Tunnelling and Underground Space Technology 46 (2015) 64–75

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Tunnelling and Underground Space Technology

journal homepage: www.elsevier .com/ locate / tust

ITA/AITES accredited material

Model test to investigate the failure mechanisms and lining stresscharacteristics of shallow buried tunnels under unsymmetrical loading

http://dx.doi.org/10.1016/j.tust.2014.11.0030886-7798/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: School of Civil Engineering, Central South University,Shaoshan South Road No. 22, 410075 Changsha, China. Tel.: +86 13787232438.

E-mail addresses: mingfenglei@aliyun.com (M. Lei), lmpeng@mail.csu.edu.cn(L. Peng), 124520238@qq.com (C. Shi).

Mingfeng Lei a,b, Limin Peng a, Chenghua Shi a,⇑a School of Civil Engineering, Central South University, Changsha, Chinab China Construction Fifth Engineering Division Corp., Ltd., Changsha, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 11 January 2014Received in revised form 9 September 2014Accepted 19 November 2014

Keywords:Unsymmetrical loading tunnelShallow buriedMechanical characteristicsFailure mechanismModeling test

The similitude criterion for the model used in this study was derived from similarity theory and elasticitymechanics equations. An experimental program was designed and used to simulate the excavation ofthree unsymmetrical loading model tunnels with different bias angles. The change laws and distributionforms of structural stress and surrounding rock pressure, and the failure mechanism of lining andsurrounding rock on shallow buried tunnels under unsymmetrical loading were then studied systemat-ically. Results show that the surrounding rock pressure and structural stress both change constantly inthe process of tunnel excavation, and the surrounding rock stress releases obviously near the excavationface, which presents a noteworthy biased feature and time–space effect. As bias angle increases, the dif-ference of surrounding rock pressure between the shallow and deep side of tunnel increases, and com-pared with the Code method, the difference obtained from the model test and field test results areincreasing at a faster pace, especially, the vertical surrounding rock pressure. Thus it can be seen thatthe solution of Code method underrates the bias feature of surrounding rock pressure, causing the tunnelto be underdesigned. The existence of unsymmetrical load transforms the state of structural stress, andthe failure form differs in location. Moreover, owing to the effect of bias angle, the development of themorphologic traits of the lining structure should be closely monitored during tunnel construction, soas to take specific measurements. The failure process over the entire construction process can bedescribed as follows: local movement ? superficial crack in tensile area of deep side ? shear slip devel-ops in deep ground. The failure mode presents as an inverted cone, with the tunnel as the top and theslope as the bottom. And owing to the effect of bias angle, the rupture angle of shallow side is smallerthan that calculated by the Code method, whereas the reverse is true for the deep side.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Limited by the geological terrain and alignment, unsymmetricalloading tunnels are often inevitable at tunnel entrances, mountain-sides and valley areas. Compared with conventional tunnels,unsymmetrical loading tunnels are more complicated inmechanism and difficult to construct, and are prone to engineeringaccidents and dangers (i.e. landsides, collapse, instability of the ini-tial liner, and cracked linings). Fundamentally, these causes can beattributed to lack of knowledge on the mechanical characteristicsof unsymmetrical loading tunnels, which in turn leads to a lackof relevant design schemes and appropriate measurements.

The problem has attracted intense research interest, and a num-ber of theoretical studies, numerical simulations and experimentalanalyses have been conducted concerning the mechanical featuresof tunnel structures, the failure mechanism of the surroundingrock, and construction methods and treatment. Zuo et al. (2011)and Bai and Wu (2012) put forward new calculation models basedon new assumptions and retaining wall models. They also derivedmodified formulas for calculating surrounding rock pressure inshallow buried and unsymmetrical loading tunnels and comparedthese formulas with the Code method (JTG D70, 2004; TB 10003-2005, J449-2005, 2005). The comparison results indicate that thenew methods coincide with the actual results measured on site,and offer a favorable supplement for the current code. Yang andWang (2008) and Pan et al. (2011) examined the mechanicalcharacteristics of unsymmetrical loading tunnels, dynamicalbehavior in construction, the interaction between surroundingrock and lining, the effects of specific parameters (i.e. bias angle),

M. Lei et al. / Tunnelling and Underground Space Technology 46 (2015) 64–75 65

structural reliability, construction techniques, and so on, by meansof numerical simulation, and many beneficial conclusions wereobtained. As regards modeling tests, Wang and Zhu (2010) and

Table 1Similarity parameters of model test.

Physical indexes Similarity ratio

Geometry 20Volume-weight 2Elastic modulus 40Poison’s ratio 1Cohesion 1Stress 40Surrounding rock pressure 40

Table 2Parameters of model and prototype materials.

Mechanical parameters Lining Surrounding rock

Prototype Model Prototype Model

Volume-weight (kN/m3) 25.00 12.58 19.00 9.53Elastic modulus (GPa) 28.00 0.72 1.00 0.028Poison’s ratio 0.20 0.20 0.45 0.45Internal friction angle (�) 55 55 18 18Cohesion (kPa) 2200 2200 30 30

Fig. 1. Model of tunnel lining structure (Unit: mm). (a) Model dimension and (b)model entity.

Zhang et al. (2009) analyzed the progressive failure mechanismand stress distribution by simulated unsymmetrical loadingtunnels. Wang et al. (2005) investigated the performance ofunsymmetrical loading tunnel structures during constructionusing in situ monitoring, whereby the project is guided directlyand provides firsthand reference for relevant research. These

Fig. 2. Model test chamber (Unit: m). (a) Front view; (b) side view and (c) realpicture.

0

1

2

3

4

5

6

1 4 7 10 13 16 19Excavation step

Pres

sure

val

ue/k

Pa

VA RH RA RILI LA LH

(a)

2

3

4

5

6

ssur

e va

lue/

kPa

VA RH RA RILI LA LH

(b)

66 M. Lei et al. / Tunnelling and Underground Space Technology 46 (2015) 64–75

studies have contributed greatly to engineering practices. Thedesign code for highway/railway tunnels (JTG D70, 2004; TB10003-2005, J449-2005, 2005) specifies the distribution modeland surrounding rock pressure calculation method for unsymmet-rical tunnels based on the rigid slider limit equilibrium method,and it has been widely used by engineers and has become theprimary reference for the unsymmetrical loading tunnels designin China.

However, research about the issues concerning shallow buriedtunnels under unsymmetrical loading remains insufficient. (a)Recent studies mainly use numerical simulation, whose resultsare affected by the deviancy of stratum parameters and are hardlysatisfactory. Furthermore, the theoretical research achievementsare extremely rare; (b) the most original and authentic data canbe obtained by means of field tests, but owing to environmentalfactors and high costs, the field test method is confined to somemajor projects. Therefore, few samples and large dispersion pres-ent intractable difficulties; (c) laboratory model experiments canresult in analytical samples with high regularity in a certaindegree. However, the high costs and long test period are unaccept-able, so there is no systematical experimental result can be foundrecently. Above all, the importance of research topics concerningthe mechanical characteristics of shallow buried tunnel underunsymmetrical loading is clarified theoretically and practically.Therefore, based on a typical shallow buried tunnel under unsym-metrical loading on the Wenxi-Jiyuan Highway in Shanxi Province,

Surrounding rock

Surrounding rockTest section

Tunnel portal

Dig direction 50

16040

Unit: cm

Pressure cell

Center line of tunnel

Bias angle

LiningStrain gauge

Surrounding rock

Ground surface

Left

Rig

ht

(a)

(b)

Fig. 3. Locations of test section and measuring points. (a) Test section and (b)measuring points.

Fig. 4. Drilling footage of model test.

0

1

1 4 7 10 13 16 19Excavation step

Pre

0

1

2

3

4

5

6

7

1 4 7 10 13 16 19Excavation step

Pres

sure

val

ue/k

Pa

VA RH RA RILI LA LH

(c)

Fig. 5. Change laws of surrounding rock pressure with excavation step. (a) 15�; (b)30� and (c) 45�. (VA—vault, LG—left haunch, LA—left arch springing, LI—left invertedarch, RI—right inverted arch, RA—right arch springing, RH—right haunch, similarlyhereinafter.)

Ground surface

2q

1e

e2

q0q1

2e

e1

Fig. 6. Distribution mode of surrounding rock pressure on shallow buried tunnelunder unsymmetrical loading.

M. Lei et al. / Tunnelling and Underground Space Technology 46 (2015) 64–75 67

China, the mechanical features and failure mechanism of shallowburied tunnel under unsymmetrical loading are discussed using amodel test in this paper.

2. Experimental design

2.1. Similarity relation

According to the three fundamental laws of the similaritytheorem and the results of an analogous modeling test (Kimet al., 2006), the ratio of similitude (C) can be deduced by meansof equation analysis to satisfy the similarity relation. Consideringthe surrounding rock as homogeneous, continuous, and isotropicmaterial, and taking only the self-weight stress into account, theequilibrium differential equations (under the Cartesian CoordinateSystem) of the original tunnel (marked with subscript ‘‘s’’) and thetunnel model (marked with subscript ‘‘m’’) can be expressed as:

@ðrxÞi@xiþ @ðsxyÞi

@yiþ @ðsxzÞi

@zi¼ 0

@ðsyzÞi@xiþ @ðryÞi

@yiþ @ðsyzÞi

@zi¼ 0

@ðsxzÞi@xiþ @ðryzÞs

@yiþ @ðrzÞi

@zi� ci ¼ 0

8>>>>><>>>>>:

; i ¼ s;m ð1Þ

Table 3Results comparison of surrounding rock pressure.

Bias angle (�) Method Vertical pressure (kPa)

qi q0 q2

15 Code 3.43 3.75Model 2.65 3.09Field 3.06 3.29DC/% 29.4 21.2DF/% 15.5 6.5 �1

30 Code 3.07 3.75Model 2.39 3.31Field 2.03 3.31DC/% 28.5 13.3DF/% �15.1 0.0

45 Code 2.56 3.73Model 2.05 2.98Field 1.05 3.37DC/% 25.0 25.0 2DF/% �48.7 13.1 4

Notes: Code-Results calculated by the Code method; Model-Experiment results from indoModel � 100%; DF = (Field �Model)/Model � 100%.

Symbolizing the similarity ratio of stress, geometry, elasticmodulus, Poisson’s ratio, and volume-weight with Cr, CL, CE, Cl,and Cc respectively, we have:

Cr ¼ ðrxÞsðrxÞm

¼ ðryÞsðryÞm

¼ ðrzÞsðrzÞm

Cr ¼ ðsxyÞsðsxyÞm

¼ ðsyzÞsðsyzÞm

¼ ðszxÞsðszxÞm

CL ¼ xsxm¼ ys

ym¼ us

um¼ ls

lm

CE ¼ EsEm;Cl ¼ ls

lm;Cc ¼ cs

cm

8>>>>>>><>>>>>>>:

ð2Þ

Substituting these similarity ratios into the basic equation ofelastic mechanics, the relationship is as below:

Cr ¼ CL � Cc;CE ¼ CL � Cc ð3Þ

Thereby obtaining the similarity criterion for the model test:

Z1 ¼ Cr=ðCL � CcÞ ¼ 1; Z2 ¼ CE=ðCL � CcÞ ¼ 1 ð4Þ

2.2. Similarity parameters

Considering the experimental conditions, the selected geometryand volume-weight similarity ratios are 20:1 and 2:1, respectively,that is, CL = 20 and Cc = 2. Consequently, the other similarityparameters can be determined as shown in Table 1.

2.3. Similarity material

The similarity material involves two kinds of mixture ratiotests: lining and surrounding rock. In terms of practical engineer-ing, Dahuyu Tunnel #2 with V-grade surrounding rock and C30concrete is used for lining and the analogous cases (Mair, 1978;Sloan and Assadi, 1993), the similarity mixture selected for thelining is gypsum, and those for the rock are clay, slag, and sand.Through a set of compressive strength cube tests on cubes withdifferent ratios, the one closest to the similarity criterion is identi-fied as the mixture ratio, namely, gypsum: water = 1:0.75, for thelining; and clay: slag: sand = 1:1:2 for the surrounding rock. Thecorresponding mechanical parameters are listed in Table 2.

2.4. Experimental model and devices

As shown in Fig. 1(a), the model size is determined by the liningsection and the similarity rate of the background project. Accord-ing to the mixture rate determined earlier, the materials are mixed

Horizontal pressure (kPa)

e01 e02 e1 e2

4.06 0.45 1.32 1.35 1.753.95 0.81 1.14 1.15 2.003.52 0.77 1.08 1.40 1.872.8 �44.3 16.2 17.2 �12.50.9 �4.7 �4.9 21.5 �6.5

4.43 1.29 1.76 1.86 2.354.19 0.91 1.38 1.22 2.804.59 1.76 1.34 1.79 2.585.7 41.4 27.2 52.0 �16.19.5 93.0 �3.2 46.2 �7.9

4.89 1.81 2.81 2.75 3.373.91 1.01 2.63 1.27 3.005.69 1.42 2.51 2.30 3.145.0 79.6 6.8 116.2 12.35.4 40.9 �4.6 80.8 4.7

or model test; Field-Back analysis results of field monitoring; DC = (Code �Model)/

Fig. 7. Results comparison of surrounding rock pressure under unsymmetrical loading. (a) 15�; (b) 30� and (c) 45�.

68 M. Lei et al. / Tunnelling and Underground Space Technology 46 (2015) 64–75

Fig. 8. Difference statistics of results obtained from the 3 methods.

M. Lei et al. / Tunnelling and Underground Space Technology 46 (2015) 64–75 69

and poured into the pre-prepared high-precision steel mold andthen shaped into models (see Fig. 1(b)). All tests are conductedwithin a self-designed test chamber (see Fig. 2), whose dimensionsare 3.5 m � 3.0 m � 2.0 m, and 1.2 cm thick toughened glass isused in the inner wall to minimize the boundary effect.

2.5. Experimental condition and test

Three types of unsymmetrical loading tunnel models, with biasangles of 15�, 30� and 45�, are considered in the normal topogra-phy, and each model is fixed with colloid wire strain gauges andsteel wire pressure cells at typical locations to monitor structuralstress and surrounding rock pressure at every excavation step.The sections and points where the gauges and cells are locatedare shown in Fig. 3.

2.6. Simulation of excavation process

The bench excavation method is used to simulate the practicalexcavation to make sure that the experimental results are consis-tent with the practical results. According to the specific excavationorder shown in Fig. 4, the upper semi-section (up-bench) 1 mprecedes the under semi-section (down-bench), with 0.2 m ascirculation footage.

2.7. Experimental procedure

Step 1: The model test chamber is constructed (see Fig. 2), andplastic film is pasted onto its inner wall and then coated with an oillayer to reduce the friction between the chamber and thesurrounding rock.

Step 2: The dosages of materials used to make the model arecalculated based on similarity ratio. The materials are weighed,homogenized in the agitator, and then poured into the high-precision mold and vibrated until compacted.

Step 3: After the test chamber is put in place, the bottom isfilled with 0.5 m high similarity material which is then compactedto prevent the breakage of the model or disturbance to straingauges, which would result in abnormal data caused by settlementunder overlying pressure.

Step 4: The lining equipped with gauges is placed in the presetposition, inside which the ‘‘soil mass’’ is constituted by blockswrapped in oil-coated plastic and shaped as excavation steps tosimulate undrilled conditions.

Step 5: The ‘‘surrounding rock’’ around the lining model is filledat different bias angles. According to the burial depth of the

example tunnel, the minimum thickness of overlying soil in test,as computed using the similarity theorem, is 0.4 m. Meanwhile,the pressure cells are embedded at the preset places.

Step 6: The prepared model is put aside for 48 h in order tomake the lining stress and surrounding rock deformation tend tostabilize (Huang et al., 2013; Seki et al., 2008; Bai et al., 2013),and then the pressure cell and strain gauge readings are recorded.

Step 7: In accordance with the excavation steps, the relevantblock is withdrawn in an orderly fashion and the correspondingsurrounding rock pressure and lining strain of each step arerecorded.

Step 8: When the excavation and test is complete according tothe preset working procedure, the external load is applied to theground surface, and the external load is gradually increased untilthe model structure is damaged. During this process, the failurecharacteristics of surrounding rock and lining structure wereobserved and recorded in detail.

3. Surrounding rock pressure analysis

3.1. Change laws of surrounding rock pressure

The surrounding rock pressure on the monitoring section at dif-ferent bias angles changes during the course of the excavation, asshown in Fig. 5. The results show that:

(1) Prior to excavation, the surrounding rock is intact and onlyinitial pressure is exerted on the pre-embedded tunnelstructure, which accounts for 20% of the final value. The ver-tical surrounding rock pressure is slightly greater than thehorizontal surrounding rock pressure.

(2) As the excavation proceeds, the pressures on the monitoringpoints are constantly changing. When the excavation of theup-bench is complete (the second step in Fig. 5), thesurrounding rock pressure on the vault and two sides ofthe tunnel haunch changes abruptly, and the pressureexerted on the vault increases faster, accounting for 60% oftotal pressure. By comparison, the variation in horizontalsurrounding rock pressure is much smaller, accounting for25% of the final release rate.

(3) When the excavation of the down-bench is complete (theninth step in Fig. 5), the release of pressure basically reachesthe extreme. Most obviously, the release rate on the tunnelspringing accounts for 60% of the total release rate, whichmeans that the tunnel invert begin to work.

3.2. Final valve analysis of surrounding rock pressure

According to the linear distribution mode (see Fig. 6), the finalsurrounding rock pressure valves at various bias angles are collatedinto Table 3 and Fig. 7. Meanwhile, in order to verify the reliabilityof the model test results, the calculated results of the Code method(JTG D70, 2004; TB 10003-2005, J449-2005, 2005) and the fieldtests results (Deng, 2012) of the same background engineeringare collated into Table 3 and Fig. 7.

It is worth noting that: (a) the filed test values in Table 3 andFig. 7 are the back analysis results according to the site monitoringmeasurement results during the construction process (Deng,2012). (b) The model test values in Table 3 and Fig. 7 are the resultsdeducted 20% from the total measured results of indoor model test.The reason is that there is some difference between the model testand real situation. In model test, the tunnel lining structure ispreset at the start of the tests, and the initial surrounding rockpressure accounted for 20% of final value according to the forego-ing analysis, acts on the tunnel lining structure before the tunnel

0

1

2

3

4

5

6

0 10 20 30 40 50

CodeModelField

Bias angle α / (°)

Ver

tical

pre

ssur

e q

1 / k

Pa

0

1

2

3

4

5

6

0 10 20 30 40 50

CodeModelField

Bias angle α / (°)

Ver

tical

pre

ssur

e q

0 / k

Pa

0

1

2

3

4

5

6

0 10 20 30 40 50

CodeModelField

Bias angle α / (°)

Ver

tical

pre

ssur

e q

2 / k

Pa

0

1

2

3

4

0 10 20 30 40 50

CodeModelField

Bias angle α / (°)

Hor

izon

tal p

ress

ure e1

/ kP

a

0

1

2

3

4

0 10 20 30 40 50

CodeModelField

Bias angle α / (°)

Hor

izon

tal p

ress

ure e2

/ kP

a

0

1

2

3

4

5

6

0 10 20 30 40 50

CodeModelField

Bias angle α / (°)

Ver

tical

pre

ssur

e q

/ kP

a

0

1

2

3

4

0 10 20 30 40 50

CodeModelField

Bias angle α / (°)

Hor

izon

tal p

ress

ure e'

1 / k

Pa

0

1

2

3

4

0 10 20 30 40 50

CodeModelField

Bias angle α / (°)

Hor

izon

tal p

ress

ure e'

2 / k

Pa 2qD

(b)(a)

(c) (d)

(e) (f)

(h)(g)q1q - =

Fig. 9. Variation tendency of surrounding rock pressure with the bias angle. (a) q1 ; (b) q0 ; (c) q2 ; (d) e1 ; (e) e2 ; (f) e01 ; (g) e02 and (h) Dq.

70 M. Lei et al. / Tunnelling and Underground Space Technology 46 (2015) 64–75

excavation. In actually, the installation of tunnel lining structurelags behind the tunnel excavation, so the initial surrounding rockpressure measured in model test is not exist in real situation.

Hence, the initial values should be deducted from the final valvesof model test results according to the comparability principle.

The results show that:

-25

-20

-15

-10

-5

0

51 4 7 10 13 16 19

Excavation stepSt

ress

val

ue/k

Pa

VA RH RARI LI LALH

-15

-12

-9

-6

-3

0

3

Excavation step

Stre

ss v

alue

/kPa

VARHRARILILALH

(a)

(b) 1 4 7 10 13 16 19

Fig. 10. Change laws of lining stress with excavation step under bias angle 15�. (a)Intrados and (b) extrados. (VA—vault, LG—left haunch, LA—left arch springing, LI—left inverted arch, RI—right inverted arch, RA—right arch springing, RH—righthaunch.)

Fig. 11. Final distribution of lining internal force under unsymmetrical loading. (a)Axial force and (b) bending moment.

M. Lei et al. / Tunnelling and Underground Space Technology 46 (2015) 64–75 71

(1) The distribution rules of surrounding rock pressure obtainedfrom the 3 methods are consistent in principle. Thesurrounding rock pressure increases with the buried deptin the transverse section of tunnel (see Fig. 7).

(2) The valves of surrounding rock pressure obtained from the 3methods are close (see Fig. 7). The statistical analysisindicates that the relative difference of the 3 methodsresults, which are less than 40%, account for more than80% (see Fig. 8), moreover, the model test results are muchcloser to the field test results. Therefore, the model testresults could be considered to be reliable.

(3) Relatively speaking, the results of the 3 methods are muchcloser given a small bias angle (see Fig. 7), and with theincreases of the bias angle, the relative differences betweenthe 3 methods increase. The results calculated by the Codemethod are big than that of the model test and field test(see Fig. 9(a)–(g)). This is because the rupture rock mass islooked upon as rigid body in the Code method, and thedissipation of internal energy caused by the cohesion ofsurrounding rock is ignored.

(4) As the bias angle increases, the difference of surroundingrock pressure between the shallow and deep side increases,and compared with the Code method, the differencesobtained from the model test and field test results areincreasing at a faster pace, especially, the vertical surround-ing rock pressure, (see Fig. 9(h)). Therefore, the Code methodcould be considered to underestimate the bias feature ofsurrounding rock pressure, which is not favorable to thetunnel structure safety.

4. Lining stress analysis

4.1. Characteristics of lining stress

Fig. 10 shows that the stress diagrams of the tunnel liningchanges along with the excavation step. The results indicate that:

(1) Before the tunnel is excavated and the surrounding rock isundisturbed, only the initial surrounding rock pressureworks on the pre-embedded tunnel structure, whichaccounts for 20% of the final stress after the excavation.And this conclusion is identical to the change laws ofsurrounding rock pressure.

(2) The structural stress constantly changes during theexcavation. When the monitoring section has completedthe excavation of the up-bench (the second step in Fig. 10),the stresses on the vault and the two sides of the tunnelhaunch have altered abruptly. The variation in the vault isthe most obvious, accounting for 50% of the total value. Bycontrast, the variation in the amplitude of the other partsis approximately 25%, which is much smaller.

-1.6

-1.2

-0.8

-0.4

0.015 20 25 30 35 40 45

Bias angle/(°)A

xial

forc

e/k

N

VA RHRA RILI LALH

-0.6

-0.3

0.0

0.3

0.6

0.915 20 25 30 35 40 45

Bias angle/(°)

Ben

ding

mom

ent/K

N-m

VA RHRA RILI LALH

(a)

(b)

Fig. 12. Change laws of lining internal force with bias angle. (a) Axial force and (b)bending moment. (VA—vault, LG—left haunch, LA—left arch springing, LI—leftinverted arch, RI—right inverted arch, RA—right arch springing, RH—right haunch.)

72 M. Lei et al. / Tunnelling and Underground Space Technology 46 (2015) 64–75

(3) When the monitoring section completes the excavation ofthe down-bench (the ninth step in Fig. 10), the stressincreases over time, and then gradually stabilizes. Themaximum growth occurs on the tunnel springing, whichaccounts for 50% of the total stress, whereas the growth onthe rest of the measuring points is only 25%.

4.2. Analysis of the final result of the lining internal force

Fig. 11 indicates the final distribution of the internal force onthe tunnel lining, and Fig. 12 shows the change in the internal forceof the measuring points on the tunnel section under different biasangles.

(1) After the excavation of the tunnel, the disturbance ofsurrounding rock is accompanied by the change in the lininginternal force. Basically, the tunnel structure is in thecompressive state, and the maximum axial force and bend-ing moment appear on the deep side from springing to thehaunch.

(2) Given the unsymmetrical load, the lining internal force isunequally distributed and non-uniformity increases as thebias angle increases. The position of the maximum axialforce on the shallow side of the tunnel moves upwards, fromthe springing to the haunch, whereas the trend is oppositefor the deep side.

(3) When the bias angle ranges from 15� to 30�, the non-uniformity of the internal force has a moderate growth butis relatively unnoticeable. By contrast, when the bias angleranges from 30� to 45�, the growth of non-uniformity is

more remarkable, which means that the bias terrain has asignificant effect on the force state of the tunnel lining, whenthe bias angle is greater than 30�.

5. Mechanism of progressive failure

5.1. Process of progressive failure

From the analysis above, under unsymmetrical loading, thesurrounding rock pressure on the deep side of the tunnel is greaterthan that on the shallow side. However, this natural balance isbroken by the excavation of the tunnel, thereby inducingdisplacement on the tunnel structure of the deep side and furthersqueezing the structure of the shallow side, which explains theunsymmetrical force distribution along the supporting structureof the tunnel. As long as the stress exceeds the surrounding rockstrength, or the structure is not armed against the surroundingrock pressure, the stability of the tunnel is endangered. The pro-gressive failure that occurred in the test is shown in Fig. 13.

(1) The surrounding rock before excavation maintains abalanced stress state. However, upon the excavation, thestress release successively and acts on the supporting struc-ture of the tunnel. Given the time–space effect, the load issmall and the resulting deformation is nearly unnoticeable,as shown in Fig. 13(a).

(2) As the tunnel excavation continues, the surrounding rockstress is further released, and the load acting on the support-ing structure increases. Given the rapid growth on the deepside, the unsymmetrical loading becomes more evident. Thedeformation is also expanded to ground surface and resultsin displacement, as shown in Fig. 13(b).

(3) Given the time–space effect, the release of surrounding rockstress continues even after the completion of the excavation.Thus, the load acting on the supporting structure increasesto some degree, which aggravates the asymmetry. If thesupporting structure is not strong enough or timely closed,it may extrude from the deep side to the shallow side. Con-sequently, the loose circle of surrounding rock on the deepside may enlarge and numerous secondary fractures mayappear, as shown in Fig. 13(c).

(4) The formation of the secondary fracture weakens thestrength of the surrounding rock, and at the same time,the drop of surrounding rock strength accelerates thedevelopment of the secondary fracture again, and so on, thena vicious circle forms. And as a result, the secondary frac-tures cross and connect one another, and finally produceseveral interconnected cracks, as shown in Fig. 13(d).

(5) At this time, the surrounding rock almost loses its self-supporting capability. The load supported by the tunnelstructure converts from the loose load into the whole weightof the surrounding rock, the rapid quantitative change in theload can break the whole structure, followed by a sharpincrease in the deformation and large areas of overlyingsurrounding rock slide, then finally collapse, as shown inFig. 13(e).

5.2. Analysis of the progressive failure mode

5.2.1. Lining structureBased on the analysis of the mechanical characteristics of the

lining structure and the progressive failure process, the failuremorphology and mode of bias tunnel are quite different from thenormal tunnel. The results of the experiment on the failure modeof the shallow buried tunnel under unsymmetrical loading areshown in Fig. 14 and Table 4.

Fig. 13. Failure process of shallow buried tunnel under unsymmetrical loading.

surface

Table 4Damage mechanism of lining structure of shallow buried tunnel under unsymmet-rical loading.

Zones Range Failure type Failure morphology

I [0, p/6 + a] Shear failure Dehiscing obliquely on crosssection

II [p/6 + a, p/2] Composite failureby tension andcompression

Concrete crashing on intradosand cracking on extrados

III [p/2, 5p/4] Tension failure Extrados is cracking by tension,and crashing on hinging andinvert is crashing bycompression

IV [5p/4, 3p/2] Tension failure Intrados is cracking by tensionV [3p/2, 2p] Tension failure Intrados is crashing by tension

M. Lei et al. / Tunnelling and Underground Space Technology 46 (2015) 64–75 73

zone

zone zone

zone zone

Ground

Fig. 14. Zoning for failure mechanism of lining structure of shallow buried tunnelunder unsymmetrical loading.

74 M. Lei et al. / Tunnelling and Underground Space Technology 46 (2015) 64–75

From the analysis, for the different parts of the lining structureof the shallow buried tunnel under unsymmetrical loading, thefailure mode is diverse, owing to its asymmetry. Meanwhile, therange varies according to the bias angle. In terms of practicaldesign and construction, the development of the surfacemorphology should be intensively monitored to allow differentialtreatments and appropriate measurements.

Fig. 15. Failure modes of unsymmetrical loading tunnel

5.2.2. Surrounding rockThe failure morphology and the rupture angle of surrounding

rock, under various bias angles in the experiment are shown andcompared in Fig. 15 and Table 5.

(a) The failure morphology of the surrounding rock comprises aspatial sliding surface, which is an inverted cone with thetunnel body as roof and the slope as bottom. The failure

at different bias angles. (a) 15 �; (b) 30� and (c) 45�.

Table 5Comparison of fracture angles between model test and Code method (Unit: �).

Bias angle Fracture angle

Shallow side Deep side

Code Model Code Model

15 61 56 66 7130 63 63 61 6845 69 66 53 66

M. Lei et al. / Tunnelling and Underground Space Technology 46 (2015) 64–75 75

range is affected by the bias angle: given a small bias angle,the failure range, depth and volume are also small; and thereverse is true for a large bias angle.

(b) In different excavation stages, the type of failure also varies.At the initial stage, given a small stress release and a smallexcavation section, the stiffness of the supporting structureis relatively large and the disturbance to soil is finite. Thus,the failure types are mainly the stress release andsettlement. With the advance of excavation, the stressrelease rates and deformation increase until the tensilestress on the ground surface on the deep side appear,thereby producing fractures on the superficial ground. Thefractures further develop into a slide plane, the failure modethen ends with shear sliding.

(c) The fracture angles are approximately 56–71�. Compared tothe fracture angles calculated by the Code method, that ofthe shallow side are smaller, approximately 56–66�, whereasthat on the deep side are larger, approximately 66–71�.Therefore, the Code method underestimates the bias featurein terms of failure morphology, as indicated by the analysisabove.

6. Conclusions

Using the similarity theory, a 20:1 geometrical similar modeltest has been designed to investigate the dynamic variation anddistribution of surrounding rock pressure and lining stress, as wellas the failure mechanism of a shallow buried tunnel underunsymmetrical loading. The main conclusions are as follows:

(1) Surrounding rock pressure and lining stress vary along withthe stages of excavation, and the release of surrounding rockstress is most distinct near the excavation face. After theexcavation of the up-bench, the stresses on the tunnel vaultand haunch abruptly increase by 50% of the final value,which is followed by the tunnel hinging after the excavationof the down-bench. The bias feature and the time–spaceeffect are clearly exhibited during the excavation.

(2) As the bias angle increases, the difference of surroundingrock pressure between the shallow and deep side of tunnelincreases. Further, compared to the Code method, thedifferences obtained from the model test and field testresults are growing at a faster pace. Hence, the Code methodcould be considered to underestimate the bias feature ofshallow buried tunnel under unsymmetrical loading, whichis not favorable to the tunnel structure safety.

(3) Given the unsymmetrical loading, the failure morphologyand the type of tunnel structure and surrounding rock varywith location. The range is likewise affected by the bias

angle. In practical engineering, the development of surfacemorphology of a tunnel structure should be closely observedand measured to facilitate proper treatments.

(4) The failure process of the entire excavation steps can bedescribed as: local displacement and deformation ? superfi-cial crack in tensile area of deep side ? shear develops indeep ground. The failure morphology is an inverted conewith the tunnel as the roof and the slope as bottom, whosefracture angle is related to the bias angle. Compared withthe Code results, the fracture angles in the experiment aresmaller than that in the Code for the shallow side, whereasthe opposite are true for the deep side. This morphologyindicates the underestimation of the bias feature in the Codemethod.

Acknowledgements

Projects funded by China Postdoctoral Science Foundation (No.2014M560652) and the National Basic Research Program of China(973 Program: 2011CB013802) are gratefully acknowledged.

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