By Mehdi Bakhshi and Verya Nasri
Mechanized tunneling by TBM has been the most dominant excavation method in the past decade in various ground conditions such as soft ground, weak rock and fractured hard rock. Precast concrete segments are installed behind a TBM to support the excavation, resist permanent ground and groundwater loads, and provide watertightness. In addition, precast segments are designed for the temporary loads from production, transportation, and construction.
Up until publication of ACI 533 guide, very little guidance had been provided for designers and contractors by local or international authorities. Publication of ACI 533.5R, led by authors of this article, as the first guide in the world published by an international code agency, addressed this need and covers all major aspects of design, manufacturing and construction of the segments together in a single publication. This guide provides procedures required for the structural concept and detail design, sealing and gasket design, connection design, durability design, and settling and monitoring tolerances. This document was drafted based on worldwide cooperation, tunneling experience and available national and international recommendations. In addition to general aspects of design, the most recent developments in design and latest technologies related to TBM tunnel lining technologies are presented.
Concrete precast tunnel segments must be designed using the Load and Resistance Factor Design (LRFD) method. Table 1 presents the governing load cases and factored load combinations for which precast concrete tunnel segments are designed. Strength reduction factors in ACI 318-19 and ACI 544.7R-16 are required for the design of reinforced concrete and fiber-reinforced concrete (FRC), respectively.
Segmental ring geometry and systems
The internal space requirements depending on the intended use of the tunnel and client requirements determine the dimension of the tunnel intrados. ACI 533.5R classifies tunnels in four main categories of railroad and subway, road, utility, and water and wastewater tunnels. The internal space requirements for each category are explained in ‘the Guide.’ Figure 1 schematically presents a typical layout of road tunnels.
ACI 533.5R provides ranges of the internal diameter (ID) ratio to the lining thickness for different tunnel sizes. This includes a range of 15-25in for 13-18 ft ID tunnels, and a range of 18-25in for tunnels with more than 18 ft ID. For tunnel diameters of 19-23 ft, a ring length of 5 ft is recommended which increases to a ring length of 6.5 ft for tunnels larger than 30 ft in diameter.
Parallel rings, parallel rings with corrective rings, right/left-tapered rings, and universal ring systems (see Figure 2) are among different segmental ring systems. Parallel rings (Figure 2(a)) are not inherently suitable for curves. In right/left rings (Figure 2(b)) generally one circumferential face of each ring is tapered perpendicular to the tunnel axis and the other face is inclined to the tunnel axis. Alternating right- and left-tapered rings in a sequence produces a straight drive. Watertightness can be guaranteed with this ring type but the requirement for different types of formwork set is a disadvantage. Currently, the universal ring system (Figure 2(c)) is the most conventional system, where often two circumferential faces of each ring are inclined to the tunnel axis, and alignment can be negotiated through the rotation of the segmental ring. The main advantage of this system is that only one type of formwork set is required .
Rings generally contain a number of segments that yield a segment slenderness ratio of 8-13. The general recommendation for tunnels with a diameter of up to 20 ft is to divide the ring into 6 segments and use 5+1 or 4+2 configurations (the latter number represent the number of key segments). When the tunnel diameter ranges between 20 to 26 ft and 26 to 36 ft, a 7-segment ring and an 8-segment ring can be adopted, respectively. For tunnel diameters between 36 to 46 ft a 9-segment ring can be adopted. Finally, for tunnels larger than 46 ft, a 9+1 configuration is the most common configuration.
The geometry of individual segments, as shown in Figure 3, can be divided into four main categories or systems: hexagonal, rectangular, trapezoidal, and rhomboidal. Because hexagonal segments (Figure 3(a)) prevent the effective use of gaskets, they compromise the watertightness of the lining and are rarely used nowadays. With rectangular systems (Figure 3(b)), staggered longitudinal joints cannot always be guaranteed, and crucifix joints may present themselves which may cause leakage. In trapezoidal system (Figure 3(c)) because of staggered longitudinal joints, the possibility of creating crucifix joints are eliminated but the installation process makes it difficult to place several key segments between the counter key segments. Rhomboidal system (Figure 3(d)) is currently the most common system as it eliminates crucifix joints, has a good sealing performance, and allows for continuous ring erection. Other major advantage is the angled segment joint which prevents rubbing of the gaskets during segment insertion and facilitates the use of fast connecting dowels in circumferential joints.
Structural design of segments
After casting and initial curing, segments are stripped from formwork. The design must consider the required strength when segments are stripped (e.g. 6 hours after casting) under their own self-weight (w).
Segment demolding is followed by segment storage, where segments are stacked to gain their required strength before transportation to the construction site. Generally, all segments comprising a full ring are piled up in one stack. The design considers the self-weight and the dead load of segments positioned above with an eccentricity of e = 4 in. between the locations of the stack support and the supports of the upper segments.
Segment handling is carried out by specially designed lifting devices such as mechanical clamping, vacuum lifters and forklifts. For handling by mechanical clamping and vacuum lifters the design procedure utilized for segment demolding and for handling by forklifts a loading scheme and eccentricity similar to segment storage is adopted.
During the segment transportation phase, precast segments are transported to the construction site and ultimately to the TBM trailing gear. Half or all segments of each ring are transported to the TBM on one carriage. Design procedure similar to storage phase and an eccentricity of 4 in. is generally recommended for design.
In addition to load factors presented in Table 1, a dynamic impact factor of 2.0 is recommended for load cases of handling and transportation. Figure 4 presents loading schemes and support conditions above-mentioned load cases.
Loads on the lining are generated during the filling of the annular space between ground and segments with semi-liquid grouts. This is modeled by applying radial pressure, which linearly varies from the minimum grout pressure at the crown to the maximum grout pressure at the invert of the tunnel. For the load combination of self-weight and grout pressure, as shown in Table 1, a load factor of 1.25 is recommended for both loads.
Load factors shown in Table 1 (Load Case 8) can be used to compute the required strength. Among other methods, this load case can be analyzed using elastic equations, beam-spring models (Figure 6), FEM and discrete element method (DEM).
Hoop forces developed in the lining are transferred through a reduced cross-sectional area along the longitudinal joints where gaskets and stress relief grooves are present. Similar to the load case of TBM thrust jack forces, analysis methods include simplified bursting equations [2, 4] (Figure 7), the analytical method of Iyengar  diagram, and 2D/3D FEM simulations.
Detailed design considerations and serviceability limit state (SLS)
ACI 533.5R Guide  summarizes available guidelines by international authorities on the recommended compressive strength of precast concrete tunnel segments. The reinforcement is categorized to three different types: a) transverse reinforcement – the main reinforcement placed perpendicular to the tunnel axis, b) longitudinal reinforcement – placed parallel to tunnel axis and often designed as minimum temperature and shrinkage reinforcement, c) joint reinforcement – placed in the vicinity of joints to resist bursting and spalling stresses. The most common reinforcement details are presented in ‘the Guide’, including the size of rebar and the minimum recommended concrete cover and rebar spacing.
Verifications for SLS in tunnel segments include stress verification, deformation verification, and cracking verification. Special attention is paid to cracking as a major contributor to reduction in serviceability due to potential water penetration. The design should ensure that flexural crack width is not greater than the allowable crack widths presented in ‘the Guide’.
Design of gaskets, connection devices and fasteners
In one-pass segmental lining, the watertightness of the tunnel is guaranteed by the segments and gaskets which are placed between segments in longitudinal and circumferential joints. In ‘the Guide’, procedures are provided for selecting gasket materials, solutions for different water pressures, appropriate safety factors considering relaxation, gasket profile considering tunnel size, tolerances and required construction gap/offset. Watertightness and load-deflection tests as well as details of gasket groove design are presented. Gasket short-term behavior is explained, and discussion regarding the design of connection systems for gasket load after short-term relaxation is made. New developments in gasket systems are introduced, including anchored gaskets and the most recently developed fiber anchorage technology for gaskets; soft corner solutions to eliminate point loading using pin-based cavities; and new repair method for post sealing of segment joint, based on direct drilling and injection through gasket profile.
Connections between segments within a ring and between rings can be divided into three categories: bolts, dowels and guiding rods. Bolt (Figure 8(a)) is generally used between segments within a ring, and between rings of rectangular systems. Because of the kinematics of the assembling process, dowel (Figure 8(b)) is only used between the rings in circumferential joints. Guiding rods (Figure 8(c)) can be used as a centering device that provides guidance and centering during segment installation with locking functionality. Guiding rods are usually utilized in conjunction with dowels. The latest developments in connection devices include integration of a screw-able socket on one side of dowel in order to reduce the installation tolerance and provide the workers with a smoother assembly process. Traditional fastening systems are post-installed anchors with drilling which may damage concrete, reinforcement, or segment gaskets with negative impacts on structural behavior, sealing performance, corrosion protection and long-term durability. ACI 533.25  presents new cast-in fastening system for segments as a durable and sustainable solution.
Tolerances, dimensional control, and Durability
Tolerances are allowable deviations of actual dimensions of segments, either as individual components or as a system from their design dimensions. In ACI 533.5R Guide , tolerances are explained in two main categories of production and construction tolerances. Production segment tolerances specified by guidelines and standards are presented, and different measurement programs and their shortcomings are discussed. 3D laser measurement using interferometer and tracker system, is presented as the best practice. Test ring is explained as a system tolerance controlling method, and ovalization and joint misalignment as two major construction tolerances.
Tunnels are typically designed for a service life of 100-125 years. In bored tunnels, durability of the tunnel is directly related to durability of segments. The most-frequent degradation mechanisms are discussed in ‘the Guide’. This includes corrosion of reinforcement by chloride attack and carbonation, sulfate and acid attacks, alkali-aggregate reactions, frost attack and freeze-and-thaw damages. Stray current-induced corrosion as a major durability concern specific to railway/subway tunnels is explained. Mitigation methods for different durability factor are also presented. Stray current corrosion mitigation method including use of FRC segments are presented and durability of segments under coupling effects of stray current with other conventional degradation factors are explained. Prescriptive approaches are introduced for the durability design considering different environmental exposure classes as the main inputs . Recommendations to ensure typical service life of tunnels are explained including concrete strength, maximum water-to-cement (w/c) ratio, minimum cement content and minimum air content.
ACI 533.5R Guide  consolidates most recent developments, international best practices, and state-of-the-art information on all aspects of design and construction of precast segments, and can be used as a general guide for segmental tunnel linings. In addition to structural design rules, this guideline addresses details of segmental ring geometry, shapes, configuration and systems, and detailed concrete design considerations. Gasket design, connection devices, tolerances, measurements, dimensional control and durability are all discussed. The prepared ‘Guide’ is the state of the practice at the current time on a continuously evolving technology field.
 ACI 533.5R: Guide for Precast Concrete Tunnel Segments. American Concrete Institute (ACI), 2020.
 ACI 318: Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute (ACI), 2019.
 ÖVBB: Guideline for Concrete Segmental Lining Systems. Austrian Society for Concrete and Construction Technology (ÖVBB), 2011.
 DAUB: Lining Segment Design: Recommendations for the Design, Production, and Installation of Segmental Rings. German Tunnelling Committee (DAUB), 2013.
 Iyengar, K. T.: Two-Dimensional Theories of Anchorage Zone Stresses in Post-Tensioned Beams. ACI 59 (1962), No. 10, pp. 1443–1466.
Mehdi Bakhshi, AVP- Lead Tunnel Engineer | AECOM
Dr. Bakhshi has a PhD in Civil Engineering from Arizona State University. He has more than 18 years of experience in civil, structures, tunnel, underground, and geotechnical engineering in national and international projects as lead tunnel engineer and senior tunnel engineer. Mehdi has published more than 75 journal and peer-reviewed conference papers related to tunneling and concrete structures.
Verya Nasri, VP- Chief Tunnel Engineer | AECOM
Dr. Nasri has a PhD in Geotechnical and Structural Engineering from École Centrale Paris. He has more than 30 years of experience as chief tunnel engineer for major tunneling projects in the New York City metropolitan area and throughout North America, Europe, Asia, Africa, and the Middle East. Dr. Nasri has more than 200 journal and conference papers on the design and construction of tunnels and underground structures.