Material reduced tunnel lining segments for moderately swelling soils

Tunnels in unfavorable ground conditions are exposed to high internal stresses due to localized loading at the outer face. Addition of extra layers of compressible material as a countermeasure needs more material and greater excavation volumes which is in conflict to the global goals of CO2 reduction. Thus, two alternative types of segments with higher bearing capacities are proposed that allow for lining thickness reduction. They are derived from multi‐load topology optimization considering relevant load cases during construction and in service. The first design incorporates centered recesses that maximize segmental stiffness. The second shifts the recesses to the outer face increasing their potential to absorb deformation. Two prototypes of each type are fabricated from high performance steel fiber reinforced concrete. Experiments show that a concrete reduction of up to 55.2% is achieved with respect to a conventional design. The volume savings give space for layers of radially compressible material.


| INTRODUCTION
Seeking a future with lower CO 2 emissions, ideas to reduce cement production require attention. Despite known difficulties to determine the emissions quantitatively, its contribution to the global CO 2 emission can be estimated to about 8%. 1 Previous studies attempted to take countermeasures merely on the material level 2,3 disregarding any potential on structural level.
In parallel, tunnel construction by mechanical means increased strongly in the last decades, and the predicted growth of cities 4 suggests that this trend will continue. Therefore, efforts should be made to reduce the amount of material required and specified by the design. This becomes even more important since segmental linings are usually produced in series. 5 Especially in swelling 6 and squeezing ground 7 conditions, the construction of tunnels is challenging throughout, during construction itself 8 and concerning the final state. 9 Here, the large deformations cause high internal Discussion on this paper must be submitted within two months of the print publication. The discussion will then be published in print, along with the authors' closure, if any, approximately nine months after the print publication. forces in the lining. This requires building tunnels with larger radial or tangential deformability to allow deformations of the ground and to reduce pressure on the lining and, consequently, keep its thickness t small. 7 The radial deformation capacity was recently addressed in studies on additional layers of compressible materials in tunnels under challenging ground conditions. [10][11][12] However, this approach comes along with an intrinsic increase of the excavation diameter, which must be compensated for if material reduction is the primary goal.
Topological optimization has been shown a promising tool to find optimal solutions on structural level. Nowadays, it is no longer just employed for the intrinsic material reduction involved, but even as an architectural design tool. 13,14 In general, it yields more slender designs exploited on higher stress levels. Practical realization becomes possible due to the (ultra) high performance concretes available today, which perform well in fabrication of solar collectors, [15][16][17] micro-reinforced concrete members, 18 non-reinforced columns, 19 and hybrid beams. 20 Others have already exploited its potential in tunneling to improve the design of ring 21,22 and longitudinal joints 23 of lining segments. Especially joints are sensitive to damage initiation. 24,25 Thus, on these, the future-oriented design should focus. 26 Figure 1 illustrates the generic cross-section of a segmental lining subjected to typical boundary conditions and introduces potential design alternatives with reduced thickness. The focus is clearly set on mechanized tunneling in general and on often faced moderately squeezing/ swelling ground conditions in particular. Under favorable ground conditions, less thickness of the lining saves not only concrete volume, but also reduces excavation quantities and effort. This directly reduces costs and execution times of projects and improves sustainability. In case of swelling/squeezing ground conditions, less concrete thickness gives space for an additional compressive layer that prevents from overloading the lining locally. The design alternatives seek a more homogeneous material utilization avoiding joint failure, as it is a common drawback of conventional designs. 23 Design performances are tested experimentally on structural scale accounting for typical service conditions of real tunnels against a true reference, the tunnel line at Wehrhahn in Düsseldorf (WHL), Germany. This metro tunnel is double tracked with an overburden approximately equal to the external diameter (9.5 m). It is made of one-pass reinforced concrete linings of 45 cm thickness. 27,28

| OPTIMIZATION OF SEGMENTS
To reduce the volume of the load-bearing structure, the segments must be redesigned. Structural optimization is employed to this end since its successful application in the construction industry kept growing in the last decades. 29 More precisely, topology optimization 30 is employed here. It offers more flexibility compared with other methods like sizing 31 and shape optimization, 32 since it enables to generate voids in the design space. 33 It allows to find the optimal material distribution (in terms of densities) that minimizes an objective function under certain constraints that limit the design space. 30 To identify promising design alternatives under practical conditions, the method has been applied to a segment (Ref) similar to that of the reference project WHL 27,28 shown in Figure 2 at top center.
The design space was defined exploiting the double symmetry of geometry and loads and neglecting the curvature of the segment. Regarding the stress state in moderately curved members as tunnel linings are, it nearly makes no difference to consider them straight. 34 Thus, a slightly arched member as the reference subjected to external radial loading can be regarded straight and subjected to axial forces ( Figure 2, bottom center).
The objective function is its structural compliance, and the material is considered linear. The design space is just restricted by the maximum volume, defined to 75% of the initial one. In fact, lower volume quantities yield to the appearance of non-manufacturable voids, and higher volume quantities would not compensate additional manufacturing efforts. The most relevant loads are considered in a single run within a multiple load optimization scheme. 35 These loads are the jack forces during construction (J-German configuration), and the ring forces at the longitudinal joints in service (R), with positive or negative eccentricity due to bending. Shear is F I G U R E 1 Cross-section of a tunnel excavated with TBM. Segments for squeezing/swelling (left) and favorable ground conditions (right); conventional segments at top contrasted to optimized segments at bottom. disregarded since it is usually not relevant. 34 The ratio of forces is set to J/R = 1.8, as in the reference tunnel. To reduce computational costs and since any material reduction at load application seems not reasonable, these regions were excluded from optimization so that no material could be removed there.
Recesses and remaining upper and lower struts evolve in the solution to meet the volume constraint. Simultaneously, the lever arm in the central region of the segment is maximized for the transmission of bending moment and axial forces in ring direction (Figure 2, bottom). Of course, the design supports the jack forces in longitudinal direction, too. The thickness of these struts results from the maximum allowable stress of the material employed. If they get too thin, buckling might become an issue.
The optimization result motivates the design of two alternative types of segments: one with one-sided barrelshaped recesses in the longitudinal direction of the tunnel (BS), and another one with partial recesses at the outer face that resemble coffer slabs (CS). The BS-type is the direct materialization of the optimization result, with (in post-processing) smoothed recesses to decrease singularities at the corners ( Figure 2, top left). This design gains from arching against the local bending induced by the external load on top. Alternatively, the recesses can be shifted towards the outer face ( Figure 2, top right). While this at first decreases the load-bearing capacity of the segments, it provides additional space for a layer of compressible material (CM). Then, the capacity merely comes from a set of struts that transfer compressive stresses and stiffen the segment. This design is in line with the ideas presented by Vigl 36 and Vigl et al. 37 In both types, HPSFRC is combined with conventional rebar to maximize confinement and increase the bearing capacity at the regions of load introduction. 23,38 It fills the entire body of the segments, similar to the studies of Liu et al. 39 Subsequently, the raw optimization result was slightly modified to cover practical needs in the experiments. In the BS-type segments, only one of the recesses is made (Figure 2, bottom left). That way, structural failure will occur on the weaker side, and the instrumentation is greatly simplified. Moreover, and in line with the experiments conducted by Hemmy, 34 the curvature of the CS-type segments is suppressed to simplify manufacturing ( Figure 2, bottom right).
Finally, an extra layer of CM is placed on both types to compensate for local load concentration. Especially for the CS-type segment, the two layers should be manufactured in a precast plant. Due to the better production conditions there, no cavities evolve at the outer surface and potential problems when filling the additional annular gap are avoided. Alternatively, the CM can be grouted in situ. In that case, its viscosity should be designed to ensure that all corners of the recesses are filled with material. Details on geometry and reinforcement layout of the segments are provided in Section 3.

| Materials
The experimental campaign comprises a total of five segments: Ref, two of type BS (BS1 and BS2), and two of type CS (CS1 and CS2). Ref is made from a normal strength F I G U R E 2 Optimization concept and segmental designs derived thereof. F.l.t.r, top: optimum with one-sided barrel-shaped recesses; double-symmetric conventional segment with load introduction and forces highlighted in one quarter; optimum with coffer segments. F.l.t.r., bottom: prototype with one recess; optimization result of a straight quarter of a reference segment in terms of material density (red color indicates full material, while pure blue indicates low density. Elements with densities below 0.001 are removed for clarity); prototype with coffer recesses. Compressive material is shown semi-transparent. concrete (NC) C40/50 according to Eurocode 2. 40 For the HPSFRC used for BS and CS, the concrete strength class C80/95 was projected. The HPSFRC in BS (HPSFRC1) consists of a cocktail of 60 kg/m 3 macro and 60 kg/m 3 microfibers (see Table 1). Such high steel fiber contents have been employed elsewhere in experimental campaigns and showed enhanced bearing capacity under partial area and strip loading. 41 The smaller dimensions of the CS-type segments force to use smaller macrofibers (Dramix ® 3D 65/35 BG) combined with microfibers as for BS (HPSFRC2 in Table 1).
General measures for fire safety include proper concrete cover and the use of polypropylene (PP) fibers. 42 To capture the impact of PP fibers on the fabrication and the load-bearing capacity, one specimen (CS2) features 2 kg/ m 3 PP fibers additionally (HPSFRC3 in Table 1). Rebar is made from B500B steel throughout.
The compressible layer is made from cementitious materials characterized by a highly plastic compression capacity for constrained transverse strains. 10 They have highly air entraining admixture (foaming agent) and expanded polystyrene beads (EPS). Figure 3 (left) qualitatively shows the characteristic stress-strain behavior in axial compression, which can be divided into three characteristic domains (I: elastic, II: plastic, and III: densification). Two variants were produced for the experiments. They differed only in the type of cement used (Table 1): CEM I 42.5 R (CM1) and CEM I 52.5 R (CM2), by which the strength, and thus the stress level in the plastic range was intentionally influenced (cf. Section 4.1). Figure 3 shows the components and volume fractions as well as a picture of a CM.

| Reference segment (Ref)
The reference is inspired from the segments employed in the reference project. 27,28 However, to match the capacity of the formwork and the test setup, the dimensions, reinforcement amounts, and bar diameters were downscaled as shown in Figure 4 (top). That way, Ref fits in an available vertical formwork with an internal radius of 3.5 m, maximum thickness t = 400 mm, and width b = 1000 mm. It covers an angle of 45 which is equivalent to 8 equal segments per ring ( Figure 5, left). To get the scheduled dimensions, internal formwork was attached therein. Throughout reinforcement has 2 cm of concrete cover. The rebar at load introduction (A s,li ) consists of stirrups (Table 1). The longitudinal joint in conventional arrangement has the gasket groove at top as established in practice (cf. Figure 2, top center). Compaction was done with internal vibrators.

| Segments with one-sided barrelshaped recess (BS)
The two BS-type segments manufactured ( Figure 4, center) had the same thickness as Ref (225 mm) but significantly reduced volume, as they incorporated a recess. With a 175 mm thick layer of CM on top, the radial deformability increases and compensates for deformations from swelling/squeezing ground. Consequently, local loading on the lining is avoided. Its thickness was chosen to fully employ the thickness provided by the formwork. BS1 has 50 mm thick struts at the recess, whereas load introduction happens through conventional longitudinal joints as in Ref. The splitting forces at load introduction as well as the tensile stresses from the deflection of the ring forces at both sides of the recess are covered via hybrid reinforcement. Thus, tensile forces are born by a cocktail of micro and macro steel fibers and conventional bars welded at their ends to two transversal bars for anchorage ( Table 1). The splitting reinforcement is determined considering centered and maximum eccentric axial loads according to the relation between bending moment and rotation angle at longitudinal joints. [43][44][45] The simplified bilinear relation yields an eccentricity of e 0 = 32 mm to the outer face for a centered contact zone at the longitudinal joint with a width equal to the half of the segmental thickness. The load introduction is idealized as a block of constant compressive stress of 51 mm width (cf. Figure 8) according to the specifications in. 46 In the second segment (BS2), the gasket groove is shifted to the center of the longitudinal joint, which splits the contact zone into two halves closer to the segmental edges. 47 As this configuration, denoted non-conventional joint, admits higher bending moments, the eccentricity was adopted to e 0 = 42 mm. It comes along with lower splitting forces that reduce the required reinforcement amount. 23 Besides the constructive leg from the longitudinal reinforcement, the region of load introduction is just reinforced with a steel fiber cocktail. The width of the struts in BS2 was set to 60 mm. This way, the region of the recess is stiffer and the capacity of the nonconventional joint can be extended to a higher level.
Fabrication of the BS-type segments employed the same vertical formwork. The recesses were accomplished using extruded polystyrene bodies (XPS-see Figure 5, center), which were removed after demolding. Due to its plastic consistency, the concrete was compacted via internal and external vibrators (see Figure 5, left). After approximately 26 days, the segments were placed back into the formwork to add the CM layer of 175 mm thickness ( Figure 5, right). Due to its high fluidity, the CM did not require mechanical vibration.

| Coffer segments (CS)
Also two specimens of this type were manufactured (Figure 4, bottom). Maintaining the thickness to depth (of the formwork) ratio of the BS-type segments at about 0.6, the aim is to determine how much bearing capacity and deformability the CS-type segments can have for a total thickness of 225 mm. This approach reduces the thickness of the HPSFRC layer to just t = 135 mm. And of course, the smaller the dimensions of the segment become, the more challenging their production is. Therefore, the feasibility of producing such thin geometries can be investigated at the same time. If the production of small segments is successful, the procedure will also be successful for bigger geometries.
The segmental length was further limited to 1.7 m to keep the slenderness of the struts lower than 60 and eliminate buckling failure. The coffers are located 200 mm away from the load introduction at the longitudinal joints to favor proper load distribution into the struts. To this end, rebar is placed in front of and behind the coffers. These bars are anchored by two transversal bars welded on each end. The longitudinal joints are conventional and reinforced with welded bars ( Table 1). The axial force is transferred eccentric at 0.6Á32 mm = 19 mm from the axis of gravity and is idealized as a constant stress block with a width of 31 mm according to. 46 Here, a 70 mm wide contact zone was taken as basis (Figure 9, right). With this at hand, the splitting reinforcement was computed. The reinforcement of the inner face consists of a regular steel mesh bent into the outer longitudinal struts and welded to the rebar at top therein. The central strut contains two bars connected to the steel mesh by welded U-shaped stirrups that prevent buckling. Despite the smaller dimensions, the cover was still 2 cm.
Casting was performed in a horizontal wooden formwork. The coffers were spared using XPS bodies removed after demolding (Figure 6, left). Due to the small dimensions, concrete compaction could just be done with F I G U R E 5 Formwork employed for fabrication of segments (left), detail of XPS body for the recess (center), and casting of compressible material (right). external vibrators. Both CS-type segments had identical geometry and rebar. As the BS-type segments, only CS1 had a CM layer of 90 mm on top that also filled the coffers to study deformability. It was cast in another wooden formwork using the already hardened segment at the bottom (cf. Figure 6, right). Only the amount of admixtures was adjusted. The naming indicates the different fibers content (cf. Section 3.1). Moreover, each specimen was made from a different batch and tested at different ages which induced some variation to the properties. While the mean compressive strength of NC and HPSFRC was determined from cylinders (f cm -150/300 mm) and cubes (f cm,cube -150 mm), for CM it was just tested on cubes. Although the same CM was used for BS2 and CS1 (CM2), both yielded different strengths due to the age at testing (11 and 27 d, respectively). Concrete's tensile strength (f ctm ) was determined from splitting tests on cylinders, 48 while the flexural tensile strengths of HPSFRCs (L1 and L2) were obtained from four point bending tests on prisms (150/150/700 mm) according to. 49 L1 and L2 denote the average flexural strength for deflections of the beams at mid-span of 0.5 and 3.5 mm, respectively. Table 2 is completed with the Young's moduli E cm .

| Material parameters
To further characterize the CMs and to capture real conditions in tunnels, axial compression tests on cylinders (150/300 mm) were performed with full lateral confinement (Figure 7), as detailed in Reference 10. At the beginning of the plastic deformation range, the stress is close to f cm,cube .

| Test setups and load concept
The curved segments were tested in a rig that mimics the real boundary conditions in tunnels in service, that is, radial loads on the outer face and axial loads on a partial area at the longitudinal joints (Figure 8, top). The simultaneous biaxial load introduction of vertical (V) and horizontal (H) loads of up to 5 MN is performed by three coupled hydraulic cylinders. The superposition of V/2 and H at the joints results in an axial force N, constant throughout the specimen. The ratio between V (controlled by displacement) and H (controlled by force) is kept constant (H/ V = 1.866) to ensure an always perpendicular load introduction at the joints. The segment is placed on steel wedges that belong to the horizontal frame with an eccentricity e. This induces a constant bending moment M = NÁe into the specimen. In its original configuration, V is introduced by means of two parallel steel frames on the specimen. Further details on setup, loading, and regarding operation and verification have been published elsewhere. 50 To test the BS-type segments, a steel plate (1760/500/40 mm) that distributes the stresses on the CM is placed on the outer face of the segment (Figure 8, center). This way, the pressure of swelling/squeezing ground is realistically captured. Thus, it becomes possible to consider the effects of ground overpressure on the CM and the bearing capacity of the HPSFRC in a single test.
The experimental procedure had three parts corresponding to the expected behavior of the CM (cf. Figure 3, left). At first, CM reacts linear. Then it plasticizes with large radial deformations but no further load increase. Finally, its compaction potential is fully exploited, and the load increase leads to failure of the HPSFRC layer.
On BS1, V was transmitted through just one of the two vertical steel frames available. While hardboard panels between test rig and longitudinal joints were enough for load transmission in Ref and BS1 (Figure 8, center), BS2 required a steel block of dimensions 180/100/750 mm in front of the specimen (Figure 8, bottom). This block distributes the force on the two contact zones, similarly to earlier studies. 23 A tooth avoids relative displacements that may occur between block and specimen due to natural arc deformation. Contact to the specimen still employs hardboard panels.
From the geometry shown in Figure 8 (bottom) and simple statics, it can be determined that 87.5% of N is applied on the upper half of the joint, and the rest on the lower half.
For Ref, V was controlled with a speed of 0.3 mm/ min up to H = 1000 kN, and then with 0.5 mm/min until failure. By contrast, for BS1 and BS2, it started with 0.5 mm/min in the initial linear range, increased to 10 mm/min in the plastic range, and finished with 0.5 mm/min again. All ranges experienced gradual and F I G U R E 7 Stress-strain curves of CMs under full lateral confinement according to 10 . controlled transition in between. Throughout, H was automatically controlled to keep H/V constant. The vertical displacement at mid-span and at the longitudinal joints were measured using linear variable displacement transducers (LVDTs) and digital image correlation (DIC). The specimens were additionally equipped with strain gauges (SGs) glued on the reinforcement at relevant locations (see Section 4.3.2).
By contrast and due to its straight geometry, testing of the CS-type segments was performed in a totally different setup employing a conventional 20 MN servo-hydraulic machine (Figure 9). Since just CS1 has a compressive layer, it was first horizontally placed (via hardboard panels) on the machine for compaction testing (Figure 9, left). The load was applied on the outer face and distributed by means of steel profiles and plates. The test was controlled by displacement (2 mm/min) and finished manually for a peak displacement of 54 mm, at a pressure p = 1.34 MPa (here considered constant), with the CM in the densification range (cf. Figure 3, left). Then, the remainder of the compressive layer was removed to now investigate the HPSFRC bearing capacity. Therefore, the specimen was placed vertically in the same machine and the load was applied through two 5 mm thick hardboard panels (Figure 9, right). The load was controlled by displacement (0.3 mm/min). Displacements were measured in the plane of the specimen as well as in the transversal direction with DIC technology. Testing of CS2 followed the same approach. BS2. Rigid body motion due to tangential displacements at the longitudinal joints is disregarded. Next to it the projected radial pressure p on the compressible material is displayed as a function of the displacement of the vertical cylinders v. The segment Ref showed an approximately linear load increase until one of the longitudinal joints failed suddenly (N = 2608.7 kN). BS1 and BS2 reached the plastic range for N = 970 kN (p = 0.55 MPa) and N = 1476 kN (p = 0.85 MPa), respectively. This equals 20% and 29% of their ultimate capacity. Thereafter, large deformations developed in the CM with minor load increase. In contrast, the HPSFRC layer experienced no considerable deformation. The maximum load available on the tester was finally reached without failure for CM in densification range. Consequently, v was fixed. After a time-induced load drop of nearly 9% loading was reactivated, and the specimens failed.

| Load-displacement behavior
Since BS1 was tested before BS2 and the latter could be expected to have even higher bearing capacity due to its geometry, the vertical frame needed strengthening. In fact, the vertical load component of the rig limited testing and prevented full utilization of its horizontal capacity due to coupling of forces (H/V = 1.866). Consequently, the second vertical steel frame was installed. Table 3 lists the maximum bearing capacities N max in the experiments and the ratio between eccentricity of load introduction and thickness. Figure 10 (right) shows BS1 after testing. Failure of BS2 was similar. The CM was compacted at mid-span to approximately 62 mm (BS1) and 79 mm (BS2), which equals 64.6% and 54.9% of the original thickness, respectively. Figure 11 (left) shows N as a function of the axial deformation Δx measured between the centers of the top and bottom faces and the transversal deflection at midspan u, obtained from DIC for both segments. The capacity of segment CS2 was 6.8% lower than CS1 with larger F I G U R E 9 Test setup of compaction test of CS1 with pressure p idealized as constant (left) and of bearing capacity tests of CS1 and CS2 (right). deflection at maximum load (10.5 vs. 9.3 mm). Figure 11 (center, right) shows the compaction of CS1. Compaction develops with load increase and shows the three expected ranges. Finally, it accumulates to residual thickness of 46 mm for p = 1.36 MPa, which equals 51.1% of the initial 90 mm. Figure 12 shows the crack patterns of the specimens. In Ref the region of load introduction is pushed into the body and spalling happens on two lateral faces while no damage was registered at the center. BS1 and BS2 broke in the upper flange of the recess. Moreover, both segments showed cracks at load introduction at the side with recess. Additionally, diagonal cracks at the corners of the recesses appeared. As planned, the half without recess exhibited no damage. Figure 12 (bottom) shows the crack pattern in CS1 and CS2. Both are characterized by concrete crushing near center, accompanied by longitudinal cracks similar to compression tests. Some flexural cracks were also observed at the inner faces. The regions of load introduction remained nearly undamaged. Figure 13 shows the strains obtained from selected gauges on the specimens. For analysis, the strains on a rebar and the surrounding concrete are assumed to be equal due to bonding. In BS1 and BS2 (Figure 13, top left and top right), the reinforcement at the side of the recess (SG 1) reached strains lower than 1‰ at maximum. At mid-span, SG 4 and 5 showed absolute strains lower than 2‰ (concrete still elastic). At the upper strut, SG 2 showed a loss of stiffness after ε ≈ 2.5‰ in both segments and final strains larger than 10‰.

| Crack patterns and strains on reinforcement
In CS1 and CS2, the reinforcement at load introduction (SG 1 to 4) as well as the bottom reinforcement (SG 5, 6, 8, 10, 11, and 13) exhibited maximum strains lower than 1‰ (Figure 13, bottom left and bottom right). The upper reinforcement in the struts (SG 7, 9, 12, and 14), on the other hand, reached strains up to 3.4‰ at maximum.

| General
With regard to the load bearing capacities in Table 3, the new designs perform better than the reference and show potential for thickness reduction, which simultaneously reduces excavation and concrete volumes, reduces costs and shortens execution times. Moreover, the tests show significantly increased deformability potential in radial direction, which provides stress relaxation in squeezing/swelling ground conditions and avoids the need of larger thickness. 7 Segments BS1 and BS2 yielded a strong increase in the bearing capacity with respect to Ref (86.7% and 97.4%, respectively). In case of BS2 even for 31% more load eccentricity. Failure happened in the central region, as intended, and not at load introduction next to the longitudinal joints. The strains in SG 2 suggest concrete crushing in the upper strut (cf. Figure 13, top left and top  CS1 and CS2 failed similarly by concrete crushing in the struts. Although u and the bending moment were maximum at mid-span, the transversal strut stiffened that region and shifted the failure to one side. The low strains in SG 1 and 2 suggest that the amount of splitting reinforcement could be reduced to further exploit its bearing capacity at maximum load.
The tests proved the addition of polypropylene fibers and high amounts of steel fibers feasible. Actually, the bearing capacity varied almost linearly with f cm and fire protection requirements 42 are met by the design.

| Volume reduction and efficiency
A look at the load-bearing capacities in Table 3 gives an idea of the material savings potential of the design alternatives compared with the reference, which arises in particular from the reduced thicknesses of the segments. It remains to determine how thick the alternatives must be to yield the same load-bearing capacity as the reference and to quantify practical volume savings. Taking the experimental loading and setup as representative for the entire ring, segments with reduced thickness are subjected to increased bending moments due to second order effects. For simplicity, the eccentricity at load introduction is assumed to vary linearly with the lining thickness. Second order effects are considered by means of a linear beam model idealizing the experimental setup of BS. If larger eccentricities would arise at the longitudinal joints, the split design still offers reserves.
Taking BS1 as a reference, the goal is to find the t that fully utilizes the critical upper strut for N = 2608.7 kN. The utilization factor follows from Equation (1), where x 1 is the thickness of the strut, α is the fraction of N in it (considering second order effects) that depends on e. The segmental width is b = 0.75 m, while A s denotes the rebar area in the strut.
To find the combination that leads to UF = 1, the model of the setup is employed to compute the second order eccentricity at the region of the strut. By nature, the procedure is iterative. Considering x 1 /t and the reinforcement ratio A s /bÁx 1 constant, it yields t = 134 mm. With that reduced t at hand, the calculation of the volume of concrete V C and excavation V E required for a total ring in both favorable (fav.) and unfavorable (sw.) ground conditions is straightforward. Table 4 summarizes the results, where the thickness of CM (t CM ) is assumed to vary proportionally with t. Therein, any contribution of the outer mortar grout of rings in the practice is neglected.
BS yields volume reduction of the concrete of 55.2% with respect to a whole ring of type Ref. The excavation volume is reduced by 4.8% if no CM is used in favorable ground conditions, while it decreases by 8.1% for unfavorable ground conditions. CS1 and CS2 possess a substantially reduced thickness but reached lower bearing capacities than Ref. This is again due to second order effects: the maximum deflection at mid-span was 9.3 and 10.5 mm for CS1 and CS2, respectively. This equals 48.9% and 55.3% of e 0 = 19 mm (cf. Figure 9, right) at the longitudinal joint. Figure 14 shows interaction diagrams constructed for the studied case, using the parabola rectangle diagram as the constitutive law for the concrete. As usual, axes show dimensionless quantities μ = M/(bÁt 2 Áf cm ) and ν = N/ (bÁtÁf cm ). Naturally, the experimental results fall on the resistance curves, and the loss in bearing capacity due to second order effects turns evident. Effectively, specimens CS1 and CS2 would reach jνj ≈ 0.36 for first order bending moments employing e 0 , which is equivalent to N = 2680 kN and N = 2570 kN, respectively. This means that they would have a normalized bearing capacity close to Ref, but second order effects diminished it by around 20%.
Analogue, a modified thickness can be computed for CS1. To this end, Figure 14 is employed to iteratively find full utilization. Then, a target load of N = 2608.7 kN is obtained considering second order effects and yields a thickness of t = 157 mm (scaling the thickness of the slab between the struts linearly). The volume reduction is computed analogue, too. Given the irregular geometry of the outer face, the average thickness t̅ is employed for the calculation. Although CS-type segments need larger t compared with BS1, the concrete volume is reduced by 53.6% with respect to Ref. The excavation volume is also reduced by 3.6% if no CM is used (fav.), while it decreases by 7% in swelling/squeezing ground conditions (sw.-cf. Table 4).
Additionally, the efficiency of the designs in terms of material utilization can be measured as the ratio between N max and the critical area A cr at the location of failure. For this, the original geometries and the maximum bearing capacities are used as basis. For BS1, the axial force at the upper strut is of interest (cf. Equation (1)) and is distributed on A cr = 750Á50 mm 2 . Here, α takes the value α = 0.683 since second order effects in the original geometry were negligible. For CS1, A cr is simply the crosssection area at the coffers. The results are normalized by f cm and integrated in Table 4. BS1 shows the best ratio with 209% increase with respect to Ref.

| Compression potential
Both design alternatives offer remarkable radial deformation potential through plasticization at low load levels. In fact, considerable structural reserves in terms of bearing capacity (80%-BS1 and 71%-BS2) remain when compaction is completed. To ensure this, the CM can and should be customized for each project. With too low strength, it would already crush under service loads and leave the system without reserves. Too high strength makes it too stiff and similar to the conventional design.
Plasticization of BS-type segments started for p ≈ f cm,cube and apparently earlier for p = 0.8Áf cm,cube in CS1. This is attributed to the variable stiffness of CM due T A B L E 4 f.l.t.r: (average) thickness of segment, concrete volume per ring, excavation volume per ring (fav.), thickness of CM layer, excavation volume per ring (sw.), critical area, and efficiency of each specimen type to coffers (Figure 15). The thinner the CM layer is, the higher its radial stiffness is. Consequently, the stiffness k 1 and the effective stress σ 1 at the struts are 1.94 times higher than at the coffers (k 2 and σ 2 ). Finally, idealizing the system as a bedded slab, p, σ 1 , and σ 2 are linked according to Equation (2): From p = 0.8 MPa (beginning of plasticization in CS1), σ 1 = 1.07 MPa results from Equation (2). Thus, the effective stress almost equals f cm,cube . With further load increase, stresses are redistributed to the coffer region and the pressure gets more homogeneously distributed throughout. Then, as for the BS-type, the material compression tests can be employed for the structural design of the CM. However, the geometry of the coffers must be assessed to predict the behavior of the CM layer. Although BS2 and CS1 reached similar compaction ratios at the end of the experiments, the maximum p on CS1 was considerably lower than on BS2 (cf. Figures 10  and 11). However, BS2 reached only 66.6% of its compaction from the start of plasticization for p = 1.36 MPa (maximum for CS1). This means that CS-type segments may reach considerably larger compaction ratios and larger p for further load increase.
Finally, both design alternatives make a strong reduction of concrete volume possible. Deciding on the best design will always depend on the project. For squeezing/ swelling ground conditions, CS-type segments possess greater potential to absorb deformation. By contrast, BStype segments provide higher stiffness, and are useful if lower radial deformations are required. A centered gasket groove as in BS2 could be advantageous. Indeed, the water tightness is less sensitive to the rotation of the joints. 47,51

| CONCLUSIONS AND RECOMMENDATIONS
In the context of an ever increasing use of concrete worldwide, this article presents new designs for tunnel lining segments in mechanized tunneling that feature reduced thickness compared with conventional designs. It is achieved through a more efficient use of material throughout. This goes along with reduced diameters of TBMs, less soil disposal, and less transportation efforts of the segments. Furthermore, this allows the installation of a layer of compressible material in tunnels subjected to local loading, as in squeezing/swelling ground conditions. The first design, with one-sided barrel-shaped recesses, prioritizes maximum stiffness. The second, with coffers, prioritizes the maximization of the thickness of the compressible material on the outer face. Their performance was tested under real conditions. The following conclusions can be drawn: • The design with one-sided barrel-shaped recesses reduces the concrete volume by 55.2% compared with a conventional reference. This reduces the tunnel's cross-section by 4.8% in favorable ground conditions, and 8.1% in unfavorable conditions. • The coffer segment reduces the concrete volume by 53.6% compared with a conventional reference and reduces the tunnel cross-section by 3.6% in favorable ground conditions, and 7% in unfavorable conditions. • The compressible layer shows 64.6% compaction for a global material utilization of 19%. Thus, a higher capacity for radial deformation is provided without considerably increasing internal loads in the bearing layer. The compressive material should be customized for each project depending on the expected loading. • The efficiency of the new designs in terms of bearing capacity with respect to critical area of failure increases up to 209% with respect to a conventional segment.
F I G U R E 1 5 Top view of CS-type segments (top), cross-section with idealized constant pressure (center), and real pressure distribution according to local stiffness in linear and in plastic range (bottom).
• The decision on a certain design depends on the project, considering the always individual boundary conditions. To maximize the deformation absorption potential, the use of coffer segments is recommended. Segments with one-sided barrel-shaped recesses can be used in more favorable ground conditions, or to provide more stiffness to the system to keep deformation limits. • Both layers, the bearing and the compressible one, are sought to be manufactured in a precast plant. That way, the quality is maximized, and in case of CS-type segments, a regular outer face is provided when grouting the annular gap. Alternatively, the TBM might install just the bearing layer, while the compressible material is filled in situ. The material properties should be carefully determined to enable proper grouting. Further experimental studies would be necessary to prove feasibility. • To simplify the fabrication of the coffer segments, their curvature was suppressed intentionally. For the small curvatures employed, the conclusions drawn from a straight segment are seen representative. Nevertheless, future campaigns could extend the fabrication methods to realize curved geometries. • The conclusions are so far drawn from unique prototypes subject to a selected load case. To generalize the findings, further experiments on segments with different geometries, materials, reinforcement, and load cases should be carried out.

ACKNOWLEDGMENT
The authors would like to thank the German Research Foundation (DFG) for their financial support for the project 77309832, which is part of the Collaborative Research Center SFB 837 "Interaction Modeling in Mechanized Tunneling" at the Ruhr University Bochum. Open access funding enabled and organized by Projekt DEAL.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.