Stability analysis of the marly formation around a tunnel in Iran

A. FahimifarDepartment of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran

H. SoroushDepartment of Petroleum Engineering, Amirkabir University of Technology, Tehran, Iran

ABSTRACT: Ahram-Frashband route is an important highway in Booshehr province in the south of Iran. In thisroute a tunnel with 2 km long is of paramount interest due to the particular problems. The most part of this tunnelis located in marly rocks which have potential of swelling and squeezing. In this study, after site investigations,physical and mechanical properties of marly rocks were measured by laboratory and in-situ tests. In order toanalyze the stability of the tunnel, both analytical and numerical methods were used and the characteristic curvesof marly formation were obtained. Equivalent Mohr-Coulomb parameters of rock (c and φ) were obtained usingthe non-linear Hoek-Brown criterion. Comparison of characteristic curves which were obtained by two methodsshowed good agreement for similar points. Analyses showed that even shotcrete with 200 mm thick could notstabilize the tunnel and the appropriate support system should be a composition of systematic steel sets at 85 cmspacing (lattice girders) and shotcrete with mesh. Also a multi-stage excavation method should be performed.

The analyses carried out using UDEC program for various sections of the tunnel.

1 INTRODUCTION

Ahram tunnel is a highway tunnel with 10 m width and8 m height which is located in Booshehr province inthe south of Iran. The tunnel length is about 2 km andthe geological formation includes sequence of gyp-sum, limestone, marl, conglomerate, and sandstonelayers.The tunnel zone, on the geomorphological pointof view, has formed from chains of relatively highmountains with an overall trend of north to south. Themaximum height in this zone is 850 m with respect tothe sea level. The relative height of tunnel axis frombeginning point to the end point varies from 326 to390 m, taking into account the tunnel slope. The tun-nel zone is a combination of layers with an azimuthof 240◦ and dip of 65◦, and the tunnel axis is perpen-dicular to the layers strike. The layers dip are towardsthe tunnel face, and therefore, there is an appropriatesituation for stability during excavation.

2 LABORATORY EXPERIMENTS

2.1 Swelling behavior of the rocks

Most of soft rocks that contain clay minerals, par-ticularly montmorilonite, are capable of swelling dueto periodical drying and wetting. In addition, theserocks are capable of squeezing and slaking in special

conditions. Shale, marl, clay stone and siltstone are themost important soft rocks which are prone to swelling.

Swelling is a physicochemical reaction which occursin the presence of water and is associated with stressrelease. In this process, volume change also occurs.

2.2 Laboratory tests

a) Swelling tests: Swelling index tests were carriedout on unconfined specimens of 54 mm diameterand 20 mm length according to the ISRM suggestedmethod (ISRM 1989). These specimens were preparedfrom the black and brick-red marls which are thepredominant swelling rocks in the site.

Swelling of the brick-red marl occurred very slowlyduring one month saturation in water and after 0.3 mmswelling remained constant. However, the black marlswelled very fast in a few hours after saturation andfinally an increase up to 5 mm observed in the speci-mens height. These tests revealed that in black marls,swelling phenomenon is a serious problem in tunnelingprocess.

b) Uniaxial compressive tests: Uniaxial compres-sive tests were performed on cylindrical specimenswith diameter of 54 mm and height to diameter ratio of2, according to the ISRM suggested method (Brown1981). The results obtained are shown in Table 1.

c) Brazilian tests: in order to approximate thetension strength of the rocks, Brazilian tests were

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Table 1. Results of uniaxial and Brazilian tests.

Young’s BrazilianUCS modulus strength

Rock type (MPa) (GPa) (MPa)

Brick-red marl 28 3.5 1.8Black marl 35 4.1 2.2Brick-red sandstone 107 9.9 5.3Black sandstone 47 4.8 10.0

Table 2. Results of slake durability tests.

Slake durabilityRock type index (%) Class

Brick-red marl 62.21 AverageBlack marl 77.33 AverageBrick-red sandstone 98.90 Very strongBlack sandstone 97.30 Strong

carried out on cylindrical specimens according to theISRM suggested methods (Brown 1981). The resultsobtained are observed in Table 1.

d) Slake durability tests and Atterberg limits: Slakedurability tests results are shown in Table 2. It isobserved that the marls surrounding the tunnel arein the average class. The average Atterberg limitsobtained for the marls are of 41% liquid limit, 24.3%plastic limit and 16.7% plastic index.

3 DESIGN OF SUPPORT SYSTEM USINGANALYTICAL METHOD

Ground-support interaction diagrams are well estab-lished aids to the understanding of tunnel supportsystem mechanics (Lombardi 1980, Ward 1978, Hoeket al. 1997). They may also be used quantitativelyto aid the selection and dimensioning of tunnel sup-port (Hoek et al. 1997, Hoek & Brown 1980). Forthis purpose, it is essential to determine the groundresponse curve for a particular rock mass, stressregime, and tunnel geometry.

In this analysis, the solution presented by Hoek &Brown (1980) was used as the analytical approach andthe corresponding calculations were performed by theMATLAB computer program.

The required support lines for marly section areplotted in Figure 1 for roof, sidewalls and floor. Sup-port system was proposed to be consisted of shotcrete,rockbolts and steel sets. Shotcrete and rockbolts (orsteel set) installed after 5 mm and 6 mm displace-ments respectively. As is observed in Figure 1, max-imum displacement is 38 mm at the tunnel floor and47 mm at the sidewalls after which the tunnel reachesequilibrium, while the tunnel roof still continues to

Figure 1. Rock-support interaction curves for marly zoneobtained by analytical method.

deform at about 0.12 MPa support pressures and less.Figure 1 shows that untensioned rockbolts with 25 mmdiameter and 4 m long is not able to limit plastic defor-mations. In fact, such a supporting system is not appro-priate for soft rocks such as marl in which deformationmechanism is not controlled by discontinuities.

Figure 1 also shows that 20 cm thickness ofshotcrete is not adequate for limiting displacements atthe tunnel roof. As is observed in this figure, only steelsets (IPE 16) with 0.85 m spacing is able to controldisplacements at an acceptable level.

4 DESIGN OF SUPPORT SYSTEM USINGNUMERICAL METHOD

The most important factor in numerical methods isselecting appropriate parameters corresponding tothe rock mass. In order to achieve the most rele-vant rock mass parameters, the approach proposed byHoek & Brown (1980) was used. In this method, havingprincipal stresses, GSI (Geological Strength Index)and intact rock parameters, the rock mass parametersincluding tensile strength, compressive strength, shearstrength and other required factors can be calculatedsatisfactory. In this research, UDEC computer pro-gram was used to model the tunnel for both continuumand discontinuum. For this purpose, tunnel geometry,material properties, height of overburden, ratio of hor-izontal to vertical in-situ stresses, joint properties andso on were entered to analysis.

Ahram tunnel has a horseshoe shape with 10 mwidth and 8 m height. The model with dimensions of100 × 100 m2 was selected and the tunnel was set outat the centre of this block (Fig. 2).

Figure 3 shows the dimensions and shape of themesh used in the models. The elements’ dimensionsincrease with increasing the distance from the tunnel.

According to this numerical analysis, in the marlysection of Ahram tunnel, maximum displacements at

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Figure 2. The zones and dimensions (in meters) of the modelconsidered in analysis of Ahram tunnel in equivalent mediain UDEC.

Figure 3. The mesh used in the model by UDEC program.

roof, floor and side walls were obtained 14.1 mm,12.2 mm and 6.5 mm respectively. Figure 4 shows thesafety factor contours before installing the support sys-tem. As is observed in this figure, safety factor of sidewalls is less than 1.5. In the side parts of the roof, it isless than 1.5 for about 10 m width.

The most important properties of marly rocks arehomogeneity, very low strength and insignificance ofdiscontinuities in the rock mass behavior. For this rea-son, rockbolts do not play an important role in stabilityof this kind of rock. In Ahram tunnel, in addition to thesteel sets as the primary support system, shotcrete lin-ing with 20 cm thick was also used as the final supportsystem. Because of very low cohesion between rocksurface and shotcrete lining in this kind of rock massand also as the shotcrete supporting system acts as apassive system, it was decided to perform the shotcretelining as closed ring.

Figures 5a, b illustrate plastic zone around the tun-nel before and after shotcrete lining performed. It is

Figure 4. Safety factor contours before installing supportsystem.

Figure 5. Displacements around the tunnel in marl, a) beforeshotcrete performance, b) after shotcrete performance.

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Figure 6. Variation of bending moment in shotcrete.

observed that after shotcreting, sidewalls become moreplastic, despite the case of not using shotcrete in whichroof and floor are mostly plastic.

For assessing the concrete support system undervarious loading conditions, variation of axial loads,shear forces and bending moments in the concretelining were evaluated. For example, Figure 6 showsvariation of the bending moment in the concrete sup-port system. The maximum amount of the bendingmoment is 152 kNm.

5 DESIGN OF REINFORCEDCONCRETE LINING

For determination of reinforced concrete lining undervarious loading conditions, 1 m of the concrete witha thickness of 0.2 cm was chosen for analysis. Thissection was analyzed using the plots corresponding tothe interaction of the axial loads and bending moments,under a combination of the effects of axial loads andbending moments.

For using the interaction plots, it is essential tocalculate the following parameters:

where Mr = ultimate bending moment of the section(N.mm); Nr = ultimate tension force of the section(N); φc = partial safety factor of concrete (= 0.6);fc = characteristic compressive strength of concrete(N/mm2); h = thickness of concrete section (mm);b = width of concrete section (mm).

Substituting bending moment and axial loadobtained from the UDEC analysis into the aboveexpressions and using the interaction plots, it is con-cluded that the selected section is not able to carrythe loads and it must be reinforced by steel bars. For

Figure 7. Stress distribution around the tunnel afterinstalling the support system.

achieving this specification, steel bars with 26 cm2

cross section are required according to the interac-tion plots. Putting the steel bars equivalent to thesteel beam sections (IPE), the required steel sets wereobtained IPE/6 (cross section area = 20.1 cm2), with76 cm spacing.

According to UDEC analysis, the maximum shearforce in the concrete lining was obtained 163 kN.In order to control the strength of concrete liningunder shear stresses, shear strength of the sectionwas calculated using the relationships proposed by theIran concrete code (Planning & Budget Organization1999), and it was compared with the shear stress inshotcrete section. The following relationship was usedin this regard.

where Vs = shear strength of the members whichare under shear, bending and axial stress (N/mm2);Vu = ultimate shear force (N), vc = shear strength ofconcrete (vc = 0.2 φc

√fc); and Mm is calculated by:

where Mm = ultimate bending moment (N.mm);Nu = ultimate axial force acting on the section (N);Bw = section width (m); d = distance between the farcompression line and center of the cross section (mm);and ρw is calculated by As/bwd in which, As is the crosssection area of the tensioned bars (mm2).

According to the above relationships, shear strengthof reinforced concrete obtained 492 kN. It is concludedthat concrete is able to bear the shear force with a safetyfactor of 3, and therefore, steel bars are not needed toincrease the shear strength of the concrete.

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Figure 8. Comparison of characteristics curves in numericaland analytical methods.

Figure 7 shows stress distribution around the tun-nel after installation of support system.As is observed,stress around the tunnel at each point is in compres-sion mode, and there is no tension stress at any point.Maximum induced compressive stresses are occurredin the walls and the edges of the tunnel.

6 COMPARISON OF THE RESULTS OFNUMERICAL AND ANALYTICALMETHODS

In Figure 8, characteristics curves obtained in analyt-ical and numerical methods have been compared. Asis observed, the tunnel roof in numerical plots showsthe maximum displacements, while the floor and wallsshow lower displacements. The elastic portions of theroof and floor curves in numerical analysis coincidewith each other (similar to analytical solution). In theplastic portions, these plots have been separated, andshow further displacements in comparison with thefloor (similar to the plot corresponding to the roof inanalytical method). The tunnel side walls also showmuch lesser displacements relative to the roof andfloor. In numerical solution, the roof and the floorlead to equilibrium after 14 and 12.5 mm displace-ments respectively. In this analysis, the pressure inthe side walls leads to zero after 7 mm displacements.However, in analytical solution, the ultimate displace-ments in all cases (in zero pressure), are more than thenumerical methods. This is due to the different tunnelshapes and failure criteria used. In numerical analy-sis, Mohr-Coulomb criterion and in analytical solutionHoek-Brown failure criterion was used.

Numerical and analytical curves are nearly parallelin the elastic portions; however, the numerical curvein this portion is above the analytical curve. This isbecause that the compressive stresses confining the

roof and floor are less in numerical method than inthe analytical method (because of non-circular tunnelsection and non-hydrostatic in-situ stress in numericalsolution).

7 SUMMARY AND CONCLUSIONS

Ahram tunnel passes through a marly formation whichis a weak and swelling soft rock. After field inves-tigations and laboratory tests and determining rockmass physical and mechanical parameters, analyticaland numerical solutions were used for analyzing of thetunnel and determining the required support system.Ground reaction curves were plotted for roof, floorand side walls using both methods. Comparison of theplots obtained in these solutions show that they donot coincide with each other. The plots correspondingto the numerical method show higher accuracy. Thisis because of the simplified assumptions used in theanalytical method.

The analytical method showed that 20 cm shotcreteis not sufficient for controlling displacements in theroof and using steel sets is essential. This fact wasverified by the numerical analysis. In addition, bothmethods proved that rockbolts are insufficient supportsystems for soft rocks.

REFERENCES

Brown, E.T. (ed.) 1981. Rock Characterization, Testing andMonitoring. Oxford: Pergamon Press.

Brown, E.T. Bray W. Ladanyi B. & Hoek E. 1983. Groundresponse curve for rock tunnels. J. Geotech. Eng. 109(1):15–39.

Gamble, J.C. 1971. Durability plasticity classification ofshales and other argillaceous rocks. Ph.D. Thesis, Uni-versity of Illinois. Illinois: USA.

Hoek, E. & Brown, E.T. 1980. Underground excavations inrock. London: The Institution of Mining and Metallurgy.

Hoek, E. Kaiser, P.K. & Bawden, W.F. 1997. Support ofUnderground Excavations in Hard Rock. A.A. Balkema.

ISRM, Commission on Swelling Rock and Working Groupon Swelling of the Commission on Testing Methods 1989.Suggested method for laboratory testing of argillaceousswelling rocks. Int. J. Rock Mech. Min. Sci. & Geomech.Abstr. 26: 415–426.

Lombardi, G. 1980. Some comments on the convergence-confinement method. Underground space. 4(4):

Pande, G.N. Beer, G. & Williams, J.R. 1990. NumericalMethod in Rock Mechanics. John Wiley & Sons.

Planning & Budget Organization 1999. Iran Concrete Code.Islamic Republic of Iran.

Shamsi Farashah, H. 2002. Characterization of rock masssurrounding Ahram-Frashband tunnel and stability anal-ysis. M.Sc. Thesis, Amirkabir University of Technology.Tehran: IRAN.

Ward, W.H. 1978. Eighteenth Rankine Lecture- Ground Sup-ports for tunnels in weak rocks. Geotechnique. 28(2):133–170.

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