Performance of the GHT Lining in the First Instrumented Plot

Transcription

1 Performance of the GHT Lining in the First Instrumented Plot BorTAS calculations Projectorganisatie HSL-Zuid Projectbureau Noordelijk Holland; dr. ir. A.G. Kooiman Holland Railconsult & CST ir. SJ Lokhorst, ir. JJM Schillings (CST) and ir. L Span Reference GP-SJL Version 1. Utrecht, December released 22, Holland Railconsult BV. All rights reserved. No part of this edition may be reproduced, stored in an automated database or published in any form or by any mean, electronic or mechanical, including photo-copying and recording, without permission in writing from Holland Railconsult BV.

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3 Summary See chapter 5. 2/36

4 Table of contents Summary 2 Introduction 4 1. Description of model and parameters Geometry Choice of parameters Variables in the calculation series Rough estimation of results 8 2. General results of calculations Tangential bending moments in the lining in the first instrumented plot Global bending moments Safety factor to failure Expected local damages in the lining in the first instrumented plot 2 5. Conclusions and recommendations References 3 Publishing details 31 Appendix 1 3/36

5 Introduction In November 21 the TBM of the bored Green Heart Tunnel left the entry shaft in Leiderdorp. A year later the TBM left escape shaft Achthoven after a foreseen maintenance period. Between the entry shaft and shaft Achthoven a series of field measurements was carried out. In the so-called (first) Instrumented Plot, surface settlements, lining deformations and grout pressures etc. were measured. The results were compared and related to the general TBM process parameters. In addition to the field measurements, calculations with the 3D Finite Element Analysis model BorTAS [2] were initiated. With this model the performance of the tunnel lining can be investigated in terms of safety factors to failure of the individual rings and in terms of expected local damage. The BorTAS parameters were chosen in line with the actual (geotechnical) situation of the tunnel in the first instrumented plot. This report describes the chosen parameters and the results of the BorTAS calculations. Also a comparison is made with results of a recent study on the lining thickness of the Green Heart Tunnel [1]. 4/36

6 1. Description of model and parameters 1.1 Geometry The three dimensional tunnel model used in these calculations consists of seven segmented rings. Each calculation starts with a model of three rings (phase ). In the following four phases of the calculation four additional rings are activated consecutively (see figure 1.1). The rings consist of nine segments and a keystone with the same geometry as the real segments. The segments consist of linear elastic volume elements. The concrete pads in the lateral joints and the ring joints are modelled as contact elements. The stiffness of the contact elements is based on the Janszen theory [3] for concrete joints. Radial boundary conditions and loading The soil and grout surrounding the rings is modelled with spring elements. The hardening of the grout is modelled by the increase of the stiffness of the springs from nearly zero to the stiffness of the surrounding soil. In each phase of the calculation the stiffness of the springs is adjusted for each ring (see figure 1.1). Phase represents the situation where the boring process is continued after a relatively long interruption (e.g. caused by maintenance). In phase the rings are supposed to be surrounded by hardened grout and soil. However, the front half of the ring 3 is still within the TBM and is therefore neither supported nor loaded in radial direction. In phase 1 ring 4 is activated. The basic radial loads are the grout loading (i.e. a hydrostatic load) and the soil loading as defined by Duddeck [4]. Alike the radial boundary conditions, the radial loading of the rings varies per phase of the calculation. This is also shown in figure 1.1. In phase the three rings are loaded with a soil loading. In the following phases each of the new rings (and also the front half of the third ring) is loaded with a load that gradually changes from the basic grout loading into the basic soil loading. Axial boundary conditions and loading In axial direction the rings are loaded with the jack forces from the TBM. In the model the TBM jacks are present with their actual geometry and stiffness. The axial forces are transferred from the TBM via the jack rods and jack soles to the pads in the ring joint of the last activated ring. During a phase the jacks change from the contracted to the ejected state. The front of the model (i.e. the TBM) has a fixed position; its displacements and rotations are prescribed as being zero. At the back of the model the first segmented ring is coupled to a beam with the same global properties and bedding as the segmented rings. 5/36

7 radial grout load radial grout/soil load radial soil load bedding with grout/soil stiffness bedding with soil stiffness Figure 1.1, schematic representation of the phased calculation procedure in BorTAS. From top to bottom the number of rings, the radial load and the radial bedding changes per phase of the calculation. 6/36

8 1.2 Choice of parameters The table below gives an overview of values of the most important parameters used for the calculation series IP1. Table 1-1. Parameter Values used calculation series IP1 No. of rings 7 (3 initial rings + 4 phased rings) Segment geometry based on design by Bouygues/Koop for GHT with lining thickness of 6 mm using plane rings. Internal diameter 13.3 m Lining thickness 6 mm Stiffness of the concrete The concrete lining is partly cracked. Partly cracked lining means that for 1/6 th of the lining a reduced elastic modulus (Ef) is used in the areas where cracking is expected. Concrete B65 (E=385 MPa & Ef=13 MPa) [5] Stiffness of joints contact elements with local stiffness based on Janszen theory Axial loading by TBM Normal force = 15 MN Moment = 8 MNm While the jacks are in the contracted state the N and M are 5% of the values above. Stiffness of TBM jacks Included Stiffness of built tunnel Included Radial grout loading hydrostatic; see section 1.3 Radial soil loading according to Duddeck; see section 1.3 Stiffness of soil see section 1.3 Stiffness of grout grout stiffness changes in a period of two phases from almost via 5% to 1% of the soil stiffness. 1.3 Variables in the calculation series In the calculation series IP1 three calculations were made. The variables are: - the grout loading, - the soil loading and - the radial grout and soil stiffness. The values for these parameters are based on the geotechnical situation in the measuring field IP1, located between the entry shaft and escape shaft Achthoven. Two calculations were made for the first instrumented plot; A third calculation was made to establish a relation with previous calculations with BorTAS [1]. In the calculation series IP1 the choice of the grout loading parameters is different from the default BorTAS settings (as used in [1]). The default settings are: 7/36

9 the radial grout pressure equals 1.4 * the groundwater pressure; the grout pressure gradient equals 8 kn/m3. In this calculation series the grout pressure equals 1. * the groundwater pressure only. The pressure gradient remains unchanged and represents the combination of the upward hydrostatic load and the downward weight of the gantry of the TBM. The grout pressure gradient of 8 kn/m3 causing an uplift of the tunnel is the net result of an expected grout pressure gradient of 1 kn/m3 corrected with the weight of the gantry of the TBM. The weight of the gantry is not a parameter in BorTAS. The calculations are identified as follows: IP1-1 is the calculation with parameters nearly identical to the calculation for a 6 mm partially cracked lining reported in [1]; Only the radial grout pressure is reduced by approx. 4%. IP1-2 is the calculation with a realistic estimation of the radial loads and soil stiffness. IP1-3 is the calculation with a conservative (i.e. a very low) estimation of the soil stiffness in the top of the ring. The values of the relevant radial load and soil stiffness parameters are shown in the table below. In the table the parameters of calculation REF are shown as reference. REF is the calculation for a 6 mm partially cracked lining reported in [1]. Table 1-2. soil load grout load Soil Stiffness Calculation S vc S wc K S gwrat S ggrad E top E tsd E bsd E bot [kpa] [kpa] [-] [-] [kn/m 3 ] [kpa] [kpa] [kpa] [kpa] REF IP IP IP where: S vc = Vertical pressure in the soil at the centre of the tunnel; S wc = Water pressure in the centre of the tunnel; K= coefficient for horizontal effective soil pressure; S gwrat = the grout pressure to water pressure ratio; S ggrad = grout pressure gradient E top, E tsd, E bsd, E bot = Soil stiffness in top sector, top-side sector, bottom side sector, bottom sector of the ring. Each sector measures 25% of the ring perimeter. 1.4 Rough estimation of results The results of the calculation series IP1 with BorTAS will be shown and discussed in the next chapters. However, a rough estimation of the bending moments and radial deformation of the tunnel lining will be made here, using an analytical solution for a continuous ring with a spring bedding (see [6]). A continuous ring (i.e. non-segmented) is subjected to a radial load approximating the radial soil load in the measuring field (see IP1-2 in the table above). However, in the analytical calculation the hydrostatic component of the loading is not included. The 8/36

10 applied load can be divided into a uniform part and a variable part. The uniform part of the load ( = 334 kpa) causes a constant radial displacement and a constant normal force only. The variable part of the loading is a cos(2 ) function along the circumference with maxima at the top and bottom and minima at the level of the horizontal axis ( 2 = 38 kpa). The variable load causes bending moments in the ring. The stiffness of lining is estimated as 7% of the Elastic modulus of the concrete i.e. 27 MPa. For the stiffness of the bedding of the soil three values are adopted: 12, 25 and 4 kpa. These values more or less agree with the variation of the bedding of the soil along the perimeter of the ring in the BorTAS calculations. In Figure 1-1 the radial deformations of a ring are presented. As expected the ovalisation of the ring increases with decreasing stiffness of the bedding. The ovalisation, i.e. the change in radius, varies between approx. 5 and 11 mm. continuous lining, radial displacement, analytical solution 15 1 Esoil=12MPa Esoil=25MPa Esoil=4MPa radial displacement [mm] Angle [degrees] Figure 1-1 Radial deformations of continuous ring for varying soil stiffness. The tangential bending moments due to the variable radial load are presented in Figure 1-2. With decreasing stiffness of the soil an increase of the bending moments is found. This is due to the fact that with a decreasing soil stiffness a larger part of the variable radial load is carried by the ring itself. The maximum bending moments vary considerably: between 16 and 33 knm/m. From the results of calculation REF presented in [1] it can be derived that the analytical results of the bending moments agree well with BorTAS results; however, the analytical results of the deformations are about 5% of the BorTAS results. Using this experience, maximum bending moments of 2 to 25 knm/m and radial deformations of 18 mm can be expected from the BorTAS calculations for calculation series IP1. 9/36

11 continuous lining, global bending moment, analytical solution 4 3 Esoil=12MPa Esoil=25MPa Esoil=4MPa 2 Bending Moment [knm/m] Angle [degrees] Figure 1-2 Tangential bending moments of continuous ring for varying soil stiffness. 1/36

12 2. General results of calculations The three tables below summarise the parameters and results of the calculation series IP1 and results presented in [1]. Table 2-1 Radial load and soil stiffness parameters. soil load grout load Soil Stiffness Calculation S vc S wc K S gwrat S ggrad E top E tsd E bsd E bot [kpa] [kpa] [-] [-] [kn/m 3 ] [kpa] [kpa] [kpa] [kpa] REF IP IP IP Table 2-2 Maximum and minimum displacements and stresses in ring 4 at the end of the calculations. Calculation Deformations [mm] Stresses [kpa] u hormax u hormin u vermax u vermin tanmax tanmin aximax aximin REF 17,7-17, 23,2-13, IP1-1 18,3-17,5 23,3-13, IP1-2 11,1-1,5 16,5-5, IP1-3 11,2-1,6 17,1-4, Table 2-3 Maximum and minimum bending moments and normal forces in ring 4 at the end of the calculations. Calculation Bending moments [knm/m[ Normal Forces [kn/m] M tanmax M tanmin M aximax M aximin N tanmax N tanmin N aximax N aximin REF IP IP IP N.B. the values in table 2-3 are local values of N and M and thus higher than the global (or smeared) values that will be presented in chapter 3. Comparison between REF and IP1-1 The only difference between REF and IP1-1 is the value of the parameter S gwrat which is the grout to water pressure ratio. The default value of this ratio 1.4 which means that the grout pressure is 4% higher than the groundwater pressure. This value was derived from results of a large scale field test at the Second Heinenoord Tunnel. Preliminary studies of HSL-South on soil-grout- lining interaction indicate that a ratio of 1.4 is doubtful. For the calculation series IP1 a ratio of 1. was chosen. The effect of lowering the ratio from 1.4 to 1. is that the average radial grout pressure reduces by approx. 4%. This causes a reduction of the average normal force in a ring surrounded by fluid grout. In the following stages of a calculation the radial load changes in two steps into the radial soil load which is the same for the two calculations. The differences in the results between the two calculations therefore must be the effect 11/36

13 of the difference in the initial radial grout load, causing different deformations and stresses in a ring surrounded by fluid grout and the stepwise changes in the load during hardening of the grout. The difference between results of both calculations are very small. This is clearly illustrated with Figure 2-1 and Figure 2-2 being almost identical. Figure 2-1 Tangential stress distribution at the end of calculation REF. Figure 2-2 Tangential stress distribution at the end of calculation IP /36

14 Comparison between IP1-1 and IP1-2 The differences in parameters between calculation IP1-1 and IP1-2 are the radial loads and the radial soil stiffness. In calculation IP1-2 the chosen values are based on the geotechnical situation in the measuring field IP1, located between the entry shaft and escape shaft Achthoven. In calculation IP1-1 the values were taken from the calculation REF which represents an arbitrary situation of the GHT. In calculation IP1-2 the radial grout load and radial soil load are significantly lower than the radial loads in calculation IP1-1. Also the soil stiffness in calculation IP1-2 varies along the perimeter whereas the stiffness in calculation IP1-1 is constant. From the tables 2-2 and 2-3 it can be seen that the differences in the radial load and the soil stiffness influence the min. and max. deformations, stresses etc. considerably. For a more global comparison see Figure 2-2 and Figure 2-3. Figure 2-3 Tangential stress distribution at the end of calculation IP /36

15 Figure 2-4 Tangential stress distribution at the end of calculation IP1-3. Comparison between IP1-2 and IP1-3 The difference between calculations IP1-2 and IP1-3 is the soil stiffness at the top sector of the tunnel (25% of the perimeter); 12 kpa and 3 kpa resp. The reduction was chosen to investigate the effect possible plastic soil deformations at the top of the tunnel. Surprisingly the results between the two calculations are very small. Comparison of ring deformations Here the vertical deformations of the ring 4 at the end of calculations IP1-2 and REF are compared. The maximum vertical displacements at the top and bottom are 5.4 / 16.5 mm for IP1-2 and 13. and 23.1 mm for REF. The ovalisation of the rings, i.e. the change in radius, is approx. 11 and 18 mm. In both calculations the rings deform into a horizontal (lying) oval shape. The ovalisation of calculation IP1-2 is about twice the ovalisation determined analytically (as was expected on the basis of a comparison between analytical results and BorTAS results in [1]). 14/36

16 Figure 3.6, Vertical deformations in calculation IP1-2 (top) and calculation REF (bottom). 15/36

17 3. Tangential bending moments in the lining in the first instrumented plot 3.1 Global bending moments This chapter deals with the distribution of the global tangential bending moments along the perimeter of a ring. The global bending moment is defined as the bending moment resulting from the total stress distribution over the width of the ring. It is the smeared or average tangential bending moment in a ring. In Figure 3-1 and Figure 3-2 the tangential bending moment at the end of calculations IP1-2 and IP1-3 are shown. At the end of the calculations the radial loads and the soil stiffness have reached their final and highest values and result in the highest bending moments. The maximum absolute bending moment is approx. 23 knm/m for both calculations. The differences between the bending moments of the two calculations are very small. As observed in chapter 2, the influence of the stiffness of the bedding of the soil in the top sector of the rings on the stress distribution is negligible. The maximum bending moments are in line with the analytically determined bending moments for the average soil stiffness of 25 kpa. Global bending moments, calculation Ring: 4 Phase: 4 Lining : Part. cracked Jacks: Ejected Bending Moment [knm/m] Angle [degrees] Figure 3-1 Tangential bending moments in ring 4 at the end of calculation IP /36

18 Global bending moments, calculation Ring: 4 Phase: 4 Lining : Part. cracked Jacks: Ejected Bending Moment [knm/m] Angle [degrees] Figure 3-2 Tangential bending moments in ring 4 at the end of calculation IP Safety factor to failure Cracking or even failure of the lining depends on the combination of normal force and bending moment that occur in the lining. To estimate the safety factor of the lining, here, the combinations of calculated normal force (N) and calculated moment (M) will be compared to the moment capacity of the lining in the ultimate limit state (M u ) at the calculated normal force (N) as proposed in [7]. For the determination of M u we refer to [1]. The combinations of N and M are plotted in Figure 3-3 to Figure 3-5. In table 3-1 the minimum safety factors for ring 4 are summarised for the calculation series IP1 and calculation REF. These factors were taken from Figure 3-3 to Figure 3-5 and from [1]. From the results of calculation REF in [1] which represents an arbitrary situation of the Green Heart Tunnel a minimum safety factor of 2.4 was derived. From calculations IP1-2 and IP1-3 which represent the actual situation in the first instrumented plot a higher minimum safety factor is found: i.e Table 3-1 Calculation REF IP1-1 IP1-2 IP1-3 Minimum Safety factor The results in table 3-1 show that for the load case defined in this project the safety factor of the tunnel lining in the first instrumented plot is higher than safety factors derived in a previous study [1] for an arbitrary situation of the GHT. 17/36

19 Global bending moments, calculation Ring: 4 Phase: 4 Lining: Part. cracked Jacks: Ejected Mu Bending Moment [knm/m] 5-5 Mu/ ; =2, Normal Force [kn/m] -4-5 Figure 3-3 Combinations of global bending moments and normal forces in ring 4 at the end of calculation IP1-2 compared with the maximum allowed bending moment in the ultimate limit state M u. Global bending moments, calculation Ring: 4 Phase: 4 Lining: Part. cracked Jacks: Ejected Mu Bending Moment [knm/m] 5-5 Mu/ ; =2, Normal Force [kn/m] -4-5 Figure 3-4 Combinations of global bending moments and normal forces in ring 4 at the end of calculation IP1-3 compared with the maximum allowed bending moment in the ultimate limit state M u. 18/36

20 Global bending moments, calculation Ring: 4 Phase: 4 Lining: Part. cracked Jacks: Ejected Mu Bending Moment [knm/m] 5-5 Mu/ ; 2, Normal Force [kn/m] -4-5 Figure 3-5 Combinations of global bending moments and normal forces in ring 4 at the end of calculation IP1-1 compared with the maximum allowed bending moment in the ultimate limit state M u. In the appendix the development of the tangential bending moment and the combinations of N and M in ring 4 in each of the four building phases is given for calculation IP1-2. From these graphs it is clear that the safety factor decreases with increasing phase of the calculation and thus with increasing radial load. 19/36

21 4. Expected local damages in the lining in the first instrumented plot In chapter 3 the analysis of the results concentrated on the tangential bending moments and normal forces. Safety factors for failure of the concrete were determined. In this chapter other types of failure of the lining will be discussed. With BorTAS, results can be generated with regard to: local concentration of tensile or compressive stresses compared to tensile or compressive strength; contact pressures in the ring joints or in the lateral joints; status of the joints, i.e. sliding of the joint contact areas or large joint rotations. The occurrence of these types of failure will be compared for the calculations IP1-2 and REF. The results presented can be regarded as the behaviour of the tunnel in the serviceability limit state. A load factor for the axial and tangential loads was not applied. Local stress concentrations The following graphs (figure 3.1) show the locations were the tensile or compressive stresses in ring 4 exceed the tensile strength or compressive strength. Only the results of phase 1 are shown here. In this phase the stresses are maximal. In the red spots at locations between the TBM jacks- the tensile strength is exceeded. Note that the stresses are fictitious since the concrete is modelled as a linear elastic material and cracking is only accounted for by a local reduction of the elastic modulus. The largest (fictitious) tensile stresses are present in calculation REF. In the legends of both graphs the minimum (compressive) and the maximum (tensile) stress is shown: SMN and SMX respectively. In calculation IP1-2 the maximum tensile stresses in tangential en axial direction are 6.7 MPa and MPa. In calculation REF the stresses are: 6.34 MPa and 4.27 MPa. The differences are small. The tangential stresses exceed the tensile strength of 4.21 MPa. 2/36

22 Figure 3.1 Maximum stresses in calculation IP1-2 (top) and calculation REF (bottom). 21/36

23 Contact pressures The segments of the lining make contact via the concrete pads in the ring joints and in the longitudinal joints. The pads are most efficient when loaded with an uniform compressive stress. Generally this will however not be the case for two reasons. One reason is that if two flat bearing pads come into contact, the resulting contact pressure is non-uniform with the highest values along the outside area, due to the stiffness of the bearing pads and the underlying concrete. The second reason is that to rotations of the joints, the contact pressures will vary over the pads. In case of large rotations the contact may locally be lost and/or the contact pressures may exceed a limit value. In BorTAS a limit value for the contact pressure of 27 MPa is used. In the following graphs the contact pressures in the pads in the ring joints (figure 3.2) and in the lateral joints (figure 3.3) are shown. At the locations where the contact pressure exceeds the limit of 27 MPa the pad is coloured blue. If the contact pressure is below 27 MPa, the colour of the pad is green. In calculation IP1-2 the maximum contact pressure in the ring joint is MPa (see SMX in legend). In the 6 mm lining the maximum pressure is MPa. In the longitudinal joints the maximum contact pressures are MPa and MPa respectively. The chosen criterion of 27 MPa is equal to the design value of the compressive strength (f b ) of a B45 concrete, see section in [5]. Since the concrete quality of the lining is B65 this criterion should be 39 MPa. This criterion is not exceeded for the load case in view. 22/36

24 Figure 3.2, contact pressures in the ring joints in calculation IP1-2 (top) and calculation REF (bottom). 23/36

25 Figure 3.3, contact pressures in the longitudinal joints in calculation IP1-2 (top) and calculation REF (bottom). 24/36

26 Leakage of joints To ensure water tightness, the segments are provided with rubber gaskets. Leakage of the joints occurs when the contact (pressure) between the rubbers of two segments is reduced due to either sliding of the joint or a large rotation of the joint. The criteria set for leakage is 2 mm due to sliding or a joint rotation of 4 mrad. In the following graphs the sliding and the rotation of the longitudinal joints is plotted for calculations IP1-2 and REF. The graphs are envelopes of the maximum values of sliding and rotations that occur in all the rings of the model. In both calculations the sliding and rotation are within the limits for a watertight lining. In calculation IP1-2, the maximum sliding and rotations are about two-third of the results in calculation REF. 25/36

27 Figure 3.4, Envelopes of maximum rotation in the longitudinal joints in calculation IP1-2 (top) and calculation REF (bottom). 26/36

28 Figure 3.5, Envelopes of maximum sliding in the longitudinal joints in calculation IP1-2 (top) and calculation REF (bottom). 27/36

29 5. Conclusions and recommendations Summary In November 21 the TBM of the Green Heart Tunnel left the entry shaft in Leiderdorp. A year later the TBM left the escape shaft Achthoven after a foreseen maintenance stop. Between the entry shaft and shaft Achthoven a series of field measurements was carried out. In so-called measurement field 1, surface settlements, lining deformations and grout pressures etc. were measured. In addition to the field measurements, calculations with the 3D Finite Element Analysis model BorTAS were initiated by HSL-South. This report describes the results of these calculations. The report focuses on the performance of the lining of the Green Heart Tunnel (GHT) at the position of the first instrumented plot. The performance of the lining is judged in terms of: safety to failure of individual rings based on combinations of tangential bending moments and normal force; local damages in the lining like local stress concentrations, crushing of pads or joints or leakage. Also a comparison is made with results of a recent study on the lining thickness of the Green Heart Tunnel [1]. The calculation series consists of three calculations where radial load and radial bedding stiffness were varied. The parameters were chosen in line with the geotechnical situation of the tunnel in the first instrumented plot. Generally, the radial load can be described as a load that gradually changes from a hydrostatic load directly behind the TBM into a soil load of neutral soil pressures according to Duddeck [4]. Parallel to the changes in load, the stiffness of the bedding increases. Both the gradual adjustments in load and bedding account for the effect of the hardening of the grout. Conclusions It is concluded that, given the defined radial load: the minimal safety factor to failure of the lining is 2.7. the reduction of the bedding stiffness at the top of the lining to model possible plastic deformations in the soil have no effect on the minimal safety factor. the safety factor to failure is higher than the safety factor determined in a previous study [1] representing an arbitrary position in the GHT (viz. 2.7 as opposed to 2.4 in [1]). in the measuring field less local damages are expected compared to an arbitrary position in the GHT. Recommendations The chosen radial loads and radial boundary conditions are typical for BorTAS vs They are a mixture of the traditional Duddeck load case for definitive situation of a tunnel lining and the assembly stage grout loading as derived from measurements at the Second Heinenoord Tunnel. Recent investigations to soil fluid grout lininginteraction indicate that the assembly stage grout loading may be quite different. This grout loading may locally show high peaks, different radial deformations of the lining and even result in plastic deformations of the surrounding soil. It is expected that this 28/36

30 grout loading result in a decrease of the safety factor to failure when compared to the factors presented in this report. It is recommended to: determine the effects of the soil-grout-lining model that was recently developed, on the safety factor to failure for the situation of the tunnel in the first instrumented plot and also for a relevant position between escape shaft Achthoven and N11. implement the soil-grout-lining model in BorTAS. 29/36

31 6. References 1. S.J. Lokhorst, J.J.M. Schillings & L.Span. Lining Thickness of the Green Heart Tunnel; a parameter study with BorTAS; Projectorganisatie HSL-Zuid document no. GP-SJL vs 1. October J.J.M. Schillings. Overview BorTAS revision 1.6; BorTAS: Bored Tunnelling Analysis System;, March Janszen P. Tragverhalten von Tunnelausbauten mit Gelenktübbings; Technische Universität Carolo-Wilhelmina, Braunschweig, June 1993, PhD Thesis. 4. Duddeck, H. Empfelungen zur Berechnungen von Tunneln im Lockergestein; Bautechnik 1, p , NEN 672; Voorschriften Beton TGB 199; Constructieve eisen en rekenmethoden VBC 1995; 6. Blom C.B.M. Design Philosophy of Concrete Linings of Shield Driven Tunnels in Soft Soils; Delft University of Technology; PhD-Thesis; To be published. 7. Haring, F.P. Spanningen in de bouwfase en de gebruiksfase van boortunnels. Afstudeerverslag Technische Universiteit Delft, faculteit Civiele Techniek en Geowetenschappen. Juni 22. 3/36

32 Publishing details Commissioned by Published by Projectorganisatie HSL-Zuid Projectbureau Noordelijk Holland; dr. ir. A.G. Kooiman Holland Railconsult & CST Major Projects Civil Structures Product Group P.O. Box GW Utrecht The Netherlands Telephone Telefax Author SJ Lokhorst Adviseur Project number GP /36

33 Appendix The appendix contains: 1. the global tangential bending moments in ring 4 in each of the four phases of calculation IP the combinations of global normal force and global bending moment in ring 4 in each of the four phases of calculation IP1-2. Global bending moments, calculation Ring: 4 Phase: 1 Lining : Part. cracked Jacks: Ejected Bending Moment [knm/m] Angle [degrees] Global bending moments, calculation Ring: 4 Phase: 2 Lining : Part. cracked Jacks: Ejected Bending Moment [knm/m] Angle [degrees]

34 Global bending moments, calculation Ring: 4 Phase: 3 Lining : Part. cracked Jacks: Ejected Bending Moment [knm/m] Angle [degrees] Global bending moments, calculation Ring: 4 Phase: 4 Lining : Part. cracked Jacks: Ejected Bending Moment [knm/m] Angle [degrees]

35 Global bending moments, calculation Ring: 4 Phase: 1 Lining: Part. cracked Jacks: Ejected Bending Moment [knm/m] 5-5 Mu Normal Force [kn/m] Global bending moments, calculation Ring: 4 Phase: 2 Lining: Part. cracked Jacks: Ejected Mu Bending Moment [knm/m] 5-5 Mu/ ; =2, Normal Force [kn/m] -4-5

36 Global bending moments, calculation Ring: 4 Phase: 3 Lining: Part. cracked Jacks: Ejected Mu Bending Moment [knm/m] 5-5 Mu/ ; =2, Normal Force [kn/m] -4-5 Global bending moments, calculation Ring: 4 Phase: 4 Lining: Part. cracked Jacks: Ejected Mu Bending Moment [knm/m] 5-5 Mu/ ; =2, Normal Force [kn/m] -4-5