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Analysis of a Rock Bolt-Reinforced Tunnel with Equivalent Mechanical Properties

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Abstract

After the excavation of a tunnel, generally, rock bolts are used as primary support. Installation of rock bolts considerably reduces the further deformation in the rock mass around the tunnel boundary. Bolts provide additional support to mass and therefore mass becomes stiffer, rigid, and stronger. The theory of rock bolts–rock mass interaction is quite complex and contains numerous factors. The complex interaction between mass and bolts leads to complex theoretical analysis, and sometimes, it is very difficult to find out the solutions. Hence, to rectify this, the continuum model of numerical analysis is used which is simple and convenient. Rock mass and rock bolts are two distinct materials, and their mechanical properties are much different from each other. In continuum analysis, generally, they are modelled separately, i.e. different mechanical properties are assigned to rock mass and rock bolt. As the whole mass is treated as equivalent continua, separate modelling of the bolt and the rock mass may give misleading results. Proper interaction between mass and bolts may not develop due to the non-existence of joints in the continuum model. Hence, if, in the continuum model, rock and bolt to be modelled together with equivalent mechanical properties, the result would be different. The present research work deals with continuum analysis of a rock bolt-reinforced tunnel in which equivalent mechanical properties of bolt and rock are used. Equivalent mechanical properties were worked out from the laboratory investigations conducted on the specimens of natural jointed rock and rock bolt. The equivalent continuum model of a rock bolt-reinforced tunnel was developed, analyzed, and compared with the conventional continuum model. The result suggested that if rock bolts are taken as an integral part of the rock mass and modelled as an equivalent continua, the result would be more rational and reliable.

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Abbreviations

UCS:

Uniaxial compressive strength

NRC:

Natural rock core

I:

Intact rock Intact rock

JR_U_45°:

Unreinforced jointed rock with joint angle 45° from the horizontal axis

JR_R_45°:

Reinforced jointed rock with 45° angle between joint and bolt

EQM:

Equivalent mechanical properties

ESR:

Excavation support ratio

EBZ:

Equivalent bolt zone

γ :

Unit weight of the material

σ i , σ cj, σ cb :

Uniaxial compressive strength of intact rock, jointed rock, and reinforced rock, respectively

E i, E j, E r :

Modulus of intact rock, jointed rock, and reinforced rock, respectively

σ 1 :

Strength of rock at σ3 confining stress

σ 1v and σ 1h :

Strength of rock in vertical and horizontal direction, respectively

dv and dh :

Deformation in rock in vertical and horizontal direction, respectively

σ 3 :

Applied confining stress

c i, c j, c r :

Cohesion of intact rock, jointed rock, and reinforced rock, respectively

ϕ i, ϕ j, ϕ r :

Friction angle of intact rock, jointed rock, and reinforced rock, respectively

T b , E b :

Tensile strength and deformation modulus of rock bolt, respectively

σ ri , E ri ,c ri, ϕ ri :

Reduced properties of mass used in continuum analysis (uniaxial compressive strength, modulus, cohesion, and friction angle, respectively)

σ equ , E equ , c equ, ϕ equ :

Equivalent properties of mass and bolts used in continuum analysis (uniaxial compressive strength, modulus, cohesion, and friction angle, respectively)

D v :

Distance starting from the crown in a vertical direction

D h :

Distance starting from the crown in a horizontal direction

B :

Width of tunnel

H :

Height of tunnel

H 0 :

Height of overburden at tunnel crown

k sv , k sh :

Stiffness of rock in any vertical and horizontal direction

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Acknowledgements

The author thanks Prof. Mahendra Singh, Department of Civil Engineering, Indian Institute of Technology, Roorkee (IIT Roorkee), India, for giving valuable suggestions and support to the completion of this paper. The author also thanks to the staff of Geotechnical Engineering Laboratory, IIT Roorkee, for providing support in experimental work. The author acknowledges the contribution of Dr. R D Dwivedi, Scientists, Central Institute of Mining and Fuel Research, Roorkee Centre, India, for providing technical support in numerical analysis.

Funding

The research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. EDRC, HCIIC, Larsen & Toubro, Haryana, 121003, Faridabad, India

    Lok Priya Srivastava

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  1. Lok Priya Srivastava
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Correspondence to Lok Priya Srivastava.

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Appendix

Appendix

See Figs.

Fig. 10
figure 10

a Axial stress (deviator) vs axial strain curves of intact rock (I) at different confining stresses b Axial stress vs axial strain curves of unreinforced joined rock (JR_U_45°) at different confining stresses c Axial stress vs axial strain curves of reinforced joined rock (JR_R_45°) at different confining stresses

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10,

Fig. 11
figure 11

a Model A, H0 = 103 m, s1 contour plot b Model B, H0 = 103 m, s1 contour plot c Model A, H0 = 103 m, d contour plot d Model B, H0 = 103 m, d contour plot

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11,

Fig. 12
figure 12

Model A, H0 = 1003 m, s1 contour plot b Model B, H0 = 1003 m, s1 contour plot c Model A, H0 = 1003 m, d contour plot d Model B, H0 = 1003 m, d contour plot

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Fig. 13
figure 13

a s1v vs dv, H0 = 103 m b s1v vs Dv, H0 = 103 m c dv vs Dv, H0 = 103 m d ksv vs Dv, H0 = 103 m

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Fig. 14
figure 14

a s1h vs dh, H0 = 103 m b s1h vs Dh, H0 = 103 m c dh vs Dh, H0 = 103 m d ksh vs Dh, H0 = 103 m

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14,

Fig. 15
figure 15

a s1v vs dv, H0 = 1003 m b s1v vs Dv, H0 = 1003 m c dv vs Dv, H0 = 1003 m d ksv vs Dv, H0 = 1003 m

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15,

Fig. 16
figure 16

a s1h vs dh, H0 = 1003 m b s1h vs Dh, H0 = 1003 m c dh vs Dh, H0 = 1003 m d ksh vs Dh, H0 = 1003 m

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16

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Srivastava, L.P. Analysis of a Rock Bolt-Reinforced Tunnel with Equivalent Mechanical Properties. Indian Geotech J 52, 815–834 (2022). https://doi.org/10.1007/s40098-022-00631-1

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