels in tunnel were studied by the uncertainty analysismethod. The results indicate that the range of resisting force of surrounding rock diminishesgradually with downgrading of surrounding rock. When the grade of surrounding rock reaches Vand VI, the resisting force will not in existence in tunnel. Under such circumstance, the resistingforce of surrounding rock will be not be considered in the internal force calculation and structuredesign. This conclusion will provide reference for underground engineering design andconstruction.

Keywords: Surrounding rock, Resisting force, Interval analysis, Tunnel

with the lining, reflecting the physical andmechanical properties of surrounding rock. Itis one of the important parameters for thedesign of tunnel lining (Zhu et al., 2011).Foryears the Buckeye method is usually adoptedin the analysis of distributing characteristicsof surrounding rock resistance, which,however, is unable to reflect all the relevantfactors, and the error of calculation results islarge (Yun et al., 2013).

The calculation of surrounding rockresistance wi ll influence the design ofunderground cavity, internal force calculation

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Int. J. Struct. & Civil Engg. Res. 2015 Huang Mingkui and Quan Jian, 2015

and structural stability analysis, therefore, therelevant research has attracted attention fromthe experts all over the world. For example,the distributing characteristics of surroundingrock resistance in unsymmetrical loadingtunnel were discussed, and its distributing lawwas obtained (Qin et al., 1964); the upper zeropoint determination method of elasticresistance was studied in vertical wall tunnel,the key idea of which is to replace elasticresistance with elastic bar. This study, however,includes complicated calculations, and theresults are not in accordance with the localdeformation theory (Fan et al., 1962). Lu etal., studied the characteristics of the liningsection of single track railway tunnel that canattain a speed of 200 km per hour, andanalyzed the influence of elastic resistancecoefficient of surrounding rock on safetycoefficient and bend moment (Lu et al., 2009).Li et al., analyzed the influence of elasticresistance coefficient on axial force andbending moment of vault and arch bottom (Liet al., 2010). These research results provideguidance for tunnel design and construction.However, because the factors influencing thesurrounding resistance are various, includingthe surrounding rock resistance coefficient, thestiffness, shape and size of lining structure, themagnitude of load and its combination, as wellas the support time of lining structure.Moreover, the different geological environmentmight influence the distribution of surroundingrock resistance, which is important for thestability of underground structure and shouldbe taken into consideration for design. Toanalyze this, based on the elastic-plastictheory, the distribution range of surroundingrock resistance is determined by uncertain

analysis method, which can provide a newmethod for internal force calculation anddesign of underground structure.

DETERMINATION OFSURROUNDING ROCKRESISTANCE AND ITSDISTRIBUTION RANGEThrough quantitative experiments and detailedin-site monitoring analysis, the research showsthat the surrounding rock not only applypressure on the lining but also restrain thedeformation of lining in the force-deformationprocess of the underground structure, whichresults in part of the structure separated fromsurrounding rock into the unbound regions andpart of the structure pushed onto thesurrounding rock into the resistance regions.In the resistance regions, the surrounding rockwill create constraint reaction, and that is thesurrounding rock resistance. In generally, thedistribution range will be determined by threeimportant points according to the structuraldeformation feature (Figure 1) (Qin et al.,2013). The intersection angle between upperzero point of elastic resistance and verticalsymmetrical centerline is about 40° to 60°. Thelower zero point of elastic resistance is locatedat the foot of the wall, where the friction is sogreat that there is no any horizontaldisplacement, and the value of elasticresistance is zero. The maximal resistancepoint is supposed to exist at around the

greatest span of the arch, and usually

take abah3

2 when calculating.

Above is the method to determine the valueand distribution range of surrounding rockresistance in structure design. The distribution

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Int. J. Struct. & Civil Engg. Res. 2015 Huang Mingkui and Quan Jian, 2015

Figure 1: Distribution Range of Surrounding Rock Resistance

range of surrounding rock resistance isdetermined through three important points,which, to some extent, can not reflect theinfluences of the lining stiffness and size,feature of load, lateral pressure coefficient andelastic resistance coefficient. Therefore, thedistribution range of surrounding rockresistance needs further research to providetechnical reference for the internal forcecalculation and structural design ofunderground chamber.

DETERMINATION OFDISTRIBUTION RANGE OFSURROUNDING ROCKRESISTANCEPrinciples of DeterminingSurrounding Rock Resistance

To simplify the analysis, there are fiveassumptions as follows (Xia et al.,2004; Qinet al., 2013): (1) the surrounding rocks aresupposed to be the homogeneous andisotropic continuous medium; (2) the shape ofunderground chamber is regarded as circularwith a radius of r

i; (3) the underground chamber

is at a certain depth and is simplified into a

hole problem in infinite body; (4) the threedimensional stress problem is simplified intoplane strain problem, and the end effect ofexcavation surface is not considered inconstruction of underground chamber; (5) theinitial stress field is shown by lateral pressurecoefficient , that is (

z,

z, where

z is the

vertical stress.

According to the assumptions above and

elastic-plastic theory, after the tunnel was

excavated, the radial displacement formula of

circular tunnel can be obtained with different

lateral pressure coefficient (Xia et al., 2004),

which is described in formula (1).

E

ru iz

r 2

1

2cos1431 ...(1)

where, E, are the elastic modulus andPoisson’s ratio of surrounding rockrespectively.

Based on formula (1), the radialdisplacement of circular tunnel is related to theinitial stress field (

z,

z) elastic modulus E,

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Int. J. Struct. & Civil Engg. Res. 2015 Huang Mingkui and Quan Jian, 2015

Poisson’s ratio and the location of calculationpoint. Under given initial stress field, theexcavation of tunnel might result in outwardexpansion of surrounding rock in a certainrange. If the surrounding rock expansion isrestrained, the surrounding rock resistance willbe created.

Assuming the displacement of surroundingrock towards the tunnel is positive, and thattowards the rock is negative, the deformationdirection of the surrounding rock can helpdetermine the value and range of theresistance, therefore, according to formula (1)the following conclusion can be obtained.

When 0ru , the surrounding rock is

displaced towards tunnel and the unboundregion is formed. According to formula (1),formula (2) can be obtained.

02cos1431

or

143

12cos ...(2)

When 0ru , the surrounding rock is

displaced towards parent rock and the resistanceregion is formed, where the surrounding rockresistance will be created. According to formula(1), formula (3) can be obtained.

02cos1431

or

143

12cos ...(3)

When 0ru , the surrounding rock

displacement is zero, which is the separationbetween the unbound region and theresistance region. According to formula (1),formula (4) can be obtained.

143

12cos ...(4)

Determination of DistributionRange of Surrounding RockResistance

Determination of Poisson’s Ratioand Lateral Pressure Coefficient

In the process of underground chamberexcavation, the surrounding rock stress isgradually changing, which will cause thechange of the values of Poisson’s ratio andlateral pressure coefficient . Based on Codefor Design of Road Tunnel (JTG D70-2004)in China, the values of Poisson’s ratio ofsurrounding rock of all levels are shown in Table1, and the values of lateral pressure coefficientof surrounding rock of all levels are shown inTable 2.

Table 1: Normal Values of Poisson’s Ratio of Surrounding Rock of All Levels

Surrounding Rock Grade I II III IV V VI

Poisson’s ratio <0.20 0.20~0.25 0.25~0.30 0.30~0.35 0.35~0.45 0.40~0.45

Table 2: Lateral Pressure Coefficients of Surrounding Rock of all Levels

Surrounding Rock Grade I, II III IV V VI

Lateral pressure coefficient 0 <0.15 0.15~0.30 0.30~0.50 0.50~1.0

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Int. J. Struct. & Civil Engg. Res. 2015 Huang Mingkui and Quan Jian, 2015

According to Table 1 and 2, under thepressure of surrounding rock, the values ofPoisson’s ratio and lateral pressurecoefficient are not constant, but vary in avariation range. Therefore, the deterministicanalysis method is not supposed to beadopted, instead, the new uncertainty analysismethod should be introduced in the analysis.In this paper, the interval analysis method willbe adopted to determine the range ofsurrounding rock resistance.

Determination of the Range ofSurrounding Rock Resistance

In the late 1950s Moore proposed anddeveloped the interval analysis method(Ramon E Moore et al., 2009). Based oninterval mathematics and Taylor seriesexpansion, the interval analysis method isused to deal with uncertainties. At first thismethod is mainly used to deal with floatingpoint arithmetic in calculation. Later it isintroduced to the analysis of engineering for itcan reflect the uncertainty of parameters inengineering. In the interval arithmetic, if thesame interval variable appears more thanonce or there are correlations between intervalvariables, this will lead to interval expansionof calculation results (Ramon E Moore et al.,2009; Huang, 2009).

To avoid the expansion, formula (4) will besimplified as formula (5) by means ofmathematical algorithms of interval analysismethod.

43

1

1

1

43

12cos

11

21

43

1

1

21

so

11

21

43

12cos

...(5)

Here the typical surrounding rock of IV

grade is taken for example, and the

calculations of the surrounding rock of other

grades can be done correspondingly. Based

on Table 1 and 2, 35.0,30.0 and

30.0,15.0 are the interval range for the

surrounding rock of IV grade.

So,

35.0,30.043

12cos

130.0,15.01

21

= 5873.1,7738.0

And because 12cos ,

0.1,7738.02cos .

Accordingly, there is point with zero

displacement in the surrounding rock of IV

grade. That is to say, under the pressure, there

are resistance regions in the surrounding rock.

Take the horizontal plane with center of the

circle as the symmetry axis, and only take the

upper section into consideration, the range of

the resistance regions in the surrounding rock

of IV grade is calculated according to formula

(3) and formula (4), namely, the range of the

resistance regions in surrounding rock of IV

grade is 0 to 19.65°.

Similarly, the range of the resistance regions

of surrounding rock at other levels can be

calculated. The results are shown in Table 3.

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Int. J. Struct. & Civil Engg. Res. 2015 Huang Mingkui and Quan Jian, 2015

Table 3: Ranges of the Resistance Regions of Surrounding Rock of all Levels

Surrounding Rock Grade I II III IV V VI

cos 2 [0.3333,0.4545] [0.4545,0.50] [0.50,1.0] [0.7738,1.0] no zero point no zero point

The ranges of the resistance 0~35.27° 0~31.48° 0~30.00° 0~19.65° no resistance no resistance

regions region region

With the decline of the surrounding rock

quality, the range of the resistance regions

gradually diminishes under the pressure of

surrounding rock. When the surrounding rock

quality downgrades to V and VI, there is no

resistance region in the surrounding rock.

Therefore, the beneficial influence of

surrounding rock resistance will not be

considered in the process of the lining design

and stability analysis when the grades of

surrounding rock are as low as V and VI.

CONCLUSIONThe surrounding rock resistance is one of theprincipal loads in structural design for tunnel.The range of distribution of resisting force willinfluence the calculation results of internal force.The determination of the reasonable range ofsurrounding rock resistance is important toavoid the uncertainty of assumption onresistance, and is of great importance forinternal force calculation and lining design ofunderground structure. In this paper, based onthe elastic-plastic theory and uncertain analysismethod, the distribution range of surroundingrock resistance of different qualities isdiscussed. The results indicate that the rangeof the resistance regions is graduallydiminished with the decline of the surroundingrock quality. When the surrounding rock qualitydowngrades to V and VI, there is no resistance

regions in surrounding rock and therefore thebeneficial influence of surrounding rockresistance will not be considered in theprocess of the lining design and stabilityanalysis when the grades of surrounding rockare as low as V and VI.

ACKNOWLEDGMENTThe author sincerely thanks the educationalcommittee fund project of Chongqingmunicipal (No. 2019501129) that supports thiswork in part.

REFERENCES1. Fan W T (1962), “Elastic resistance

calculation of lining arch of upright wallrailway tunnel”, Railway Standard Design.No.Supp.2, pp.29-30.

2. Huang M K (2009), “Interval analysismethod of the mechanical property forconcrete-filled steel tube”, SichuanBuilding Science, Vol. 35, No. 2, pp. 32-35.

3. Qin S J-Han J C and Zhang J F (1964),“Determine elastic resistance distributionlaw of unsymmetrically loaded tunnel byasymptotic method”, Railway StandardDesign. No. 1, pp. 10-14.

4. Song K Z and Wang M S (2013),“Influence of elastic resistance of wall rockon tunnel l ining internal forces”,

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Int. J. Struct. & Civil Engg. Res. 2015 Huang Mingkui and Quan Jian, 2015

Hydrogeology & Engineering Geology,Vol. 40, No. 1, pp. 79-82.

5. Lu M L (2009), “Analysis on influencingfactors for internal force of railway tunnellining”, Tunnel Construction, Vol. 29, No.1, pp. 33-37.

6. Li P F, Zhang D L, Zhao Y , et al. (2010),“Study of mechanical characteristics ofsecondary lining of large-Section loesstunnel”, Chinese Journal of RockMechanics and Engineering, Vol. 29, No.8, pp. 1690-1696.

7. Q in R H and W ang C (2013), Tunnel, 3rd

Edition, Chongqing University Press.

8. Ramon E.Moore, Baker Kearfott R andMichael J Cloud (2009), Introduction to

Interval analysis, Society for Industrialand Applied Mathematics, Philadelphia.

9. Xiao Y X and Wang Y D (2004),Mechanical Calculation of TunnelStructure, China Communications Press.

10. Yun Y F and Wu D L (2013), “Method ofdetermining the elastic resistance forarched tunnel”, Chinese Journal ofUnderground Space and Engineering,Vol. 9, No. 3, pp. 878-883.

11. Zhu J M, Peng X P and Xu J H (2011),“Determination of rock resistantcoefficient in lining tunnels based on SMPfailure criterion “, Chinese Journal ofGeotechnical Engineering, Vol. 32, No.5, pp. 700-704.