continuum and discontinuum modelling in tunnel engineering

Rud.-gco1.-naft. zb., Vol. 12, Zagreb, 2000.52 Rarlu, G., Barla M.: Continuum and discontinuum modellingm., r[-I6.1where o~,~ and a o,, are the uniaxial compressivestrength values (peak and residual) and mipp and mi,, arethe corresponding Hoek-Brown empirical constants.For very good quality rock masses, which is the casefor a significant tunnel length (Figure ll), typical rockmass properties can be defined on the basis of the GeologicalStrength Index (GSI) as follows:Intact rock strengthoCi = 144 MPaHoek-Brown constant m, =7.0Geological Strength Index GSI = 70Hoek-Brown constant mb =2.4Hoek-Brown constant s =0.02Rock mass compressive strength o,,= 27.2 MPaDeformation modulus E, =35 GPa3.4. In situ stress conditionsIn view of the high overburden and closer valley side,associated with evidence of deformation and thin slabbingin isolated sections along the tunnel length, it wasrecommended that stress measurements by means of flat-jack tests and hydraulic minifracture tests be carriedout. At present only the flat-jack test data are available Gas follows, derived from measurements around the sec- -r=02 /tion of the tunnel at ch 950 m, where the overburden isapproximately 400 m:Figure 16. (a) Mmum princrpul .!tre.r\ contours. (6) Computed andmeusured tangential strrsse.s Fht-jack slot tests, wtth overbur-Angle with respect toJack presyureden of 400 m approximatelyFlat-jack slot horizontal axisPI[MPalvalues of oCi and s = 1. The stability of the tunnel wasMI 0 34.8 assessed by computation of the strength factor contoursas shown in Figure 17. The implication is that the rockM2 +50 3.3mass inside the unit strength factor contour (SF(m,ol = 1)M3 -45 23.5 will be unstable, unless well retained.Based on a stress concentration study in linearly elas-the above simplifiedtic conditions around the tunnel using the finite element linearly elastic costitutive model, no influence of hy-method and the phase2 code cur aband c ku *, drostatic head considered, etc.) the tunnel experi-1997), as shown in ~i~~~~ 1 , the initial stresses in the ences localized failure at the sidewalls which deepensplane perpendicular to the tunnel axis were evaluated to inside the rock mass as the micaschist intact rockbe as follows: uniaxial compressive strength decreases from 100MPa to 75 MPa. This would signify that in the highlyol = maximum principal stress =13 MPaanisotropic stress regime of the tunnel, as evidencedo3 = minimum principal stress = 2.6 MPawith a I?, value equal to 0.2, localized slabbing insta-O1 = angle of ol with respect to the vertical axis =15O bility cannot be ruled out, if the rock strength is in therange 100-75 MPa.3.5. Continuum modelling3.5.1. The m = 0 approachIn order to determine to what extent the adoption ofa continuum modelling approach can provide a reasonableinterpretation of tunnel instability, numerical analyseswere first carried out to assess the stability conditionsby using a constant deviatoric stress criterion as proposedby (M a r t i n et a 1. (1997).The initial stresses o, and 03 at the cross section ofinterest (ch 2360 m) were assumed to be proportionallyhigher in relation to the higher overburden of 650 m.Also, the stress ratio (q,) of the minimum stress tomaximum stress (03/01) in the plane of the tunnel crosssection was considered equal to 0.2, as in the section ofthe flat-jack measurements.The m = 0 analyses were performed by using thephases2 code and the Hoek-Brown criterion for different3.5.2. The elastic-brittle-plastic modelThe analyses above considered overstressing of therockmass around the tunnel periphery, without accountingfor the presence of discontinuities. Therefore, it wasdecided to analyse the same instability problem by introducingthese features in the numerical model.As shown in Figure 18, the model comprises twoparallel discontinuities near the right sidewall, dippingtoward the tunnel. In order to account for the rock massdisturbance due to jointing in the proximity of the discontinuitiesand the apparently more massive rock onthe left sidewall, where relatively little slabbing and overstressingwas present, it was decided to introduce threedifferent regions in the model with the following materialproperties, according to the Hoek-Brown failurecriterion: