3D simulations of a NATM tunnel in stiff clays with soil ...

3D simulations of a NATM tunnel in stiff clays with soil parametersoptimised using monitoring data from exploratory adit

T. Svoboda & D. MasınCharles University in Prague, Czech Republic

ABSTRACT: The paper demonstrates the application of a hypoplastic model in class A predictions of a NATMtunnel in an urban environment. The tunnel, excavated in a stiff clay, is 14 m wide with 6 m to 21 m of overbur-den thickness. The constitutive model was calibrated using laboratory data (oedometric and triaxial tests) andthe parameters were optimised using monitoring data from an exploratory drift. Based on the optimised dataset, the future tunnel was simulated. After the tunnel excavation, it could be concluded that the model predictedcorrectly surface settlements, surface horizontal displacements, and the distribution of vertical displacementswith depth. It overpredicted horizontal displacements in the vicinity of the tunnel.

1 INTRODUCTIONThe main issue of tunnelling in urban environment,typically characterised by a low overburden thicknessand presence of surface infrastructure, is the controlof settlements induced by tunnel excavation. The firststep in the design of any protective measure reducingthe tunnel impact on surrounding buildings is an ac-curate prediction of the tunnelling-induced displace-ment field.

The present paper demonstrates the application ofan advanced constitutive model (Masın 2005) in pre-dictions of a complex tunnelling problem in urbanenvironment. The goal was to provide class A pre-dictions of the displacement field induced by a 14 mwide road tunnel in stiff clay, with an overburden of 6m to 21 m. The parameters of the constitutive modelwere calibrated on laboratory data and optimised us-ing monitoring data from an exploratory drift. Thedrift was located in top heading of the future tun-nel. Based on the optimised data set, class A predic-tions of the displacement field induced by the tunnelwere performed in 2008 and early 2009. In November2009, the full profile of the tunnel passed the simu-lated cross-section, which allowed us to compare thepredictions with the data from the geotechnical mon-itoring.

2 KRALOVO POLE TUNNELSThe Kralovo Pole tunnels (often referred to as Do-brovskeho tunnels) form a part of the northern sectionof the ring road of Brno town in the Czech Repub-

lic. The tunnels consist of two parallel tubes with aseparation distance of about 70 m and lengths of ap-proximately 1250 m. The tunnel cross-section heightand width are about 12 m and 14 m respectively, andthe overburden thickness varies from 6 m to 21 m.The tunnels are driven in a developed urban environ-ment (see Fig. 1). The displacement field induced bythe tunnel excavation was thus an important issue thedesigners had to cope with.

Figure 1. Temporary portals of the Kralovo Pole tunnels (Horak2009).

The geological sequence in the area is shownin Fig. 2. From the stratigraphical point of view,the area is formed by Miocene marine deposits ofthe Carpathian fore-trough, the thickness of whichreaches several hundreds meters in this location

(Pavlık et al. 2004). The top part of the overburdenconsists of anthropogenic materials. The natural Qua-ternary cover consists of loess loam and clayey loamwith the thickness of 3 to 10 m. The base of the Qua-ternary cover is formed by a discontinuous layer offluvial sandy gravel, often with a loamy admixture.The majority of the tunnel is driven through the Ter-tiary calcareous silty clay. The clays are of stiff to verystiff consistency and high plasticity.

Figure 2. Longitudinal geological cross-section along the tunnels(Pavlık et al. 2004).

Before the Kralovo Pole project, there was only lit-tle experience with the response of the Brno clay totunnelling. In order to clarify the geological condi-tions of the site, and in order to study the mechanicalresponse of the Brno clay, a comprehensive geotech-nical site investigation programme was designed, thecrucial part of it being an excavation of three ex-ploratory drifts. The drifts were triangular in crosssection with the side-length of 5 m and were designedto form parts of the top headings of the future tun-nels (Fig. 3). The total length of the three drifts wasover 2000 m. For technological reasons, they were notdriven along the complete length of the future tunnels.

Figure 3. Exploratory drifts situated in the top headings of thefuture Kralovo Pole tunnels.

The tunnels were driven by the New Austrian Tun-neling Method (NATM), with sub-division of the faceinto six separate headings (Fig. 4). The face subdi-vision, and the relatively complicated excavation se-quence, were adopted in order to minimise the surfacesettlements imposed by the tunnel.

Figure 4. Sketch of the excavation sequence of the tunnel (Horak2009).

3 LABORATORY EXPERIMENTS AND CON-STITUTIVE MODEL CALIBRATION

The behaviour of loess loams and sandy gravels wasfound not to influence significantly the predicted tun-nel performance (Svoboda et al. 2010), the laboratoryexperiments thus focused on the behaviour of Brnoclay. Triaxial CIUP tests and oedometric tests wereperformed in order to calibrate the selected consti-tutive model. The triaxial specimens were equippedwith submersible local LVDT axial strain transduc-ers in order to evaluate the soil stiffness in the smallstrain range. In addition, one specimen was equippedwith bender elements to measure the soil stiffnessin the very small strain range by means of propaga-tion of shear waves. Oedometric tests have been per-formed on undisturbed and reconstituted specimens.The specimens were loaded up to axial pressures of13 MPa in order to find the position of the normalcompression line and in order to evaluate the apparentoverconsolidation ratio, which is also used for estima-tion of the coefficient of earth pressure at rest K0.

The mechanical behaviour of the Brno clay wassimulated using the hypoplastic model for clays(Masın 2005) enhanced by the concept of intergran-ular strains (Niemunis and Herle 1997). This modelwas selected to represent the advanced constitutivemodels, which are capable of predicting the non-linear soil behaviour, with high stiffness at very smallstrains and a nonlinear decrease of stiffness withincreasing strain level. The implementation of themodel into various finite element programs (such asPlaxis, ABAQUS, Tochnog Professional) is freelyavailable on the internet (Gudehus et al. 2008).

For details of the model calibration, see Svobodaet al. (2010). The parameters of the model are sum-marised in Table 1.

Table 1. Brno clay parameters of the clay hypoplastic model.

ϕc λ∗ κ∗ N r19.9◦ 0.128 0.01 1.506 0.45mR mT R βr χ

16.75 16.75 0.0001 0.2 0.8

4 SIMULATION OF THE EXPLORATORYDRIFT

The finite element predictions of the exploratory driftand of the whole tunnel were performed using soft-ware Tochnog Professional. The geometry of the ex-ploratory drift and the finite element mesh consistingof 4680 8-noded brick elements are shown in Fig.5. The evaluated cross-section corresponded to thefront boundary of the finite element model. It waschecked that no additional displacements at the eval-uated cross-section were caused by the further ad-vance of the drift face. Steady state conditions werethus reached. The mesh density was selected to beapproximately the same for the drift and full tunnelsimulations (Sec. 5). The analyses were performed asundrained using penalty approach with bulk modu-lus of water equal to Kw = 100 MPa. This procedureis described in Masın (2009). No interface elementshave been used between the tunnel lining and the soil;therefore sliding of the lining with respect to soil hasnot been allowed which is a reasonable assumptionfor shotcrete lining. On the vertical sides of the mesh,normal horizontal movements have been restrained,whereas the base has been fixed in all directions.

The bottom 27.7m thick stratum represent the Brnoclay and it has been simulated using the hypoplas-tic model with parameters from Tab. 1. The overly-ing layers of loams and gravels were simulated us-ing the Mohr-Coulomb model with the parameters ob-tained during the site investigation (Pavlık and Rupp2003) (Table 2). The shotcrete lining was simulatedusing continuum elements in the 3D model. Its wasmodelled by a linear elasticity with time dependentstiffness calculated using an empirical relationship(Oreste 2003)

E = Ef(1− e−αt/tr

)(1)

whereEf is the final Young modulus, α is a parameterand tr = 1 day is the reference time. The same param-eters as the ones adopted by Masın (2009) were usedin the simulations (Ef = 14.5 GPa and α = 0.14).The simulated excavation sequence represented theone adopted on the site. An excavation step of 1.2 mwas followed by the lining installation.

The initial conditions of the simulation consistedof the determination of vertical stresses, the void ratioand the coefficient of earth pressure at rest K0. Thevertical stress was calculated from the unit weight

Table 2. Mohr-Coulomb model parameters of the layers overly-ing the Brno clay strata.

ϕ c ψ E ν[◦] [MPa] [◦] [MPa] [-]

backfill 20 10 4 10 0.35loess 28 2 2 45 0.4sandy gravel 30 5 8 60 0.35

Figure 5. Finite element mesh used in the analyses of the ex-ploratory drift.

of soil: γ=18.8 kN/m3 for clay, 19.5 kN/m3 for sec-ondary loess and 19.6 kN/m3 for sandy gravels. Watertable corresponded to the Brno clay - sandy gravel in-terface. The initial void ratio of the Brno clay e=0.83was derived from the undisturbed samples from bothboreholes.

Because no reliable in-situ measurements of K0

were available in the Brno clay massif, two extremevalues of K0 were considered in the analyses. First,the value ofK0 was determined from Mayne and Kul-hawy (1982) empirical relationship:

K0 = (1− sinϕc)OCRsinϕc (2)

The overconsolidation stress of 1800 kPa was esti-mated on the basis of the oedometer tests on theundisturbed Brno clay samples, with the correspond-ing overconsolidation ratio (OCR) of 6.5, leading toK0=1.25. The calculation of K0 according to Eq. (2)assumes that the apparent soil overconsolidation wascaused by the actual soil unloading resulting from theerosion of overlying geological layers. Creep repre-sents the second possible interpretation of the mea-sured overconsolidation. This interpretation wouldlead to the K0 value calculated from the Jaky (1948)relationship:

K0 = 1− sinϕc (3)

leading toK0 = 0.66.K0 of the layers overlying Brnoclay was always calculated from (3) using the frictionangles from Tab. 2.

The procedure of the analyses was as follows. First,the drift was simulated using the 3D finite elementmethod. The next step was optimisation of the modelparameters to account for inaccuracies of the descrip-tion of soil massif based on small-size laboratoryspecimens. As the optimisation was CPU demandingand not feasible in 3D, an equivalent 2D model to the

presented 3D model was developed. After the optimi-sation stage, the drift was simulated in 3D using theoptimised parameter set. The 2D model was based onthe load reduction method (Schikora and Fink 1982).The load reduction factor λd was calculated to ensurethat the 3D analyses and the equivalent 2D analysespredicted as closely as possible the surface settlementtroughs. The actual factors λd for the drift simulationswere λd = 0.50 (for K0 = 1.25) and λd = 0.53 (forK0 = 0.66). The adequacy of the 2D representationhad been demonstrated in a separate paper (Svobodaand Masın 2010). The 3D and equivalent 2D mod-els gave comparable predictions of the displacementfields, apart from the displacements in the very closevicinity of the tunnels.

4.1 Optimisation of the model parametersIn geotechnical practice, a common problem is thatdue to the size effects, sampling disturbance and limi-tations of experimental devices laboratory specimensdo not represent the behaviour of the soil massif withsufficient accuracy. For this reason, the soil param-eters calibrated by means of laboratory experimentshave been corrected using an inverse analysis of theexploratory drift. The corrected parameters were thenused for the class A predictions of the deformationsdue to the tunnel.

In the optimisation stage we focused on the shearstiffness. Namely, the parameter r controlling thelarge-strain shear stiffness as well as the small-strainshear stiffness was optimised. As the value of K0 hasalso remarkable influence on the results, all the sim-ulations were performed with two extreme K0 values(as explained above). The inverse analysis has beenperformed using the software UCODE. In the inverseanalysis, the parameter values are automatically ad-justed until the model’s computed results match theobserved behaviour of the system (Finno and Calvello2005). In the analyses, results of the simulations werecompared with the measurement of the vertical dis-placements at several locations. Three locations wereat the surface, where the vertical displacements weremeasured by means of geodetic survey. The fourthmonitoring point was located just above the driftcrown and it was monitored by means of an exten-someter. The differences between the simulation andthe monitoring data were expressed in terms of anobjective function S(b) (Finno and Calvello 2005)which takes the form:

S(b) = [y− y′(b)]Tω[y− y′(b)] (4)

where b is a vector containing the values of param-eters, y is a vector of observations, y′(b) is a vectorof the computed values corresponding to the obser-vations and ω is the weight matrix. The weight ma-trix evaluates the significance of each measurement.

Typically, the weight of each observation is taken asthe inverse of its error variance (Finno and Calvello2005). In the present case, with a low number of ob-servations, however, each of the four observations isgiven the same weight equal to unity. UCODE per-forms the optimisation using by means of minimisa-tion of the objective function S(b) using the modifiedGauss-Newton method.

The surface settlement troughs predicted with theoriginal and optimised parameter sets, compared withthe monitoring data, are shown in Fig. 6. Clearly, themodel predicts reasonably both the settlement troughshape and magnitude already with the original param-eter set. The optimisation procedure leads to a slightincrease of the parameter r (Tab. 3) and a further im-provement in predictions.

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measurementor. p., K0=1.25or. p., K0=0.66opt. r, K0=1.25opt. r, K0=0.66

Figure 6. Surface settlement troughs due to exploratory drift pre-dicted with the original parameter set (”or. p.”) and with opti-mised value of the parameter r (”opt. r”).

Table 3. Original and optimised values of the parameter r.

parameter set roriginal param. 0.45optimised r, K0 = 1.25 0.51optimised r, K0 = 0.66 0.49

5 3D SIMULATIONS OF THE KRALOVO POLETUNNELS

As the last step in the investigation, the whole tun-nel was simulated in 3D with the optimised parameterset. The results represent class A predictions, as theywere performed in the period 2008 to early 2009, andthus before the tunnel excavation passed the simulatedcross-section (November 2009).

In 3D, the finite element mesh consisting of 18 3528-noded elements was used. The mesh and the mod-elled geometry are shown in Fig. 7. As in the case ofthe drift simulations, the evaluated cross-section was

located at the front tunnel boundary. Steady-state con-ditions with no additional displacements with furtheradvance of the tunnel face were reached. Other detailsof the analyses (drainage conditions, boundary condi-tions) were the same as in the exploratory drift simu-lations (Sec. 4). The tunnel lining was modelled usingcontinuum elements with the thickness of 0.35 m asa linear elastic material with time dependent stiffness(as in the case of the exploratory drift). A 100 me-ters long simulated portion of the tunnel correspondedto the tunnel chainage 0.790-0.890 km (Fig. 2). Themodels considered the complex excavation sequencewith the tunnel face subdivided into 6 segments (Fig-ure 8). The excavation was performed in steps 1 to 6(Fig. 8) with an unsupported span of 1.2 m. A constantdistance of 8 m was kept between the individual faces,except the distance between the top heading and thebottom, which was 16 m.

Figure 7. Finite element mesh used in the analyses of the wholetunnel.

Figure 8. The excavation sequence as represented by the model.

The surface settlement troughs for both K0 val-ues are presented in Figure 9a. Due to the scatterof the monitoring data, several measurements at thechainages close to the simulated cross-section are pre-sented. The agreement between the simulated andmeasured settlements is very good. The settlementmagnitude is better predicted represented by the sim-ulation with the higher K0, while the trough shape isbetter predicted by the low K0. Both predictions areon the safe side of the monitoring data (displacementsare slightly overpredicted).

Figure 9b shows measurements of an extensome-ter located above the tunnel crown. The differencebetween the monitoring data and the simulations isapproximately constant with depth, and correspondsto the slight overestimation of the surface settlementsin Fig. 9a. Fig. 9b thus indicates that the hypoplasticmodel predicted correctly also the distribution of ver-tical displacements with depth, not only surface set-tlements.

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K0=1.25K0=0.660.740km0.825km0.880km0.920km1.010km

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(b)Figure 9. Surface settlement trough (a) and extensometer mea-surements (b). Class A predictions compared with the monitor-ing data.

Although the model predicted correctly the verti-cal displacement field, it significantly overestimatedhorizontal displacements in a vicinity of the tunnelin the tunnel depth. This is demonstrated in Fig. 10,showing the inclinometric measurements from an in-clinometer located 3 m from the tunnel side. One ofthe possible reasons for this discrepancy is an ab-sence of the small-strain stiffness anisotropy in thehypoplastic model. A similar problem was pointedout by Masın (2009), who concluded that incorpora-tion of the small-strain stiffness anisotropy into thehypoplastic model would improve the predicted shapeof the settlement trough. This indicates a direction for

the future development of the hypoplastic model. It is,however, necessary to stress out that although the hor-izontal displacements were overpredicted in the tun-nel depth, their magnitude in the vicinity of the sur-face was predicted correctly. the correct predictionsof the surface displacements are important in estimat-ing the damage to the surrounding buildings.

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Figure 10. Inclinometric measurement, inclinometer located 3 mfrom the tunnel side.

6 CONCLUSIONSIt was shown that the application of an advanced soilconstitutive model, in combination with quality ex-perimental data and 3D finite element analysis, maylead to accurate forward predictions of the displace-ment field induced by a tunnel with low overburdenthickness. The hypoplastic model for clays enhancedby the intergranular strain concept gave accurate pre-dictions of the surface settlement, surface horizon-tal displacements, and the distribution of vertical dis-placements with depths. For both K0 values adoptedthe model overpredicted the horizontal displacementsin the vicinity of the tunnel.

ACKNOWLEDGMENTThe authors greatly appreciate the financial supportby the research grants GACR P105/11/1884, GACR103/09/1262, GAUK 134907 and MSM0021620855.

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