J. Mt. Sci. (2017) 14(6): 1124-1139 e-mail: jms@imde.ac.cn http://jms.imde.ac.cn DOI: 10.1007/s11629-016-3999-y

1124

Abstract: This paper focuses on the analytical derivation and the numerical simulation analyses to predict the interaction influences between a landslide and a new tunnel in mountain areas. Based on the slip-line theory, the disturbance range induced by tunneling and the minimum safe distance between the tunnel vault and the sliding belt are obtained in consideration of the mechanical analyses of relaxed rocks over the tunnel opening. The influence factors for the minimum safe crossing distance are conducted, including the tunnel radius, the friction angle of surrounding rocks, the inclination angle of sliding belt, and the friction coefficient of surrounding rocks. Secondly, taking account of the compressive zone and relaxed rocks caused by tunneling, the Sarma method is employed to calculate the safety factor of landslide. Finally, the analytical solutions for interaction between the tunnel and the landslide are compared with a series of numerical simulations, considering the cases for different perpendicular distances between the tunnel vault and the sliding belt. Results

show that the distance between the tunnel vault and the slip zone has significant influence on the rock stress and strain. For the case of the minimum crossing distance, a plastic zone in the landslide traversed by tunneling would be formed with rather large range, which seriously threatens the stability of landslide. This work demonstrates that the minimum safe crossing distance obtained from numerical simulation is in a good agreement with that calculated by the proposed analytical solutions. Keywords: Tunnel excavation; Landslide; Safe crossing distance; Analytical method; Numerical simulation

Received: 20 April2016 Revised: 04 May 2016 Accepted: 02 September 2016

Interaction analyses between tunnel and landslide in

mountain area

ZHANG Zhi-guo1,2,3,4* http://orcid.org/0000-0003-1208-2800; e-mail: zgzhang@usst.edu.cn

ZHAO Qi-hua2 http://orcid.org/0000-0002-8187-8311; e-mail: zhqh@cdut.edu.cn

XU Chen3 http://orcid.org/0000-0002-7688-6587; e-mail: xcusst@yahoo.com

XU Xiao-yang3 http://orcid.org/0000-0003-4836-4201; e-mail: pitn_188017@sohu.com

* Corresponding author

1 State Key Laboratory Breeding Base of Mountain Bridge and Tunnel Engineering, Chongqing Jiaotong University, Chongqing 400074, China

2 State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, China

3 School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, China

4 Key Laboratory of Geohazard Prevention of Hilly Mountains, Ministry of Land and Resources, Fuzhou 350002, China

Citation: Zhang ZG, Zhao QH, Xu C, et al. (2017) Evaluation on interaction influences between tunnel and landslide in mountain area. Journal of Mountain Science 14(6). DOI: 10.1007/s11629-016-3999-y

© Science Press and Institute of Mountain Hazards and Environment, CAS and Springer-Verlag Berlin Heidelberg 2017

Notations:

λ Lateral earth pressure coefficient P Load r Polar radius r0 Radius of tunnel φ Internal friction angle θ0 Initial angle of the slip line θ Polar angle

-To be continued-

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Introduction

The development of urban areas and expanded land use in mountain regions has increased the incidence of landslide disasters which in turn affects tunneling systems. The landslide-tunneling

interaction is a rather complex issue, since it may be influenced by not only the geological condition, the tunnel structure design, the construction environment, but also the construction deficiency without in-time treatments. The crossing distance between the tunnel and the landslide is one of the important influence parameters in tunnel excavation. Currently, many studies have focused on the problem of tunnel excavation (Asano et al. 2003; Dimmock and Mair 2008; Liu et al. 2008; Yoo 2013; Sun et al. 2012; Ng et al. 2013a, 2013b, 2014; Thum and Paoli 2015; Xiao et al. 2016) or the landslide stability (Chen et al. 2001; Zheng et al. 2006; Hungr and McDougall 2009; Preuth et al. 2010; Zheng 2012; Raghuvanshi et al. 2014; Tiwari et al. 2015; Singh et al. 2016). However, few attention has been paid to the combined investigation of the two kinds of engineering problems. In particular, when dealing with ancient landslides crossed by new tunnels, challenges are considerable, especially in simplified analytical method for tunnel crossing influences. Accurate prediction of effects of tunneling on landslide stability poses a major challenge during the tunnel design and construction.

Some attempts have been made to enhance landslide risk and stability research. Methods for solving the problem may be classified into two categories: numerical methods (Chen et al. 2001; Zheng et al. 2006; Hungr and McDougall 2009; Zheng 2012) and monitoring methods (Preuth et al. 2010; Raghuvanshi et al. 2014). However, few investigations are conducted on the problem of landslides induced by tunneling and the estimations heavily rely on the numerical simulation analyses (Jiao et al. 2013; Zhang et al. 2014; Giovanni et al. 2015; Bandini et al. 2015) and geological-condition monitoring (Noferini et al. 2007; Zhang et al. 2015). Minimal attention has been given to the interaction analyses between the tunnel and the landslide based on the closed-form method.

In this paper, the minimum tunnel-landslide crossing distance and the stability of landslides are studied based on slip-line theory (Sokolovski 1954). Combined with the mechanical analysis of the relaxed rocks compressive zone above the tunnel, the analytical expression for the minimum safe distance between the tunnel and the landslide is derived and the influence factors are discussed. In

-Continued-

l Radial disturbance range S Length of relaxed rock zone

H Perpendicular distance between tunnel vault and the sliding belt

ymax Vertical distance between tunnel vault and the sliding belt

T0, 0T Forces on relaxed rocks from surrounding rocks

q Pressure on relaxed rocks from upper rock mass

y0 Maximum distance between compressive zone and sliding belt

α Inclination angle of the sliding belt f Friction coefficient of rockmass

Xi, Xi+1 Normal pressures on both sides of the sliding body element i

Yi , Yi+1 Shear pressures on both sides of the sliding body element i

Wi Weight of the sliding body element i K Critical acceleration coefficient

KWi Horizontal tectonic stress of the sliding body element i

Vi Vertical tectonic stress of the sliding body element i

Ti Shear force imposed on the sliding body element i

Ni Normal pressure imposed on the sliding body element i

bi Projection length in horizontal direction

di, di+1 Left and right side lengths of the sliding body element i

δi, δi+1 Included angle between the left/right side of the sliding body element i and vertical direction

αi Included angle between the bottom surface of the sliding body element i and horizontal direction

ji Internal fraction angle on the left side of

the sliding body element i

φi Internal fraction angle at the bottom of the sliding body element i

jic

Cohesion on the left side of the sliding body element i

ci Cohesion at the bottom of the sliding body element i

F Safety factor

D Equivalent diameter of tunnel in numerical model

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addition, the stability of landslide above the tunnel is analyzed based on the Sarma method (Sarma 1973). Numerical analyses are employed to simulate the plastic zones of tunnel and surrounding rocks with different working conditions while the landslide is crossed orthogonally by tunneling. The applicability of the analytical method proposed in this paper for estimating the minimum safe crossing distance is verified with numerical analyses.

1 Minimum Safe Crossing Distance

1.1 Radial disturbance range of tunnel

The tunnel disturbance range can be obtained from the slip-line theory, which is developed based on the classical plastic mechanics. The slip line is defined as the trajectory of the maximum shear stress in the plastic deformation body. As the maximum shear stress is orthogonal, the slip line is composed of two groups of perpendicular wire mesh. It is available for the slip line field to give a critical solution of soil at the limit equilibrium state. According to Zheng et al. (2012) and Wang et al. (2013), the traditional plastic theory with associated flow rule is not applicable to the deformation mechanism of rock, and the length of slip-line is then obtained considering the non-associated flow rule.

It is a geometric axisymmetric condition when assuming the tunnel is circular and the lateral earth pressure coefficient λ=1. If the load P is symmetrical, the stress around the tunnel cavity will also be symmetrical. In general, this paper adopts the conventional geomechanics sign notation wherein the compressive stresses and pressures are considered to be positive. From symmetry analysis, the orientations of principal stresses around the tunnel are radial and tangential. The minimum principle stress is the radical stress. In addition, it is a non-symmetric problem if the lateral earth pressure coefficient λ ≠ 1. The rotation of principal stress axes are varied to a certain degree. Therefore, the principal stresses are not strictly located at radial and tangential direction. According to numerical calculation results (Zheng et al. 2012), when the included angle between radial and horizontal direction is within 45°, the

orientations of principal stresses can be approximated as radial and tangential.

For a circular tunnel, the slip line field is very simple. According to the slip line theory with non-associated flow rule, the included angle between the plastic slip line and displacement vector is φ/2. The coordinate system is established as shown in Figure 1.

For an arbitrary point P (r, θ), the geometrical equation can be established as:

2tan

d

d

r

r (1)

Therefore,

d

2tan

d

r

r (2)

where, r is the polar radius of the slip line, θ is the angle of the slip line, φ is the internal friction angle of surrounding rocks.

Therefore, the parameter r can be obtained by integrating θ from θ0 to θ, and r from r0 to r:

00

d2

tandr

r r

r (3)

2

tan

0

0e

rr

)2

( 0

(4)

where, θ0 is initial angle of the slip line, as shown in Figure 1. r0 is the radius of tunnel.

Modeling tests show that the value λ has little influence on the parameter θ0 (Zheng et al. 2012). According to symmetry analysis, there must be an exact solution for θ0=π/4 when λ=1. For the cases that λ≠1, we assume that the parameter θ0 approximately equals to π/4.

Figure 1 Calculation model and coordinate system for slip-line theory.

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According to the assumptions above, when the angle between radial and horizontal direction is within 45°, the orientations of principal stresses can be approximated as radial and tangential. Therefore, Eq. (4) is applicable to both λ=1 and λ≠1. According to Zheng et al. (2012), when the parameter λ=0.75 or 0.5, good approximate results can be obtained. However, great errors will appear while the parameter λ=0.25. Given the parameter θ0=π/4, the radial disturbance range l can be obtained by specifying θ=π/2:

1e 2

tan4

0

rl (5)

where, φ is the internal friction angle of surrounding rocks; r0 is the radius of tunnel. The radial disturbance range l will be obtained from Eq. (5) with a given φ.

1.2 Arch height of compressive zone of relaxed rocks

The sliding body will creep down along the sliding belt under the gravity if there is no excavation under the landslide, but this creep has little effect on the disturbance of the sliding bed. However, the disturbed zone, plastic zone and stress relaxation zone will be formed condition on excavation completion under the landslide. For the tunnel-landslide system, with unsymmetrical load, the rock pressure is larger at the top of the landslide above the tunnel than that at the foot of the landslide. The original static equilibrium of rock is broken by tunneling, and the tunnel structure at the top of the landslide began to sand down. At the same time, the tunnel structure at the toe of landslide is extruded and the tunnel is in deviated stress state. With the increase of deformation, the disturbance range of surrounding rock increases, the relaxed zone of surrounding rocks and the compressive zone are formed in the end. The formation of relaxed rocks will weaken the shear strength of rock mass around the relaxed rocks, and the disturbance range will extend up to the upper landslide, thus the stability of the landslide is reduced. According to Mohr-Coulomb yield criterion, with the failure of rocks, there is an angle of 45˚-φ/2 between the fracture surfaces and the direction of the maximum principal stress. The length of relaxed rock zone, S, is the projection

length of tunnel disturbance range in the upper sliding belt, and the arch formed by relaxed rocks compressive zone is tangent to the circle of disturbed zone, as shown in Figure 2. Due to the interaction of tunnel and landslide, if the tunnel vault is close to sliding surface, the effect of relaxed rocks between compressive zone and sliding belt on tunnel stresses must be taken into consideration. The stress of tunnel comes not only from the earth pressure of surrounding rock but also from the extrusion pressure of relaxed rocks above the compressive zone.

The horseshoe shaped tunnel is very common in highway tunnels. In this paper, the tunnel is simplified to a cylinder with an equivalent area in cross-section. The radial disturbance range of the tunnel can be calculated by Eq.(5). Figure 2 shows the schematic diagram for compressive zone and disturbance range considering the interaction of tunnel and landslide, the tunnel cross-section is simplified to an equivalent circle as shown in the figure. H is the perpendicular distance between tunnel vault and the sliding belt, ymax is the vertical distance between tunnel vault and the sliding belt, the S is the length of the relaxed rocks range at the sliding belt, and the l is the radial disturbance range, and α is inclination angle of the sliding belt.

An arch is formed within the relaxed rocks when the tunnel excavation is completed and the extrusion of the slide body is appeared. The simplified calculation diagram of the relaxed rocks between compressive zone and sliding surface is shown in Figure 3. For an arbitrary point M (x, y) in the compressive zone, the geometrical equation is established as:

0 0 0

1 1( ) ( ) 0

2 2 4

ST y y T y qx qS x (6)

where, T0 and T0' are forces on relaxed rocks from surrounding rocks, as shown in Figure 3; q is the pressure on relaxed rocks from upper rock mass; y0 is the maximum distance between compressive zone and sliding belt; S is the length of the relaxed rocks range at the sliding belt, and the value can be described through geometrical relations:

02( ) / cosS l r (7) The force T′ from surrounding rocks should

meet the relationship:

0 0'2 2

qS fT T (8)

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where, f is the friction coefficient of rockmass, f = tanφ; φ is the internal fraction angle of surrounding rocks; S is the length of the relaxed soil range at the sliding belt.

Combining the Eqs. (7) and (8), the maximum arch height of the relaxed rock compressive zone y0 can be obtained:

πtan

4 20 0

0

e

2 cos cos

l r rSy

f f f

(9)

where, S is the length of the relaxed soil range at the sliding belt. r0 is the radius of tunnel; l is the radial disturbance range; φ is the internal friction angle of surrounding rocks.

1.3 Minimum safe crossing distance

If the tunneling is far from the relaxed rocks, the interaction between tunnel and rockmass can be ignored. While the tunneling is close to the relaxed rocks, the extrusion force on tunnel from the relaxed rocks must be considered. Therefore, the minimum safe distance between tunnel vault and the sliding belt must be greater than the critical value, and the critical safe distance between tunnel vault and sliding belt is related to the radial disturbance range l and maximum arch height of the relaxed rock compressive zone y0, as follows:

πtanπ 4 2tan

04 2max 0 0

ecos cos (e 1)cos

cos

rH y l y r

f

(10) where, H is the perpendicular distance between tunnel vault and the sliding belt; α is inclination angle of the sliding belt; r0 is the radius of tunnel.

1.4 Influence factors of minimum safe crossing distance

The minimum safe crossing distance can be predicted by the presented method to examine the influence of different factors, including tunnel radius r0, friction angle of surrounding rocks φ, inclination angle of the sliding belt α and the friction coefficient of surrounding rocks f. Figure 4 shows the influences of these factors on the minimum safe crossing distance. The basic calculation parameters are as follows: slip angle is 31.4°, the radius of tunnel is 6.2 m, friction angle of rocks is 42°, and friction coefficient of rocks is 0.9.

In this paper, other parameters keep constant when studying a certain influence factor.

Figure 4(a) shows that the safety factor increases linearly with tunnel radius. The disturbance range extends as the tunnel radius increases. Therefore, the safe crossing distance should be increased. Figure 4(b) shows that the safe crossing distance is negatively related to the internal friction angle. An increased internal friction angle leads to an improvement of the shear strength, therefore, the safe crossing distance is decreased.

A growth curve is obtained in Figure 4(c) to express the relationship between the inclination of sliding surface and the minimum safe crossing distance. As shown in the figure, along with the increase of sliding surface inclination, the growth rate of the minimum safe distance has greatly

Figure 2 Rock compressive zone and disturbed range.

Figure 3 Simplified calculation diagram for relaxed rocks.

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increased. Figure 4(d) shows a negative correlation between the minimum safe crossing distance and the friction coefficient of rock. Therefore, the minimum safe crossing distance decreases with the increase of friction coefficient.

2 Landslide Safety Analysis

Due to the formation of rocks compressive zone and relaxed rocks, the stability of the landslide will be affected by tunneling, which has already existed above the tunnel. The most common methods to analyze slope stability may broadly include: Swedish slice method (Fellenius 1927), simplified Bishop method (Bishop 1955),

Janbu method (Janbu 1973), Sarma method (Sarma 1973). The Sarma method considers that the sliding body could move only if it is broken into blocks, and the boundaries of these elements need not keep vertical. This method is suitable for slope stability analysis in rocks. In this paper, the landslide is assumed to be traversed down by a tunnel in the minimum safe crossing distance. The calculation diagram for the sliding body is shown in Figure 5. As shown in the figure, Xi and Xi+1 are the normal pressures on both sides of the sliding body element i; Yi and Yi+1 are the shear pressures on both sides of the sliding body element i; Wi is the weight of the sliding body element i; KWi is the horizontal tectonic stress of the sliding body element i; K is the critical acceleration coefficient;

(a) Tunnel radius (b) Friction angle of surrounding rocks

(c) Inclination angle of the sliding belt (d) Friction coefficient of surrounding rocks

Figure 4 Influence factors of minimum safe crossing distance.

5 6 7 8 9 10 11 128

12

16

20

24

Saf

e di

atan

ce

H/m

Tunnel radius r0/m

30 35 40 45 50 55 606.0

6.5

7.0

7.5

8.0

8.5

9.0

Saf

e di

atan

ce

H/m

Friction angle surrounding rocks φ/o

20 25 30 35 40 45 50 5511

12

13

14

15

16

Saf

e di

stan

ce H

/m

Inclination angle of the sliding belt α/o

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.16

8

10

12

14

16S

afe

dist

ance

H/m

Friction coefficient of surrounding rocks f

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Vi is the vertical tectonic stress of the sliding body element i; Ti is shear force imposed on the sliding body element i from the sliding belt; Ni is normal pressure imposed on the sliding body element i from the sliding belt; bi is the projection length in horizontal direction for the bottom surface of the sliding body element i; di and di+1 are the left and right side lengths of the sliding body element i, respectively; δi is the included angle between the left side of the sliding body element i and vertical direction, and δi+1 is the included angle between the right side of the sliding body element i and vertical direction; i is the included angle between the bottom surface of the sliding body element i and horizontal direction.

The equilibrium equation of the sliding body element i in horizontal direction is:

Ti cos i+Xi cos δi +Yi sin δi -KWi-Ni sin i

-Yi+1 sin δi+1 -Xi+1 cosδi+1 =0 (11)

The equilibrium equation of the sliding body element i in vertical direction is:

Ti sin Xi sin +Yi cos δi +Ni cos iYi+1 cosδi+1 +Xi+1 sin =0 (12)

According to Mohr-Coulomb failure criterion, for the bottom and left and right sides of the sliding body element i:

iiiiii bcNT cos/tan (13)

ij

ij

iii dcXY tan (14)

11111 tan ij

ij

iii dcXY (15) where, is the internal fraction angle on the left side of the sliding body element i; is the internal fraction angle at the bottom of the sliding body element i. Note that when the sliding body element i is located above the relaxed rocks caused by the tunnel excavation, should take the value of internal friction angle of the disturbed sliding zone;

is the cohesion on the left side of the sliding body element i; is the cohesion at the bottom of the sliding body element i. Similarly, when the sliding body element i is located above the relaxed rocks, should take the value of cohesion of the disturbed sliding zone. di and di+1 are the lengths for the left and right sides of the sliding body element i, respectively; i is the included angle between the bottom surface of the sliding body element i and horizontal direction.

By introducing Eqs.(13) ~ (15) into Eq.(11) and Eq.(12), the following relation is obtained:

1i i i i iX a PK X e (16)

and then

1211

2311121

23111211

)(

)(

eeeeX

eeeePeePePPK

eeeeaeeaeaaX

nn

nnnnnnnn

nnnnnnnnn

(17)

If there is no applied load, the critical acceleration coefficient can be described as:

2311121

2311121

eeeePeePePP

eeeeaeeaeaaK

nnnnnnnn

nnnnnnnn

(18)

where,αi=mi[(Wi+Vi) sin φi-αi +Ri cosφi

+Si+1 sin i-αi-δi+1 -Si sin φi- i-δi ;

)sec(cos 111 ij

iiij

iim ;

; ij

ii dcS ;

( )cos( )i i i i i iP m W V ; seciii bcR

The boundary conditions are：

; =0 (19)

In calculation, the safety factor F is assumed as a certain value firstly. Then, replace the value ci by ci/F, replace the value tanφi by tanφi/F, replace the

j

ii

i

j

icic

ic

sec cos( )j j

i i i i i i ie m

1 1 0j j

n 1 1n

Figure 5 Calculation diagram of landslide safety.

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value j

ic by j

ic /F, replace the value jitan by

jitan /F. Finally, the safety factor F and all other

parameters, including Pi, ei, ai, mi, Si, are calculated by iterative method.

Note that when critical acceleration coefficient K=0, the calculated value of F corresponds to the slope safety factor with no seismic force. When K is equal to a seismic acceleration, the calculated value of F corresponds to the slope safety factor considering the seismic force.

3 Verifications

In order to verify the analytical method proposed in this paper, the stability of the landslide is calculated by a series of case studies, and some typical cases in different tunnel-landslide distance are considered by numerical analysis. Figure 6 shows the profile of calculation model. The physical parameters are shown in Table 1. The thickness of the lining is 0.7 m. The inclinations of the sliding faces are taken as α1=10.6°, α2=31.4°, α3=62.8°, respectively, as shown in Figure 6. The length of the sliding belts are taken as l1=35.30 m, l2=123.98 m, l3=50.34 m, respectively. The horseshoe section tunnel can be simplified as an equivalent cylindrical tunnel with the diameter D of 12.40 m.

3.1 Analytical analysis for minimum safe crossing distance and landslide stability

The minimum safe distance H=12.77 m is obtained by introducing these parameters into Eq. (9) and the stability of landslide will be analyzed in this case. According to the geometry of the sliding body, the sliding body is divided into five parts and the calculation model is built, as shown in Figure 7. According to Eq.(17), the calculated results are shown in Table 2. Note that the parameter δi in Table 2 is positive if the calculated surface is in a clockwise direction from the vertical direction.

As shown in Table 2, while the landslide safety factor F3=1.2, the calculated corresponding critical acceleration coefficient K=0.0289; and while the landslide safety factor F4=1.3, the calculated corresponding critical acceleration coefficient K=-0.0129. Therefore, the value of landslide safety factor F is between 1.2 and 1.3 while the critical acceleration coefficient K=0. The precise value of landslide safety factor F at K=0 is obtained by numerical analysis. In numerical analysis, assuming xi=Fi firstly. The values F2=1.1, F3=1.2, F4=1.3 are selected in function interpolation; and the corresponding values of K2, K3 and K4 are 0.0791, 0.0289, -0.0129, respectively. Then, assuming yi=f(xi), the values of x2, x3 and x4 are 1.1, 1.2, 1.3, respectively; and the corresponding values

Figure 6 Profile of calculation model. Figure 7 Calculation model.

Table 1 Physical parameters

Surrounding rocks Sliding body Sliding belt Liner Sliding belt above the relaxed rocks Elastic modulus(GPa) 4.0 1.5 0.5 25 0.4 Density(kN/m3) 23 20 20 25 18 Poisson's ratio 0.32 0.4 0.45 0.2 0.47 Internal friction angle(°) 42 35 33 - 26 Cohesion(MPa) 0.50 0.05 0.01 - 0.008

Slidingbody

Surroundingrock

Slidingbelt

Tunnelα1

α2

α3

l2

l1

l3

-11.2 °

-27.5 °

27.5 ° -30.6 °

1

23

4

5

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of y2, y3 and y4 are 0.0791, 0.0289, -0.0129, respectively.

The problem can be transformed into solving the root of the equation f(xi)=0. The approximate root x0 is between 1.1 and 1.2. Eq.(20) gives the Lagrange interpolation polynomial, which is obtained from the inverse function of y=f(x) by quadratic interpolation method.

1 4 5

3

3 4 3 5

1 13 5 3 4

4 5

4 3 4 5 5 3 5 4

( )( )( ) ( )

( )( )

( )( ) ( )( )( ) ( )

( )( ) ( )( )

y y y yL y f y

y y y y

y y y y y y y yf y f y

y y y y y y y y

(20)

By introducing y=0, y2=0.0791, y3=0.0289,

y4=-0.0129 into Eq.(20), the safety factor F is obtained:

F=L 0 =1.2675 (21)

Similarly, the safety factors for K=0.05, K=0.1 and K=0.15 can be calculated by the proposed method according to Table 3, Table 4 and Table 5, respectively. The calculated results are:

F1=L 0.05 =1.156 (22) F2=L 0.1 =1.0639 (23)

F =L 0.15 =0.989 (24)

With the increase of K, the landslide stability decreased gradually. When K=0.15, the landslide is unstable.

3.2 Numerical models

The numerical model is built as shown in Figure 8. The dimension of the model is 300 m in x direction and 30 m in z direction. In y direction, the maximum height is 187.5 m, the height at the right boundary is 154.2 m. The distance from the center of the tunnel to the left boundary is 155.4 m. The surrounding rockmass is assumed to be homogeneous, isotropic and perfectly elastic-plastic Mohr-Coulomb material, while the tunnel lining is a linear elastic material. Six cases are selected in this paper considering different perpendicular distances between tunnel vault and the sliding surface H, including H=0, H1=0.25D, H2=0.5D, H3=1.0D, H4=1.5D and H5=2.0D.

3.3 Comparison for calculated results

Numerical analysis is employed to verify the

applicability of the analytical method proposed in this paper for estimating the minimum safe crossing distance.

The minimum safe crossing distance for analytical method can be obtained according to the Eq.(9), the calculated result is H=12.77 m. Therefore, the ratio of H to D for analytical method is approximately equal to 1. Figure 9 shows the comparison for plastic zone of surrounding rocks and landslide in six cases which are calculated by numerical method. The criterion for plastic zone of surrounding rock is developed from the strength theory of rock material. It indicates that the stress state is transformed from elastic to plastic when the rock is yield. The size of plastic zone reflects the stress state of surrounding rock. In this paper, the influence of the tunnel-landslide interaction is represented by the change of the plastic state diagram.

The landslide stability is obviously affected by tunnel position. As shown in Figure 9(a), the plastic zone of the landslide is very large when the sliding belt is traversed by tunneling. In this case, the surrounding rocks of the tunnel are very unstable, which might cause tunnel collapse. The tunnel vault and tunnel invert are mainly in shear-tension state and in tension state, respectively. The surrounding rocks on both sides of the tunnel are in shear state. For the landslide, the surface of the sliding body is mainly in tension state; the toe of the landslide is in shear-tension state; and the sliding belt is mainly in shear state. Figure 9(b) shows the plastic zone distribution of the tunnel and the landslide when H=0.25D. The plastic area of the landslide in Figure 9(b) is reduced compared with that in Figure 9(a), which indicates that the interaction between landslide and tunnel has weakened.

The tunnel vault and tunnel invert are mainly in tension state. The surrounding rocks on both sides of the tunnel are in shear-tension state. For the landslide, the surface of the sliding body is mainly in tension state, the toe of the landslide is in complex shear-tension state, and the sliding belt is mainly in shear state. Figure 9(c) shows the plastic zone distribution of the tunnel and the landslide when H=0.5D. The plastic zone at the upper part of the landslide is further narrowed. The tunnel vault and tunnel invert are mainly in tension state. The surrounding rocks on both sides of the tunnel are

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J. Mt. Sci. (2017) 14(6): 1124-1139

1133

J. M

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2017

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J. Mt. Sci. (2017) 14(6): 1124-1139

1134

J. Mt. Sci. (2017) 14(6): 1124-1139

1135

in shear-tension state. For the landslide, the surface of the sliding body is mainly in tension state; the toe of the landslide is in shear-tension state; and the sliding belt is mainly in shear state.

Figure 9(d), 9(e) and 9(f) show the plastic zones distribution of the tunnel and the landslide when H=1.0D, 1.5D and 2.0D, respectively. The tunnel vault and tunnel invert are mainly in tension state. At a very small range of both sides of the tunnel, the surrounding rocks are in shear-tension state. For the landslide, the surface of the sliding body is mainly in tension state; the toe of the landslide is in shear-tension state; and the sliding belt is mainly in shear state.

According to the analysis above, the plastic zone is very large when H (the distance between

the tunnel and the sliding belt) is less than the minimum safe crossing distance. It has a great influence on the deformation of the tunnel and landslide. While the distance between the tunnel and the sliding belt is larger than the minimum safe crossing distance, the plastic zone is much smaller, which indicates that the interaction between tunnel and landslide is weakened.

In addition, the failure states and failure ranges of landslide and rockmass surrounding tunnel are very similar in three cases of which H4=1.5D, H5=2.0D, H3=1.0D. According to numerical simulation results, the influence of tunneling on the stability of the landslide is very similar while H ＞ 1.0D. By comparison, the minimum safe crossing distance obtained from

(a) The sliding belt is traversed by tunneling (b) H1=0.25D

(c) H2=0.5D (d) H3=1.0D

(e) H4=1.5D (f) H5=2.0D

Figure 8 Numerical model for different cases.

J. Mt. Sci. (2017) 14(6): 1124-1139

1136

numerical simulation (H=1.0D) is in a good agreement with that calculated by the proposed analytical method in this paper (the ratio of H to D is approximately equal to 1.0).

In order to provide a further explanation of the relaxed rocks compressive zone caused by tunneling, this paper extracts the stress contour image of different crossing distance, as shown in Figure 10. According to Figure 10, the relaxed zone of rocks above the tunnel is formed due to stress release caused by tunneling. When tunnel is close to the sliding belt, the relaxed zone goes through to the landslide surface, thereby, the stability of landslide is affected. With increase of the distance

between the tunnel and the sliding belt, the stress of rock situated between sliding belt and tunnel increases, which indicates that influence of tunneling is reduced on the upper rocks. In particular, there is little effect on the stresses of rocks above tunnel when H>1.0D. The results by analytical derivation have a good agreement with the numerical simulation results.

4 Conclusions

This paper deals with the problem of the interaction mechanics between the tunnel and

(a) The sliding belt is traversed by tunneling (b) H1=0.25D

(c) H2=0.5D (d) H3=1.0D

(e) H4=1.5D (f) H5=2.0D

Figure 9 Plastic zone of different crossing distance.

J. Mt. Sci. (2017) 14(6): 1124-1139

1137

adjacent landslide. The analysis aims to provide an efficient analytical method in assessing the minimum safe crossing distance between the tunnel and the sliding belt. The disturbed range of surrounding rocks induced by tunneling is derived based on the slip-line theory. The analytical expression for the minimum safe crossing distance between the tunnel and the sliding belt is obtained by the mechanical analysis of relaxed rocks between sliding belt and the compressive zone of relaxed rock. The minimum safe crossing distance is in association with the tunnel radius, the internal

fraction angle of surrounding rocks, the sliding belt inclination and the rock friction coefficient.

The stability of landslide above the tunnel is studied based on the Sarma method and the expression for safety factor is obtained. The stability of landslide depends on the critical acceleration coefficient, the friction angle and the cohesion of landslide, the friction angle and cohesion of sliding belt, as well as the internal fraction angle and cohesion of disturbed sliding belt.

The analytical method proposed in this paper

(a) The sliding belt is traversed by tunneling (b) H1=0.25D

(c) H2=0.5D (d) H3=1.0D

(e) H4=1.5D (f) H5=2.0D

Figure 10 Normal stress contour image of different crossing distance.

J. Mt. Sci. (2017) 14(6): 1124-1139

1138

was verified by a numerical simulation. Six cases were selected in the numerical analyses considering different perpendicular distances between tunnel vault and the sliding belt, including 0.25D, 0.5D, 1.0D, 1.5D, 2.0D and condition that the sliding belt is traversed by tunneling. Numerical results show that the plastic zone of landslide is very large when the sliding belt is traversed by tunneling. The tunnel vault and tunnel invert are mainly in shear-tension state and in tension state, respectively. The surrounding rocks

on both sides of the tunnel are in shear state. For the landslide, the surface of the sliding body is mainly in tension state. The toe of the landslide is in shear-tension state and the sliding belt is mainly in shear state. The distance between tunnel vault and the slip zone has a significant influence on the stress and strain of rock. The plastic zones of the landslide and the rockmass surrounding tunnel are within rather large range when the distance is less than the minimum safe crossing distance.

Acknowledgements

The authors acknowledge the financial support provided by Natural Science Foundation of China (Grant No. 51008188), and by Shanghai Natural Science Foundation (Grant No. 15ZR1429400), and by Open Project Program of State Key Laboratory Breeding Base of Mountain Bridge and Tunnel Engineering (Grant No. CQSLBF-Y15-1), and by

Open Project Program of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Grant No. SKLGP2015K015), and by the Open Project Program of Key Laboratory of Geohazard Prevention of Hilly Mountains, Ministry of Land and Resources (Grant No. 2015k005).

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