EPB-TBM tunnel under internal pressure: Assessment of serviceability
N. A. Labanda, A. O. Sfriso, D. Tsingas, R. Aradas, M. Martini
EEPB-TBM tunnel under internal pressure: Assessment of serviceability
N. A. Labanda & A. O. Sfriso
SRK Consulting & Universidad de Buenos Aires, Argentina
D. Tsingas & R. Aradas
Jacobs, Argentina
M. Martini
Salini-Impregilo S.p.A., Italy
ABSTRACT: The Mantanza-Riachuelo basin recovery is one of the most ambitious environmental projectsunder construction in Argentina. In this context, the sanitary bureau of the metropolitan area of Buenos Aires(AySA) is building a sewage collection network to transport the waste water of the population in the southernarea of the city, composed by almost five million people. The most complex tunnel in this big project is named
Lot 3 , an outfall EPB-TBM tunnel starting at a shaft located at the
Rio de la Plata margin and running underthe river 12 km to a discharge area.The tunnel runs through soft clay belonging to the post-pampeano formation and dense sands of the
Puelchese formation. In operation, it will be pressurized by a pumping station which will produce a piezometer head that,in the first 2000 m, might be eventually higher than the confining pressure around the tunnel.This paper presents the numerical analysis of the structural forces acting on the tunnel rings using a risk-orientedapproach that considers the stochastic nature of materials, stratigraphy and tunnel-ground interaction. The com-pression of the lining is evaluated and compared with field measurements in order to predict the structural forcesand the risk of the rings going into tension beyond the structural capacity of the system.1 INTRODUCTIONThe
Matanza-Riachuelo river flows along the riparianlands between the City and the Province of BuenosAires (Argentina). It is a water stream 64 km longthat flows into the
Rio de la Plata . The river is heavilycontaminated with industrial and residential wastewa-ter discharged from both margins with limited -if any-pre-discharge water treatment process.The
Matanza-Riachuelo basin recovery project isan ambitious plan to manage the wastewater from theleft margin of the
Rio de la Plata through a sewer-age interceptor tunnel, a treatment plant and a dis-charge tunnel into the
Rio de la Plata . The projectis divided into several contracts. One of them, named
Lot 3 , holds the outfall tunnel, an EPB-TBM tunnelrunning 35 meters below the riverbed of the
Rio dela Plata . A global scheme of the outfall, which is thesubject of this paper, is presented in Figure 1.The tunnel has an internal diameter of 4.3 m anda total length of 12 km, including a 1.5 km diffusorzone with 34 standpipe risers, 28 m long, that day-light in the riverbed. It is being driven through soft
Figure 1: Location of Matanza-Riachuelo outfall (Buenos Aires,Argentina). The thin red line is the border between the City ofBuenos Aires and the Province of Buenos Aires. The Riachueloriver is along the south border. a r X i v : . [ phy s i c s . g e o - ph ] S e p lays of the Postpampeano formation and dense sandsfrom the
Puelchense formation. Water flows by grav-ity from a pumping station onshore built into the ac-cess shaft. Figure 2 shows the longitudinal elevationof the tunnel proposed in pre-feasibility stage.The tunnel will be subjected to a maximum inter-nal pressure of 550 kPa and an external water pres-sure from 330 to 420 kPa, resulting in a net outwardspressure 130 to 220 kPa. Further information aboutthe tunnel and its design can be found in Aradas et al.(2019).EPB-TBMs employ muck to balance water andsoil pressure at the tunnel face. By managing the ex-cavation parameters i.e., screw conveyor speed, ad-vance rate, thrust force, face support pressure, etc., theground relaxation and, consequently, structural forcesin the lining can be somewhat controlled. This aspect,usually not of high interest, is important in the case ofsegmental pressurized tunnels working at high inter-nal pressure.A common feature found when reviewing case his-tories of pressurized tunnels in soft ground is the rec-ommendation to neglect the contribution of the exter-nal ground confinement as a safety redundancy. Thishypothesis, despite being conservative from the per-spective of confinement, produces an unrealistic esti-mate of the deformation of the lining ring and there-fore of the resulting bending moments. On the otherhand, the adoption of a nonzero effective externalground pressure is challenging as it is largely depen-dent on the TBM-soil interaction during excavationand on the long-term creep behavior of the soil.An assessment of the compression induced in thesegmental rings by ground pressure via stochastic nu-merical models and calibrated using back-analysis af-ter field measurements is presented in this paper. Tworings are studied in this proposal: N ◦ and N ◦ ,embedded in soft clays and dense sands, respectively.2 CONSTITUTIVE MODELING FOR SOILAND LINING CONCRETEThe tunnel was designed in pre-feasibility stage tobe driven through dense sands, as shown in Fig-ure 2, where yellow layers represent the Puelchense formation. However, field conditions departed fromthis assumption in several places. For instance, high-plasticity clays belonging to the
Paranaense forma-tion were detected in the conveyor belt (Figure 3) be-twen chainages PK 0+294 to PK 0+586.Ring N ◦ placed at PK 0+316 and consequently,embedded in clay, and Ring N ◦ placed at PK0+681, embedded in dense sand, were instrumentedwith strain gauges whose results allow for evaluatingthe compression load of the tunnel lining in two dif-ferent grounds.The Hardening soil small (HSsmall) constitutivemodel was used to simulate the mechanical behaviorof soils and calibrated by in situ and lab tests and local
Table 1: Constitutive models and parameters used.Unit Soft clay Sandy soilsModel - HSsmall HSsmallDrainage - Undrained (A) Drained γ kN/m φ (cid:48) ◦ P.D. 32 c (cid:48) kP a ψ ◦ G ref M P a
P.D. 200 γ . - − − E refur M P a
P.D. 120 E ref M P a
P.D. 40 E refoed M P a
P.D. 40 m - 1.0 0.5 ν ur - 0.20 0.20OCR - 1.00 1.00 K nc - − sin φ (cid:48) − sin φ (cid:48) R inter - 0.90 0.70 k − m/s 0.005 1.00 experience. Statistical variability of the friction anglewas estimated using the 6-sigma method. A correla-tion between the compression index C c and the liquidlimit ω L for Postpampeano clays was first reportedby (Sfriso 1997) with a
COV = 0 . , and was laterupdated by (Ledesma 2008) as presented in Figure4, with a COV = 0 . . Swelling index C s , relevantfor the estimation of the interaction forces, correlateswith C c by: C s = 15 | C c and C c = 0 .
009 ( ω L − ± . (1)HSsmall requires the definition of elastic and hard-ening parameters E refoed , E refur , E ref and G ref , amongother parameters. They were computed as E refoed = 2 . e ) p ref C c , (2) E refur = 2 . e )(1 + ν ur )(1 − ν ur ) p ref (1 − ν ur ) K C s , (3) E ref = 1 . | . E refoed , (4) G ref = 52(1 + ν ) E refur , (5)being ν ur the Poisson modulus, K the at rest earthpressure coefficient, p ref the reference pressure and e the initial void ratio.Uncertainties in the properties of the clay where thering N ◦ is placed were dealt with by consideringa stochastic approach to bracket the prediction of thestructural forces acting on the lining. The parametersemployed are presented in Table 1, where some prop-erties are defined using probability distributions thatwill be described in the next section. A deterministicset of parameters were used for dense sand becauseits influence is negligible for the ring under analysis. igure 2: Matanza-Riachuelo outfall: longitudinal elevation of the tunnel proposed in pre-feasibility stage.Figure 3: High-plasticity clay detected in the TBM’s conveyorbelt.Figure 4: Compression index C c versus liquid limit for the post-pampeano formation. The structural stiffness of the lining was reduced toaccount for the segment joints using the Muir-Woodexpression (Muir Wood 1975) I red = I real (cid:18) n (cid:19) , (6)where I red is the reduced moment of inertia, I real isthe real moment of inertia and n is the number of lin-ing segments in each ring.3 STATISTICAL CHARACTERIZATION3.1 Soil parameters
The proposed risk analysis requires that the variabilityof soil parameters be defined together with the bound- P r obab ili t y d i s t r i bu t i on f [(cid:176)] f = 25(cid:176) s = 1(cid:176) P r obab ili t y d i s t r i bu t i on s = 0.065 Figure 5: Probability distribution for friction angle and com-pressibility index of the Postpampeano formation. | s - s | [ k P a ] e axial Triaxial lab test (p = 50 kPa) Triaxial lab test (p = 100 kPa) Triaxial lab test (p = 200 kPa)HSsmall results for p = 50 kPa HSsmall results for p = 100 kPa HSsmall results for p = 200 kPa
Figure 6: Drained triaxial test, comparisons between laboratorytests and HSsmall simulations. aries presented in equation (4). A statistical character-ization for the effective friction angle φ (cid:48) and the com-pression index C c is presented in Figure 5. Probabil-ity distributions were obtained using the experimentaldata shown in Figure 4 and classical correlations forthe friction angle.Considering values • ± σ • for parameters C c , φ (cid:48) and boundary multipliers in equations (1) and (4), = 16 permutations can be performed to reproducedrained triaxial tests, where • is the mean value and σ • is the standard deviation of the considered param-eter. Results are presented in Figure 6 and comparedwith three experimental tests for this project. Goodfitting is obtained for consolidation mean pressures of p = 50 kP a , p = 100 kP a and p = 200 kP a .3.2 Lining segment concrete
The Young’s modulus of concrete is required to com-pute stresses and forces out of microstrains measuredy the monitoring system. A histogram of 480 sim-ple compression tests, a normal probability functionand a cumulative probability function are shown inFigure 7. In order to compute the concrete stiffnessat low strains E cise , the following expression is used(Comite-Euro-International-Du-Beton 1993) E ci = E co (cid:34) f cm f cmo (cid:35) / , (7)with E co = 21500 M P a , f cmo = 10 M P a and f cm un-confined compression resistance of the sample.Considering a mean value f cm = 59 . M P a and astandard deviation σ f cm = 4 . M P a , deformationsmeasured by strain gauges can be translated intostructural forces. -3 P r obab ili t y d i s t r i bu t i on ( N o r m a li z ed ) x - Simple compression tests Normal probability distribution f'c = 59.6 [MPa] s = 4.94 [MPa] C u m u l a t i v e p r obab ili t y d i s t r i bu t i on ( N o r m a li z ed ) s = 4.94 [MPa] Figure 7: Histogram of unconfined compression test results for480 samples of lining concrete. Probability distribution and cu-mulative distribution.
Water level in the river
Variable water level in the river is one of the key con-tributors to uncertainty of the compression forces act-ing on the tunnel lining, making its statistical charac-terization a critical aspect of the analysis. The Argen-tine Naval Hydrographic Service provided the time-history evolution of the river over the last few years.Taking the data corresponding to the first semester of2018, where the rings under analysis were installed,a normal probability function is fitted and presentedin Figure 8, and compared with field measurements.A mean elevation . m and a standard deviation . m were considered in the analyses. P r ob a b ilit y d i s t r i bu ti on ( N o r m a li ze d ) River elevation
River elevation measurements Normal probability distributionMean elevation 0.9453 mStandard deviation 0.5473 m 1.00.90.80.70.60.50.40.30.20.10.0 C u m u l a ti v e p r ob a b ilit y d i s t r i bu ti on ( N o r m a li ze d ) River elevation
River elevation measurements Normal probability distributionMean elevation 0.9453 mStandard deviation 0.5473 m
Figure 8: Water level in the
Rio de la Plata . Probability distribu-tion and cumulative distribution.
Ground relaxation estimate by 3D modeling inring N ◦ A three dimensional model of the excavation was de-veloped to estimate the ground relaxation induced bythe TBM drive in ring N ◦ . The TBM shield wassimulated considering a face contraction c ref = 0 . and a tail-to-face contraction increment c inc,axial =0 . /m . A grout pressure equal to the total fieldstress plus 0.5 bar was applied in the TBMs tail. Theface pressure was calibrated with data provided by thesensors in the TBM, imposing a normal surface loadequal to the measured value presented in Figure 9. -1.5-1.0-0.50.00.51.01.5 D i s t an c e t o T B M s a x i s [ m ] Ring 33 - Sensors 1-2-3 Ring 38 - Sensors 1-2-3 Ring 80 - Sensors 1-2-3 Ring 85 - Sensors 1-2-3 Ring 142 - Sensors 1-2-3 Ring 147 - Sensors 1-2-3 Ring 232 - Sensors 1-2-3 Ring 237 - Sensors 1-2-3 Ring 33 - Sensors 4-5-6 Ring 38 - Sensors 4-5-6 Ring 80 - Sensors 4-5-6 Ring 85 - Sensors 4-5-6 Ring 142 - Sensors 4-5-6 Ring 147- Sensors 4-5-6 Ring 232 - Sensors 4-5-6 Ring 237 - Sensors 4-5-6 3D Model pressure
S1S2 S3 S4S5S6
Figure 9: Sensor data from the TBM face.
The 3D model is presented in Figure 10. Due tothe high computational effort required by this kindof simulations, mean values for all materials wereused and a single model is analyzed. The excavationsequence was repeated until a reasonably stabilizedzone was obtained.
Figure 10: 3D model of settlements after excavation.
Settlements in the tunnel crown and effective verti-cal stresses in the stabilized section are plotted in Fig-ure 11. The mean value for settlement is close to 30m, while the effective vertical stress is around 145kPa. These values were used to fit a ground relaxationfactor in the two dimensional models presented in thenext section.4.2
Structural forces in ring N ◦ In order to evaluate the risk of tension forces beingdeveloped in the ring, a 2D model was developed andthe influence of uncertainties in input data in equa-tions 1 and 4, river water level and concrete qualitywere studied.The numerical model and construction stages aresummarized in Figure 12. The excavation sequencewas simulated in 2D by partial stress relaxation usingthe β -method, i.e. applying Σ M stage = 1 − β < .Grout pressure in TBMs tail was simulated as a dis-tributed load, the (impervious) lining was activatedand consolidation until 99 % dissipation of excesspore pressure -the expected condition by the time thetunnel starts operating- was allowed for. In operation,an internal head of 15.5 m, 14.0 to 15.1 meters abovethe river level was applied. = 32 models were gen-erated by performing all permutations of data pre-sented in Table 2. Table 2: Parameter ranges used to compute ground relaxationcurves. Unit Lower bound Upper Bound C c - 0.367 0.497 C s (eq. 1) - 0.1 0.2 E ref (eq. 4) - 1.25 1.90 φ (cid:48) ◦
24 26River Elevation m Figure 13 shows the obtained ground relaxationcurves and both displacement and effective verticalstress measured in the tunnel crown, plotted in termsof Σ M stage . The purpose of these curves is to obtain,in a 2D model, a stress state similar to the stabilizedsection of a 3D model.By getting into the graph with the mean crown dis-placement obtained in the 3D model, and intersect-ing curves corresponding to the 2D crown displace-ment (in blue), a range of Σ M stage values were ob-tained. The range of effective contact stresses ob-tained reasonably contains the mean value obtainedin the 3D model. Values adopted for the analysis are Σ M stage = [0 . , . , . , . , . , . .Tables 2 and 3 show values employed to calcu-late structural forces in the lining. Together with the Σ M stage values, a set of x = 384 numericalmodels were obtained. Table 3: Concrete parameters used in permutations to computestructural forces.Unit Lower bound Upper Bound f cm M P a
Figure 14 plots translation and ovalization compo-nents of the tunnel lining obtained with all permuta-tions, during construction. The model shows that, for low relaxation values, a little rebound of the tunnel isobserved and an ovalization pattern where the verticalstress is larger than the horizontal stress is obtained.While the ground relaxation increases, a tunnel set-tlement and an invertion in the tunnel ovalization isobtained.Figure 15 shows the obtained structural forces forall models in the construction stage, comparing thosewith field data measured in ring N ◦ using straingauges. The actual concrete stiffness was used totranslate deformations into forces, as indicated withmarkers for the mean value and lines for the standarddeviation band.It can be seen that the proposed procedure prodcuesa good fitting with field data for both bending mo-ments and normal forces. For low Σ M stage values,hihger normal forces and lower bending moments areobtained, being the last in agreement with the oval-ization pattern. If Σ M stage is higher, normal forcesdecrease and bending moments increase.Figure 16 shows a comparison of the mobilizedshear stress τ mob for a 2D model and a stabilized sec-tion of the 3D model. For sake of simplicity, a singlerepresentative 2D model is shown but similar stresspatterns are obtained in all permutations. It is inter-esting to see that the mobilized shear, a measure ofthe tunnel arching effect, is similar in both cases.After ensuring the validation of the proposedmethodology, a study of the tunnel lining in operationwas performed and the risk of tension forces beingdeveloped was analyzed.4.3 Structural forces in operation in ring N ◦ Lining forces in operation in ring N ◦ are evalu-ated in this section. Figure 17 shows the translationand ovalization for the tunnel under internal pressure.Results are similar than those obtained for the con-struction stage, with a small increment in tunnel set-tlements due to the waste water weight. Ovalizationremains almost equal by virtue of the hydrostatic notgenerating higher deformations compared with theconstruction stage.Figure 18 plots the structural forces for all con-sidered permutations. Results show that bending mo-ments and shear forces are almost the same than dur-ing construction. Normal compression forces, how-ever, decrease dramatically from values − ± kN before the internal pressure to − ± kN in service. Despite this fact, even for high relaxationvalues i.e. Σ M stage = 0 . , lining is still under com-pression, and tension in connecting bolts is avoided.4.4 Structural forces in ring N ◦ Structural forces and deformations in the most ad-verse chainage of the tunnel, represented by ring N ◦ , is presented in this section. E ff ec ti v e v e r ti ca l s t r e ss s z ' [ k P a ] Stabilized zone in tunnel crown [m] -32x10 -3 -30-28-26-24-22-20-18-16-14-12-10 V e r ti ca l d i s p l ace m e n t [ m ] Vertical crown displacement Mean displacement 0.027 m Vertical effective stress Mean effective stress 145 kPa
Figure 11: Settlements of tunnel crown and effective vertical stress in stabilized section.Figure 12: 2D model of ring N ◦ . (a) Excavation using Σ M stage < (b) grout pressure (c) Activation of lining andconsolidation (d) Internal pressure in operation.Figure 13: Ground relaxation curves for = 32 permutations insoil parameters and river water level. Ring N ◦ . The procedure for the back analysis used in thiscase is different than the used in the previous case,avoiding 3D calculations and fixing the ground re-laxation by means of Σ M stage and field measure-ments. The simulation procedure is the same than inthe previous case. Soil properties for the soft clay andoverlying materials were defined using the mean val-ues presented in previous sections, while parametersfor dense sand were considered to be permuted usingbounds presented in Table 4.A two dimensional base model considering thestratigraphy corresponding to chainage PK 0+681 ispresented in Figure 19. The construction procedure isthe same than in the previous case.The effective friction angle φ (cid:48) was defined as thesum of the constant volume friction angle φ cv = 30 ◦ and the dilatancy angle ψ presented above.Ground relaxation curves for current stratigraphy Construction stage - Displacements x 10
MStage = 0.35MStage = 0.40MStage = 0.45MStage = 0.50MStage = 0.55MStage = 0.60Undeformed Tunnel
Construction stage - Displacements x 30
MStage = 0.35MStage = 0.40MStage = 0.45MStage = 0.50MStage = 0.55MStage = 0.60Undeformed Tunnel
Figure 14: Translation and ovalization of ring N ◦ duringconstruction. Angle to equator [°] -80-60-40-200204060 B end i ng M o m en t [ k N m ] Bending moments - Construction stage
MStage = 0.35MStage = 0.40MStage = 0.45MStage = 0.50MStage = 0.55MStage = 0.60Field measurement
Angle to equator[°] -2800-2600-2400-2200-2000-1800-1600-1400 N o r m a l [ k N ] Normal - Construction stage
MStage = 0.35MStage = 0.40MStage = 0.45MStage = 0.50MStage = 0.55MStage = 0.60Field measurement
Angle to equator [°] -60-40-200204060 S hea r [ k N ] Shear - Construction stage
MStage = 0.35MStage = 0.40MStage = 0.45MStage = 0.50MStage = 0.55MStage = 0.60
Figure 15: Structural forces of ring N ◦ in construction stageand comparison with field measurements.Table 4: Parameters used to compute ground relaxation curves indense sands. Unit Lower bound Upper Bound ψ ◦ E ref [kPa] 82000 98000 E refur [kPa] 200000 240000 G ref [kPa] 280000 400000River Elevation m are shown in Figure 20. Displacement are consider-ably lower than those observed for soft clays in Figure13. Also, a lower ground mobilization is required toachieve the same confinement pressure on the lining.Concrete parameters presented in Table 3, togetherwith relaxations Σ M stage = [0 . , . , . , pro-duce sets of paramteres that were employed to dothe stochastic analysis. Results are expressed in termsof bending moments, normal and shear forces duringconstruction, and are shown together with field mea-surements for ring N ◦ in Figure 21. Good fitting is igure 16: Comparison of τ mob between the 2D model and astabilized section of the 3D model. Normal operation - Displacements x 10
MStage = 0.35MStage = 0.40MStage = 0.45MStage = 0.50MStage = 0.55MStage = 0.60Undeformed Tunnel
Normal operation - Displacements x 30
MStage = 0.35MStage = 0.40MStage = 0.45MStage = 0.50MStage = 0.55MStage = 0.60Undeformed Tunnel
Figure 17: Translation and ovalization of ring N ◦ in normaloperation stage. found between numerical and experimental results inbending moments, while predictions in normal forcestend to underestimate the compression forces in thelining.Tunnel translation and ovalization during construc-tion are plotted in Figure 22, where vertical displace-ments are negligible while ovalization tends to in-crease with ground relaxation.4.5 Structural forces in operation, ring N ◦ Using the calibrated numerical model, an assessmentof serviceability in operation (under internal pressure)is presented in this section.Bending moments, normal and shear forces in thelining are presented in Figure 23, while translationand ovalization are shown in Figure 24.Similar to ring N ◦ , internal pressure in the tun-nel does not change much the bending moments,shear forces and lining deformations. However, nor-mal forces were affected, being the internal pressureproduced by the waste water transportation similar oreven higher than the ground and water pressure ap-plied in the tunnel lining. In this aspect, the behavioris different than the section embedded in clay; densesands produce less pre-compression in the lining, thusincreasing the probability to experience tensile forcesin the joint bolts. Angle to equator [°] -100-50050100 B end i ng M o m en t [ k N m ] Bending moments - Normal operation
MStage = 0.35MStage = 0.40MStage = 0.45MStage = 0.50MStage = 0.55MStage = 0.60
Angle to equator[°] -350-300-250-200-150-100-500 N o r m a l [ k N ] Normal - Normal operation
MStage = 0.35MStage = 0.40MStage = 0.45MStage = 0.50MStage = 0.55MStage = 0.60
Angle to equator [°] -100-50050100 S hea r [ k N ] Shear - Normal operation
MStage = 0.35MStage = 0.40MStage = 0.45MStage = 0.50MStage = 0.55MStage = 0.60
Figure 18: Structural forces of ring N ◦ in normal operation.Figure 19: 2D base model for ring N ◦ . (a) Excavaction with Σ M stage (b) grout pressure application (c) Lining construction(d) Tunnel under internal pressure in normal operation. -220-200-180-160-140-120-100-80-60-40-20 E ff ec ti v e v e r ti ca l s t r e ss s y ' [ k P a ] S Mstage -15x10 -3 -14-13-12-11-10-9-8-7-6-5-4-3-2-1 V e r ti ca l d i s p l ace m e n t [ m ] Relaxation curves for Puelche formation Stress in crown vs S Mstage Displacement in crown vs Mstage
Figure 20: Ground relaxation curves for = 32 permutations insoil parameters and river water level. Ring N ◦ . Angle to equator [°] -60-40-2002040 B end i ng M o m en t [ k N m ] Bending moments - Construction stage
MStage = 0.35MStage = 0.45MStage = 0.55Field measurement
Angle to equator[°] -3500-3000-2500-2000-1500-1000 N o r m a l [ k N ] Normal - Construction stage
MStage = 0.35MStage = 0.45MStage = 0.55Field measurement
Angle to equator [°] -40-2002040 S hea r [ k N ] Shear - Construction stage
MStage = 0.35MStage = 0.45MStage = 0.55
Figure 21: Structural forces of ring N ◦ in construction stageand comparisons with field measurements. Construction stage - Displacements x 50
MStage = 0.35MStage = 0.45MStage = 0.55Undeformed Tunnel
Construction stage - Displacements x 100
MStage = 0.35MStage = 0.45MStage = 0.55Undeformed Tunnel
Figure 22: Translation and ovalization of ring N ◦ duringconstruction. Angle to equator [°] -40-2002040 B end i ng M o m en t [ k N m ] Bending moments - Normal operation
MStage = 0.35MStage = 0.45MStage = 0.55
Angle to equator[°] -300-200-1000100200 N o r m a l [ k N ] Normal - Normal operation
MStage = 0.35MStage = 0.45MStage = 0.55
Angle to equator [°] -40-2002040 S hea r [ k N ] Shear - Normal operation
MStage = 0.35MStage = 0.45MStage = 0.55
Figure 23: Structural forces of ring N ◦ in operation. Normal operation - Displacements x 50
MStage = 0.35MStage = 0.45MStage = 0.55Undeformed Tunnel
Normal operation - Displacements x 100
MStage = 0.35MStage = 0.45MStage = 0.55Undeformed Tunnel
Figure 24: Translation and ovalization of ring N ◦ in opera-tion. Σ M stage , aset of x = 384 Rio de laPlata and Salini-Impregilo-Chediak for permission topublish the data contained in this paper.REFERENCES
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