Indian Journal of Engineering & Materials Sciences Vol. 7, April 2000, pp. 57-60

Stability analysis of twin tunnels by finite element method

C S Singha & B K Shrivastvab

aHindalco Industries Limited, Court Road, P.O. & District Lohardaga, Bihar 835 302 hDepartment of Mining Engineering, Institute of Technology, Banaras Hindu University, Varanasi 221 005, India

Received 29 June 1998; accepted 7 February 2000

The tunnels are generally made for mining, civil and other engineering works. The techniques to construct twin tunnel s become a matter of great concern to rock designers , especially for the stability of the structure. The stability of tunnel s depends upon a number of parameters. The present studies deal with the simulation of the twin tunnels in general and methods of their construction in particular, by analyzing the stability of twin tunnels based on finite element method. Three different types of techniques have been adopted for the construction of such tunnels, viz., (i) simultaneous excavation , (ii ) alternate excavation , and (iii) simultaneous sequential excavation. The reported studies show that the simultaneous sequential excavation method of construction of twin tunnels is more appropriate in comparison to the other two methods of construction.

The methods of construction of twin tunnels play an important role on their stability. The tunnels are generally' utilized for roadways, ventilation, transportation and other app lied engineering purposes. Sometimes, it becomes a pre-requisite for the development of underground openings. In a rock stress environment, the stress field has a tendency to interact when twin tunnels are in close proximity . Thus, over stressing the parting of a pillar between twin tunnel s makes a vulnerable zone. The safety of twin tunnel systems, therefore, lies in controlling the final state of stress pattern in the parting pillar so as to keep it within safety limits.

Laboratory studies have been made to analyze the stability of twin tunnels by physical modelling l.2 . Conventional approaches presume that the construction of tunnel is completed in one stage and gravity load withheld until the final shape is attained.

It has already been proved analytically' that the conventional approach is valid only if the state of stress in the structure is determined at all stages during the construction process. The numerical approach by finite element method (FEM) is one such method having the flexibility of incorporating the arbitrary construction sequence and thereby simulating the structure in nearly true condition . Numerous procedures have been developed from time to time to analyze such situations based on various assumptions4

-17

• An attempt has been made here to explain in some detail the stability analysis of twin tunnel driveages by this approach.

Simulation of Twin Tunnels The method of construction of tunnel s could be

simulated in a number of ways . However, an attempt has been made to study the effects of excavation sequence on the resulting stress environment produced in the surrounding rockmass. A numerical model has already been developed 17 to study the non­dimensional principal stress, i.e. , a/ali and ai al i , where, al and a, are maximum and minimum principal stresses, respectively, and ali is in situ maximum principal stress . The compressive stress has been taken as positive and tensile stress has been taken as negative. Three types of simulation of tunnels have been considered as s~own in Fig. 1.

Fig. 1 depicts ' Twin Square Horizontal Openings' . In the first case, the twin tunnels are excavated simultaneously (i.e. at the same time) . In the second

SAND-STONE

COAL ~ ~ '- -' ' _ _ -l _ ...1

SAND-STONE

I B B I

,-- ... r- '" §:] I : : ~ '- - -' L_-' L __ J

§:] §] ~ (A) SIMULTANEOUS EXCAVATION (6) ALTERNATE EXCA\lA.TION (el SEOUEHTIAL EXCAVATION

Fig. I-Twin square horizontal openings

58 INDIAN 1. ENG. MATER. SCI., APRIL 2000

case, alternate excavations are made (i.e. second tunnel is excavated after finishing the first) and, in the third case, simultaneous sequential excavations are made (i.e. one section is excavated simultaneously for both the tunnel s and then enlarged to bigger dimension). The sequence simulated for finite element analysis is based on the assumption that tunnels are in coal bed embedded in a layered strata of sandstone.

The area is discretised into 324 elements having 361 nodes. The body forces are considerably less in comparison to in situ stresses as the excavation is considered to be deep enough. The boundary is assumed to be six times the sides away from the

Fig. 2-Contours of maximum principal stress around twin horizontal square tunnels during simultaneous excavation

(~l Oii

\·2

L ,: U 1--1 0 0 I

Fig. 3-Contours of maximum principal stress during alternate excavation

center of the opening. It is also assumed that the simulation of excavation is initially under a stressed environment. This is fo llowed by the reversal of stresses, i.e., computed stress under stress environment is applied in an opposite direction along the excavation boundary and finally these stresses are applied as equi valent nodal point forces . The sum of initial stresses (pre-mining stresses) , and stresses caused due to excavation (induced stresses) yield the final state of stresses. For the present analysis, the ratio of horizontal to vertical in situ stresses has been taken as 1.0. However, the stress values also depend upon this ratio. The physico-mechanical properties used for the present study are summari zed in Table I.

Results and Discussion Figs 2-4 show the contours of maximum principal

stress whereas Figs 5-7 show the contours of minimum principal stress -around twin horizontal tunnels . The area affected by tensile stress around the tunnels has been hatched. At the comers of the tunnel , there is a high compressive stress in all the three conditions but the magnitude of stress is less in case of simultaneous sequential excavation method tn

comparison to other two methods of construction.

Table I-Physico-mechanical properties of rockmass

Rockmass

Sandstone Coal

Young's modulus

(MN/m2x I 04)

0.972 0.408

8 8 \-1

Poisson's Unit wei~ht ratio (MN/m' )

0.20 0.02450 0.30 0.01274

0 0

Fig. 4-Contours of maxi mum principal stress during sequential excavation

SINGH & SHRIVASTAVA: STABILITY ANALYSIS OF TWIN TUNNELS BY FINITE ELEMENT METHOD 59

Fig. 5-Contours of minimum principal stress during simultaneous excavation

o [J 1--1 0 0

(~) Oli

Fig. 6-Contours of minimum principal stress during alternate excavation

The parting pillar between the two tunnels also experiences high stress concentrations. The maximum, minimum and maximum shear stress concentrations for the three different methods of construction of twin horizontal tunnels are summarized in Table 2. The sequential excavation method (i.e. excavating both the tunnels simultaneously and then enlarging them to a bigger size) seems to be most stable in comparison to other two methods, as evident from Table 2. It may be said that such a system of sequential excavation gives better results from stability point of view, particularly in terms of shear and tensile stress component of ultimate analysis. Since, rocks are usually weak in tension and or shear, lowering of their values would

,--8_8--'.' ._\- 1'-------'0_0_

0 ·9

--__________ O~----__ --__ ~

Fig. 7-Contours of minimum principal stress during sequential excavation

Table 2-Stress concentrations in parting pillar of twin horizontal tunnels

Method of Maximum Minimum Maximum construction principal principal shear stress

stress stress (MPa) (MPa) (MPa)

Simultaneous 2.50 -0.88 1.69 Alternate 2.78 -1.\0 1.94 Simultaneous 2.00 -1.00 1.50 sequential

be of great significance for the stabi lity of twin tunnels ,

Conclusions It is concluded that the simultaneous sequential

method of construction of twin horizontal tunnels has pronounced effect on stress environment. It has also been observed that during the application of this method, the tunnels seem to be more stable, The usual practice of alternate excavation induces high stress concentrations in parting pillars compared to others, This study suggests that the simultaneous sequential method of excavation should be adopted for the stability of such structures.

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60 INDIAN 1. ENG. MATER. SCI. , APRIL 2000

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